Sample records for gait dynamics fractals

  1. Entrainment to a real time fractal visual stimulus modulates fractal gait dynamics.

    PubMed

    Rhea, Christopher K; Kiefer, Adam W; D'Andrea, Susan E; Warren, William H; Aaron, Roy K

    2014-08-01

    Fractal patterns characterize healthy biological systems and are considered to reflect the ability of the system to adapt to varying environmental conditions. Previous research has shown that fractal patterns in gait are altered following natural aging or disease, and this has potential negative consequences for gait adaptability that can lead to increased risk of injury. However, the flexibility of a healthy neurological system to exhibit different fractal patterns in gait has yet to be explored, and this is a necessary step toward understanding human locomotor control. Fifteen participants walked for 15min on a treadmill, either in the absence of a visual stimulus or while they attempted to couple the timing of their gait with a visual metronome that exhibited a persistent fractal pattern (contained long-range correlations) or a random pattern (contained no long-range correlations). The stride-to-stride intervals of the participants were recorded via analog foot pressure switches and submitted to detrended fluctuation analysis (DFA) to determine if the fractal patterns during the visual metronome conditions differed from the baseline (no metronome) condition. DFA α in the baseline condition was 0.77±0.09. The fractal patterns in the stride-to-stride intervals were significantly altered when walking to the fractal metronome (DFA α=0.87±0.06) and to the random metronome (DFA α=0.61±0.10) (both p<.05 when compared to the baseline condition), indicating that a global change in gait dynamics was observed. A variety of strategies were identified at the local level with a cross-correlation analysis, indicating that local behavior did not account for the consistent global changes. Collectively, the results show that a gait dynamics can be shifted in a prescribed manner using a visual stimulus and the shift appears to be a global phenomenon. Copyright © 2014 Elsevier B.V. All rights reserved.

  2. Association between stride time fractality and gait adaptability during unperturbed and asymmetric walking.

    PubMed

    Ducharme, Scott W; Liddy, Joshua J; Haddad, Jeffrey M; Busa, Michael A; Claxton, Laura J; van Emmerik, Richard E A

    2018-04-01

    Human locomotion is an inherently complex activity that requires the coordination and control of neurophysiological and biomechanical degrees of freedom across various spatiotemporal scales. Locomotor patterns must constantly be altered in the face of changing environmental or task demands, such as heterogeneous terrains or obstacles. Variability in stride times occurring at short time scales (e.g., 5-10 strides) is statistically correlated to larger fluctuations occurring over longer time scales (e.g., 50-100 strides). This relationship, known as fractal dynamics, is thought to represent the adaptive capacity of the locomotor system. However, this has not been tested empirically. Thus, the purpose of this study was to determine if stride time fractality during steady state walking associated with the ability of individuals to adapt their gait patterns when locomotor speed and symmetry are altered. Fifteen healthy adults walked on a split-belt treadmill at preferred speed, half of preferred speed, and with one leg at preferred speed and the other at half speed (2:1 ratio asymmetric walking). The asymmetric belt speed condition induced gait asymmetries that required adaptation of locomotor patterns. The slow speed manipulation was chosen in order to determine the impact of gait speed on stride time fractal dynamics. Detrended fluctuation analysis was used to quantify the correlation structure, i.e., fractality, of stride times. Cross-correlation analysis was used to measure the deviation from intended anti-phasing between legs as a measure of gait adaptation. Results revealed no association between unperturbed walking fractal dynamics and gait adaptability performance. However, there was a quadratic relationship between perturbed, asymmetric walking fractal dynamics and adaptive performance during split-belt walking, whereby individuals who exhibited fractal scaling exponents that deviated from 1/f performed the poorest. Compared to steady state preferred walking

  3. When human walking becomes random walking: fractal analysis and modeling of gait rhythm fluctuations

    NASA Astrophysics Data System (ADS)

    Hausdorff, Jeffrey M.; Ashkenazy, Yosef; Peng, Chang-K.; Ivanov, Plamen Ch.; Stanley, H. Eugene; Goldberger, Ary L.

    2001-12-01

    We present a random walk, fractal analysis of the stride-to-stride fluctuations in the human gait rhythm. The gait of healthy young adults is scale-free with long-range correlations extending over hundreds of strides. This fractal scaling changes characteristically with maturation in children and older adults and becomes almost completely uncorrelated with certain neurologic diseases. Stochastic modeling of the gait rhythm dynamics, based on transitions between different “neural centers”, reproduces distinctive statistical properties of the gait pattern. By tuning one model parameter, the hopping (transition) range, the model can describe alterations in gait dynamics from childhood to adulthood - including a decrease in the correlation and volatility exponents with maturation.

  4. Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington's disease

    NASA Technical Reports Server (NTRS)

    Hausdorff, J. M.; Mitchell, S. L.; Firtion, R.; Peng, C. K.; Cudkowicz, M. E.; Wei, J. Y.; Goldberger, A. L.

    1997-01-01

    Fluctuations in the duration of the gait cycle (the stride interval) display fractal dynamics and long-range correlations in healthy young adults. We hypothesized that these stride-interval correlations would be altered by changes in neurological function associated with aging and certain disease states. To test this hypothesis, we compared the stride-interval time series of 1) healthy elderly subjects and young controls and of 2) subjects with Huntington's disease and healthy controls. Using detrended fluctuation analysis we computed alpha, a measure of the degree to which one stride interval is correlated with previous and subsequent intervals over different time scales. The scaling exponent alpha was significantly lower in elderly subjects compared with young subjects (elderly: 0.68 +/- 0.14; young: 0.87 +/- 0.15; P < 0.003). The scaling exponent alpha was also smaller in the subjects with Huntington's disease compared with disease-free controls (Huntington's disease: 0.60 +/- 0.24; controls: 0.88 +/-0.17; P < 0.005). Moreover, alpha was linearly related to degree of functional impairment in subjects with Huntington's disease (r = 0.78, P < 0.0005). These findings demonstrate that strike-interval fluctuations are more random (i.e., less correlated) in elderly subjects and in subjects with Huntington's disease. Abnormal alterations in the fractal properties of gait dynamics are apparently associated with changes in central nervous system control.

  5. Fractal and Multifractal Analysis of Human Gait

    NASA Astrophysics Data System (ADS)

    Muñoz-Diosdado, A.; del Río Correa, J. L.; Angulo-Brown, F.

    2003-09-01

    We carried out a fractal and multifractal analysis of human gait time series of young and old individuals, and adults with three illnesses that affect the march: The Parkinson's and Huntington's diseases and the amyotrophic lateral sclerosis (ALS). We obtained cumulative plots of events, the correlation function, the Hurst exponent and the Higuchi's fractal dimension of these time series and found that these fractal markers could be a factor to characterize the march, since we obtained different values of these quantities for youths and adults and they are different also for healthy and ill persons and the most anomalous values belong to ill persons. In other physiological signals there is complexity lost related with the age and the illness, in the case of the march the opposite occurs. The multifractal analysis could be also a useful tool to understand the dynamics of these and other complex systems.

  6. Kinematic variability, fractal dynamics and local dynamic stability of treadmill walking

    PubMed Central

    2011-01-01

    Background Motorized treadmills are widely used in research or in clinical therapy. Small kinematics, kinetics and energetics changes induced by Treadmill Walking (TW) as compared to Overground Walking (OW) have been reported in literature. The purpose of the present study was to characterize the differences between OW and TW in terms of stride-to-stride variability. Classical (Standard Deviation, SD) and non-linear (fractal dynamics, local dynamic stability) methods were used. In addition, the correlations between the different variability indexes were analyzed. Methods Twenty healthy subjects performed 10 min TW and OW in a random sequence. A triaxial accelerometer recorded trunk accelerations. Kinematic variability was computed as the average SD (MeanSD) of acceleration patterns among standardized strides. Fractal dynamics (scaling exponent α) was assessed by Detrended Fluctuation Analysis (DFA) of stride intervals. Short-term and long-term dynamic stability were estimated by computing the maximal Lyapunov exponents of acceleration signals. Results TW did not modify kinematic gait variability as compared to OW (multivariate T2, p = 0.87). Conversely, TW significantly modified fractal dynamics (t-test, p = 0.01), and both short and long term local dynamic stability (T2 p = 0.0002). No relationship was observed between variability indexes with the exception of significant negative correlation between MeanSD and dynamic stability in TW (3 × 6 canonical correlation, r = 0.94). Conclusions Treadmill induced a less correlated pattern in the stride intervals and increased gait stability, but did not modify kinematic variability in healthy subjects. This could be due to changes in perceptual information induced by treadmill walking that would affect locomotor control of the gait and hence specifically alter non-linear dependencies among consecutive strides. Consequently, the type of walking (i.e. treadmill or overground) is important to consider in each protocol

  7. Nonlinear dynamical model of human gait

    NASA Astrophysics Data System (ADS)

    West, Bruce J.; Scafetta, Nicola

    2003-05-01

    We present a nonlinear dynamical model of the human gait control system in a variety of gait regimes. The stride-interval time series in normal human gait is characterized by slightly multifractal fluctuations. The fractal nature of the fluctuations becomes more pronounced under both an increase and decrease in the average gait. Moreover, the long-range memory in these fluctuations is lost when the gait is keyed on a metronome. Human locomotion is controlled by a network of neurons capable of producing a correlated syncopated output. The central nervous system is coupled to the motocontrol system, and together they control the locomotion of the gait cycle itself. The metronomic gait is simulated by a forced nonlinear oscillator with a periodic external force associated with the conscious act of walking in a particular way.

  8. Understanding the complexity of human gait dynamics

    NASA Astrophysics Data System (ADS)

    Scafetta, Nicola; Marchi, Damiano; West, Bruce J.

    2009-06-01

    Time series of human gait stride intervals exhibit fractal and multifractal properties under several conditions. Records from subjects walking at normal, slow, and fast pace speed are analyzed to determine changes in the fractal scalings as a function of the stress condition of the system. Records from subjects with different age from children to elderly and patients suffering from neurodegenerative disease are analyzed to determine changes in the fractal scalings as a function of the physical maturation or degeneration of the system. A supercentral pattern generator model is presented to simulate the above two properties that are typically found in dynamical network performance: that is, how a dynamical network responds to stress and to evolution.

  9. Complexity, fractal dynamics and determinism in treadmill ambulation: Implications for clinical biomechanists.

    PubMed

    Hollman, John H; Watkins, Molly K; Imhoff, Angela C; Braun, Carly E; Akervik, Kristen A; Ness, Debra K

    2016-08-01

    Reduced inter-stride complexity during ambulation may represent a pathologic state. Evidence is emerging that treadmill training for rehabilitative purposes may constrain the locomotor system and alter gait dynamics in a way that mimics pathological states. The purpose of this study was to examine the dynamical system components of gait complexity, fractal dynamics and determinism during treadmill ambulation. Twenty healthy participants aged 23.8 (1.2) years walked at preferred walking speeds for 6min on a motorized treadmill and overground while wearing APDM 6 Opal inertial monitors. Stride times, stride lengths and peak sagittal plane trunk velocities were measured. Mean values and estimates of complexity, fractal dynamics and determinism were calculated for each parameter. Data were compared between overground and treadmill walking conditions. Mean values for each gait parameter were statistically equivalent between overground and treadmill ambulation (P>0.05). Through nonlinear analyses, however, we found that complexity in stride time signals (P<0.001), and long-range correlations in stride time and stride length signals (P=0.005 and P=0.024, respectively), were reduced on the treadmill. Treadmill ambulation induces more predictable inter-stride time dynamics and constrains fluctuations in stride times and stride lengths, which may alter feedback from destabilizing perturbations normally experienced by the locomotor control system during overground ambulation. Treadmill ambulation, therefore, may provide less opportunity for experiencing the adaptability necessary to successfully ambulate overground. Investigators and clinicians should be aware that treadmill ambulation will alter dynamic gait characteristics. Copyright © 2016 Elsevier Ltd. All rights reserved.

  10. Fractal analyses reveal independent complexity and predictability of gait

    PubMed Central

    Dierick, Frédéric; Nivard, Anne-Laure

    2017-01-01

    Locomotion is a natural task that has been assessed for decades and used as a proxy to highlight impairments of various origins. So far, most studies adopted classical linear analyses of spatio-temporal gait parameters. Here, we use more advanced, yet not less practical, non-linear techniques to analyse gait time series of healthy subjects. We aimed at finding more sensitive indexes related to spatio-temporal gait parameters than those previously used, with the hope to better identify abnormal locomotion. We analysed large-scale stride interval time series and mean step width in 34 participants while altering walking direction (forward vs. backward walking) and with or without galvanic vestibular stimulation. The Hurst exponent α and the Minkowski fractal dimension D were computed and interpreted as indexes expressing predictability and complexity of stride interval time series, respectively. These holistic indexes can easily be interpreted in the framework of optimal movement complexity. We show that α and D accurately capture stride interval changes in function of the experimental condition. Walking forward exhibited maximal complexity (D) and hence, adaptability. In contrast, walking backward and/or stimulation of the vestibular system decreased D. Furthermore, walking backward increased predictability (α) through a more stereotyped pattern of the stride interval and galvanic vestibular stimulation reduced predictability. The present study demonstrates the complementary power of the Hurst exponent and the fractal dimension to improve walking classification. Our developments may have immediate applications in rehabilitation, diagnosis, and classification procedures. PMID:29182659

  11. GAIT DYNAMICS, FRACTALS AND FALLS: FINDING MEANING IN THE STRIDE-TO-STRIDE FLUCTUATIONS OF HUMAN WALKING

    PubMed Central

    Hausdorff, Jeffrey M

    2007-01-01

    Until recently, quantitative studies of walking have typically focused on properties of a typical or average stride, ignoring the stride-to-stride fluctuations and considering these fluctuations to be noise. Work over the past two decades has demonstrated, however, that the alleged noise actually conveys important information. The magnitude of the stride-to-stride fluctuations and their changes over time during a walk – gait dynamics – may be useful in understanding the physiology of gait, in quantifying age-related and pathologic alterations in the locomotor control system, and in augmenting objective measurement of mobility and functional status Indeed, alterations in gait dynamics may help to determine disease severity, medication utility, and fall risk, and to objectively document improvements in response to therapeutic interventions, above and beyond what can be gleaned from measures based on the average, typical stride. This review discusses support for the idea that gait dynamics has meaning and may be useful in providing insight into the neural control of locomtion and for enhancing functional assessment of aging, chronic disease, and their impact on mobility. PMID:17618701

  12. Fractals, Coherence and Brain Dynamics

    NASA Astrophysics Data System (ADS)

    Vitiello, Giuseppe

    2010-11-01

    I show that the self-similarity property of deterministic fractals provides a direct connection with the space of the entire analytical functions. Fractals are thus described in terms of coherent states in the Fock-Bargmann representation. Conversely, my discussion also provides insights on the geometrical properties of coherent states: it allows to recognize, in some specific sense, fractal properties of coherent states. In particular, the relation is exhibited between fractals and q-deformed coherent states. The connection with the squeezed coherent states is also displayed. In this connection, the non-commutative geometry arising from the fractal relation with squeezed coherent states is discussed and the fractal spectral properties are identified. I also briefly discuss the description of neuro-phenomenological data in terms of squeezed coherent states provided by the dissipative model of brain and consider the fact that laboratory observations have shown evidence that self-similarity characterizes the brain background activity. This suggests that a connection can be established between brain dynamics and the fractal self-similarity properties on the basis of the relation discussed in this report between fractals and squeezed coherent states. Finally, I do not consider in this paper the so-called random fractals, namely those fractals obtained by randomization processes introduced in their iterative generation. Since self-similarity is still a characterizing property in many of such random fractals, my conjecture is that also in such cases there must exist a connection with the coherent state algebraic structure. In condensed matter physics, in many cases the generation by the microscopic dynamics of some kind of coherent states is involved in the process of the emergence of mesoscopic/macroscopic patterns. The discussion presented in this paper suggests that also fractal generation may provide an example of emergence of global features, namely long range

  13. Detrended Fluctuation Analysis and Adaptive Fractal Analysis of Stride Time Data in Parkinson's Disease: Stitching Together Short Gait Trials

    PubMed Central

    Liebherr, Magnus; Haas, Christian T.

    2014-01-01

    Variability indicates motor control disturbances and is suitable to identify gait pathologies. It can be quantified by linear parameters (amplitude estimators) and more sophisticated nonlinear methods (structural information). Detrended Fluctuation Analysis (DFA) is one method to measure structural information, e.g., from stride time series. Recently, an improved method, Adaptive Fractal Analysis (AFA), has been proposed. This method has not been applied to gait data before. Fractal scaling methods (FS) require long stride-to-stride data to obtain valid results. However, in clinical studies, it is not usual to measure a large number of strides (e.g., strides). Amongst others, clinical gait analysis is limited due to short walkways, thus, FS seem to be inapplicable. The purpose of the present study was to evaluate FS under clinical conditions. Stride time data of five self-paced walking trials ( strides each) of subjects with PD and a healthy control group (CG) was measured. To generate longer time series, stride time sequences were stitched together. The coefficient of variation (CV), fractal scaling exponents (DFA) and (AFA) were calculated. Two surrogate tests were performed: A) the whole time series was randomly shuffled; B) the single trials were randomly shuffled separately and afterwards stitched together. CV did not discriminate between PD and CG. However, significant differences between PD and CG were found concerning and . Surrogate version B yielded a higher mean squared error and empirical quantiles than version A. Hence, we conclude that the stitching procedure creates an artificial structure resulting in an overestimation of true . The method of stitching together sections of gait seems to be appropriate in order to distinguish between PD and CG with FS. It provides an approach to integrate FS as standard in clinical gait analysis and to overcome limitations such as short walkways. PMID:24465708

  14. Fractal fluctuations in spatiotemporal variables when walking on a self-paced treadmill.

    PubMed

    Choi, Jin-Seung; Kang, Dong-Won; Seo, Jeong-Woo; Tack, Gye-Rae

    2017-12-08

    This study investigated the fractal dynamic properties of stride time (ST), stride length (SL) and stride speed (SS) during walking on a self-paced treadmill (STM) in which the belt speed is automatically controlled by the walking speed. Twelve healthy young subjects participated in the study. The subjects walked at their preferred walking speed under four conditions: STM, STM with a metronome (STM+met), fixed-speed (conventional) treadmill (FTM), and FTM with a metronome (FTM+met). To compare the fractal dynamics between conditions, the mean, variability, and fractal dynamics of ST, SL, and SS were compared. Moreover, the relationship among the variables was examined under each walking condition using three types of surrogates. The mean values of all variables did not differ between the two treadmills, and the variability of all variables was generally larger for STM than for FTM. The use of a metronome resulted in a decrease in variability in ST and SS for all conditions. The fractal dynamic characteristics of SS were maintained with STM, in contrast to FTM, and only the fractal dynamic characteristics of ST disappeared when using a metronome. In addition, the fractal dynamic patterns of the cross-correlated surrogate results were identical to those of all variables for the two treadmills. In terms of the fractal dynamic properties, STM walking was generally closer to overground walking than FTM walking. Although further research is needed, the present results will be useful in research on gait fractal dynamics and rehabilitation. Copyright © 2017 Elsevier Ltd. All rights reserved.

  15. Persistent fluctuations in stride intervals under fractal auditory stimulation.

    PubMed

    Marmelat, Vivien; Torre, Kjerstin; Beek, Peter J; Daffertshofer, Andreas

    2014-01-01

    Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.

  16. Persistent Fluctuations in Stride Intervals under Fractal Auditory Stimulation

    PubMed Central

    Marmelat, Vivien; Torre, Kjerstin; Beek, Peter J.; Daffertshofer, Andreas

    2014-01-01

    Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals. PMID:24651455

  17. Fractal dynamics of earthquakes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bak, P.; Chen, K.

    1995-05-01

    Many objects in nature, from mountain landscapes to electrical breakdown and turbulence, have a self-similar fractal spatial structure. It seems obvious that to understand the origin of self-similar structures, one must understand the nature of the dynamical processes that created them: temporal and spatial properties must necessarily be completely interwoven. This is particularly true for earthquakes, which have a variety of fractal aspects. The distribution of energy released during earthquakes is given by the Gutenberg-Richter power law. The distribution of epicenters appears to be fractal with dimension D {approx} 1--1.3. The number of after shocks decay as a function ofmore » time according to the Omori power law. There have been several attempts to explain the Gutenberg-Richter law by starting from a fractal distribution of faults or stresses. But this is a hen-and-egg approach: to explain the Gutenberg-Richter law, one assumes the existence of another power-law--the fractal distribution. The authors present results of a simple stick slip model of earthquakes, which evolves to a self-organized critical state. Emphasis is on demonstrating that empirical power laws for earthquakes indicate that the Earth`s crust is at the critical state, with no typical time, space, or energy scale. Of course the model is tremendously oversimplified; however in analogy with equilibrium phenomena they do not expect criticality to depend on details of the model (universality).« less

  18. Fractal dynamics in physiology: Alterations with disease and aging

    PubMed Central

    Goldberger, Ary L.; Amaral, Luis A. N.; Hausdorff, Jeffrey M.; Ivanov, Plamen Ch.; Peng, C.-K.; Stanley, H. Eugene

    2002-01-01

    According to classical concepts of physiologic control, healthy systems are self-regulated to reduce variability and maintain physiologic constancy. Contrary to the predictions of homeostasis, however, the output of a wide variety of systems, such as the normal human heartbeat, fluctuates in a complex manner, even under resting conditions. Scaling techniques adapted from statistical physics reveal the presence of long-range, power-law correlations, as part of multifractal cascades operating over a wide range of time scales. These scaling properties suggest that the nonlinear regulatory systems are operating far from equilibrium, and that maintaining constancy is not the goal of physiologic control. In contrast, for subjects at high risk of sudden death (including those with heart failure), fractal organization, along with certain nonlinear interactions, breaks down. Application of fractal analysis may provide new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as to monitoring the aging process. Similar approaches show promise in assessing other regulatory systems, such as human gait control in health and disease. Elucidating the fractal and nonlinear mechanisms involved in physiologic control and complex signaling networks is emerging as a major challenge in the postgenomic era. PMID:11875196

  19. Effect of Interpersonal Interaction on Festinating Gait Rehabilitation in Patients with Parkinson's Disease.

    PubMed

    Uchitomi, Hirotaka; Ogawa, Ken-Ichiro; Orimo, Satoshi; Wada, Yoshiaki; Miyake, Yoshihiro

    2016-01-01

    Although human walking gait rhythms are generated by native individual gait dynamics, these gait dynamics change during interactions between humans. A typical phenomenon is synchronization of gait rhythms during cooperative walking. Our previous research revealed that fluctuation characteristics in stride interval of subjects with Parkinson's disease changed from random to 1/f fluctuation as fractal characteristics during cooperative walking with the gait assist system Walk-Mate, which emulates a human interaction using interactive rhythmic cues. Moreover, gait dynamics were relearned through Walk-Mate gait training. However, the system's clinical efficacy was unclear because the previous studies did not focus on specific gait rhythm disorder symptoms. Therefore, this study aimed to evaluate the effect of Walk-Mate on festinating gait among subjects with Parkinson's disease. Three within-subject experimental conditions were used: (1) preinteraction condition, (2) interaction condition, and (3) postinteraction condition. The only difference between conditions was the interactive rhythmic cues generated by Walk-Mate. Because subjects with festinating gait gradually and involuntarily decreased their stride interval, the regression slope of stride interval as an index of severity of preinteraction festinating gait was elevated. The regression slope in the interaction condition was more gradual than during the preinteraction condition, indicating that the interactive rhythmic cues contributed to relieving festinating gait and stabilizing gait dynamics. Moreover, the gradual regression slope was carried over to the postinteraction condition, indicating that subjects with festinating gait have the potential to relearn stable gait dynamics. These results suggest that disordered gait dynamics are clinically restored through interactive rhythmic cues and that Walk-Mate may have the potential to assist therapists in more effective rehabilitation. UMIN Clinical Trials Registry

  20. Fractal dimension and nonlinear dynamical processes

    NASA Astrophysics Data System (ADS)

    McCarty, Robert C.; Lindley, John P.

    1993-11-01

    Mandelbrot, Falconer and others have demonstrated the existence of dimensionally invariant geometrical properties of non-linear dynamical processes known as fractals. Barnsley defines fractal geometry as an extension of classical geometry. Such an extension, however, is not mathematically trivial Of specific interest to those engaged in signal processing is the potential use of fractal geometry to facilitate the analysis of non-linear signal processes often referred to as non-linear time series. Fractal geometry has been used in the modeling of non- linear time series represented by radar signals in the presence of ground clutter or interference generated by spatially distributed reflections around the target or a radar system. It was recognized by Mandelbrot that the fractal geometries represented by man-made objects had different dimensions than the geometries of the familiar objects that abound in nature such as leaves, clouds, ferns, trees, etc. The invariant dimensional property of non-linear processes suggests that in the case of acoustic signals (active or passive) generated within a dispersive medium such as the ocean environment, there exists much rich structure that will aid in the detection and classification of various objects, man-made or natural, within the medium.

  1. Effect of Interpersonal Interaction on Festinating Gait Rehabilitation in Patients with Parkinson’s Disease

    PubMed Central

    Uchitomi, Hirotaka; Ogawa, Ken-ichiro; Orimo, Satoshi; Wada, Yoshiaki; Miyake, Yoshihiro

    2016-01-01

    Although human walking gait rhythms are generated by native individual gait dynamics, these gait dynamics change during interactions between humans. A typical phenomenon is synchronization of gait rhythms during cooperative walking. Our previous research revealed that fluctuation characteristics in stride interval of subjects with Parkinson’s disease changed from random to 1/f fluctuation as fractal characteristics during cooperative walking with the gait assist system Walk-Mate, which emulates a human interaction using interactive rhythmic cues. Moreover, gait dynamics were relearned through Walk-Mate gait training. However, the system’s clinical efficacy was unclear because the previous studies did not focus on specific gait rhythm disorder symptoms. Therefore, this study aimed to evaluate the effect of Walk-Mate on festinating gait among subjects with Parkinson’s disease. Three within-subject experimental conditions were used: (1) preinteraction condition, (2) interaction condition, and (3) postinteraction condition. The only difference between conditions was the interactive rhythmic cues generated by Walk-Mate. Because subjects with festinating gait gradually and involuntarily decreased their stride interval, the regression slope of stride interval as an index of severity of preinteraction festinating gait was elevated. The regression slope in the interaction condition was more gradual than during the preinteraction condition, indicating that the interactive rhythmic cues contributed to relieving festinating gait and stabilizing gait dynamics. Moreover, the gradual regression slope was carried over to the postinteraction condition, indicating that subjects with festinating gait have the potential to relearn stable gait dynamics. These results suggest that disordered gait dynamics are clinically restored through interactive rhythmic cues and that Walk-Mate may have the potential to assist therapists in more effective rehabilitation. Trial Registration

  2. Down syndrome's brain dynamics: analysis of fractality in resting state.

    PubMed

    Hemmati, Sahel; Ahmadlou, Mehran; Gharib, Masoud; Vameghi, Roshanak; Sajedi, Firoozeh

    2013-08-01

    To the best knowledge of the authors there is no study on nonlinear brain dynamics of down syndrome (DS) patients, whereas brain is a highly complex and nonlinear system. In this study, fractal dimension of EEG, as a key characteristic of brain dynamics, showing irregularity and complexity of brain dynamics, was used for evaluation of the dynamical changes in the DS brain. The results showed higher fractality of the DS brain in almost all regions compared to the normal brain, which indicates less centrality and higher irregular or random functioning of the DS brain regions. Also, laterality analysis of the frontal lobe showed that the normal brain had a right frontal laterality of complexity whereas the DS brain had an inverse pattern (left frontal laterality). Furthermore, the high accuracy of 95.8 % obtained by enhanced probabilistic neural network classifier showed the potential of nonlinear dynamic analysis of the brain for diagnosis of DS patients. Moreover, the results showed that the higher EEG fractality in DS is associated with the higher fractality in the low frequencies (delta and theta), in broad regions of the brain, and the high frequencies (beta and gamma), majorly in the frontal regions.

  3. A Brief Historical Introduction to Fractals and Fractal Geometry

    ERIC Educational Resources Information Center

    Debnath, Lokenath

    2006-01-01

    This paper deals with a brief historical introduction to fractals, fractal dimension and fractal geometry. Many fractals including the Cantor fractal, the Koch fractal, the Minkowski fractal, the Mandelbrot and Given fractal are described to illustrate self-similar geometrical figures. This is followed by the discovery of dynamical systems and…

  4. Nonlinear dynamics, fractals, cardiac physiology and sudden death

    NASA Technical Reports Server (NTRS)

    Goldberger, Ary L.

    1987-01-01

    The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.

  5. Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Agarwal, S.; Wettlaufer, J. S.

    2014-12-01

    We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.

  6. The analysis of the influence of fractal structure of stimuli on fractal dynamics in fixational eye movements and EEG signal

    NASA Astrophysics Data System (ADS)

    Namazi, Hamidreza; Kulish, Vladimir V.; Akrami, Amin

    2016-05-01

    One of the major challenges in vision research is to analyze the effect of visual stimuli on human vision. However, no relationship has been yet discovered between the structure of the visual stimulus, and the structure of fixational eye movements. This study reveals the plasticity of human fixational eye movements in relation to the ‘complex’ visual stimulus. We demonstrated that the fractal temporal structure of visual dynamics shifts towards the fractal dynamics of the visual stimulus (image). The results showed that images with higher complexity (higher fractality) cause fixational eye movements with lower fractality. Considering the brain, as the main part of nervous system that is engaged in eye movements, we analyzed the governed Electroencephalogram (EEG) signal during fixation. We have found out that there is a coupling between fractality of image, EEG and fixational eye movements. The capability observed in this research can be further investigated and applied for treatment of different vision disorders.

  7. Autonomous Evolution of Dynamic Gaits with Two Quadruped Robots

    NASA Technical Reports Server (NTRS)

    Hornby, Gregory S.; Takamura, Seichi; Yamamoto, Takashi; Fujita, Masahiro

    2004-01-01

    A challenging task that must be accomplished for every legged robot is creating the walking and running behaviors needed for it to move. In this paper we describe our system for autonomously evolving dynamic gaits on two of Sony's quadruped robots. Our evolutionary algorithm runs on board the robot and uses the robot's sensors to compute the quality of a gait without assistance from the experimenter. First we show the evolution of a pace and trot gait on the OPEN-R prototype robot. With the fastest gait, the robot moves at over 10/min/min., which is more than forty body-lengths/min. While these first gaits are somewhat sensitive to the robot and environment in which they are evolved, we then show the evolution of robust dynamic gaits, one of which is used on the ERS-110, the first consumer version of AIBO.

  8. Wearable Device-Based Gait Recognition Using Angle Embedded Gait Dynamic Images and a Convolutional Neural Network.

    PubMed

    Zhao, Yongjia; Zhou, Suiping

    2017-02-28

    The widespread installation of inertial sensors in smartphones and other wearable devices provides a valuable opportunity to identify people by analyzing their gait patterns, for either cooperative or non-cooperative circumstances. However, it is still a challenging task to reliably extract discriminative features for gait recognition with noisy and complex data sequences collected from casually worn wearable devices like smartphones. To cope with this problem, we propose a novel image-based gait recognition approach using the Convolutional Neural Network (CNN) without the need to manually extract discriminative features. The CNN's input image, which is encoded straightforwardly from the inertial sensor data sequences, is called Angle Embedded Gait Dynamic Image (AE-GDI). AE-GDI is a new two-dimensional representation of gait dynamics, which is invariant to rotation and translation. The performance of the proposed approach in gait authentication and gait labeling is evaluated using two datasets: (1) the McGill University dataset, which is collected under realistic conditions; and (2) the Osaka University dataset with the largest number of subjects. Experimental results show that the proposed approach achieves competitive recognition accuracy over existing approaches and provides an effective parametric solution for identification among a large number of subjects by gait patterns.

  9. Wearable Device-Based Gait Recognition Using Angle Embedded Gait Dynamic Images and a Convolutional Neural Network

    PubMed Central

    Zhao, Yongjia; Zhou, Suiping

    2017-01-01

    The widespread installation of inertial sensors in smartphones and other wearable devices provides a valuable opportunity to identify people by analyzing their gait patterns, for either cooperative or non-cooperative circumstances. However, it is still a challenging task to reliably extract discriminative features for gait recognition with noisy and complex data sequences collected from casually worn wearable devices like smartphones. To cope with this problem, we propose a novel image-based gait recognition approach using the Convolutional Neural Network (CNN) without the need to manually extract discriminative features. The CNN’s input image, which is encoded straightforwardly from the inertial sensor data sequences, is called Angle Embedded Gait Dynamic Image (AE-GDI). AE-GDI is a new two-dimensional representation of gait dynamics, which is invariant to rotation and translation. The performance of the proposed approach in gait authentication and gait labeling is evaluated using two datasets: (1) the McGill University dataset, which is collected under realistic conditions; and (2) the Osaka University dataset with the largest number of subjects. Experimental results show that the proposed approach achieves competitive recognition accuracy over existing approaches and provides an effective parametric solution for identification among a large number of subjects by gait patterns. PMID:28264503

  10. Dynamics of Fractal Cluster Gels with Embedded Active Colloids

    NASA Astrophysics Data System (ADS)

    Szakasits, Megan E.; Zhang, Wenxuan; Solomon, Michael J.

    2017-08-01

    We find that embedded active colloids increase the ensemble-averaged mean squared displacement of particles in otherwise passively fluctuating fractal cluster gels. The enhancement in dynamics occurs by a mechanism in which the active colloids contribute to the average dynamics both directly through their own active motion and indirectly through their excitation of neighboring passive colloids in the fractal network. Fractal cluster gels are synthesized by addition of magnesium chloride to an initially stable suspension of 1.0 μ m polystyrene colloids in which a dilute concentration of platinum coated Janus colloids has been dispersed. The Janus colloids are thereby incorporated into the fractal network. We measure the ensemble-averaged mean squared displacement of all colloids in the gel before and after the addition of hydrogen peroxide, a fuel that drives diffusiophoretic motion of the Janus particles. The gel mean squared displacement increases by up to a factor of 3 for an active to passive particle ratio of 1 ∶20 and inputted active energy—defined based on the hydrogen peroxide's effect on colloid swim speed and run length—that is up to 9.5 times thermal energy, on a per particle basis. We model the enhancement in gel particle dynamics as the sum of a direct contribution from the displacement of the Janus particles themselves and an indirect contribution from the strain field that the active colloids induce in the surrounding passive particles.

  11. The effects of smartphone multitasking on gait and dynamic balance

    PubMed Central

    Lee, Jeon Hyeong; Lee, Myoung Hee

    2018-01-01

    [Purpose] This study was performed to analyze the influence of smartphone multitasking on gait and dynamic balance. [Subjects and Methods] The subjects were 19 male and 20 female university students. There were 4 types of gait tasks: General Gait (walking without a task), Task Gait 1 (walking while writing a message), Task Gait 2 (walking while writing a message and listening to music), Task Gait 3 (walking while writing a message and having a conversation). To exclude the learning effect, the order of tasks was randomized. The Zebris FDM-T treadmill system (Zebris Medical GmbH, Germany) was used to measure left and right step length and width, and a 10 m walking test (10MWT) was conducted for gait velocity. In addition, a Timed Up and Go test (TUG) was used to measure dynamic balance. All the tasks were performed 3 times, and the mean of the measured values was analyzed. [Results] There were no statistically significant differences in step length and width. There were statistically significant differences in the 10MWT and TUG tests. [Conclusion] Using a smartphone while walking decreases a person’s dynamic balance and walking ability. It is considered that accident rates are higher when using a smartphone. PMID:29545698

  12. The effects of smartphone multitasking on gait and dynamic balance.

    PubMed

    Lee, Jeon Hyeong; Lee, Myoung Hee

    2018-02-01

    [Purpose] This study was performed to analyze the influence of smartphone multitasking on gait and dynamic balance. [Subjects and Methods] The subjects were 19 male and 20 female university students. There were 4 types of gait tasks: General Gait (walking without a task), Task Gait 1 (walking while writing a message), Task Gait 2 (walking while writing a message and listening to music), Task Gait 3 (walking while writing a message and having a conversation). To exclude the learning effect, the order of tasks was randomized. The Zebris FDM-T treadmill system (Zebris Medical GmbH, Germany) was used to measure left and right step length and width, and a 10 m walking test (10MWT) was conducted for gait velocity. In addition, a Timed Up and Go test (TUG) was used to measure dynamic balance. All the tasks were performed 3 times, and the mean of the measured values was analyzed. [Results] There were no statistically significant differences in step length and width. There were statistically significant differences in the 10MWT and TUG tests. [Conclusion] Using a smartphone while walking decreases a person's dynamic balance and walking ability. It is considered that accident rates are higher when using a smartphone.

  13. Nonlinear analysis of gait kinematics to track changes in oxygen consumption in prolonged load carriage walking: a pilot study.

    PubMed

    Schiffman, Jeffrey M; Chelidze, David; Adams, Albert; Segala, David B; Hasselquist, Leif

    2009-09-18

    Linking human mechanical work to physiological work for the purpose of developing a model of physical fatigue is a complex problem that cannot be solved easily by conventional biomechanical analysis. The purpose of the study was to determine if two nonlinear analysis methods can address the fundamental issue of utilizing kinematic data to track oxygen consumption from a prolonged walking trial: we evaluated the effectiveness of dynamical systems and fractal analysis in this study. Further, we selected, oxygen consumption as a measure to represent the underlying physiological measure of fatigue. Three male US Army Soldier volunteers (means: 23.3 yr; 1.80 m; 77.3 kg) walked for 120 min at 1.34 m/s with a 40-kg load on a level treadmill. Gait kinematic data and oxygen consumption (VO(2)) data were collected over the 120-min period. For the fractal analysis, utilizing stride interval data, we calculated fractal dimension. For the dynamical systems analysis, kinematic angle time series were used to estimate phase space warping based features at uniform time intervals: smooth orthogonal decomposition (SOD) was used to extract slowly time-varying trends from these features. Estimated fractal dimensions showed no apparent trend or correlation with independently measured VO(2). While inter-individual difference did exist in the VO(2) data, dominant SOD time trends tracked and correlated with the VO(2) for all volunteers. Thus, dynamical systems analysis using gait kinematics may be suitable to develop a model to predict physiologic fatigue based on biomechanical work.

  14. Quantifying dynamic characteristics of human walking for comprehensive gait cycle.

    PubMed

    Mummolo, Carlotta; Mangialardi, Luigi; Kim, Joo H

    2013-09-01

    Normal human walking typically consists of phases during which the body is statically unbalanced while maintaining dynamic stability. Quantifying the dynamic characteristics of human walking can provide better understanding of gait principles. We introduce a novel quantitative index, the dynamic gait measure (DGM), for comprehensive gait cycle. The DGM quantifies the effects of inertia and the static balance instability in terms of zero-moment point and ground projection of center of mass and incorporates the time-varying foot support region (FSR) and the threshold between static and dynamic walking. Also, a framework of determining the DGM from experimental data is introduced, in which the gait cycle segmentation is further refined. A multisegmental foot model is integrated into a biped system to reconstruct the walking motion from experiments, which demonstrates the time-varying FSR for different subphases. The proof-of-concept results of the DGM from a gait experiment are demonstrated. The DGM results are analyzed along with other established features and indices of normal human walking. The DGM provides a measure of static balance instability of biped walking during each (sub)phase as well as the entire gait cycle. The DGM of normal human walking has the potential to provide some scientific insights in understanding biped walking principles, which can also be useful for their engineering and clinical applications.

  15. Nonlinear stochastic interacting dynamics and complexity of financial gasket fractal-like lattice percolation

    NASA Astrophysics Data System (ADS)

    Zhang, Wei; Wang, Jun

    2018-05-01

    A novel nonlinear stochastic interacting price dynamics is proposed and investigated by the bond percolation on Sierpinski gasket fractal-like lattice, aim to make a new approach to reproduce and study the complexity dynamics of real security markets. Fractal-like lattices correspond to finite graphs with vertices and edges, which are similar to fractals, and Sierpinski gasket is a well-known example of fractals. Fractional ordinal array entropy and fractional ordinal array complexity are introduced to analyze the complexity behaviors of financial signals. To deeper comprehend the fluctuation characteristics of the stochastic price evolution, the complexity analysis of random logarithmic returns and volatility are preformed, including power-law distribution, fractional sample entropy and fractional ordinal array complexity. For further verifying the rationality and validity of the developed stochastic price evolution, the actual security market dataset are also studied with the same statistical methods for comparison. The empirical results show that this stochastic price dynamics can reconstruct complexity behaviors of the actual security markets to some extent.

  16. Fractal Dynamics of Heartbeat Interval Fluctuations in Health and Disease

    NASA Astrophysics Data System (ADS)

    Meyer, M.; Marconi, C.; Rahmel, A.; Grassi, B.; Ferretti, G.; Skinner, J. E.; Cerretelli, P.

    The dynamics of heartbeat interval time series were studied by a modified random walk analysis recently introduced as Detrended Fluctuation Analysis. In this analysis, the intrinsic fractal long-range power-law correlation properties of beat-to-beat fluctuations generated by the dynamical system (i.e. cardiac rhythm generator), after decomposition from extrinsic uncorrelated sources, can be quantified by the scaling exponent which, in healthy subjects, is about 1.0. The finding of a scaling coefficient of 1.0, indicating scale-invariant long-range power-law correlations (1/ƒnoise) of heartbeat fluctuations, would reflect a genuinely self-similar fractal process that typically generates fluctuations on a wide range of time scales. Lack of a characteristic time scale suggests that the neuroautonomic system underlying the control of heart rate dynamics helps prevent excessive mode-locking (error tolerance) that would restrict its functional responsiveness (plasticity) to environmental stimuli. The 1/ƒ dynamics of heartbeat interval fluctuations are unaffected by exposure to chronic hypoxia suggesting that the neuroautonomic cardiac control system is preadapted to hypoxia. Functional (hypothermia, cardiac disease) and/or structural (cardiac transplantation, early cardiac development) inactivation of neuroautonomic control is associated with the breakdown or absence of fractal complexity reflected by anticorrelated random walk-like dynamics, indicating that in these conditions the heart is unadapted to its environment.

  17. Fractal analysis on human dynamics of library loans

    NASA Astrophysics Data System (ADS)

    Fan, Chao; Guo, Jin-Li; Zha, Yi-Long

    2012-12-01

    In this paper, the fractal characteristic of human behaviors is investigated from the perspective of time series constructed with the amount of library loans. The values of the Hurst exponent and length of non-periodic cycle calculated through rescaled range analysis indicate that the time series of human behaviors and their sub-series are fractal with self-similarity and long-range dependence. Then the time series are converted into complex networks by the visibility algorithm. The topological properties of the networks such as scale-free property and small-world effect imply that there is a close relationship among the numbers of repetitious behaviors performed by people during certain periods of time. Our work implies that there is intrinsic regularity in the human collective repetitious behaviors. The conclusions may be helpful to develop some new approaches to investigate the fractal feature and mechanism of human dynamics, and provide some references for the management and forecast of human collective behaviors.

  18. Dynamic markers of altered gait rhythm in amyotrophic lateral sclerosis

    NASA Technical Reports Server (NTRS)

    Hausdorff, J. M.; Lertratanakul, A.; Cudkowicz, M. E.; Peterson, A. L.; Kaliton, D.; Goldberger, A. L.

    2000-01-01

    Amyotrophic lateral sclerosis (ALS) is a disorder marked by loss of motoneurons. We hypothesized that subjects with ALS would have an altered gait rhythm, with an increase in both the magnitude of the stride-to-stride fluctuations and perturbations in the fluctuation dynamics. To test for this locomotor instability, we quantitatively compared the gait rhythm of subjects with ALS with that of normal controls and with that of subjects with Parkinson's disease (PD) and Huntington's disease (HD), pathologies of the basal ganglia. Subjects walked for 5 min at their usual pace wearing an ankle-worn recorder that enabled determination of the duration of each stride and of stride-to-stride fluctuations. We found that the gait of patients with ALS is less steady and more temporally disorganized compared with that of healthy controls. In addition, advanced ALS, HD, and PD were associated with certain common, as well as apparently distinct, features of altered stride dynamics. Thus stride-to-stride control of gait rhythm is apparently compromised with ALS. Moreover, a matrix of markers based on gait dynamics may be useful in characterizing certain pathologies of motor control and, possibly, in quantitatively monitoring disease progression and evaluating therapeutic interventions.

  19. Multi-fractal characterization of bacterial swimming dynamics: a case study on real and simulated Serratia marcescens

    PubMed Central

    Bogdan, Paul; Wei, Guopeng; Marculescu, Radu; Zhuang, Jiang; Carlsen, Rika Wright; Sitti, Metin

    2017-01-01

    To add to the current state of knowledge about bacterial swimming dynamics, in this paper, we study the fractal swimming dynamics of populations of Serratia marcescens bacteria both in vitro and in silico, while accounting for realistic conditions like volume exclusion, chemical interactions, obstacles and distribution of chemoattractant in the environment. While previous research has shown that bacterial motion is non-ergodic, we demonstrate that, besides the non-ergodicity, the bacterial swimming dynamics is multi-fractal in nature. Finally, we demonstrate that the multi-fractal characteristic of bacterial dynamics is strongly affected by bacterial density and chemoattractant concentration. PMID:28804259

  20. Adaptive control of dynamic balance in human gait on a split-belt treadmill.

    PubMed

    Buurke, Tom J W; Lamoth, Claudine J C; Vervoort, Danique; van der Woude, Lucas H V; den Otter, Rob

    2018-05-17

    Human bipedal gait is inherently unstable and staying upright requires adaptive control of dynamic balance. Little is known about adaptive control of dynamic balance in reaction to long-term, continuous perturbations. We examined how dynamic balance control adapts to a continuous perturbation in gait, by letting people walk faster with one leg than the other on a treadmill with two belts (i.e. split-belt walking). In addition, we assessed whether changes in mediolateral dynamic balance control coincide with changes in energy use during split-belt adaptation. In nine minutes of split-belt gait, mediolateral margins of stability and mediolateral foot roll-off changed during adaptation to the imposed gait asymmetry, especially on the fast side, and returned to baseline during washout. Interestingly, no changes in mediolateral foot placement (i.e. step width) were found during split-belt adaptation. Furthermore, the initial margin of stability and subsequent mediolateral foot roll-off were strongly coupled to maintain mediolateral dynamic balance throughout the gait cycle. Consistent with previous results net metabolic power was reduced during split-belt adaptation, but changes in mediolateral dynamic balance control were not correlated with the reduction of net metabolic power during split-belt adaptation. Overall, this study has shown that a complementary mechanism of relative foot positioning and mediolateral foot roll-off adapts to continuously imposed gait asymmetry to maintain dynamic balance in human bipedal gait. © 2018. Published by The Company of Biologists Ltd.

  1. Multiscale entropy analysis of human gait dynamics

    NASA Astrophysics Data System (ADS)

    Costa, M.; Peng, C.-K.; L. Goldberger, Ary; Hausdorff, Jeffrey M.

    2003-12-01

    We compare the complexity of human gait time series from healthy subjects under different conditions. Using the recently developed multiscale entropy algorithm, which provides a way to measure complexity over a range of scales, we observe that normal spontaneous walking has the highest complexity when compared to slow and fast walking and also to walking paced by a metronome. These findings have implications for modeling locomotor control and for quantifying gait dynamics in physiologic and pathologic states.

  2. Dynamic Simulation of Human Gait Model With Predictive Capability.

    PubMed

    Sun, Jinming; Wu, Shaoli; Voglewede, Philip A

    2018-03-01

    In this paper, it is proposed that the central nervous system (CNS) controls human gait using a predictive control approach in conjunction with classical feedback control instead of exclusive classical feedback control theory that controls based on past error. To validate this proposition, a dynamic model of human gait is developed using a novel predictive approach to investigate the principles of the CNS. The model developed includes two parts: a plant model that represents the dynamics of human gait and a controller that represents the CNS. The plant model is a seven-segment, six-joint model that has nine degrees-of-freedom (DOF). The plant model is validated using data collected from able-bodied human subjects. The proposed controller utilizes model predictive control (MPC). MPC uses an internal model to predict the output in advance, compare the predicted output to the reference, and optimize the control input so that the predicted error is minimal. To decrease the complexity of the model, two joints are controlled using a proportional-derivative (PD) controller. The developed predictive human gait model is validated by simulating able-bodied human gait. The simulation results show that the developed model is able to simulate the kinematic output close to experimental data.

  3. Effect of arm swing strategy on local dynamic stability of human gait.

    PubMed

    Punt, Michiel; Bruijn, Sjoerd M; Wittink, Harriet; van Dieën, Jaap H

    2015-02-01

    Falling causes long term disability and can even lead to death. Most falls occur during gait. Therefore improving gait stability might be beneficial for people at risk of falling. Recently arm swing has been shown to influence gait stability. However at present it remains unknown which mode of arm swing creates the most stable gait. To examine how different modes of arm swing affect gait stability. Ten healthy young male subjects volunteered for this study. All subjects walked with four different arm swing instructions at seven different gait speeds. The Xsens motion capture suit was used to capture gait kinematics. Basic gait parameters, variability and stability measures were calculated. We found an increased stability in the medio-lateral direction with excessive arm swing in comparison to normal arm swing at all gait speeds. Moreover, excessive arm swing increased stability in the anterior-posterior and vertical direction at low gait speeds. Ipsilateral and inphase arm swing did not differ compared to a normal arm swing. Excessive arm swing is a promising gait manipulation to improve local dynamic stability. For excessive arm swing in the ML direction there appears to be converging evidence. The effect of excessive arm swing on more clinically relevant groups like the more fall prone elderly or stroke survivors is worth further investigating. Excessive arm swing significantly increases local dynamic stability of human gait. Copyright © 2014 Elsevier B.V. All rights reserved.

  4. Fractal dynamics of heartbeat time series of young persons with metabolic syndrome

    NASA Astrophysics Data System (ADS)

    Muñoz-Diosdado, A.; Alonso-Martínez, A.; Ramírez-Hernández, L.; Martínez-Hernández, G.

    2012-10-01

    Many physiological systems have been in recent years quantitatively characterized using fractal analysis. We applied it to study heart variability of young subjects with metabolic syndrome (MS); we examined the RR time series (time between two R waves in ECG) with the detrended fluctuation analysis (DFA) method, the Higuchi's fractal dimension method and the multifractal analysis to detect the possible presence of heart problems. The results show that although the young persons have MS, the majority do not present alterations in the heart dynamics. However, there were cases where the fractal parameter values differed significantly from the healthy people values.

  5. Unification of two fractal families

    NASA Astrophysics Data System (ADS)

    Liu, Ying

    1995-06-01

    Barnsley and Hurd classify the fractal images into two families: iterated function system fractals (IFS fractals) and fractal transform fractals, or local iterated function system fractals (LIFS fractals). We will call IFS fractals, class 2 fractals and LIFS fractals, class 3 fractals. In this paper, we will unify these two approaches plus another family of fractals, the class 5 fractals. The basic idea is given as follows: a dynamical system can be represented by a digraph, the nodes in a digraph can be divided into two parts: transient states and persistent states. For bilevel images, a persistent node is a black pixel. A transient node is a white pixel. For images with more than two gray levels, a stochastic digraph is used. A transient node is a pixel with the intensity of 0. The intensity of a persistent node is determined by a relative frequency. In this way, the two families of fractals can be generated in a similar way. In this paper, we will first present a classification of dynamical systems and introduce the transformation based on digraphs, then we will unify the two approaches for fractal binary images. We will compare the decoding algorithms of the two families. Finally, we will generalize the discussion to continuous-tone images.

  6. Stride dynamics, gait variability and prospective falls risk in active community dwelling older women.

    PubMed

    Paterson, Kade; Hill, Keith; Lythgo, Noel

    2011-02-01

    Measures of walking instability such as stride dynamics and gait variability have been shown to identify future fallers in older adult populations with gait limitations or mobility disorders. This study investigated whether measures of walking instability can predict future fallers (over a prospective 12 month period) in a group of healthy and active older women. Ninety-seven healthy active women aged between 55 and 90 years walked for 7 min around a continuous walking circuit. Gait data recorded by a GAITRite(®) walkway and foot-mounted accelerometers were used to calculate measures of stride dynamics and gait variability. The participant's physical function and balance were assessed. Fall incidence was monitored over the following 12 months. Inter-limb differences (p≤0.04) in stride dynamics were found for fallers (one or more falls) aged over 70 years, and multiple fallers (two or more falls) aged over 55 years, but not in non-fallers or a combined group of single and non-fallers. No group differences were found in the measures of physical function, balance or gait, including variability. Additionally, no gait variable predicted falls. Reduced coordination of inter-limb dynamics was found in active healthy older fallers and multiple fallers despite no difference in other measures of intrinsic falls risk. Evaluating inter-limb dynamics may be a clinically sensitive technique to detect early gait instability and falls risk in high functioning older adults, prior to change in other measures of physical function, balance and gait. Copyright © 2010 Elsevier B.V. All rights reserved.

  7. Fractal nematic colloids

    NASA Astrophysics Data System (ADS)

    Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.

    2017-01-01

    Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter.

  8. Fractal nematic colloids

    PubMed Central

    Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.

    2017-01-01

    Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter. PMID:28117325

  9. A proof-of-concept study for measuring gait speed, steadiness, and dynamic balance under various footwear conditions outside of the gait laboratory.

    PubMed

    Wrobel, James S; Edgar, Sarah; Cozzetto, Dana; Maskill, James; Peterson, Paul; Najafi, Bijan

    2010-01-01

    This pilot study examined the effect of custom and prefabricated foot orthoses on self-selected walking speed, walking speed variability, and dynamic balance in the mediolateral direction. The gait of four healthy participants was analyzed with a body-worn sensor system across a distance of at least 30 m outside of the gait laboratory. Participants walked at their habitual speed in four conditions: barefoot, regular shoes, prefabricated foot orthoses, and custom foot orthoses. In the custom foot orthoses condition, gait speed was improved on average 13.5% over the barefoot condition and 9.8% over the regular shoe condition. The mediolateral range of motion of center of mass was reduced 55% and 56% compared with the shoes alone and prefabricated foot orthoses conditions, respectively. This may suggest better gait efficiency and lower energy cost with custom foot orthoses. This tendency remained after normalizing center of mass by gait speed, suggesting that irrespective of gait speed, custom foot orthoses improve center of mass motion in the mediolateral direction compared with other footwear conditions. Gait intercycle variability, measured by intercycle coefficient of variation of gait speed, was decreased on average by 25% and 19% compared with the barefoot and shoes-alone conditions, respectively. The decrease in gait unsteadiness after wearing custom foot orthoses may suggest improved proprioception from the increased contact area of custom foot orthoses versus the barefoot condition. These findings may open new avenues for objective assessment of the impact of prescribed footwear on dynamic balance and spatiotemporal parameters of gait and assess gait adaptation after use of custom foot orthoses.

  10. Gait ataxia in humans: vestibular and cerebellar control of dynamic stability.

    PubMed

    Schniepp, Roman; Möhwald, Ken; Wuehr, Max

    2017-10-01

    During human locomotion, vestibular feedback control is fundamental for maintaining dynamic stability and adapting the gait pattern to external circumstances. Within the supraspinal locomotor network, the cerebellum represents the key site for the integration of vestibular feedback information. The cerebellum is further important for the fine-tuning and coordination of limb movements during walking. The aim of this review article is to highlight the shared structural and functional sensorimotor principles in vestibular and cerebellar locomotion control. Vestibular feedback for the maintenance of dynamic stability is integrated into the locomotor pattern via midline, caudal cerebellar structures (vermis, flocculonodular lobe). Hemispheric regions of the cerebellum facilitate feed-forward control of multi-joint coordination and higher locomotor functions. Characteristic features of the gait disorder in patients with vestibular deficits or cerebellar ataxia are increased levels of spatiotemporal gait variability in the fore-aft and the medio-lateral gait dimension. In the fore-aft dimension, pathologic increases of gait fluctuations critically depend on the locomotion speed and predominantly manifest during slow walking velocities. This feature is associated with an increased risk of falls in both patients with vestibular hypofunction as well as patients with cerebellar ataxia. Pharmacological approaches for the treatment of vestibular or cerebellar gait ataxia are currently not available. However, new promising options are currently tested in randomized, controlled trials (fampridine/FACEG; acetyl-DL-leucine/ALCAT).

  11. Cardiac interbeat interval dynamics from childhood to senescence : comparison of conventional and new measures based on fractals and chaos theory

    NASA Technical Reports Server (NTRS)

    Pikkujamsa, S. M.; Makikallio, T. H.; Sourander, L. B.; Raiha, I. J.; Puukka, P.; Skytta, J.; Peng, C. K.; Goldberger, A. L.; Huikuri, H. V.

    1999-01-01

    BACKGROUND: New methods of R-R interval variability based on fractal scaling and nonlinear dynamics ("chaos theory") may give new insights into heart rate dynamics. The aims of this study were to (1) systematically characterize and quantify the effects of aging from early childhood to advanced age on 24-hour heart rate dynamics in healthy subjects; (2) compare age-related changes in conventional time- and frequency-domain measures with changes in newly derived measures based on fractal scaling and complexity (chaos) theory; and (3) further test the hypothesis that there is loss of complexity and altered fractal scaling of heart rate dynamics with advanced age. METHODS AND RESULTS: The relationship between age and cardiac interbeat (R-R) interval dynamics from childhood to senescence was studied in 114 healthy subjects (age range, 1 to 82 years) by measurement of the slope, beta, of the power-law regression line (log power-log frequency) of R-R interval variability (10(-4) to 10(-2) Hz), approximate entropy (ApEn), short-term (alpha(1)) and intermediate-term (alpha(2)) fractal scaling exponents obtained by detrended fluctuation analysis, and traditional time- and frequency-domain measures from 24-hour ECG recordings. Compared with young adults (<40 years old, n=29), children (<15 years old, n=27) showed similar complexity (ApEn) and fractal correlation properties (alpha(1), alpha(2), beta) of R-R interval dynamics despite lower spectral and time-domain measures. Progressive loss of complexity (decreased ApEn, r=-0.69, P<0.001) and alterations of long-term fractal-like heart rate behavior (increased alpha(2), r=0.63, decreased beta, r=-0.60, P<0.001 for both) were observed thereafter from middle age (40 to 60 years, n=29) to old age (>60 years, n=29). CONCLUSIONS: Cardiac interbeat interval dynamics change markedly from childhood to old age in healthy subjects. Children show complexity and fractal correlation properties of R-R interval time series comparable to those

  12. The developmental dynamics of gait maturation with a focus on spatiotemporal measures.

    PubMed

    Kraan, C M; Tan, A H J; Cornish, K M

    2017-01-01

    Gait analysis is recognised as a powerful clinical tool for studying relationships between motor control and brain function. By drawing on the literature investigating gait in individuals with neurological disorders, this review provides insight into the neural processes that contribute to and regulate specific spatiotemporal sub-components of gait and how they may mature across early to late childhood. This review also discusses the roles of changing anthropomorphic characteristics, and maturing sensory and higher-order cognitive processes in differentiating the developmental trajectories of the sub-components of gait. Importantly, although studies have shown that cognitive-gait interference is larger in children compared to adults, the contributing neurocognitive mechanisms may vary across age groups who have different types of attentional or cognitive vulnerabilities. These findings have implications for current models of gait maturation by highlighting the need for a dynamic model that focuses on the integration of various factors that contribute to gait though experience and practice. This is essential to elucidating why gait and other motor deficits are often contiguous with cognitive neurodevelopmental disorders. Copyright © 2016. Published by Elsevier B.V.

  13. Detection of chaotic dynamics in human gait signals from mobile devices

    NASA Astrophysics Data System (ADS)

    DelMarco, Stephen; Deng, Yunbin

    2017-05-01

    The ubiquity of mobile devices offers the opportunity to exploit device-generated signal data for biometric identification, health monitoring, and activity recognition. In particular, mobile devices contain an Inertial Measurement Unit (IMU) that produces acceleration and rotational rate information from the IMU accelerometers and gyros. These signals reflect motion properties of the human carrier. It is well-known that the complexity of bio-dynamical systems gives rise to chaotic dynamics. Knowledge of chaotic properties of these systems has shown utility, for example, in detecting abnormal medical conditions and neurological disorders. Chaotic dynamics has been found, in the lab, in bio-dynamical systems data such as electrocardiogram (heart), electroencephalogram (brain), and gait data. In this paper, we investigate the following question: can we detect chaotic dynamics in human gait as measured by IMU acceleration and gyro data from mobile phones? To detect chaotic dynamics, we perform recurrence analysis on real gyro and accelerometer signal data obtained from mobile devices. We apply the delay coordinate embedding approach from Takens' theorem to reconstruct the phase space trajectory of the multi-dimensional gait dynamical system. We use mutual information properties of the signal to estimate the appropriate delay value, and the false nearest neighbor approach to determine the phase space embedding dimension. We use a correlation dimension-based approach together with estimation of the largest Lyapunov exponent to make the chaotic dynamics detection decision. We investigate the ability to detect chaotic dynamics for the different one-dimensional IMU signals, across human subject and walking modes, and as a function of different phone locations on the human carrier.

  14. Effect of body weight support variation on muscle activities during robot assisted gait: a dynamic simulation study.

    PubMed

    Hussain, Shahid; Jamwal, Prashant K; Ghayesh, Mergen H

    2017-05-01

    While body weight support (BWS) intonation is vital during conventional gait training of neurologically challenged subjects, it is important to evaluate its effect during robot assisted gait training. In the present research we have studied the effect of BWS intonation on muscle activities during robotic gait training using dynamic simulations. Two dimensional (2-D) musculoskeletal model of human gait was developed conjointly with another 2-D model of a robotic orthosis capable of actuating hip, knee and ankle joints simultaneously. The musculoskeletal model consists of eight major muscle groups namely; soleus (SOL), gastrocnemius (GAS), tibialis anterior (TA), hamstrings (HAM), vasti (VAS), gluteus maximus (GLU), uniarticular hip flexors (iliopsoas, IP), and Rectus Femoris (RF). BWS was provided at levels of 0, 20, 40 and 60% during the simulations. In order to obtain a feasible set of muscle activities during subsequent gait cycles, an inverse dynamics algorithm along with a quadratic minimization algorithm was implemented. The dynamic parameters of the robot assisted human gait such as joint angle trajectories, ground contact force (GCF), human limb joint torques and robot induced torques at different levels of BWS were derived. The patterns of muscle activities at variable BWS were derived and analysed. For most part of the gait cycle (GC) the muscle activation patterns are quite similar for all levels of BWS as is apparent from the mean of muscle activities for the complete GC. Effect of BWS variation during robot assisted gait on muscle activities was studied by developing dynamic simulation. It is expected that the proposed dynamic simulation approach will provide important inferences and information about the muscle function variations consequent upon a change in BWS during robot assisted gait. This information shall be quite important while investigating the influence of BWS intonation on neuromuscular parameters of interest during robotic gait training.

  15. The relationship between 2D static features and 2D dynamic features used in gait recognition

    NASA Astrophysics Data System (ADS)

    Alawar, Hamad M.; Ugail, Hassan; Kamala, Mumtaz; Connah, David

    2013-05-01

    In most gait recognition techniques, both static and dynamic features are used to define a subject's gait signature. In this study, the existence of a relationship between static and dynamic features was investigated. The correlation coefficient was used to analyse the relationship between the features extracted from the "University of Bradford Multi-Modal Gait Database". This study includes two dimensional dynamic and static features from 19 subjects. The dynamic features were compromised of Phase-Weighted Magnitudes driven by a Fourier Transform of the temporal rotational data of a subject's joints (knee, thigh, shoulder, and elbow). The results concluded that there are eleven pairs of features that are considered significantly correlated with (p<0.05). This result indicates the existence of a statistical relationship between static and dynamics features, which challenges the results of several similar studies. These results bare great potential for further research into the area, and would potentially contribute to the creation of a gait signature using latent data.

  16. Micro and MACRO Fractals Generated by Multi-Valued Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Banakh, T.; Novosad, N.

    2014-08-01

    Given a multi-valued function Φ : X \\mumap X on a topological space X we study the properties of its fixed fractal \\malteseΦ, which is defined as the closure of the orbit Φω(*Φ) = ⋃n∈ωΦn(*Φ) of the set *Φ = {x ∈ X : x ∈ Φ(x)} of fixed points of Φ. A special attention is paid to the duality between micro-fractals and macro-fractals, which are fixed fractals \\maltese Φ and \\maltese {Φ -1} for a contracting compact-valued function Φ : X \\mumap X on a complete metric space X. With help of algorithms (described in this paper) we generate various images of macro-fractals which are dual to some well-known micro-fractals like the fractal cross, the Sierpiński triangle, Sierpiński carpet, the Koch curve, or the fractal snowflakes. The obtained images show that macro-fractals have a large-scale fractal structure, which becomes clearly visible after a suitable zooming.

  17. Fractals in physiology and medicine

    NASA Technical Reports Server (NTRS)

    Goldberger, Ary L.; West, Bruce J.

    1987-01-01

    The paper demonstrates how the nonlinear concepts of fractals, as applied in physiology and medicine, can provide an insight into the organization of such complex structures as the tracheobronchial tree and heart, as well as into the dynamics of healthy physiological variability. Particular attention is given to the characteristics of computer-generated fractal lungs and heart and to fractal pathologies in these organs. It is shown that alterations in fractal scaling may underlie a number of pathophysiological disturbances, including sudden cardiac death syndromes.

  18. Paradigms of Complexity: Fractals and Structures in the Sciences

    NASA Astrophysics Data System (ADS)

    Novak, Miroslav M.

    The Table of Contents for the book is as follows: * Preface * The Origin of Complexity (invited talk) * On the Existence of Spatially Uniform Scaling Laws in the Climate System * Multispectral Backscattering: A Fractal-Structure Probe * Small-Angle Multiple Scattering on a Fractal System of Point Scatterers * Symmetric Fractals Generated by Cellular Automata * Bispectra and Phase Correlations for Chaotic Dynamical Systems * Self-Organized Criticality Models of Neural Development * Altered Fractal and Irregular Heart Rate Behavior in Sick Fetuses * Extract Multiple Scaling in Long-Term Heart Rate Variability * A Semi-Continous Box Counting Method for Fractal Dimension Measurement of Short Single Dimension Temporal Signals - Preliminary Study * A Fractional Brownian Motion Model of Cracking * Self-Affine Scaling Studies on Fractography * Coarsening of Fractal Interfaces * A Fractal Model of Ocean Surface Superdiffusion * Stochastic Subsurface Flow and Transport in Fractal Fractal Conductivity Fields * Rendering Through Iterated Function Systems * The σ-Hull - The Hull Where Fractals Live - Calculating a Hull Bounded by Log Spirals to Solve the Inverse IFS-Problem by the Detected Orbits * On the Multifractal Properties of Passively Convected Scalar Fields * New Statistical Textural Transforms for Non-Stationary Signals: Application to Generalized Mutlifractal Analysis * Laplacian Growth of Parallel Needles: Their Mullins-Sekerka Instability * Entropy Dynamics Associated with Self-Organization * Fractal Properties in Economics (invited talk) * Fractal Approach to the Regional Seismic Event Discrimination Problem * Fractal and Topological Complexity of Radioactive Contamination * Pattern Selection: Nonsingular Saffman-Taylor Finger and Its Dynamic Evolution with Zero Surface Tension * A Family of Complex Wavelets for the Characterization of Singularities * Stabilization of Chaotic Amplitude Fluctuations in Multimode, Intracavity-Doubled Solid-State Lasers * Chaotic

  19. Fractals and foods.

    PubMed

    Peleg, M

    1993-01-01

    Fractal geometry and related concepts have had only a very minor impact on food research. The very few reported food applications deal mainly with the characterization of the contours of agglomerated instant coffee particles, the surface morphology of treated starch particles, the microstructure of casein gels viewed as a product limited diffusion aggregation, and the jagged mechanical signatures of crunchy dry foods. Fractal geometry describes objects having morphological features that are scale invariant. A demonstration of the self-similarity of fractal objects can be found in the familiar morphology of cauliflower and broccoli, both foods. Processes regulated by nonlinear dynamics can exhibit a chaotic behavior that has fractal characteristics. Examples are mixing of viscous fluids, turbulence, crystallization, agglomeration, diffusion, and possibly food spoilage.

  20. Generating high-speed dynamic running gaits in a quadruped robot using an evolutionary search.

    PubMed

    Krasny, Darren P; Orin, David E

    2004-08-01

    Over the past several decades, there has been a considerable interest in investigating high-speed dynamic gaits for legged robots. While much research has been published, both in the biomechanics and engineering fields regarding the analysis of these gaits, no single study has adequately characterized the dynamics of high-speed running as can be achieved in a realistic, yet simple, robotic system. The goal of this paper is to find the most energy-efficient, natural, and unconstrained gallop that can be achieved using a simulated quadrupedal robot with articulated legs, asymmetric mass distribution, and compliant legs. For comparison purposes, we also implement the bound and canter. The model used here is planar, although we will show that it captures much of the predominant dynamic characteristics observed in animals. While it is not our goal to prove anything about biological locomotion, the dynamic similarities between the gaits we produce and those found in animals does indicate a similar underlying dynamic mechanism. Thus, we will show that achieving natural, efficient high-speed locomotion is possible even with a fairly simple robotic system. To generate the high-speed gaits, we use an efficient evolutionary algorithm called set-based stochastic optimization. This algorithm finds open-loop control parameters to generate periodic trajectories for the body. Several alternative methods are tested to generate periodic trajectories for the legs. The combined solutions found by the evolutionary search and the periodic-leg methods, over a range of speeds up to 10.0 m/s, reveal "biological" characteristics that are emergent properties of the underlying gaits.

  1. Assessment of stability during gait in patients with spinal deformity-A preliminary analysis using the dynamic stability margin.

    PubMed

    Simon, Anne-Laure; Lugade, Vipul; Bernhardt, Kathie; Larson, A Noelle; Kaufman, Kenton

    2017-06-01

    Daily living activities are dynamic, requiring spinal motion through space. Current assessment of spinal deformities is based on static measurements from full-spine standing radiographs. Tools to assess dynamic stability during gait might be useful to enhance the standard evaluation. The aim of this study was to evaluate gait dynamic imbalance in patients with spinal deformity using the dynamic stability margin (DSM). Twelve normal subjects and 17 patients with spinal deformity were prospectively recruited. A kinematic 3D gait analysis was performed for the control group (CG) and the spinal deformity group (SDG). The DSM (distance between the extrapolated center of mass and the base of support) and time-distance parameters were calculated for the right and left side during gait. The relationship between DSM and step length was assessed using three variables: gait stability, symmetry, and consistency. Variables' accuracy was validated by a discriminant analysis. Patients with spinal deformity exhibited gait instability according to the DSM (0.25m versus 0.31m) with decreased velocity (1.1ms -1 versus 1.3ms -1 ) and decreased step length (0.32m versus 0.38m). According to the discriminant analysis, gait stability was the more accurate variable (area under the curve AUC=0.98) followed by gait symmetry and consistency. However, gait consistency showed 100% of specificity, sensitivity, and accuracy of precision. The DSM showed that patients with spinal malalignment exhibit decreased gait stability, symmetry, and consistency besides gait time-distance parameter changes. Additional work is required to determine how to apply the DSM for preoperative and postoperative spinal deformity management. Copyright © 2017. Published by Elsevier B.V.

  2. Gait dynamics to optimize fall risk assessment in geriatric patients admitted to an outpatient diagnostic clinic

    PubMed Central

    de Groot, Maartje H.; van Campen, Jos P.; Beijnen, Jos H.; Hortobágyi, Tibor; Vuillerme, Nicolas; Lamoth, Claudine C. J.

    2017-01-01

    Fall prediction in geriatric patients remains challenging because the increased fall risk involves multiple, interrelated factors caused by natural aging and/or pathology. Therefore, we used a multi-factorial statistical approach to model categories of modifiable fall risk factors among geriatric patients to identify fallers with highest sensitivity and specificity with a focus on gait performance. Patients (n = 61, age = 79; 41% fallers) underwent extensive screening in three categories: (1) patient characteristics (e.g., handgrip strength, medication use, osteoporosis-related factors) (2) cognitive function (global cognition, memory, executive function), and (3) gait performance (speed-related and dynamic outcomes assessed by tri-axial trunk accelerometry). Falls were registered prospectively (mean follow-up 8.6 months) and one year retrospectively. Principal Component Analysis (PCA) on 11 gait variables was performed to determine underlying gait properties. Three fall-classification models were then built using Partial Least Squares–Discriminant Analysis (PLS-DA), with separate and combined analyses of the fall risk factors. PCA identified ‘pace’, ‘variability’, and ‘coordination’ as key properties of gait. The best PLS-DA model produced a fall classification accuracy of AUC = 0.93. The specificity of the model using patient characteristics was 60% but reached 80% when cognitive and gait outcomes were added. The inclusion of cognition and gait dynamics in fall classification models reduced misclassification. We therefore recommend assessing geriatric patients’ fall risk using a multi-factorial approach that incorporates patient characteristics, cognition, and gait dynamics. PMID:28575126

  3. Gait dynamics to optimize fall risk assessment in geriatric patients admitted to an outpatient diagnostic clinic.

    PubMed

    Kikkert, Lisette H J; de Groot, Maartje H; van Campen, Jos P; Beijnen, Jos H; Hortobágyi, Tibor; Vuillerme, Nicolas; Lamoth, Claudine C J

    2017-01-01

    Fall prediction in geriatric patients remains challenging because the increased fall risk involves multiple, interrelated factors caused by natural aging and/or pathology. Therefore, we used a multi-factorial statistical approach to model categories of modifiable fall risk factors among geriatric patients to identify fallers with highest sensitivity and specificity with a focus on gait performance. Patients (n = 61, age = 79; 41% fallers) underwent extensive screening in three categories: (1) patient characteristics (e.g., handgrip strength, medication use, osteoporosis-related factors) (2) cognitive function (global cognition, memory, executive function), and (3) gait performance (speed-related and dynamic outcomes assessed by tri-axial trunk accelerometry). Falls were registered prospectively (mean follow-up 8.6 months) and one year retrospectively. Principal Component Analysis (PCA) on 11 gait variables was performed to determine underlying gait properties. Three fall-classification models were then built using Partial Least Squares-Discriminant Analysis (PLS-DA), with separate and combined analyses of the fall risk factors. PCA identified 'pace', 'variability', and 'coordination' as key properties of gait. The best PLS-DA model produced a fall classification accuracy of AUC = 0.93. The specificity of the model using patient characteristics was 60% but reached 80% when cognitive and gait outcomes were added. The inclusion of cognition and gait dynamics in fall classification models reduced misclassification. We therefore recommend assessing geriatric patients' fall risk using a multi-factorial approach that incorporates patient characteristics, cognition, and gait dynamics.

  4. Dynamic fractals in spatial evolutionary games

    NASA Astrophysics Data System (ADS)

    Kolotev, Sergei; Malyutin, Aleksandr; Burovski, Evgeni; Krashakov, Sergei; Shchur, Lev

    2018-06-01

    We investigate critical properties of a spatial evolutionary game based on the Prisoner's Dilemma. Simulations demonstrate a jump in the component densities accompanied by drastic changes in average sizes of the component clusters. We argue that the cluster boundary is a random fractal. Our simulations are consistent with the fractal dimension of the boundary being equal to 2, and the cluster boundaries are hence asymptotically space filling as the system size increases.

  5. A fractal approach to dynamic inference and distribution analysis

    PubMed Central

    van Rooij, Marieke M. J. W.; Nash, Bertha A.; Rajaraman, Srinivasan; Holden, John G.

    2013-01-01

    Event-distributions inform scientists about the variability and dispersion of repeated measurements. This dispersion can be understood from a complex systems perspective, and quantified in terms of fractal geometry. The key premise is that a distribution's shape reveals information about the governing dynamics of the system that gave rise to the distribution. Two categories of characteristic dynamics are distinguished: additive systems governed by component-dominant dynamics and multiplicative or interdependent systems governed by interaction-dominant dynamics. A logic by which systems governed by interaction-dominant dynamics are expected to yield mixtures of lognormal and inverse power-law samples is discussed. These mixtures are described by a so-called cocktail model of response times derived from human cognitive performances. The overarching goals of this article are twofold: First, to offer readers an introduction to this theoretical perspective and second, to offer an overview of the related statistical methods. PMID:23372552

  6. Fractals for Geoengineering

    NASA Astrophysics Data System (ADS)

    Oleshko, Klaudia; de Jesús Correa López, María; Romero, Alejandro; Ramírez, Victor; Pérez, Olga

    2016-04-01

    The effectiveness of fractal toolbox to capture the scaling or fractal probability distribution, and simply fractal statistics of main hydrocarbon reservoir attributes, was highlighted by Mandelbrot (1995) and confirmed by several researchers (Zhao et al., 2015). Notwithstanding, after more than twenty years, it's still common the opinion that fractals are not useful for the petroleum engineers and especially for Geoengineering (Corbett, 2012). In spite of this negative background, we have successfully applied the fractal and multifractal techniques to our project entitled "Petroleum Reservoir as a Fractal Reactor" (2013 up to now). The distinguishable feature of Fractal Reservoir is the irregular shapes and rough pore/solid distributions (Siler, 2007), observed across a broad range of scales (from SEM to seismic). At the beginning, we have accomplished the detailed analysis of Nelson and Kibler (2003) Catalog of Porosity and Permeability, created for the core plugs of siliciclastic rocks (around ten thousand data were compared). We enriched this Catalog by more than two thousand data extracted from the last ten years publications on PoroPerm (Corbett, 2012) in carbonates deposits, as well as by our own data from one of the PEMEX, Mexico, oil fields. The strong power law scaling behavior was documented for the major part of these data from the geological deposits of contrasting genesis. Based on these results and taking into account the basic principles and models of the Physics of Fractals, introduced by Per Back and Kan Chen (1989), we have developed new software (Muukíl Kaab), useful to process the multiscale geological and geophysical information and to integrate the static geological and petrophysical reservoir models to dynamic ones. The new type of fractal numerical model with dynamical power law relations among the shapes and sizes of mesh' cells was designed and calibrated in the studied area. The statistically sound power law relations were established

  7. LETTER TO THE EDITOR: Fractal diffusion coefficient from dynamical zeta functions

    NASA Astrophysics Data System (ADS)

    Cristadoro, Giampaolo

    2006-03-01

    Dynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero.

  8. Statically vs dynamically balanced gait: Analysis of a robotic exoskeleton compared with a human.

    PubMed

    Barbareschi, Giulia; Richards, Rosie; Thornton, Matt; Carlson, Tom; Holloway, Catherine

    2015-01-01

    In recent years exoskeletons able to replicate human gait have begun to attract growing popularity for both assistive and rehabilitative purposes. Although wearable robots often need the use of external support in order to maintain stability, the REX exoskeleton by REX Bionics is able to self-balance through the whole cycle. However this statically balanced gait presents important differences with the dynamically balanced gait of human subjects. This paper will examine kinematic and kinetic differences between the gait analysis performed on a subject wearing the REX exoskeleton and human gait analysis data as presented in literature. We will also provide an insight on the impact that these differences can have for both rehabilitative and assistive applications.

  9. Fractal Physiology and the Fractional Calculus: A Perspective

    PubMed Central

    West, Bruce J.

    2010-01-01

    This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a

  10. Possibilities of fractal analysis of the competitive dynamics: Approaches and procedures

    NASA Astrophysics Data System (ADS)

    Zagornaya, T. O.; Medvedeva, M. A.; Panova, V. L.; Isaichik, K. F.; Medvedev, A. N.

    2017-11-01

    The possibilities of the fractal approach are used for the study of non-linear nature of the competitive dynamics of the market of trading intermediaries. Based on a statistical study of the functioning of retail indicators in the region, the approach to the analysis of the characteristics of the competitive behavior of market participants is developed. The authors postulate the principles of studying the dynamics of competition as a result of changes in the characteristics of the vector and the competitive behavior of market agents.

  11. Fractals in biology and medicine

    NASA Technical Reports Server (NTRS)

    Havlin, S.; Buldyrev, S. V.; Goldberger, A. L.; Mantegna, R. N.; Ossadnik, S. M.; Peng, C. K.; Simons, M.; Stanley, H. E.

    1995-01-01

    Our purpose is to describe some recent progress in applying fractal concepts to systems of relevance to biology and medicine. We review several biological systems characterized by fractal geometry, with a particular focus on the long-range power-law correlations found recently in DNA sequences containing noncoding material. Furthermore, we discuss the finding that the exponent alpha quantifying these long-range correlations ("fractal complexity") is smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the normal heart is characterized by long-range "anticorrelations" which are absent in the diseased heart.

  12. Dynamic Modeling of GAIT System Reveals Transcriptome Expansion and Translational Trickle Control Device

    PubMed Central

    Yao, Peng; Potdar, Alka A.; Arif, Abul; Ray, Partho Sarothi; Mukhopadhyay, Rupak; Willard, Belinda; Xu, Yichi; Yan, Jun; Saidel, Gerald M.; Fox, Paul L.

    2012-01-01

    SUMMARY Post-transcriptional regulatory mechanisms superimpose “fine-tuning” control upon “on-off” switches characteristic of gene transcription. We have exploited computational modeling with experimental validation to resolve an anomalous relationship between mRNA expression and protein synthesis. Differential GAIT (Gamma-interferon Activated Inhibitor of Translation) complex activation repressed VEGF-A synthesis to a low, constant rate despite high, variable VEGFA mRNA expression. Dynamic model simulations indicated the presence of an unidentified, inhibitory GAIT element-interacting factor. We discovered a truncated form of glutamyl-prolyl tRNA synthetase (EPRS), the GAIT constituent that binds the 3’-UTR GAIT element in target transcripts. The truncated protein, EPRSN1, prevents binding of functional GAIT complex. EPRSN1 mRNA is generated by a remarkable polyadenylation-directed conversion of a Tyr codon in the EPRS coding sequence to a stop codon (PAY*). By low-level protection of GAIT element-bearing transcripts, EPRSN1 imposes a robust “translational trickle” of target protein expression. Genome-wide analysis shows PAY* generates multiple truncated transcripts thereby contributing to transcriptome expansion. PMID:22386318

  13. An Approach to Study Elastic Vibrations of Fractal Cylinders

    NASA Astrophysics Data System (ADS)

    Steinberg, Lev; Zepeda, Mario

    2016-11-01

    This paper presents our study of dynamics of fractal solids. Concepts of fractal continuum and time had been used in definitions of a fractal body deformation and motion, formulation of conservation of mass, balance of momentum, and constitutive relationships. A linearized model, which was written in terms of fractal time and spatial derivatives, has been employed to study the elastic vibrations of fractal circular cylinders. Fractal differential equations of torsional, longitudinal and transverse fractal wave equations have been obtained and solution properties such as size and time dependence have been revealed.

  14. Estimating dynamic permeability in fractal pore network saturated by Maxwellian fluid

    NASA Astrophysics Data System (ADS)

    Sun, W.

    2017-12-01

    The frequency dependent flow of fluid in porous media is an important issue in geophysical prospecting. Oscillating flow in pipe leads to frequency dependent dynamic permeability and has been studied in pore network containing Newtonian fluid. But there is little work on oscillating complex fluid in pipe network, especially in irregular network. Here we formulated frequency dependent permeability for Maxwellian fluid and estimated the permeability in three-dimensional fractal network model. We consider an infinitely long cylindrical pipe with rigid solid wall. The pipe is filled with Maxwellian fluids. Based on the mass conservation equation, the equilibrium equation of force and Maxwell constitutive relationship, we formulated the flux by integration of axial velocity component over the pipe's cross section. Then we extend single pipe formulation to a 3D irregular network. Flux balance condition yields a set of linear equations whose unknowns are the fluid pressure at each node. By evaluating the total flow flux through the network, the dynamic permeability can be calculated.We investigated the dynamic permeability of brine and CPyCl/NaSal in a 3D porous sample with a cubic side length 1 cm. The pore network is created by a Voronoi cell filling method. The porosity, i.e., volume ratio between pore/pipe network and the overall cubic, is set as 0.1. The irregular pore network has a fractal structure. The dimension d of the pore network is defined by the relation between node number M within a sphere and the radius r of the sphere,M=rd.The results show that both brine and Maxwellian fluid's permeability maintain a stable value at low frequency, then decreases with fluctuating peaks. The dynamic permeability in pore networks saturated by Maxwellian fluid (CPyCl/NaSal (60 mM)) show larger peaks during the decline process at high frequency, which represents the typical resonance behavior. Dynamic permeability shows clear dependence on the dimension of the fractal

  15. Generation of Adaptive Gait Patterns for Quadruped Robot with CPG Network including Motor Dynamic Model

    NASA Astrophysics Data System (ADS)

    Son, Yurak; Kamano, Takuya; Yasuno, Takashi; Suzuki, Takayuki; Harada, Hironobu

    This paper describes the generation of adaptive gait patterns using new Central Pattern Generators (CPGs) including motor dynamic models for a quadruped robot under various environment. The CPGs act as the flexible oscillators of the joints and make the desired angle of the joints. The CPGs are mutually connected each other, and the sets of their coupling parameters are adjusted by genetic algorithm so that the quadruped robot can realize the stable and adequate gait patterns. As a result of generation, the suitable CPG networks for not only a walking straight gait pattern but also rotation gait patterns are obtained. Experimental results demonstrate that the proposed CPG networks are effective to automatically adjust the adaptive gait patterns for the tested quadruped robot under various environment. Furthermore, the target tracking control based on image processing is achieved by combining the generated gait patterns.

  16. Deterministic chaos and fractal complexity in the dynamics of cardiovascular behavior: perspectives on a new frontier.

    PubMed

    Sharma, Vijay

    2009-09-10

    Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts.

  17. Deterministic Chaos and Fractal Complexity in the Dynamics of Cardiovascular Behavior: Perspectives on a New Frontier

    PubMed Central

    Sharma, Vijay

    2009-01-01

    Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts. PMID:19812706

  18. Fractal scaling analysis of groundwater dynamics in confined aquifers

    NASA Astrophysics Data System (ADS)

    Tu, Tongbi; Ercan, Ali; Kavvas, M. Levent

    2017-10-01

    Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA) and multiscale multifractal analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.

  19. Heart rate dynamics in patients with stable angina pectoris and utility of fractal and complexity measures

    NASA Technical Reports Server (NTRS)

    Makikallio, T. H.; Ristimae, T.; Airaksinen, K. E.; Peng, C. K.; Goldberger, A. L.; Huikuri, H. V.

    1998-01-01

    Dynamic analysis techniques may uncover abnormalities in heart rate (HR) behavior that are not easily detectable with conventional statistical measures. However, the applicability of these new methods for detecting possible abnormalities in HR behavior in various cardiovascular disorders is not well established. Conventional measures of HR variability were compared with short-term (< or = 11 beats, alpha1) and long-term (> 11 beats, alpha2) fractal correlation properties and with approximate entropy of RR interval data in 38 patients with stable angina pectoris without previous myocardial infarction or cardiac medication at the time of the study and 38 age-matched healthy controls. The short- and long-term fractal scaling exponents (alpha1, alpha2) were significantly higher in the coronary patients than in the healthy controls (1.34 +/- 0.15 vs 1.11 +/- 0.12 [p <0.001] and 1.10 +/- 0.08 vs 1.04 +/- 0.06 [p <0.01], respectively), and they also had lower approximate entropy (p <0.05), standard deviation of all RR intervals (p <0.01), and high-frequency spectral component of HR variability (p <0.05). The short-term fractal scaling exponent performed better than other heart rate variability parameters in differentiating patients with coronary artery disease from healthy subjects, but it was not related to the clinical or angiographic severity of coronary artery disease or any single nonspectral or spectral measure of HR variability in this retrospective study. Patients with stable angina pectoris have altered fractal properties and reduced complexity in their RR interval dynamics relative to age-matched healthy subjects. Dynamic analysis may complement traditional analyses in detecting altered HR behavior in patients with stable angina pectoris.

  20. Climbing favours the tripod gait over alternative faster insect gaits

    NASA Astrophysics Data System (ADS)

    Ramdya, Pavan; Thandiackal, Robin; Cherney, Raphael; Asselborn, Thibault; Benton, Richard; Ijspeert, Auke Jan; Floreano, Dario

    2017-02-01

    To escape danger or catch prey, running vertebrates rely on dynamic gaits with minimal ground contact. By contrast, most insects use a tripod gait that maintains at least three legs on the ground at any given time. One prevailing hypothesis for this difference in fast locomotor strategies is that tripod locomotion allows insects to rapidly navigate three-dimensional terrain. To test this, we computationally discovered fast locomotor gaits for a model based on Drosophila melanogaster. Indeed, the tripod gait emerges to the exclusion of many other possible gaits when optimizing fast upward climbing with leg adhesion. By contrast, novel two-legged bipod gaits are fastest on flat terrain without adhesion in the model and in a hexapod robot. Intriguingly, when adhesive leg structures in real Drosophila are covered, animals exhibit atypical bipod-like leg coordination. We propose that the requirement to climb vertical terrain may drive the prevalence of the tripod gait over faster alternative gaits with minimal ground contact.

  1. Climbing favours the tripod gait over alternative faster insect gaits

    PubMed Central

    Ramdya, Pavan; Thandiackal, Robin; Cherney, Raphael; Asselborn, Thibault; Benton, Richard; Ijspeert, Auke Jan; Floreano, Dario

    2017-01-01

    To escape danger or catch prey, running vertebrates rely on dynamic gaits with minimal ground contact. By contrast, most insects use a tripod gait that maintains at least three legs on the ground at any given time. One prevailing hypothesis for this difference in fast locomotor strategies is that tripod locomotion allows insects to rapidly navigate three-dimensional terrain. To test this, we computationally discovered fast locomotor gaits for a model based on Drosophila melanogaster. Indeed, the tripod gait emerges to the exclusion of many other possible gaits when optimizing fast upward climbing with leg adhesion. By contrast, novel two-legged bipod gaits are fastest on flat terrain without adhesion in the model and in a hexapod robot. Intriguingly, when adhesive leg structures in real Drosophila are covered, animals exhibit atypical bipod-like leg coordination. We propose that the requirement to climb vertical terrain may drive the prevalence of the tripod gait over faster alternative gaits with minimal ground contact. PMID:28211509

  2. Emergence of fractal scaling in complex networks

    NASA Astrophysics Data System (ADS)

    Wei, Zong-Wen; Wang, Bing-Hong

    2016-09-01

    Some real-world networks are shown to be fractal or self-similar. It is widespread that such a phenomenon originates from the repulsion between hubs or disassortativity. Here we show that this common belief fails to capture the causality. Our key insight to address it is to pinpoint links critical to fractality. Those links with small edge betweenness centrality (BC) constitute a special architecture called fractal reference system, which gives birth to the fractal structure of those reported networks. In contrast, a small amount of links with high BC enable small-world effects, hiding the intrinsic fractality. With enough of such links removed, fractal scaling spontaneously arises from nonfractal networks. Our results provide a multiple-scale view on the structure and dynamics and place fractality as a generic organizing principle of complex networks on a firmer ground.

  3. Exterior dimension of fat fractals

    NASA Technical Reports Server (NTRS)

    Grebogi, C.; Mcdonald, S. W.; Ott, E.; Yorke, J. A.

    1985-01-01

    Geometric scaling properties of fat fractal sets (fractals with finite volume) are discussed and characterized via the introduction of a new dimension-like quantity which is called the exterior dimension. In addition, it is shown that the exterior dimension is related to the 'uncertainty exponent' previously used in studies of fractal basin boundaries, and it is shown how this connection can be exploited to determine the exterior dimension. Three illustrative applications are described, two in nonlinear dynamics and one dealing with blood flow in the body. Possible relevance to porous materials and ballistic driven aggregation is also noted.

  4. Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics

    NASA Technical Reports Server (NTRS)

    Iyengar, N.; Peng, C. K.; Morin, R.; Goldberger, A. L.; Lipsitz, L. A.

    1996-01-01

    We postulated that aging is associated with disruption in the fractallike long-range correlations that characterize healthy sinus rhythm cardiac interval dynamics. Ten young (21-34 yr) and 10 elderly (68-81 yr) rigorously screened healthy subjects underwent 120 min of continuous supine resting electrocardiographic recording. We analyzed the interbeat interval time series using standard time and frequency domain statistics and using a fractal measure, detrended fluctuation analysis, to quantify long-range correlation properties. In healthy young subjects, interbeat intervals demonstrated fractal scaling, with scaling exponents (alpha) from the fluctuation analysis close to a value of 1.0. In the group of healthy elderly subjects, the interbeat interval time series had two scaling regions. Over the short range, interbeat interval fluctuations resembled a random walk process (Brownian noise, alpha = 1.5), whereas over the longer range they resembled white noise (alpha = 0.5). Short (alpha s)- and long-range (alpha 1) scaling exponents were significantly different in the elderly subjects compared with young (alpha s = 1.12 +/- 0.19 vs. 0.90 +/- 0.14, respectively, P = 0.009; alpha 1 = 0.75 +/- 0.17 vs. 0.99 +/- 0.10, respectively, P = 0.002). The crossover behavior from one scaling region to another could be modeled as a first-order autoregressive process, which closely fit the data from four elderly subjects. This implies that a single characteristic time scale may be dominating heartbeat control in these subjects. The age-related loss of fractal organization in heartbeat dynamics may reflect the degradation of integrated physiological regulatory systems and may impair an individual's ability to adapt to stress.

  5. Long-range correlations and fractal dynamics in C. elegans: Changes with aging and stress

    NASA Astrophysics Data System (ADS)

    Alves, Luiz G. A.; Winter, Peter B.; Ferreira, Leonardo N.; Brielmann, Renée M.; Morimoto, Richard I.; Amaral, Luís A. N.

    2017-08-01

    Reduced motor control is one of the most frequent features associated with aging and disease. Nonlinear and fractal analyses have proved to be useful in investigating human physiological alterations with age and disease. Similar findings have not been established for any of the model organisms typically studied by biologists, though. If the physiology of a simpler model organism displays the same characteristics, this fact would open a new research window on the control mechanisms that organisms use to regulate physiological processes during aging and stress. Here, we use a recently introduced animal-tracking technology to simultaneously follow tens of Caenorhabdits elegans for several hours and use tools from fractal physiology to quantitatively evaluate the effects of aging and temperature stress on nematode motility. Similar to human physiological signals, scaling analysis reveals long-range correlations in numerous motility variables, fractal properties in behavioral shifts, and fluctuation dynamics over a wide range of timescales. These properties change as a result of a superposition of age and stress-related adaptive mechanisms that regulate motility.

  6. Fractal 1/f Dynamics Suggest Entanglement of Measurement and Human Performance

    ERIC Educational Resources Information Center

    Holden, John G.; Choi, Inhyun; Amazeen, Polemnia G.; Van Orden, Guy

    2011-01-01

    Variability of repeated measurements in human performances exhibits fractal 1/f noise. Yet the relative strength of this fractal pattern varies widely across conditions, tasks, and individuals. Four experiments illustrate how subtle details of the conditions of measurement change the fractal patterns observed across task conditions. The results…

  7. Fractional Stability of Trunk Acceleration Dynamics of Daily-Life Walking: Toward a Unified Concept of Gait Stability

    PubMed Central

    Ihlen, Espen A. F.; van Schooten, Kimberley S.; Bruijn, Sjoerd M.; Pijnappels, Mirjam; van Dieën, Jaap H.

    2017-01-01

    Over the last decades, various measures have been introduced to assess stability during walking. All of these measures assume that gait stability may be equated with exponential stability, where dynamic stability is quantified by a Floquet multiplier or Lyapunov exponent. These specific constructs of dynamic stability assume that the gait dynamics are time independent and without phase transitions. In this case the temporal change in distance, d(t), between neighboring trajectories in state space is assumed to be an exponential function of time. However, results from walking models and empirical studies show that the assumptions of exponential stability break down in the vicinity of phase transitions that are present in each step cycle. Here we apply a general non-exponential construct of gait stability, called fractional stability, which can define dynamic stability in the presence of phase transitions. Fractional stability employs the fractional indices, α and β, of differential operator which allow modeling of singularities in d(t) that cannot be captured by exponential stability. The fractional stability provided an improved fit of d(t) compared to exponential stability when applied to trunk accelerations during daily-life walking in community-dwelling older adults. Moreover, using multivariate empirical mode decomposition surrogates, we found that the singularities in d(t), which were well modeled by fractional stability, are created by phase-dependent modulation of gait. The new construct of fractional stability may represent a physiologically more valid concept of stability in vicinity of phase transitions and may thus pave the way for a more unified concept of gait stability. PMID:28900400

  8. Influence of footwear midsole material hardness on dynamic balance control during unexpected gait termination.

    PubMed

    Perry, Stephen D; Radtke, Alison; Goodwin, Chris R

    2007-01-01

    The purpose of this study was to determine the influence of different midsole hardnesses on dynamic balance control during unexpected gait termination. Twelve healthy young female adults were asked to walk along an 8-m walkway, looking straight ahead. During 25% of the trials, they were signaled (via an audio buzzer) to terminate gait within the next two steps. The four experimental conditions were: (1) soft (A15); (2) standard (A33); (3) hard (A50); (4) barefoot. Center of mass (COM) position relative to the lateral base of support (BOS), center of mass-center of pressure (COM-COP) difference and vertical loading rate were used to evaluate the influence of midsole material on dynamic balance control. The results were a decrease in the medial-lateral range of COM with respect to the lateral BOS, a reduction in the maximum COM-COP difference and an increase in the vertical loading rate due to the presence and hardness level of the midsole material when compared to the barefoot condition. The primary outcomes of this study have illustrated the influence of midsole hardness as an impediment to dynamic balance control during responses to gait termination. In conclusion, the present study suggests that variations in midsole material and even the presence of it, impairs the dynamic balance control system.

  9. Vibrotactile tilt feedback improves dynamic gait index: a fall risk indicator in older adults.

    PubMed

    Wall, Conrad; Wrisley, Diane M; Statler, Kennyn D

    2009-07-01

    The purpose of this study was to determine the effectiveness of vibrotactile feedback of body tilt in improving dynamic gait index (DGI) a fall risk indicator in community dwelling older adults. Twelve healthy elderly subjects (three males and nine females, age 79.7+/-5.4 yrs) were tested in an institutional balance rehabilitation laboratory to investigate changes between the feedback off and on conditions. Subjects were acutely exposed to a vibrotactile display that indicated the magnitude and direction of their body tilt from the vertical. DGI and mediolateral (ML) sway were determined during locomotion with, and without, vibrotactile tilt feedback (VTTF). All subjects were at risk for falls based on their initial DGI Score (range: 15-19, mean 17.4+/-1.56), which was taken with the vibratory stimulus turned off. Subjects learned to use the trunk tilt information from the vibrotactile feedback vest through 20-30 min of gait and balance training consisting of activities that challenged their balance. Subjects were then retested on the DGI. Statistically significant changes were demonstrated for the DGI total score while using the vibrotactile tilt feedback. DGI total scores improved from 17.1+/-0.4 to 20.8+/-0.3 (p<0.05). We conclude that vibrotactile tilt feedback improves both control of mediolateral sway during gait and dynamic gait index. Both are fall risk indicators for this population.

  10. Fractal Folding and Medium Viscoelasticity Contribute Jointly to Chromosome Dynamics

    NASA Astrophysics Data System (ADS)

    Polovnikov, K. E.; Gherardi, M.; Cosentino-Lagomarsino, M.; Tamm, M. V.

    2018-02-01

    Chromosomes are key players of cell physiology, their dynamics provides valuable information about its physical organization. In both prokaryotes and eukaryotes, the short-time motion of chromosomal loci has been described with a Rouse model in a simple or viscoelastic medium. However, little emphasis has been put on the influence of the folded organization of chromosomes on the local dynamics. Clearly, stress propagation, and thus dynamics, must be affected by such organization, but a theory allowing us to extract such information from data, e.g., on two-point correlations, is lacking. Here, we describe a theoretical framework able to answer this general polymer dynamics question. We provide a scaling analysis of the stress-propagation time between two loci at a given arclength distance along the chromosomal coordinate. The results suggest a precise way to assess folding information from the dynamical coupling of chromosome segments. Additionally, we realize this framework in a specific model of a polymer whose long-range interactions are designed to make it fold in a fractal way and immersed in a medium characterized by subdiffusive fractional Langevin motion with a tunable scaling exponent. This allows us to derive explicit analytical expressions for the correlation functions.

  11. Effect of Fractal Dimension on the Strain Behavior of Particulate Media

    NASA Astrophysics Data System (ADS)

    Altun, Selim; Sezer, Alper; Goktepe, A. Burak

    2016-12-01

    In this study, the influence of several fractal identifiers of granular materials on dynamic behavior of a flexible pavement structure as a particulate stratum is considered. Using experimental results and numerical methods as well, 15 different grain-shaped sands obtained from 5 different sources were analyzed as pavement base course materials. Image analyses were carried out by use of a stereomicroscope on 15 different samples to obtain quantitative particle shape information. Furthermore, triaxial compression tests were conducted to determine stress-strain and shear strength parameters of sands. Additionally, the dynamic response of the particulate media to standard traffic loads was computed using finite element modeling (FEM) technique. Using area-perimeter, line divider and box counting methods, over a hundred grains for each sand type were subjected to fractal analysis. Relationships among fractal dimension descriptors and dynamic strain levels were established for assessment of importance of shape descriptors of sands at various scales on the dynamic behavior. In this context, the advantage of fractal geometry concept to describe irregular and fractured shapes was used to characterize the sands used as base course materials. Results indicated that fractal identifiers can be preferred to analyze the effect of shape properties of sands on dynamic behavior of pavement base layers.

  12. Recognition using gait.

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Koch, Mark William

    2007-09-01

    Gait or an individual's manner of walking, is one approach for recognizing people at a distance. Studies in psychophysics and medicine indicate that humans can recognize people by their gait and have found twenty-four different components to gait that taken together make it a unique signature. Besides not requiring close sensor contact, gait also does not necessarily require a cooperative subject. Using video data of people walking in different scenarios and environmental conditions we develop and test an algorithm that uses shape and motion to identify people from their gait. The algorithm uses dynamic time warping to match stored templatesmore » against an unknown sequence of silhouettes extracted from a person walking. While results under similar constraints and conditions are very good, the algorithm quickly degrades with varying conditions such as surface and clothing.« less

  13. The fractal geometry of Hartree-Fock

    NASA Astrophysics Data System (ADS)

    Theel, Friethjof; Karamatskou, Antonia; Santra, Robin

    2017-12-01

    The Hartree-Fock method is an important approximation for the ground-state electronic wave function of atoms and molecules so that its usage is widespread in computational chemistry and physics. The Hartree-Fock method is an iterative procedure in which the electronic wave functions of the occupied orbitals are determined. The set of functions found in one step builds the basis for the next iteration step. In this work, we interpret the Hartree-Fock method as a dynamical system since dynamical systems are iterations where iteration steps represent the time development of the system, as encountered in the theory of fractals. The focus is put on the convergence behavior of the dynamical system as a function of a suitable control parameter. In our case, a complex parameter λ controls the strength of the electron-electron interaction. An investigation of the convergence behavior depending on the parameter λ is performed for helium, neon, and argon. We observe fractal structures in the complex λ-plane, which resemble the well-known Mandelbrot set, determine their fractal dimension, and find that with increasing nuclear charge, the fragmentation increases as well.

  14. Beyond Fractals and 1/f Noise: Multifractal Analysis of Complex Physiological Time Series

    NASA Astrophysics Data System (ADS)

    Ivanov, Plamen Ch.; Amaral, Luis A. N.; Ashkenazy, Yosef; Stanley, H. Eugene; Goldberger, Ary L.; Hausdorff, Jeffrey M.; Yoneyama, Mitsuru; Arai, Kuniharu

    2001-03-01

    We investigate time series with 1/f-like spectra generated by two physiologic control systems --- the human heartbeat and human gait. We show that physiological fluctuations exhibit unexpected ``hidden'' structures often described by scaling laws. In particular, our studies indicate that when analyzed on different time scales the heartbeat fluctuations exhibit cascades of branching patterns with self-similar (fractal) properties, characterized by long-range power-law anticorrelations. We find that these scaling features change during sleep and wake phases, and with pathological perturbations. Further, by means of a new wavelet-based technique, we find evidence of multifractality in the healthy human heartbeat even under resting conditions, and show that the multifractal character and nonlinear properties of the healthy heart are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure. In contrast to the heartbeat, we find that the interstride interval time series of healthy human gait, a voluntary process under neural regulation, is described by a single fractal dimension (such as classical 1/f noise) indicating monofractal behavior. Thus our approach can help distinguish physiological and physical signals with comparable frequency spectra and two-point correlations, and guide modeling of their control mechanisms.

  15. Fractality à la carte: a general particle aggregation model.

    PubMed

    Nicolás-Carlock, J R; Carrillo-Estrada, J L; Dossetti, V

    2016-01-19

    In nature, fractal structures emerge in a wide variety of systems as a local optimization of entropic and energetic distributions. The fractality of these systems determines many of their physical, chemical and/or biological properties. Thus, to comprehend the mechanisms that originate and control the fractality is highly relevant in many areas of science and technology. In studying clusters grown by aggregation phenomena, simple models have contributed to unveil some of the basic elements that give origin to fractality, however, the specific contribution from each of these elements to fractality has remained hidden in the complex dynamics. Here, we propose a simple and versatile model of particle aggregation that is, on the one hand, able to reveal the specific entropic and energetic contributions to the clusters' fractality and morphology, and, on the other, capable to generate an ample assortment of rich natural-looking aggregates with any prescribed fractal dimension.

  16. Energy Expenditure of Trotting Gait Under Different Gait Parameters

    NASA Astrophysics Data System (ADS)

    Chen, Xian-Bao; Gao, Feng

    2017-07-01

    Robots driven by batteries are clean, quiet, and can work indoors or in space. However, the battery endurance is a great problem. A new gait parameter design energy saving strategy to extend the working hours of the quadruped robot is proposed. A dynamic model of the robot is established to estimate and analyze the energy expenditures during trotting. Given a trotting speed, optimal stride frequency and stride length can minimize the energy expenditure. However, the relationship between the speed and the optimal gait parameters is nonlinear, which is difficult for practical application. Therefore, a simplified gait parameter design method for energy saving is proposed. A critical trotting speed of the quadruped robot is found and can be used to decide the gait parameters. When the robot is travelling lower than this speed, it is better to keep a constant stride length and change the cycle period. When the robot is travelling higher than this speed, it is better to keep a constant cycle period and change the stride length. Simulations and experiments on the quadruped robot show that by using the proposed gait parameter design approach, the energy expenditure can be reduced by about 54% compared with the 100 mm stride length under 500 mm/s speed. In general, an energy expenditure model based on the gait parameter of the quadruped robot is built and the trotting gait parameters design approach for energy saving is proposed.

  17. Effects of altering heel wedge properties on gait with the Intrepid Dynamic Exoskeletal Orthosis.

    PubMed

    Ikeda, Andrea J; Fergason, John R; Wilken, Jason M

    2018-06-01

    The Intrepid Dynamic Exoskeletal Orthosis is a custom-made dynamic response carbon fiber device. A heel wedge, which sits in the shoe, is an integral part of the orthosis-heel wedge-shoe system. Because the device restricts ankle movement, the system must compensate to simulate plantarflexion and allow smooth forward progression during gait. To determine the influence of wedge height and durometer on the walking gait of individuals using the Intrepid Dynamic Exoskeletal Orthosis. Repeated measures. Twelve individuals walked over level ground with their Intrepid Dynamic Exoskeletal Orthosis and six different heel wedges of soft or firm durometer and 1, 2, or 3 cm height. Center of pressure velocity, joint moments, and roll-over shape were calculated for each wedge. Height and durometer significantly affected time to peak center of pressure velocity, time to peak internal dorsiflexion and knee extension moments, time to ankle moment zero crossing, and roll-over shape center of curvature anterior-posterior position. Wedge height had a significant influence on peak center of pressure velocity, peak dorsiflexion moment, time to peak knee extension moment, and roll-over shape radius and vertical center of curvature. Changes in wedge height and durometer systematically affected foot loading. Participants preferred wedges which produced ankle moment zero crossing timing, peak internal knee extension moment timing, and roll-over shape center of curvature anterior-posterior position close to that of able-bodied individuals. Clinical relevance Adjusting the heel wedge is a simple, straightforward way to adjust the orthosis-heel wedge-shoe system. Changing wedge height and durometer significantly alters loading of the foot and has great potential to improve an individual's gait.

  18. A New Fractal Model of Chromosome and DNA Processes

    NASA Astrophysics Data System (ADS)

    Bouallegue, K.

    Dynamic chromosome structure remains unknown. Can fractals and chaos be used as new tools to model, identify and generate a structure of chromosomes?Fractals and chaos offer a rich environment for exploring and modeling the complexity of nature. In a sense, fractal geometry is used to describe, model, and analyze the complex forms found in nature. Fractals have also been widely not only in biology but also in medicine. To this effect, a fractal is considered an object that displays self-similarity under magnification and can be constructed using a simple motif (an image repeated on ever-reduced scales).It is worth noting that the problem of identifying a chromosome has become a challenge to find out which one of the models it belongs to. Nevertheless, the several different models (a hierarchical coiling, a folded fiber, and radial loop) have been proposed for mitotic chromosome but have not reached a dynamic model yet.This paper is an attempt to solve topological problems involved in the model of chromosome and DNA processes. By combining the fractal Julia process and the numerical dynamical system, we have finally found out four main points. First, we have developed not only a model of chromosome but also a model of mitosis and one of meiosis. Equally important, we have identified the centromere position through the numerical model captured below. More importantly, in this paper, we have discovered the processes of the cell divisions of both mitosis and meiosis. All in all, the results show that this work could have a strong impact on the welfare of humanity and can lead to a cure of genetic diseases.

  19. Dynamic stability requirements during gait and standing exergames on the wii fit® system in the elderly

    PubMed Central

    2012-01-01

    Background In rehabilitation, training intensity is usually adapted to optimize the trained system to attain better performance (overload principle). However, in balance rehabilitation, the level of intensity required during training exercises to optimize improvement in balance has rarely been studied, probably due to the difficulty in quantifying the stability level during these exercises. The goal of the present study was to test whether the stabilizing/destabilizing forces model could be used to analyze how stability is challenged during several exergames, that are more and more used in balance rehabilitation, and a dynamic functional task, such as gait. Methods Seven healthy older adults were evaluated with three-dimensional motion analysis during gait at natural and fast speed, and during three balance exergames (50/50 Challenge, Ski Slalom and Soccer). Mean and extreme values for stabilizing force, destabilizing force and the ratio of the two forces (stability index) were computed from kinematic and kinetic data to determine the mean and least level of dynamic, postural and overall balance stability, respectively. Results Mean postural stability was lower (lower mean destabilizing force) during the 50/50 Challenge game than during all the other tasks, but peak postural instability moments were less challenging during this game than during any of the other tasks, as shown by the minimum destabilizing force values. Dynamic stability was progressively more challenged (higher mean and maximum stabilizing force) from the 50/50 Challenge to the Soccer and Slalom games, to the natural gait speed task and to the fast gait speed task, increasing the overall stability difficulty (mean and minimum stability index) in the same manner. Conclusions The stabilizing/destabilizing forces model can be used to rate the level of balance requirements during different tasks such as gait or exergames. The results of our study showed that postural stability did not differ much

  20. Modeling and simulation of normal and hemiparetic gait

    NASA Astrophysics Data System (ADS)

    Luengas, Lely A.; Camargo, Esperanza; Sanchez, Giovanni

    2015-09-01

    Gait is the collective term for the two types of bipedal locomotion, walking and running. This paper is focused on walking. The analysis of human gait is of interest to many different disciplines, including biomechanics, human-movement science, rehabilitation and medicine in general. Here we present a new model that is capable of reproducing the properties of walking, normal and pathological. The aim of this paper is to establish the biomechanical principles that underlie human walking by using Lagrange method. The constraint forces of Rayleigh dissipation function, through which to consider the effect on the tissues in the gait, are included. Depending on the value of the factor present in the Rayleigh dissipation function, both normal and pathological gait can be simulated. First of all, we apply it in the normal gait and then in the permanent hemiparetic gait. Anthropometric data of adult person are used by simulation, and it is possible to use anthropometric data for children but is necessary to consider existing table of anthropometric data. Validation of these models includes simulations of passive dynamic gait that walk on level ground. The dynamic walking approach provides a new perspective of gait analysis, focusing on the kinematics and kinetics of gait. There have been studies and simulations to show normal human gait, but few of them have focused on abnormal, especially hemiparetic gait. Quantitative comparisons of the model predictions with gait measurements show that the model can reproduce the significant characteristics of normal gait.

  1. Gait-force model and inertial measurement unit-based measurements: A new approach for gait analysis and balance monitoring.

    PubMed

    Li, Xinan; Xu, Hongyuan; Cheung, Jeffrey T

    2016-12-01

    This work describes a new approach for gait analysis and balance measurement. It uses an inertial measurement unit (IMU) that can either be embedded inside a dynamically unstable platform for balance measurement or mounted on the lower back of a human participant for gait analysis. The acceleration data along three Cartesian coordinates is analyzed by the gait-force model to extract bio-mechanics information in both the dynamic state as in the gait analyzer and the steady state as in the balance scale. For the gait analyzer, the simple, noninvasive and versatile approach makes it appealing to a broad range of applications in clinical diagnosis, rehabilitation monitoring, athletic training, sport-apparel design, and many other areas. For the balance scale, it provides a portable platform to measure the postural deviation and the balance index under visual or vestibular sensory input conditions. Despite its simple construction and operation, excellent agreement has been demonstrated between its performance and the high-cost commercial balance unit over a wide dynamic range. The portable balance scale is an ideal tool for routine monitoring of balance index, fall-risk assessment, and other balance-related health issues for both clinical and household use.

  2. Fractal universe and quantum gravity.

    PubMed

    Calcagni, Gianluca

    2010-06-25

    We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.

  3. Non-linear dynamics of human locomotion: effects of rhythmic auditory cueing on local dynamic stability.

    PubMed

    Terrier, Philippe; Dériaz, Olivier

    2013-01-01

    It has been observed that times series of gait parameters [stride length (SL), stride time (ST), and stride speed (SS)], exhibit long-term persistence and fractal-like properties. Synchronizing steps with rhythmic auditory stimuli modifies the persistent fluctuation pattern to anti-persistence. Another non-linear method estimates the degree of resilience of gait control to small perturbations, i.e., the local dynamic stability (LDS). The method makes use of the maximal Lyapunov exponent, which estimates how fast a non-linear system embedded in a reconstructed state space (attractor) diverges after an infinitesimal perturbation. We propose to use an instrumented treadmill to simultaneously measure basic gait parameters (time series of SL, ST, and SS from which the statistical persistence among consecutive strides can be assessed), and the trajectory of the center of pressure (from which the LDS can be estimated). In 20 healthy participants, the response to rhythmic auditory cueing (RAC) of LDS and of statistical persistence [assessed with detrended fluctuation analysis (DFA)] was compared. By analyzing the divergence curves, we observed that long-term LDS (computed as the reverse of the average logarithmic rate of divergence between the 4th and the 10th strides downstream from nearest neighbors in the reconstructed attractor) was strongly enhanced (relative change +73%). That is likely the indication of a more dampened dynamics. The change in short-term LDS (divergence over one step) was smaller (+3%). DFA results (scaling exponents) confirmed an anti-persistent pattern in ST, SL, and SS. Long-term LDS (but not short-term LDS) and scaling exponents exhibited a significant correlation between them (r = 0.7). Both phenomena probably result from the more conscious/voluntary gait control that is required by RAC. We suggest that LDS and statistical persistence should be used to evaluate the efficiency of cueing therapy in patients with neurological gait disorders.

  4. Music and fractals

    NASA Astrophysics Data System (ADS)

    Wuorinen, Charles

    2015-03-01

    Any of the arts may produce exemplars that have fractal characteristics. There may be fractal painting, fractal poetry, and the like. But these will always be specific instances, not necessarily displaying intrinsic properties of the art-medium itself. Only music, I believe, of all the arts possesses an intrinsically fractal character, so that its very nature is fractally determined. Thus, it is reasonable to assert that any instance of music is fractal...

  5. Fractal rigidity in migraine

    NASA Astrophysics Data System (ADS)

    Latka, Miroslaw; Glaubic-Latka, Marta; Latka, Dariusz; West, Bruce J.

    2004-04-01

    We study the middle cerebral artery blood flow velocity (MCAfv) in humans using transcranial Doppler ultrasonography (TCD). Scaling properties of time series of the axial flow velocity averaged over a cardiac beat interval may be characterized by two exponents. The short time scaling exponent (STSE) determines the statistical properties of fluctuations of blood flow velocities in short-time intervals while the Hurst exponent describes the long-term fractal properties. In many migraineurs the value of the STSE is significantly reduced and may approach that of the Hurst exponent. This change in dynamical properties reflects the significant loss of short-term adaptability and the overall hyperexcitability of the underlying cerebral blood flow control system. We call this effect fractal rigidity.

  6. Fractal Bread.

    ERIC Educational Resources Information Center

    Esbenshade, Donald H., Jr.

    1991-01-01

    Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)

  7. Fractal and Chaos Analysis for Dynamics of Radon Exhalation from Uranium Mill Tailings

    NASA Astrophysics Data System (ADS)

    Li, Yongmei; Tan, Wanyu; Tan, Kaixuan; Liu, Zehua; Xie, Yanshi

    2016-08-01

    Tailings from mining and milling of uranium ores potentially are large volumes of low-level radioactive materials. A typical environmental problem associated with uranium tailings is radon exhalation, which can significantly pose risks to environment and human health. In order to reduce these risks, it is essential to study the dynamical nature and underlying mechanism of radon exhalation from uranium mill tailings. This motivates the conduction of this study, which is based on the fractal and chaotic methods (e.g. calculating the Hurst exponent, Lyapunov exponent and correlation dimension) and laboratory experiments of the radon exhalation rates. The experimental results show that the radon exhalation rate from uranium mill tailings is highly oscillated. In addition, the nonlinear analyses of the time series of radon exhalation rate demonstrate the following points: (1) the value of Hurst exponent much larger than 0.5 indicates non-random behavior of the radon time series; (2) the positive Lyapunov exponent and non-integer correlation dimension of the time series imply that the radon exhalation from uranium tailings is a chaotic dynamical process; (3) the required minimum number of variables should be five to describe the time evolution of radon exhalation. Therefore, it can be concluded that the internal factors, including heterogeneous distribution of radium, and randomness of radium decay, as well as the fractal characteristics of the tailings, can result in the chaotic evolution of radon exhalation from the tailings.

  8. Enhanced Graphene Photodetector with Fractal Metasurface.

    PubMed

    Fang, Jieran; Wang, Di; DeVault, Clayton T; Chung, Ting-Fung; Chen, Yong P; Boltasseva, Alexandra; Shalaev, Vladimir M; Kildishev, Alexander V

    2017-01-11

    Graphene has been demonstrated to be a promising photodetection material because of its ultrabroadband optical absorption, compatibility with CMOS technology, and dynamic tunability in optical and electrical properties. However, being a single atomic layer thick, graphene has intrinsically small optical absorption, which hinders its incorporation with modern photodetecting systems. In this work, we propose a gold snowflake-like fractal metasurface design to realize broadband and polarization-insensitive plasmonic enhancement in graphene photodetector. We experimentally obtain an enhanced photovoltage from the fractal metasurface that is an order of magnitude greater than that generated at a plain gold-graphene edge and such an enhancement in the photovoltage sustains over the entire visible spectrum. We also observed a relatively constant photoresponse with respect to polarization angles of incident light, as a result of the combination of two orthogonally oriented concentric hexagonal fractal geometries in one metasurface.

  9. A study of the passive gait of a compass-like biped robot: Symmetry and chaos

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Goswami, A.; Espiau, B.; Thuilot, B.

    1998-12-01

    The focus of this work is a systematic study of the passive gait of a compass-like planar, biped robot on inclined slopes. The robot is kinematically equivalent to a double pendulum, possessing two kneeless legs with point masses and a third point mass at the hip joint. Three parameters, namely, the ground-slope angle and the normalized mass and length of the robot describe its gait. The authors show that in response to a continuous change in any one of its parameters, the symmetric and steady stable gait of the unpowered robot gradually evolves through a regime of bifurcations characterized bymore » progressively complicated asymmetric gaits, eventually arriving at an apparently chaotic gait where not two steps are identical. The robot can maintain this gait indefinitely. A necessary (but not sufficient) condition for the stability of such gaits is the contraction of the phase-fluid volume. For this frictionless robot, the volume contraction, which the authors compute, is caused by the dissipative effects of the ground-impact model. In the chaotic regime, the fractal dimension of the robot`s strange attractor (2.07) compared to its state-space dimension (4) also reveals strong contraction. The authors present a novel graphical technique based on the first return map that compactly captures the entire evolution of the gait, from symmetry to chaos. Additional passive dissipative elements in the robot joint results in a significant improvement in the stability and the versatility of the gait, and provide a rich repertoire for simple controls laws.« less

  10. Contrast Density and mass function for spherical collapse of Lemaitre-Tolman-Bondi metric from fractal point of view

    NASA Astrophysics Data System (ADS)

    Chacón-Cardona, C. A.; Casas-Miranda, R. A.

    2014-10-01

    Recent works about large structure in the universe put in doubt the homogeneity transition almost universally accepted, (Joyce et al.2005), (Gaite 2007), (Chacón-Cardona & Casas-Miranda 2012). In the present work we develop theoretically the density contrast for the spherical collapse of an over-density of dark matter which evolve in a inhomogeneous universe inside a fractal cosmology presented by (Bondi 1947).

  11. Gait phenotypes in paediatric hereditary spastic paraplegia revealed by dynamic time warping analysis and random forests

    PubMed Central

    Martín-Gonzalo, Juan Andrés; Rodríguez-Andonaegui, Irene; López-López, Javier; Pascual-Pascual, Samuel Ignacio

    2018-01-01

    The Hereditary Spastic Paraplegias (HSP) are a group of heterogeneous disorders with a wide spectrum of underlying neural pathology, and hence HSP patients express a variety of gait abnormalities. Classification of these phenotypes may help in monitoring disease progression and personalizing therapies. This is currently managed by measuring values of some kinematic and spatio-temporal parameters at certain moments during the gait cycle, either in the doctor´s surgery room or after very precise measurements produced by instrumental gait analysis (IGA). These methods, however, do not provide information about the whole structure of the gait cycle. Classification of the similarities among time series of IGA measured values of sagittal joint positions throughout the whole gait cycle can be achieved by hierarchical clustering analysis based on multivariate dynamic time warping (DTW). Random forests can estimate which are the most important isolated parameters to predict the classification revealed by DTW, since clinicians need to refer to them in their daily practice. We acquired time series of pelvic, hip, knee, ankle and forefoot sagittal angular positions from 26 HSP and 33 healthy children with an optokinetic IGA system. DTW revealed six gait patterns with different degrees of impairment of walking speed, cadence and gait cycle distribution and related with patient’s age, sex, GMFCS stage, concurrence of polyneuropathy and abnormal visual evoked potentials or corpus callosum. The most important parameters to differentiate patterns were mean pelvic tilt and hip flexion at initial contact. Longer time of support, decreased values of hip extension and increased knee flexion at initial contact can differentiate the mildest, near to normal HSP gait phenotype and the normal healthy one. Increased values of knee flexion at initial contact and delayed peak of knee flexion are important factors to distinguish GMFCS stages I from II-III and concurrence of polyneuropathy

  12. Universal characteristics of fractal fluctuations in prime number distribution

    NASA Astrophysics Data System (ADS)

    Selvam, A. M.

    2014-11-01

    The frequency of occurrence of prime numbers at unit number spacing intervals exhibits self-similar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows, stock market fluctuations and population dynamics. The physics of long-range correlations exhibited by fractals is not yet identified. A recently developed general systems theory visualizes the eddy continuum underlying fractals to result from the growth of large eddies as the integrated mean of enclosed small scale eddies, thereby generating a hierarchy of eddy circulations or an inter-connected network with associated long-range correlations. The model predictions are as follows: (1) The probability distribution and power spectrum of fractals follow the same inverse power law which is a function of the golden mean. The predicted inverse power law distribution is very close to the statistical normal distribution for fluctuations within two standard deviations from the mean of the distribution. (2) Fractals signify quantum-like chaos since variance spectrum represents probability density distribution, a characteristic of quantum systems such as electron or photon. (3) Fractal fluctuations of frequency distribution of prime numbers signify spontaneous organization of underlying continuum number field into the ordered pattern of the quasiperiodic Penrose tiling pattern. The model predictions are in agreement with the probability distributions and power spectra for different sets of frequency of occurrence of prime numbers at unit number interval for successive 1000 numbers. Prime numbers in the first 10 million numbers were used for the study.

  13. Fractal geometry in an expanding, one-dimensional, Newtonian universe.

    PubMed

    Miller, Bruce N; Rouet, Jean-Louis; Le Guirriec, Emmanuel

    2007-09-01

    Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with new, larger, sample sizes from recent surveys, it is difficult to extract information concerning fractal properties with confidence. Similarly, three-dimensional N-body simulations with a billion particles only provide a thousand particles per dimension, far too small for accurate conclusions. With one-dimensional models these limitations can be overcome by carrying out simulations with on the order of a quarter of a million particles without compromising the computation of the gravitational force. Here the multifractal properties of two of these models that incorporate different features of the dynamical equations governing the evolution of a matter dominated universe are compared. For each model at least two scaling regions are identified. By employing criteria from dynamical systems theory it is shown that only one of them can be geometrically significant. The results share important similarities with galaxy observations, such as hierarchical clustering and apparent bifractal geometry. They also provide insights concerning possible constraints on length and time scales for fractal structure. They clearly demonstrate that fractal geometry evolves in the mu (position, velocity) space. The observed patterns are simply a shadow (projection) of higher-dimensional structure.

  14. The Effects of Aging and Dual Tasking on Human Gait Complexity During Treadmill Walking: A Comparative Study Using Quantized Dynamical Entropy and Sample Entropy.

    PubMed

    Ahmadi, Samira; Wu, Christine; Sepehri, Nariman; Kantikar, Anuprita; Nankar, Mayur; Szturm, Tony

    2018-01-01

    Quantized dynamical entropy (QDE) has recently been proposed as a new measure to quantify the complexity of dynamical systems with the purpose of offering a better computational efficiency. This paper further investigates the viability of this method using five different human gait signals. These signals are recorded while normal walking and while performing secondary tasks among two age groups (young and older age groups). The results are compared with the outcomes of previously established sample entropy (SampEn) measure for the same signals. We also study how analyzing segmented and spatially and temporally normalized signal differs from analyzing whole data. Our findings show that human gait signals become more complex as people age and while they are cognitively loaded. Center of pressure (COP) displacement in mediolateral direction is the best signal for showing the gait changes. Moreover, the results suggest that by segmenting data, more information about intrastride dynamical features are obtained. Most importantly, QDE is shown to be a reliable measure for human gait complexity analysis.

  15. Quadrupedal rodent gait compensations in a low dose monoiodoacetate model of osteoarthritis.

    PubMed

    Lakes, Emily H; Allen, Kyle D

    2018-06-01

    Rodent gait analysis provides robust, quantitative results for preclinical musculoskeletal and neurological models. In prior work, surgical models of osteoarthritis have been found to result in a hind limb shuffle-stepping gait compensation, while a high dose monoiodoacetate (MIA, 3 mg) model resulted in a hind limb antalgic gait. However, it is unknown whether the antalgic gait caused by MIA is associated with severity of degeneration from the high dosage or the whole-joint degeneration associated with glycolysis inhibition. This study evaluates rodent gait changes resulting from a low dose, 1 mg unilateral intra-articular injection of MIA compared to saline injected and naïve rats. Spatiotemporal and dynamic gait parameters were collected from a total of 42 male Lewis rats spread across 3 time points: 1, 2, and 4 weeks post-injection. To provide a detailed analysis of this low dose MIA model, gait analysis was used to uniquely quantify both fore and hind limb gait parameters. Our data indicate that 1 mg of MIA caused relatively minor degeneration and a shuffle-step gait compensation, similar to the compensation observed in prior surgical models. These data from a 1 mg MIA model show a different gait compensation compared to a previously studied 3 mg model. This 1 mg MIA model resulted in gait compensations more similar to a previously studied surgical model of osteoarthritis. Additionally, this study provides detailed 4 limb analysis of rodent gait that includes spatiotemporal and dynamic data from the same gait trial. These data highlight the importance of measuring dynamic data in combination with spatiotemporal data, since compensatory gait patterns may not be captured by spatial, temporal, or dynamic characterizations alone. Copyright © 2018 Elsevier B.V. All rights reserved.

  16. Ulam method and fractal Weyl law for Perron-Frobenius operators

    NASA Astrophysics Data System (ADS)

    Ermann, L.; Shepelyansky, D. L.

    2010-06-01

    We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show numerically that the spectrum is characterized by the fractal Weyl law recently established for nonunitary operators describing poles of quantum chaotic scattering with the Weyl exponent ν = d-1, where d is the fractal dimension of corresponding strange set of trajectories nonescaping in future times. In contrast, for dissipative maps we numerically find the Weyl exponent ν = d/2 where d is the fractal dimension of strange attractor. The Weyl exponent can be also expressed via the relation ν = d0/2 where d0 is the fractal dimension of the invariant sets. We also discuss the properties of eigenvalues and eigenvectors of such operators characterized by the fractal Weyl law.

  17. Gait parameter control timing with dynamic manual contact or visual cues.

    PubMed

    Rabin, Ely; Shi, Peter; Werner, William

    2016-06-01

    We investigated the timing of gait parameter changes (stride length, peak toe velocity, and double-, single-support, and complete step duration) to control gait speed. Eleven healthy participants adjusted their gait speed on a treadmill to maintain a constant distance between them and a fore-aft oscillating cue (a place on a conveyor belt surface). The experimental design balanced conditions of cue modality (vision: eyes-open; manual contact: eyes-closed while touching the cue); treadmill speed (0.2, 0.4, 0.85, and 1.3 m/s); and cue motion (none, ±10 cm at 0.09, 0.11, and 0.18 Hz). Correlation analyses revealed a number of temporal relationships between gait parameters and cue speed. The results suggest that neural control ranged from feedforward to feedback. Specifically, step length preceded cue velocity during double-support duration suggesting anticipatory control. Peak toe velocity nearly coincided with its most-correlated cue velocity during single-support duration. The toe-off concluding step and double-support durations followed their most-correlated cue velocity, suggesting feedback control. Cue-tracking accuracy and cue velocity correlations with timing parameters were higher with the manual contact cue than visual cue. The cue/gait timing relationships generalized across cue modalities, albeit with greater delays of step-cycle events relative to manual contact cue velocity. We conclude that individual kinematic parameters of gait are controlled to achieve a desired velocity at different specific times during the gait cycle. The overall timing pattern of instantaneous cue velocities associated with different gait parameters is conserved across cues that afford different performance accuracies. This timing pattern may be temporally shifted to optimize control. Different cue/gait parameter latencies in our nonadaptation paradigm provide general-case evidence of the independent control of gait parameters previously demonstrated in gait adaptation paradigms

  18. Gait parameter control timing with dynamic manual contact or visual cues

    PubMed Central

    Shi, Peter; Werner, William

    2016-01-01

    We investigated the timing of gait parameter changes (stride length, peak toe velocity, and double-, single-support, and complete step duration) to control gait speed. Eleven healthy participants adjusted their gait speed on a treadmill to maintain a constant distance between them and a fore-aft oscillating cue (a place on a conveyor belt surface). The experimental design balanced conditions of cue modality (vision: eyes-open; manual contact: eyes-closed while touching the cue); treadmill speed (0.2, 0.4, 0.85, and 1.3 m/s); and cue motion (none, ±10 cm at 0.09, 0.11, and 0.18 Hz). Correlation analyses revealed a number of temporal relationships between gait parameters and cue speed. The results suggest that neural control ranged from feedforward to feedback. Specifically, step length preceded cue velocity during double-support duration suggesting anticipatory control. Peak toe velocity nearly coincided with its most-correlated cue velocity during single-support duration. The toe-off concluding step and double-support durations followed their most-correlated cue velocity, suggesting feedback control. Cue-tracking accuracy and cue velocity correlations with timing parameters were higher with the manual contact cue than visual cue. The cue/gait timing relationships generalized across cue modalities, albeit with greater delays of step-cycle events relative to manual contact cue velocity. We conclude that individual kinematic parameters of gait are controlled to achieve a desired velocity at different specific times during the gait cycle. The overall timing pattern of instantaneous cue velocities associated with different gait parameters is conserved across cues that afford different performance accuracies. This timing pattern may be temporally shifted to optimize control. Different cue/gait parameter latencies in our nonadaptation paradigm provide general-case evidence of the independent control of gait parameters previously demonstrated in gait adaptation paradigms

  19. Effects of a multichannel dynamic functional electrical stimulation system on hemiplegic gait and muscle forces

    PubMed Central

    Qian, Jing-guang; Rong, Ke; Qian, Zhenyun; Wen, Chen; Zhang, Songning

    2015-01-01

    [Purpose] The purpose of the study was to design and implement a multichannel dynamic functional electrical stimulation system and investigate acute effects of functional electrical stimulation of the tibialis anterior and rectus femoris on ankle and knee sagittal-plane kinematics and related muscle forces of hemiplegic gait. [Subjects and Methods] A multichannel dynamic electrical stimulation system was developed with 8-channel low frequency current generators. Eight male hemiplegic patients were trained for 4 weeks with electric stimulation of the tibia anterior and rectus femoris muscles during walking, which was coupled with active contraction. Kinematic data were collected, and muscle forces of the tibialis anterior and rectus femoris of the affected limbs were analyzed using a musculoskelatal modeling approach before and after training. A paired sample t-test was used to detect the differences between before and after training. [Results] The step length of the affected limb significantly increased after the stimulation was applied. The maximum dorsiflexion angle and maximum knee flexion angle of the affected limb were both increased significantly during stimulation. The maximum muscle forces of both the tibia anterior and rectus femoris increased significantly during stimulation compared with before functional electrical stimulation was applied. [Conclusion] This study established a functional electrical stimulation strategy based on hemiplegic gait analysis and musculoskeletal modeling. The multichannel functional electrical stimulation system successfully corrected foot drop and altered circumduction hemiplegic gait pattern. PMID:26696734

  20. Extreme value laws for fractal intensity functions in dynamical systems: Minkowski analysis

    NASA Astrophysics Data System (ADS)

    Mantica, Giorgio; Perotti, Luca

    2016-09-01

    Typically, in the dynamical theory of extremal events, the function that gauges the intensity of a phenomenon is assumed to be convex and maximal, or singular, at a single, or at most a finite collection of points in phase-space. In this paper we generalize this situation to fractal landscapes, i.e. intensity functions characterized by an uncountable set of singularities, located on a Cantor set. This reveals the dynamical rôle of classical quantities like the Minkowski dimension and content, whose definition we extend to account for singular continuous invariant measures. We also introduce the concept of extremely rare event, quantified by non-standard Minkowski constants and we study its consequences to extreme value statistics. Limit laws are derived from formal calculations and are verified by numerical experiments. Dedicated to the memory of Joseph Ford, on the twentieth anniversary of his departure.

  1. Use of a dynamic gait trainer for a child with thoracic level spinal cord injury

    PubMed Central

    Paleg, Ginny

    2017-01-01

    Paediatric spinal cord injury (SCI) can result in permanent mobility impairment with consequences for activity, participation and quality of life. This case documents the effect of an overground supported stepping intervention using a dynamic gait trainer. To our knowledge, there are no published studies on this intervention for children with SCI and similar interventions have only been reported in children at American Spinal Injury Association Impairment Scale (AIS) levels B and C. A child with a T10 (thoracic level, vertebra 10), AIS level A injury, sustained at 2 years of age, continued to make gains in all areas including participation, activity, body structure and function over the following 4 years. Use of a dynamic gait trainer improved the participant’s ability to be active and participate despite lack of further neuromuscular recovery. This novel approach with a commonly available device allowed the child to be active and participate in the absence of neural recovery. PMID:29021141

  2. The effects of core stabilization exercise on dynamic balance and gait function in stroke patients.

    PubMed

    Chung, Eun-Jung; Kim, Jung-Hee; Lee, Byoung-Hee

    2013-07-01

    [Purpose] The purpose of this study was to determine the effects of core stabilization exercise on dynamic balance and gait function in stroke patients. [Subjects] The subjects were 16 stroke patients, who were randomly divided into two groups: a core stabilization exercise group of eight subjects and control group of eight subjects. [Methods] Subjects in both groups received general training five times per week. Subjects in the core stabilization exercise group practiced an additional core stabilization exercise program, which was performed for 30 minutes, three times per week, during a period of four weeks. All subjects were evaluated for dynamic balance (Timed Up and Go test, TUG) and gait parameters (velocity, cadence, step length, and stride length). [Results] Following intervention, the core exercise group showed a significant change in TUG, velocity, and cadence. The only significant difference observed between the core group and control group was in velocity. [Conclusion] The results of this study suggest the feasibility and suitability of core stabilization exercise for stroke patients.

  3. The influence of passive-dynamic ankle-foot orthosis bending axis location on gait performance in individuals with lower-limb impairments.

    PubMed

    Ranz, Ellyn C; Russell Esposito, Elizabeth; Wilken, Jason M; Neptune, Richard R

    2016-08-01

    Passive-dynamic ankle-foot orthoses are commonly prescribed to augment impaired ankle muscle function, however their design and prescription are largely qualitative. One design includes a footplate and cuff, and flexible strut connecting the two. During gait, deflection occurs along the strut, with the greatest deflection at a central bending axis. The vertical location of the axis can affect lower extremity biomechanics. The goal of this study was to investigate the influence of bending axis location on gait performance. For thirteen participants with unilateral ankle muscle weakness, an additive manufacturing framework was used to fabricate passive-dynamic ankle-foot orthosis struts with central and off-center bending axes. Participants walked overground while electromyographic, kinetic and kinematic data were collected for three different bending axes: proximal (high), central (middle) and distal (low), and the participants indicated their order of bending axis preference after testing. Gait measures and preference effect sizes were examined during six regions of the gait cycle. A few differences between bending axes were observed: in the first double-leg support peak plantarflexion angle, peak dorsiflexion moment and positive hip work, in the early single-leg support peak knee extension moment and positive ankle and knee work, and in the late single-leg support gastrocnemius activity and vertical ground reaction force impulse. In addition, preference was strongly related to various gait measures. Despite the observed statistical differences, altering bending axis location did not produce large and consistent changes in gait performance. Thus, individual preference and comfort may be more important factors guiding prescription. Copyright © 2016 Elsevier Ltd. All rights reserved.

  4. Does footwear type impact the number of steps required to reach gait steady state?: an innovative look at the impact of foot orthoses on gait initiation.

    PubMed

    Najafi, Bijan; Miller, Daniel; Jarrett, Beth D; Wrobel, James S

    2010-05-01

    Many studies have attempted to better elucidate the effect of foot orthoses on gait dynamics. To our knowledge, most previous studies exclude the first few steps of gait and begin analysis at steady state walking. These unanalyzed steps of gait may contain important information about the dynamic and complex processes required to achieve equilibrium for a given gait velocity. The purpose of this study was to quantify gait initiation and determine how many steps were required to reach steady state walking under three footwear conditions: barefoot, habitual shoes, and habitual shoes with a prefabricated foot orthoses. Fifteen healthy subjects walked 50m at habitual speed in each condition. Wearing habitual shoes with the prefabricated orthoses enabled subjects to reach steady state walking in fewer steps (3.5 steps+/-2.0) compared to the barefoot condition (5.2 steps+/-3.0; p=0.02) as well as compared to the habitual shoes condition (4.7 steps+/-1.6; p=0.05). Interestingly, the subjects' dynamic medial-lateral balance was significantly improved (22%, p<0.05) by using foot orthoses compared to other footwear conditions. These findings suggest that foot orthoses may help individuals reach steady state more quickly and with a better dynamic balance in the medial-lateral direction, independent of foot type. The findings of this pilot study may open new avenues for objectively assessing the impact of prescription footwear on dynamic balance and spatio-temporal parameters of gait. Further work to better assess the impact of foot orthoses on gait initiation in patients suffering from gait and instability pathologies may be warranted. Copyright 2010 Elsevier B.V. All rights reserved.

  5. Fractal vector optical fields.

    PubMed

    Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

    2016-07-15

    We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.

  6. Fractal analysis of narwhal space use patterns.

    PubMed

    Laidre, Kristin L; Heide-Jørgensen, Mads P; Logsdon, Miles L; Hobbs, Roderick C; Dietz, Rune; VanBlaricom, Glenn R

    2004-01-01

    Quantifying animal movement in response to a spatially and temporally heterogeneous environment is critical to understanding the structural and functional landscape influences on population viability. Generalities of landscape structure can easily be extended to the marine environment, as marine predators inhabit a patchy, dynamic system, which influences animal choice and behavior. An innovative use of the fractal measure of complexity, indexing the linearity of movement paths over replicate temporal scales, was applied to satellite tracking data collected from narwhals (Monodon monoceros) (n = 20) in West Greenland and the eastern Canadian high Arctic. Daily movements of individuals were obtained using polar orbiting satellites via the ARGOS data location and collection system. Geographic positions were filtered to obtain a daily good quality position for each whale. The length of total pathway was measured over seven different temporal length scales (step lengths), ranging from one day to one week, and a seasonal mean was calculated. Fractal dimension (D) was significantly different between seasons, highest during summer (D = 1.61, SE 0.04) and winter (D = 1.69, SE 0.06) when whales made convoluted movements in focal areas. Fractal dimension was lowest during fall (D = 1.34, SE 0.03) when whales were migrating south ahead of the forming sea ice. There were no significant effects of size category or sex on fractal dimension by season. The greater linearity of movement during the migration period suggests individuals do not intensively forage on patchy resources until they arrive at summer or winter sites. The highly convoluted movements observed during summer and winter suggest foraging or searching efforts in localized areas. Significant differences between the fractal dimensions on two separate wintering grounds in Baffin Bay suggest differential movement patterns in response to the dynamics of sea ice.

  7. Most suitable mother wavelet for the analysis of fractal properties of stride interval time series via the average wavelet coefficient

    PubMed Central

    Zhang, Zhenwei; VanSwearingen, Jessie; Brach, Jennifer S.; Perera, Subashan

    2016-01-01

    Human gait is a complex interaction of many nonlinear systems and stride intervals exhibit self-similarity over long time scales that can be modeled as a fractal process. The scaling exponent represents the fractal degree and can be interpreted as a biomarker of relative diseases. The previous study showed that the average wavelet method provides the most accurate results to estimate this scaling exponent when applied to stride interval time series. The purpose of this paper is to determine the most suitable mother wavelet for the average wavelet method. This paper presents a comparative numerical analysis of sixteen mother wavelets using simulated and real fractal signals. Simulated fractal signals were generated under varying signal lengths and scaling exponents that indicate a range of physiologically conceivable fractal signals. The five candidates were chosen due to their good performance on the mean square error test for both short and long signals. Next, we comparatively analyzed these five mother wavelets for physiologically relevant stride time series lengths. Our analysis showed that the symlet 2 mother wavelet provides a low mean square error and low variance for long time intervals and relatively low errors for short signal lengths. It can be considered as the most suitable mother function without the burden of considering the signal length. PMID:27960102

  8. Dynamic parameters of three-point crutch gait in female patients after total hip arthroplasty.

    PubMed

    Murawa, Michał; Dworak, Lechosław B; Kabaciński, Jarosław; Syczewska, Małgorzata; Rzepnicka, Agata

    2016-01-01

    Patient recovery after a surgical procedure depends, among other factors, on the amount of the body weight with which patient loads lower limb. Research studies report different results of the degree of body weight with which lower limb is loaded during three-point crutch gait. The aim of this study was to evaluate the level of the ground reaction forces (GRF) during crutch gait used by patients after total hip arthroplasty (THA) in the first week after discharge from the orthopaedic units. Ten female patients diagnosed with primary unilateral coxarthrosis participated in a single measurement session. In order to record kinematic and dynamic variables of this gait pattern motion analysis system was used together with two force plates. The static test of body weight distribution between lower limbs was performed on a dual-top stabilometric plate. The average peak values of loading on the operated (O) limb during mid stance and terminal stance of three-point crutch gait were 64.6% and 64.3% of body weight (BW), respectively, whereas in the case of the nonoperated (NO) limb 103.5%BW and 108.8%BW, respectively. The maximum loads on the crutches were significantly higher (by 9%BW) on the NO side as compared to the O side ( p < 0.05). During the static test, average values of body weight distribution on the O and NO limb were 36%BW and 64%BW, respectively. The patients showed surprisingly similar level of loading on the O limb. The weight bearing on the O limb was lower during static trial than during three-point crutch gait.

  9. Passive-dynamic ankle-foot orthosis replicates soleus but not gastrocnemius muscle function during stance in gait: Insights for orthosis prescription.

    PubMed

    Arch, Elisa S; Stanhope, Steven J; Higginson, Jill S

    2016-10-01

    Passive-dynamic ankle-foot orthosis characteristics, including bending stiffness, should be customized for individuals. However, while conventions for customizing passive-dynamic ankle-foot orthosis characteristics are often described and implemented in clinical practice, there is little evidence to explain their biomechanical rationale. To develop and combine a model of a customized passive-dynamic ankle-foot orthosis with a healthy musculoskeletal model and use simulation tools to explore the influence of passive-dynamic ankle-foot orthosis bending stiffness on plantar flexor function during gait. Dual case study. The customized passive-dynamic ankle-foot orthosis characteristics were integrated into a healthy musculoskeletal model available in OpenSim. Quasi-static forward dynamic simulations tracked experimental gait data under several passive-dynamic ankle-foot orthosis conditions. Predicted muscle activations were calculated through a computed muscle control optimization scheme. Simulations predicted that the passive-dynamic ankle-foot orthoses substituted for soleus but not gastrocnemius function. Induced acceleration analyses revealed the passive-dynamic ankle-foot orthosis acts like a uniarticular plantar flexor by inducing knee extension accelerations, which are counterproductive to natural knee kinematics in early midstance. These passive-dynamic ankle-foot orthoses can provide plantar flexion moments during mid and late stance to supplement insufficient plantar flexor strength. However, the passive-dynamic ankle-foot orthoses negatively influenced knee kinematics in early midstance. Identifying the role of passive-dynamic ankle-foot orthosis stiffness during gait provides biomechanical rationale for how to customize passive-dynamic ankle-foot orthoses for patients. Furthermore, these findings can be used in the future as the basis for developing objective prescription models to help drive the customization of passive-dynamic ankle-foot orthosis

  10. Local dynamic stability and gait variability during attentional tasks in young adults.

    PubMed

    Magnani, Rina Márcia; Lehnen, Georgia Cristina; Rodrigues, Fábio Barbosa; de Sá E Souza, Gustavo Souto; de Oliveira Andrade, Adriano; Vieira, Marcus Fraga

    2017-06-01

    Cell phone use while walking may be a cognitive distraction and reduce visual and motor attention. Thus, the aim of this study was to verify the effects of attentional dual-tasks while using a cell phone in different conditions. Stability, regularity, and linear variability of trunk kinematics, and gait spatiotemporal parameters in young adults were measured. Twenty young subjects of both genders were asked to walk on a treadmill for 4min under the following conditions: (a) looking forward at a fixed target 2.5m away (walking); (b) talking on a cell phone with unilateral handling (talking); (c) texting messages on a cell phone with unilateral handling (texting); and (d) looking forward at the aforementioned target while listening to music without handling the phone (listening). Local dynamic stability measured in terms of the largest Lyapunov exponent decreased while handling a cell phone (talking and texting). Gait variability and regularity increased when talking on a cell phone, but no variable changed in the listening condition. Under all dual-task conditions, there were significant increases in stride width and its variability. We conclude that young adults who use a cell phone when walking adapt their gait pattern conservatively, which can be because of increased attentional demand during cell phone use. Copyright © 2017 Elsevier B.V. All rights reserved.

  11. Quantifying gait deviations in individuals with rheumatoid arthritis using the Gait Deviation Index.

    PubMed

    Esbjörnsson, A-C; Rozumalski, A; Iversen, M D; Schwartz, M H; Wretenberg, P; Broström, E W

    2014-01-01

    In this study we evaluated the usability of the Gait Deviation Index (GDI), an index that summarizes the amount of deviation in movement from a standard norm, in adults with rheumatoid arthritis (RA). The aims of the study were to evaluate the ability of the GDI to identify gait deviations, assess inter-trial repeatability, and examine the relationship between the GDI and walking speed, physical disability, and pain. Sixty-three adults with RA and 59 adults with typical gait patterns were included in this retrospective case-control study. Following a three-dimensional gait analysis (3DGA), representative gait cycles were selected and GDI scores calculated. To evaluate the effect of walking speed, GDI scores were calculated using both a free-speed and a speed-matched reference set. Physical disability was assessed using the Health Assessment Questionnaire (HAQ) and subjects rated their pain during walking. Adults with RA had significantly increased gait deviations compared to healthy individuals, as shown by lower GDI scores [87.9 (SD = 8.7) vs. 99.4 (SD = 8.3), p < 0.001]. This difference was also seen when adjusting for walking speed [91.7 (SD = 9.0) vs. 99.9 (SD = 8.6), p < 0.001]. It was estimated that a change of ≥ 5 GDI units was required to account for natural variation in gait. There was no evident relationship between GDI and low/high RA-related physical disability and pain. The GDI seems to useful for identifying and summarizing gait deviations in individuals with RA. Thus, we consider that the GDI provides an overall measure of gait deviation that may reflect lower extremity pathology and may help clinicians to understand the impact of RA on gait dynamics.

  12. Neuromorphic walking gait control.

    PubMed

    Still, Susanne; Hepp, Klaus; Douglas, Rodney J

    2006-03-01

    We present a neuromorphic pattern generator for controlling the walking gaits of four-legged robots which is inspired by central pattern generators found in the nervous system and which is implemented as a very large scale integrated (VLSI) chip. The chip contains oscillator circuits that mimic the output of motor neurons in a strongly simplified way. We show that four coupled oscillators can produce rhythmic patterns with phase relationships that are appropriate to generate all four-legged animal walking gaits. These phase relationships together with frequency and duty cycle of the oscillators determine the walking behavior of a robot driven by the chip, and they depend on a small set of stationary bias voltages. We give analytic expressions for these dependencies. This chip reduces the complex, dynamic inter-leg control problem associated with walking gait generation to the problem of setting a few stationary parameters. It provides a compact and low power solution for walking gait control in robots.

  13. Dynamic balance control in elders: gait initiation assessment as a screening tool

    NASA Technical Reports Server (NTRS)

    Chang, H.; Krebs, D. E.; Wall, C. C. (Principal Investigator)

    1999-01-01

    OBJECTIVE: To determine whether measurements of center of gravity-center of pressure separation (CG-CP moment arm) during gait initiation can differentiate healthy from disabled subjects with sufficient specificity and sensitivity to be useful as a screening test for dynamic balance in elderly patients. SUBJECTS: Three groups of elderly subjects (age, 74.97+/-6.56 yrs): healthy elders (HE, n = 21), disabled elders (DE, n = 20), and elders with vestibular hypofunction (VH, n = 18). DESIGN: Cross-sectional, intact-groups research design. Peak CG-CP moment arm measures how far the subject will tolerate the whole-body CG to deviate from the ground reaction force's CP; it represents dynamic balance control. Screening test cutoff points at 16 to 18 cm peak CG-CP moment arm predicted group membership. RESULTS: The magnitude of peak CG-CP moment arm was significantly greater in HE than in DE and VH subjects (p<.01) and was not different between the DE and VH groups. The peak CG-CP moment arm occurred at the end of single stance phase in all groups. As a screening test, the peak moment arm has greater than 50% sensitivity and specificity to discriminate the HE group from the DE and VH groups with peak CG-CP moment arm cutoff points between 16 and 18 cm. CONCLUSIONS: Examining dynamic balance through the use of the CG-CP moment arm during single stance in gait initiation discriminates between nondisabled and disabled older persons and warrants further investigation as a potential tool to identify people with balance dysfunction.

  14. A 3D model for rain-induced landslides based on molecular dynamics with fractal and fractional water diffusion

    NASA Astrophysics Data System (ADS)

    Martelloni, Gianluca; Bagnoli, Franco; Guarino, Alessio

    2017-09-01

    We present a three-dimensional model of rain-induced landslides, based on cohesive spherical particles. The rainwater infiltration into the soil follows either the fractional or the fractal diffusion equations. We analytically solve the fractal partial differential equation (PDE) for diffusion with particular boundary conditions to simulate a rainfall event. We developed a numerical integration scheme for the PDE, compared with the analytical solution. We adapt the fractal diffusion equation obtaining the gravimetric water content that we use as input of a triggering scheme based on Mohr-Coulomb limit-equilibrium criterion. This triggering is then complemented by a standard molecular dynamics algorithm, with an interaction force inspired by the Lennard-Jones potential, to update the positions and velocities of particles. We present our results for homogeneous and heterogeneous systems, i.e., systems composed by particles with same or different radius, respectively. Interestingly, in the heterogeneous case, we observe segregation effects due to the different volume of the particles. Finally, we analyze the parameter sensibility both for the triggering and the propagation phases. Our simulations confirm the results of a previous two-dimensional model and therefore the feasible applicability to real cases.

  15. The fractal forest: fractal geometry and applications in forest science.

    Treesearch

    Nancy D. Lorimer; Robert G. Haight; Rolfe A. Leary

    1994-01-01

    Fractal geometry is a tool for describing and analyzing irregularity. Because most of what we measure in the forest is discontinuous, jagged, and fragmented, fractal geometry has potential for improving the precision of measurement and description. This study reviews the literature on fractal geometry and its applications to forest measurements.

  16. Structural parameters of young star clusters: fractal analysis

    NASA Astrophysics Data System (ADS)

    Hetem, A.

    2017-07-01

    A unified view of star formation in the Universe demand detailed and in-depth studies of young star clusters. This work is related to our previous study of fractal statistics estimated for a sample of young stellar clusters (Gregorio-Hetem et al. 2015, MNRAS 448, 2504). The structural properties can lead to significant conclusions about the early stages of cluster formation: 1) virial conditions can be used to distinguish warm collapsed; 2) bound or unbound behaviour can lead to conclusions about expansion; and 3) fractal statistics are correlated to the dynamical evolution and age. The technique of error bars estimation most used in the literature is to adopt inferential methods (like bootstrap) to estimate deviation and variance, which are valid only for an artificially generated cluster. In this paper, we expanded the number of studied clusters, in order to enhance the investigation of the cluster properties and dynamic evolution. The structural parameters were compared with fractal statistics and reveal that the clusters radial density profile show a tendency of the mean separation of the stars increase with the average surface density. The sample can be divided into two groups showing different dynamic behaviour, but they have the same dynamic evolution, since the entire sample was revealed as being expanding objects, for which the substructures do not seem to have been completely erased. These results are in agreement with the simulations adopting low surface densities and supervirial conditions.

  17. A system framework of inter-enterprise machining quality control based on fractal theory

    NASA Astrophysics Data System (ADS)

    Zhao, Liping; Qin, Yongtao; Yao, Yiyong; Yan, Peng

    2014-03-01

    In order to meet the quality control requirement of dynamic and complicated product machining processes among enterprises, a system framework of inter-enterprise machining quality control based on fractal was proposed. In this system framework, the fractal-specific characteristic of inter-enterprise machining quality control function was analysed, and the model of inter-enterprise machining quality control was constructed by the nature of fractal structures. Furthermore, the goal-driven strategy of inter-enterprise quality control and the dynamic organisation strategy of inter-enterprise quality improvement were constructed by the characteristic analysis on this model. In addition, the architecture of inter-enterprise machining quality control based on fractal was established by means of Web service. Finally, a case study for application was presented. The result showed that the proposed method was available, and could provide guidance for quality control and support for product reliability in inter-enterprise machining processes.

  18. [Features of fractal dynamics EEG of alpha-rhythm in patients with neurotic and neurosis-like disorders].

    PubMed

    Shul'ts, E V; Baburin, I N; Karavaeva, T A; Karvasarskiĭ, B D; Slezin, V B

    2011-01-01

    Fifty-five patients with neurotic and neurosis-like disorders and 20 healthy controls, aged 17-64 years, have been examined. The basic research method was electroencephalography (EEG) with the fractal analysis of alpha power fluctuations. In patients, the changes in the fractal structure were of the same direction: the decrease of fractal indexes of low-frequency fluctuations and the increase of fractal indexes of mid-frequency fluctuations. Patients with neurosis-like disorders, in comparison to those with neurotic disorders, were characterized by more expressed (quantitative) changes in fractal structures of more extended character. It suggests the presence of deeper pathological changes in patients with neurosis-like disorders.

  19. Spontaneous imbibition in fractal tortuous micro-nano pores considering dynamic contact angle and slip effect: phase portrait analysis and analytical solutions.

    PubMed

    Li, Caoxiong; Shen, Yinghao; Ge, Hongkui; Zhang, Yanjun; Liu, Tao

    2018-03-02

    Shales have abundant micro-nano pores. Meanwhile, a considerable amount of fracturing liquid is imbibed spontaneously in the hydraulic fracturing process. The spontaneous imbibition in tortuous micro-nano pores is special to shale, and dynamic contact angle and slippage are two important characteristics. In this work, we mainly investigate spontaneous imbibition considering dynamic contact angle and slip effect in fractal tortuous capillaries. We introduce phase portrait analysis to analyse the dynamic state and stability of imbibition. Moreover, analytical solutions to the imbibition equation are derived under special situations, and the solutions are verified by published data. Finally, we discuss the influences of slip length, dynamic contact angle and gravity on spontaneous imbibition. The analysis shows that phase portrait is an ideal tool for analysing spontaneous imbibition because it can evaluate the process without solving the complex governing ordinary differential equations. Moreover, dynamic contact angle and slip effect play an important role in fluid imbibition in fractal tortuous capillaries. Neglecting slip effect in micro-nano pores apparently underestimates imbibition capability, and ignoring variations in contact angle causes inaccuracy in predicting imbibition speed at the initial stage of the process. Finally, gravity is one of the factors that control the stabilisation of the imbibition process.

  20. Self-organized network of fractal-shaped components coupled through statistical interaction.

    PubMed

    Ugajin, R

    2001-09-01

    A dissipative dynamics is introduced to generate self-organized networks of interacting objects, which we call coupled-fractal networks. The growth model is constructed based on a growth hypothesis in which the growth rate of each object is a product of the probability of receiving source materials from faraway and the probability of receiving adhesives from other grown objects, where each object grows to be a random fractal if isolated, but connects with others if glued. The network is governed by the statistical interaction between fractal-shaped components, which can only be identified in a statistical manner over ensembles. This interaction is investigated using the degree of correlation between fractal-shaped components, enabling us to determine whether it is attractive or repulsive.

  1. Use of a dynamic gait trainer for a child with thoracic level spinal cord injury.

    PubMed

    Altizer, Wendy; Noritz, Garey; Paleg, Ginny

    2017-10-10

    Paediatric spinal cord injury (SCI) can result in permanent mobility impairment with consequences for activity, participation and quality of life. This case documents the effect of an overground supported stepping intervention using a dynamic gait trainer. To our knowledge, there are no published studies on this intervention for children with SCI and similar interventions have only been reported in children at American Spinal Injury Association Impairment Scale (AIS) levels B and C.A child with a T10 (thoracic level, vertebra 10), AIS level A injury, sustained at 2 years of age, continued to make gains in all areas including participation, activity, body structure and function over the following 4 years. Use of a dynamic gait trainer improved the participant's ability to be active and participate despite lack of further neuromuscular recovery. This novel approach with a commonly available device allowed the child to be active and participate in the absence of neural recovery. © BMJ Publishing Group Ltd (unless otherwise stated in the text of the article) 2017. All rights reserved. No commercial use is permitted unless otherwise expressly granted.

  2. Fractal astronomy.

    NASA Astrophysics Data System (ADS)

    Beech, M.

    1989-02-01

    The author discusses some of the more recent research on fractal astronomy and results presented in several astronomical studies. First, the large-scale structure of the universe is considered, while in another section one drops in scale to examine some of the smallest bodies in our solar system; the comets and meteoroids. The final section presents some thoughts on what influence the fractal ideology might have on astronomy, focusing particularly on the question recently raised by Kadanoff, "Fractals: where's the physics?"

  3. On fractality and chaos in Moroccan family business stock returns and volatility

    NASA Astrophysics Data System (ADS)

    Lahmiri, Salim

    2017-05-01

    The purpose of this study is to examine existence of fractality and chaos in returns and volatilities of family business companies listed on the Casablanca Stock Exchange (CSE) in Morocco, and also in returns and volatility of the CSE market index. Detrended fluctuation analysis based Hurst exponent and fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) model are used to quantify fractality in returns and volatility time series respectively. Besides, the largest Lyapunov exponent is employed to quantify chaos in both time series. The empirical results from sixteen family business companies follow. For return series, fractality analysis show that most of family business returns listed on CSE exhibit anti-persistent dynamics, whilst market returns have persistent dynamics. Besides, chaos tests show that business family stock returns are not chaotic while market returns exhibit evidence of chaotic behaviour. For volatility series, fractality analysis shows that most of family business stocks and market index exhibit long memory in volatility. Furthermore, results from chaos tests show that volatility of family business returns is not chaotic, whilst volatility of market index is chaotic. These results may help understanding irregularities patterns in Moroccan family business stock returns and volatility, and how they are different from market dynamics.

  4. The Ndynamics package—Numerical analysis of dynamical systems and the fractal dimension of boundaries

    NASA Astrophysics Data System (ADS)

    Avellar, J.; Duarte, L. G. S.; da Mota, L. A. C. P.; de Melo, N.; Skea, J. E. F.

    2012-09-01

    A set of Maple routines is presented, fully compatible with the new releases of Maple (14 and higher). The package deals with the numerical evolution of dynamical systems and provide flexible plotting of the results. The package also brings an initial conditions generator, a numerical solver manager, and a focusing set of routines that allow for better analysis of the graphical display of the results. The novelty that the package presents an optional C interface is maintained. This allows for fast numerical integration, even for the totally inexperienced Maple user, without any C expertise being required. Finally, the package provides the routines to calculate the fractal dimension of boundaries (via box counting). New version program summary Program Title: Ndynamics Catalogue identifier: %Leave blank, supplied by Elsevier. Licensing provisions: no. Programming language: Maple, C. Computer: Intel(R) Core(TM) i3 CPU M330 @ 2.13 GHz. Operating system: Windows 7. RAM: 3.0 GB Keywords: Dynamical systems, Box counting, Fractal dimension, Symbolic computation, Differential equations, Maple. Classification: 4.3. Catalogue identifier of previous version: ADKH_v1_0. Journal reference of previous version: Comput. Phys. Commun. 119 (1999) 256. Does the new version supersede the previous version?: Yes. Nature of problem Computation and plotting of numerical solutions of dynamical systems and the determination of the fractal dimension of the boundaries. Solution method The default method of integration is a fifth-order Runge-Kutta scheme, but any method of integration present on the Maple system is available via an argument when calling the routine. A box counting [1] method is used to calculate the fractal dimension [2] of the boundaries. Reasons for the new version The Ndynamics package met a demand of our research community for a flexible and friendly environment for analyzing dynamical systems. All the user has to do is create his/her own Maple session, with the system to

  5. Study on the Adsorption Phenomenon in Shale with the Combination of Molecular Dynamic Simulation and Fractal Analysis

    NASA Astrophysics Data System (ADS)

    Zhang, Liehui; Li, Jianchao; Jia, Du; Zhao, Yulong; Xie, Chunyu; Tao, Zhengwu

    As one of the key status of gas in shale reservoir, adsorption gas accounts for considerable percentage of total gas amount. Due to the complexity and nanostructure of shale gas reservoir, it is very challenging to represent adsorption gas through traditional methods. However, the integration of the fractal theory and molecular dynamics (MD) simulation may provide a new perspective of understanding such nanostructure and the micro-phenomenon happening in it. The key purpose of this paper is to investigate the adsorption phenomenon in shale kerogen. By using MD simulation and grand canonical Monte Carlo (GCMC) algorithm, the adsorption of methane in 2, 5 and 10nm slit-like pores is simulated for different temperature and pressure status. According to the results, the average gas density in smaller pores is higher than that in bigger pores, and multilayer adsorption presents on some areas of pore surfaces. Then, the simulation results are analyzed using the multilayer fractal adsorption model. The analysis indicates that the number of adsorption layer increases with pressure increase: four-layer adsorption presents in 10nm pores while three-layer adsorption shows up in 2nm and 5nm pores due to pore volume limit. Fractal dimension of pore wall surface generated in this study is in the range of 2.31-2.63. Moreover, high temperature could decrease the adsorption behavior in reservoir condition.

  6. The effect of subtalar inversion/eversion on the dynamic function of the tibialis anterior, soleus, and gastrocnemius during the stance phase of gait.

    PubMed

    Wang, Ruoli; Gutierrez-Farewik, Elena M

    2011-05-01

    The purpose of this study was to determine how gait deviation in one plane (i.e. excessive subtalar inversion/eversion) can affect the dynamic function of the tibialis anterior, gastrocnemius, and soleus to accelerate the subtalar, ankle, knee and hip joints, as well as the body center of mass. Induced acceleration analysis was performed based on a subject-specific three-dimensional linkage model configured by stance phase gait data and driven by one unit of muscle force. Eight healthy adult subjects were examined in gait analysis. The subtalar inversion/eversion was modeled by offsetting up to 20° from the normal subtalar angle while other configurations remained unaltered. This study showed that the gastrocnemius, soleus and tibialis anterior generally functioned as their anatomical definition in normal gait, but counterintuitive function was occasionally found in the bi-articular gastrocnemius. The plantarflexors play important roles in the body support and forward progression. Excessive subtalar eversion was found to enlarge the plantarflexors and tibialis anterior's function. Induced acceleration analysis demonstrated its ability to isolate the contributions of individual muscle to a given factor, and as a means of studying effect of pathological gait on the dynamic muscle functions. Copyright © 2011 Elsevier B.V. All rights reserved.

  7. A fractal model for nuclear organization: current evidence and biological implications

    PubMed Central

    Bancaud, Aurélien; Lavelle, Christophe; Huet, Sébastien; Ellenberg, Jan

    2012-01-01

    Chromatin is a multiscale structure on which transcription, replication, recombination and repair of the genome occur. To fully understand any of these processes at the molecular level under physiological conditions, a clear picture of the polymorphic and dynamic organization of chromatin in the eukaryotic nucleus is required. Recent studies indicate that a fractal model of chromatin architecture is consistent with both the reaction-diffusion properties of chromatin interacting proteins and with structural data on chromatin interminglement. In this study, we provide a critical overview of the experimental evidence that support a fractal organization of chromatin. On this basis, we discuss the functional implications of a fractal chromatin model for biological processes and propose future experiments to probe chromatin organization further that should allow to strongly support or invalidate the fractal hypothesis. PMID:22790985

  8. Concurrent musculoskeletal dynamics and finite element analysis predicts altered gait patterns to reduce foot tissue loading.

    PubMed

    Halloran, Jason P; Ackermann, Marko; Erdemir, Ahmet; van den Bogert, Antonie J

    2010-10-19

    Current computational methods for simulating locomotion have primarily used muscle-driven multibody dynamics, in which neuromuscular control is optimized. Such simulations generally represent joints and soft tissue as simple kinematic or elastic elements for computational efficiency. These assumptions limit application in studies such as ligament injury or osteoarthritis, where local tissue loading must be predicted. Conversely, tissue can be simulated using the finite element method with assumed or measured boundary conditions, but this does not represent the effects of whole body dynamics and neuromuscular control. Coupling the two domains would overcome these limitations and allow prediction of movement strategies guided by tissue stresses. Here we demonstrate this concept in a gait simulation where a musculoskeletal model is coupled to a finite element representation of the foot. Predictive simulations incorporated peak plantar tissue deformation into the objective of the movement optimization, as well as terms to track normative gait data and minimize fatigue. Two optimizations were performed, first without the strain minimization term and second with the term. Convergence to realistic gait patterns was achieved with the second optimization realizing a 44% reduction in peak tissue strain energy density. The study demonstrated that it is possible to alter computationally predicted neuromuscular control to minimize tissue strain while including desired kinematic and muscular behavior. Future work should include experimental validation before application of the methodology to patient care. Copyright © 2010 Elsevier Ltd. All rights reserved.

  9. More symmetrical gait after split-belt treadmill walking does not modify dynamic and postural balance in individuals post-stroke.

    PubMed

    Miéville, Carole; Lauzière, Séléna; Betschart, Martina; Nadeau, Sylvie; Duclos, Cyril

    2018-04-24

    Spontaneous gait is often asymmetrical in individuals post-stroke, despite their ability to walk more symmetrically on demand. Given the sensorimotor deficits in the paretic limb, this asymmetrical gait may facilitate balance maintenance. We used a split-belt walking protocol to alter gait asymmetry and determine the effects on dynamic and postural balance. Twenty individuals post-stroke walked on a split-belt treadmill. In two separate periods, the effects of walking with the non-paretic leg, and then the paretic one, on the faster belt on spatio-temporal symmetry and balance were compared before and after these perturbation periods. Kinematic and kinetic data were collected using a motion analysis system and an instrumented treadmill to determine symmetry ratios of spatiotemporal parameters and dynamic and postural balance. Balance, quantified by the concepts of stabilizing and destabilizing forces, was compared before and after split-belt walking for subgroups of participants who improved and worsened their symmetry. The side on the slow belt during split-belt walking, but not the changes in asymmetry, affected balance. Difficulty in maintaining balance was higher during stance phase of the leg that was on the slow belt and lower on the contralateral side after split-belt walking, mostly because the center of pressure was closer (higher difficulty) or further (lower difficulty) from the limit of the base of support, respectively. Changes in spatiotemporal parameters may be sought without additional alteration of balance during gait post-stroke. Copyright © 2018 Elsevier Ltd. All rights reserved.

  10. Adaptive gait responses to awareness of an impending slip during treadmill walking.

    PubMed

    Yang, Feng; Kim, JaeEun; Munoz, Jose

    2016-10-01

    The awareness of potential slip risk has been shown to cause protective changes to human gait during overground walking. It remains unknown if such adaptations to walking pattern also exist when ambulating on a treadmill. This study sought to determine whether and to what extent individuals, when being aware of a potential slip risk during treadmill walking, could adjust their gait pattern to improve their dynamic stability against backward balance loss in response to the impending slip hazard. Fifty-four healthy young subjects (age: 23.9±4.7years) participated in this study. Subjects' gait pattern was measured under two conditions: walking on a treadmill without (or normal walking) and with (or aware walking) the awareness of the potential slip perturbation. During both walking conditions, subjects' full body kinematics were gathered by using a motion capture system. Spatial gait parameters and the dynamic gait stability against backward balance were compared between the two walking conditions. The results revealed that subjects proactively adopted a "cautious gait" during aware walking compared with the normal walking. The cautious gait, which was achieved by taking a shorter step and a more flatfoot landing, positioned the body center of mass closer to the base of support, improving participants' dynamic stability and increasing their resistance against a possible slip-related fall. The finding from this study could provide insights into the dynamic stability control when individuals anticipate potential slip risk during treadmill walking. Copyright © 2016 Elsevier B.V. All rights reserved.

  11. Monte Carlo Sampling in Fractal Landscapes

    NASA Astrophysics Data System (ADS)

    Leitão, Jorge C.; Lopes, J. M. Viana Parente; Altmann, Eduardo G.

    2013-05-01

    We design a random walk to explore fractal landscapes such as those describing chaotic transients in dynamical systems. We show that the random walk moves efficiently only when its step length depends on the height of the landscape via the largest Lyapunov exponent of the chaotic system. We propose a generalization of the Wang-Landau algorithm which constructs not only the density of states (transient time distribution) but also the correct step length. As a result, we obtain a flat-histogram Monte Carlo method which samples fractal landscapes in polynomial time, a dramatic improvement over the exponential scaling of traditional uniform-sampling methods. Our results are not limited by the dimensionality of the landscape and are confirmed numerically in chaotic systems with up to 30 dimensions.

  12. Fractal dimension of spatially extended systems

    NASA Astrophysics Data System (ADS)

    Torcini, A.; Politi, A.; Puccioni, G. P.; D'Alessandro, G.

    1991-10-01

    Properties of the invariant measure are numerically investigated in 1D chains of diffusively coupled maps. The coarse-grained fractal dimension is carefully computed in various embedding spaces, observing an extremely slow convergence towards the asymptotic value. This is in contrast with previous simulations, where the analysis of an insufficient number of points led the authors to underestimate the increase of fractal dimension with increasing the dimension of the embedding space. Orthogonal decomposition is also performed confirming that the slow convergence is intrinsically related to local nonlinear properties of the invariant measure. Finally, the Kaplan-Yorke conjecture is tested for short chains, showing that, despite the noninvertibility of the dynamical system, a good agreement is found between Lyapunov dimension and information dimension.

  13. Chaos, Fractals and Their Applications

    NASA Astrophysics Data System (ADS)

    Thompson, J. Michael T.

    2016-12-01

    This paper gives an up-to-date account of chaos and fractals, in a popular pictorial style for the general scientific reader. A brief historical account covers the development of the subject from Newton’s laws of motion to the astronomy of Poincaré and the weather forecasting of Lorenz. Emphasis is given to the important underlying concepts, embracing the fractal properties of coastlines and the logistics of population dynamics. A wide variety of applications include: NASA’s discovery and use of zero-fuel chaotic “superhighways” between the planets; erratic chaotic solutions generated by Euler’s method in mathematics; atomic force microscopy; spontaneous pattern formation in chemical and biological systems; impact mechanics in offshore engineering and the chatter of cutting tools; controlling chaotic heartbeats. Reference is made to a number of interactive simulations and movies accessible on the web.

  14. Design of patient-specific gait modifications for knee osteoarthritis rehabilitation.

    PubMed

    Fregly, Benjamin J; Reinbolt, Jeffrey A; Rooney, Kelly L; Mitchell, Kim H; Chmielewski, Terese L

    2007-09-01

    Abstract-Gait modification is a nonsurgical approach for reducing the external knee adduction torque in patients with knee osteoarthritis (OA). The magnitude of the first adduction torque peak in particular is strongly associated with knee OA progression. While toeing out has been shown to reduce the second peak, no clinically realistic gait modifications have been identified that effectively reduce both peaks simultaneously. This study predicts novel patient-specific gait modifications that achieve this goal without changing the foot path. The modified gait motion was designed for a single patient with knee OA using dynamic optimization of a patient-specific, full-body gait model. The cost function minimized the knee adduction torque subject to constraints limiting how much the new gait motion could deviate from the patient's normal gait motion. The optimizations predicted a "medial-thrust" gait pattern that reduced the first adduction torque peak between 32% and 54% and the second peak between 34% and 56%. The new motion involved three synergistic kinematic changes: slightly decreased pelvis obliquity, slightly increased leg flexion, and slightly increased pelvis axial rotation. After gait retraining, the patient achieved adduction torque reductions of 39% to 50% in the first peak and 37% to 55% in the second one. These reductions are comparable to those reported after high tibial osteotomy surgery. The associated kinematic changes were consistent with the predictions except for pelvis obliquity, which showed little change. This study demonstrates that it is feasible to design novel patient-specific gait modifications with potential clinical benefit using dynamic optimization of patient-specific, full-body gait models. Further investigation is needed to assess the extent to which similar gait modifications may be effective for other patients with knee OA.

  15. Fractal pharmacokinetics.

    PubMed

    Pereira, Luis M

    2010-06-01

    Pharmacokinetics (PK) has been traditionally dealt with under the homogeneity assumption. However, biological systems are nowadays comprehensively understood as being inherently fractal. Specifically, the microenvironments where drug molecules interact with membrane interfaces, metabolic enzymes or pharmacological receptors, are unanimously recognized as unstirred, space-restricted, heterogeneous and geometrically fractal. Therefore, classical Fickean diffusion and the notion of the compartment as a homogeneous kinetic space must be revisited. Diffusion in fractal spaces has been studied for a long time making use of fractional calculus and expanding on the notion of dimension. Combining this new paradigm with the need to describe and explain experimental data results in defining time-dependent rate constants with a characteristic fractal exponent. Under the one-compartment simplification this strategy is straightforward. However, precisely due to the heterogeneity of the underlying biology, often at least a two-compartment model is required to address macroscopic data such as drug concentrations. This simple modelling step-up implies significant analytical and numerical complications. However, a few methods are available that make possible the original desideratum. In fact, exploring the full range of parametric possibilities and looking at different drugs and respective biological concentrations, it may be concluded that all PK modelling approaches are indeed particular cases of the fractal PK theory.

  16. Launching the chaotic realm of iso-fractals: A short remark

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    O'Schmidt, Nathan; Katebi, Reza; Corda, Christian

    In this brief note, we introduce the new, emerging sub-discipline of iso-fractals by highlighting and discussing the preliminary results of recent works. First, we note the abundance of fractal, chaotic, non-linear, and self-similar structures in nature while emphasizing the importance of studying such systems because fractal geometry is the language of chaos. Second, we outline the iso-fractal generalization of the Mandelbrot set to exemplify the newly generated Mandelbrot iso-sets. Third, we present the cutting-edge notion of dynamic iso-spaces and explain how a mathematical space can be iso-topically lifted with iso-unit functions that (continuously or discretely) change; in the discrete casemore » examples, we mention that iteratively generated sequences like Fibonacci’s numbers and (the complex moduli of) Mandelbrot’s numbers can supply a deterministic chain of iso-units to construct an ordered series of (magnified and/or de-magnified) iso-spaces that are locally iso-morphic. Fourth, we consider the initiation of iso-fractals with Inopin’s holographic ring (IHR) topology and fractional statistics for 2D and 3D iso-spaces. In total, the reviewed iso-fractal results are a significant improvement over traditional fractals because the application of Santilli’s iso-mathematics arms us an extra degree of freedom for attacking problems in chaos. Finally, we conclude by proposing some questions and ideas for future research work.« less

  17. Differential effects of absent visual feedback control on gait variability during different locomotion speeds.

    PubMed

    Wuehr, M; Schniepp, R; Pradhan, C; Ilmberger, J; Strupp, M; Brandt, T; Jahn, K

    2013-01-01

    Healthy persons exhibit relatively small temporal and spatial gait variability when walking unimpeded. In contrast, patients with a sensory deficit (e.g., polyneuropathy) show an increased gait variability that depends on speed and is associated with an increased fall risk. The purpose of this study was to investigate the role of vision in gait stabilization by determining the effects of withdrawing visual information (eyes closed) on gait variability at different locomotion speeds. Ten healthy subjects (32.2 ± 7.9 years, 5 women) walked on a treadmill for 5-min periods at their preferred walking speed and at 20, 40, 70, and 80 % of maximal walking speed during the conditions of walking with eyes open (EO) and with eyes closed (EC). The coefficient of variation (CV) and fractal dimension (α) of the fluctuations in stride time, stride length, and base width were computed and analyzed. Withdrawing visual information increased the base width CV for all walking velocities (p < 0.001). The effects of absent visual information on CV and α of stride time and stride length were most pronounced during slow locomotion (p < 0.001) and declined during fast walking speeds. The results indicate that visual feedback control is used to stabilize the medio-lateral (i.e., base width) gait parameters at all speed sections. In contrast, sensory feedback control in the fore-aft direction (i.e., stride time and stride length) depends on speed. Sensory feedback contributes most to fore-aft gait stabilization during slow locomotion, whereas passive biomechanical mechanisms and an automated central pattern generation appear to control fast locomotion.

  18. Reply to "Comment on 'Hydrodynamics of fractal continuum flow' and 'Map of fluid flow in fractal porous medium into fractal continuum flow'".

    PubMed

    Balankin, Alexander S; Elizarraraz, Benjamin Espinoza

    2013-11-01

    The aim of this Reply is to elucidate the difference between the fractal continuum models used in the preceding Comment and the models of fractal continuum flow which were put forward in our previous articles [Phys. Rev. E 85, 025302(R) (2012); 85, 056314 (2012)]. In this way, some drawbacks of the former models are highlighted. Specifically, inconsistencies in the definitions of the fractal derivative, the Jacobian of transformation, the displacement vector, and angular momentum are revealed. The proper forms of the Reynolds' transport theorem and angular momentum principle for the fractal continuum are reaffirmed in a more illustrative manner. Consequently, we emphasize that in the absence of any internal angular momentum, body couples, and couple stresses, the Cauchy stress tensor in the fractal continuum should be symmetric. Furthermore, we stress that the approach based on the Cartesian product measured and used in the preceding Comment cannot be employed to study the path-connected fractals, such as a flow in a fractally permeable medium. Thus, all statements of our previous works remain unchallenged.

  19. Scattering from fractals

    NASA Astrophysics Data System (ADS)

    Hurd, Alan J.

    The realization that structures in Nature often can be described by Mandelbrot's fractals has led to a revolution in many areas of physics. The interaction of waves with fractal systems has, understandably, become intensely studied since scattering is the method of choice to probe delicate fractal structures such as chainlike particle aggregates. Not all of these waves are electromagnetic. Neutron scattering, for example, is an important complementary tool to structural studies by X-ray and light scattering. Since the phenomenology of small-angle neutron scattering (SANS), as it is applied to fractal systems, is identical to that of small-angle X-ray scattering (SAXS), it falls within the scope of this paper.

  20. Fractal avalanche ruptures in biological membranes

    NASA Astrophysics Data System (ADS)

    Gözen, Irep; Dommersnes, Paul; Czolkos, Ilja; Jesorka, Aldo; Lobovkina, Tatsiana; Orwar, Owe

    2010-11-01

    Bilayer membranes envelope cells as well as organelles, and constitute the most ubiquitous biological material found in all branches of the phylogenetic tree. Cell membrane rupture is an important biological process, and substantial rupture rates are found in skeletal and cardiac muscle cells under a mechanical load. Rupture can also be induced by processes such as cell death, and active cell membrane repair mechanisms are essential to preserve cell integrity. Pore formation in cell membranes is also at the heart of many biomedical applications such as in drug, gene and short interfering RNA delivery. Membrane rupture dynamics has been studied in bilayer vesicles under tensile stress, which consistently produce circular pores. We observed very different rupture mechanics in bilayer membranes spreading on solid supports: in one instance fingering instabilities were seen resulting in floral-like pores and in another, the rupture proceeded in a series of rapid avalanches causing fractal membrane fragmentation. The intermittent character of rupture evolution and the broad distribution in avalanche sizes is consistent with crackling-noise dynamics. Such noisy dynamics appear in fracture of solid disordered materials, in dislocation avalanches in plastic deformations and domain wall magnetization avalanches. We also observed similar fractal rupture mechanics in spreading cell membranes.

  1. Performance of an inverted pendulum model directly applied to normal human gait.

    PubMed

    Buczek, Frank L; Cooney, Kevin M; Walker, Matthew R; Rainbow, Michael J; Concha, M Cecilia; Sanders, James O

    2006-03-01

    In clinical gait analysis, we strive to understand contributions to body support and propulsion as this forms a basis for treatment selection, yet the relative importance of gravitational forces and joint powers can be controversial even for normal gait. We hypothesized that an inverted pendulum model, propelled only by gravity, would be inadequate to predict velocities and ground reaction forces during gait. Unlike previous ballistic and passive dynamic walking studies, we directly compared model predictions to gait data for 24 normal children. We defined an inverted pendulum from the average center-of-pressure to the instantaneous center-of-mass, and derived equations of motion during single support that allowed a telescoping action. Forward and inverse dynamics predicted pendulum velocities and ground reaction forces, and these were statistically and graphically compared to actual gait data for identical strides. Results of forward dynamics replicated those in the literature, with reasonable predictions for velocities and anterior ground reaction forces, but poor predictions for vertical ground reaction forces. Deviations from actual values were explained by joint powers calculated for these subjects. With a telescoping action during inverse dynamics, predicted vertical forces improved dramatically and gained a dual-peak pattern previously missing in the literature, yet expected for normal gait. These improvements vanished when telescoping terms were set to zero. Because this telescoping action is difficult to explain without muscle activity, we believe these results support the need for both gravitational forces and joint powers in normal gait. Our approach also begins to quantify the relative contributions of each.

  2. Fractal Electronic Circuits Assembled From Nanoclusters

    NASA Astrophysics Data System (ADS)

    Fairbanks, M. S.; McCarthy, D.; Taylor, R. P.; Brown, S. A.

    2009-07-01

    Many patterns in nature can be described using fractal geometry. The effect of this fractal character is an array of properties that can include high internal connectivity, high dispersivity, and enhanced surface area to volume ratios. These properties are often desirable in applications and, consequently, fractal geometry is increasingly employed in technologies ranging from antenna to storm barriers. In this paper, we explore the application of fractal geometry to electrical circuits, inspired by the pervasive fractal structure of neurons in the brain. We show that, under appropriate growth conditions, nanoclusters of Sb form into islands on atomically flat substrates via a process close to diffusion-limited aggregation (DLA), establishing fractal islands that will form the basis of our fractal circuits. We perform fractal analysis of the islands to determine the spatial scaling properties (characterized by the fractal dimension, D) of the proposed circuits and demonstrate how varying growth conditions can affect D. We discuss fabrication approaches for establishing electrical contact to the fractal islands. Finally, we present fractal circuit simulations, which show that the fractal character of the circuit translates into novel, non-linear conduction properties determined by the circuit's D value.

  3. Three-dimensional dynamic analysis of knee joint during gait in medial knee osteoarthritis using loading axis of knee.

    PubMed

    Nishino, Katsutoshi; Omori, Go; Koga, Yoshio; Kobayashi, Koichi; Sakamoto, Makoto; Tanabe, Yuji; Tanaka, Masaei; Arakawa, Masaaki

    2015-07-01

    We recently developed a new method for three-dimensional evaluation of mechanical factors affecting knee joint in order to help identify factors that contribute to the progression of knee osteoarthritis (KOA). This study aimed to verify the clinical validity of our method by evaluating knee joint dynamics during gait. Subjects were 41 individuals (14 normal knees; 8 mild KOAs; 19 severe KOAs). The positions of skin markers attached to the body were captured during gait, and bi-planar X-ray images of the lower extremities were obtained in standing position. The positional relationship between the markers and femorotibial bones was determined from the X-ray images. Combining this relationship with gait capture allowed for the estimation of relative movement between femorotibial bones. We also calculated the point of intersection of loading axis of knee on the tibial proximal surface (LAK point) to analyze knee joint dynamics. Knee flexion range in subjects with severe KOA during gait was significantly smaller than that in those with normal knees (p=0.011), and knee adduction in those with severe KOA was significantly larger than in those with mild KOA (p<0.000). LAK point was locally loaded on the medial compartment of the tibial surface as KOA progressed, with LAK point of subjects with severe KOA rapidly shifting medially during loading response. Local loading and medial shear force were applied to the tibial surface during stance phase as medial KOA progressed. Our findings suggest that our method is useful for the quantitative evaluation of mechanical factors that affect KOA progression. Copyright © 2015 Elsevier B.V. All rights reserved.

  4. Self-stabilized Fractality of Sea-coasts Through Damped Erosion

    NASA Astrophysics Data System (ADS)

    Sapoval, B.; Baldassari, A.; Gabrielli, A.

    2004-05-01

    Coastline morphology is of current interest in geophysical research and coastline erosion has important economic consequences. At the same time, although the geometry of seacoasts is often used as an introductory archetype of fractal morphology in nature there has been no explanation about which physical mechanism could justify that empirical observation. The present work propose a minimal, but robust, model of evolution of rocky coasts towards fractality. The model describes how a stationary fractal geometry arises spontaneously from the mutual self-stabilization of a rocky coast morphology and sea eroding power. If, on one hand, erosion generally increases the geometrical irregularity of the coast, on the other hand this increase creates a stronger damping of the sea and a consequent diminution of its eroding power. The increased damping argument relies on the studies of fractal acoustical cavities, which have shown that viscous damping is augmented on a longer, irregular, surface. A minimal two-dimensional model of erosion is introduced which leads to the through a complex dynamics of the earth-sea interface, to the appearance of a stationary fractal seacoast with dimension close to 4/3. Fractal geometry plays here the role of a morphological attractor directly related to percolation geometry. The model reproduces at least qualitatively some of the features of real coasts using only simple ingredients: the randomness of the lithology and the decrease of the erosion power of the sea. B. Sapoval, Fractals (Aditech, Paris, 1989). B. Sapoval, O. Haeberlé, and S.Russ, J. Acoust. Soc. Am., 2014 (1997). B. Hébert B., B. Sapoval, and S.Russ, J. Acoust. Soc. Am., 1567 (1999).

  5. Universal Inverse Power-Law Distribution for Fractal Fluctuations in Dynamical Systems: Applications for Predictability of Inter-Annual Variability of Indian and USA Region Rainfall

    NASA Astrophysics Data System (ADS)

    Selvam, A. M.

    2017-01-01

    Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and, therefore, the statistical normal distribution with implicit assumption of independence, fixed mean and standard deviation cannot be used for description and quantification of fractal data sets. The author has developed a general systems theory based on classical statistical physics for fractal fluctuations which predicts the following. (1) The fractal fluctuations signify an underlying eddy continuum, the larger eddies being the integrated mean of enclosed smaller-scale fluctuations. (2) The probability distribution of eddy amplitudes and the variance (square of eddy amplitude) spectrum of fractal fluctuations follow the universal Boltzmann inverse power law expressed as a function of the golden mean. (3) Fractal fluctuations are signatures of quantum-like chaos since the additive amplitudes of eddies when squared represent probability densities analogous to the sub-atomic dynamics of quantum systems such as the photon or electron. (4) The model predicted distribution is very close to statistical normal distribution for moderate events within two standard deviations from the mean but exhibits a fat long tail that are associated with hazardous extreme events. Continuous periodogram power spectral analyses of available GHCN annual total rainfall time series for the period 1900-2008 for Indian and USA stations show that the power spectra and the corresponding probability distributions follow model predicted universal inverse power law form signifying an eddy continuum structure underlying the observed inter-annual variability of rainfall. On a global scale, man-made greenhouse gas related atmospheric warming would result in intensification of natural climate variability, seen immediately in high frequency fluctuations such as QBO and ENSO and even shorter timescales. Model concepts and results of analyses are discussed with reference

  6. Gait dynamics in Pisa syndrome and Camptocormia: The role of stride length and hip kinematics.

    PubMed

    Tramonti, C; Di Martino, S; Unti, E; Frosini, D; Bonuccelli, U; Rossi, B; Ceravolo, R; Chisari, C

    2017-09-01

    This is an observational cross-sectional study evaluating gait dynamics in patients with Parkinson's Disease (PD) and severe postural deformities, PD without axial deviations and healthy subjects. Ten PS individuals with Pisa syndrome (PS) and nine subjects with Camptocormia (CC) performed 3-D Gait Analysis and were evaluated with walking and balance scales. Correlations with clinical and functional scales were investigated. Spatio-temporal and kinematic data were compared to ten PD subjects without postural deformities (PP) and ten healthy matched individuals (CG). Data obtained showed decreased walking velocity, stride and step length in PP, PS and CC groups compared to controls. The correlation analysis showed that stride and step length were associated with reduced functional abilities and disease severity in PS and CC groups. Kinematic data revealed marked reduction in range of movements (ROMs) at all lower-extremity joints in PS group. While, in CC group the main differences were pronounced in hip and knee joints. PS and CC groups presented a more pronounced reduction in hip articular excursion compared to PP subjects, revealing an increased hip flexion pattern during gait cycle. Moreover, the increased hip and knee flexion pattern adversely affected functional performance during walking tests. Results obtained provide evidence that step length, along with stride length, can be proposed as simple and clear indicators of disease severity and reduced functional abilities. The reduction of ROMs at hip joint represented an important mechanism contributing to decreased walking velocity, balance impairment and reduced gait performance in PD patients with postural deformities. Copyright © 2017 Elsevier B.V. All rights reserved.

  7. An intermittent control model of flexible human gait using a stable manifold of saddle-type unstable limit cycle dynamics

    PubMed Central

    Fu, Chunjiang; Suzuki, Yasuyuki; Kiyono, Ken; Morasso, Pietro; Nomura, Taishin

    2014-01-01

    than directly to the LC. The proposed intermittent control strategy might have a high affinity for the inverted pendulum analogy of biped gait, providing a dynamic view of how the step-to-step transition from one pendular stance to the next can be achieved stably in a robust manner by a well-timed neural intervention that exploits the stable modes embedded in the unstable dynamics. PMID:25339687

  8. An intermittent control model of flexible human gait using a stable manifold of saddle-type unstable limit cycle dynamics.

    PubMed

    Fu, Chunjiang; Suzuki, Yasuyuki; Kiyono, Ken; Morasso, Pietro; Nomura, Taishin

    2014-12-06

    than directly to the LC. The proposed intermittent control strategy might have a high affinity for the inverted pendulum analogy of biped gait, providing a dynamic view of how the step-to-step transition from one pendular stance to the next can be achieved stably in a robust manner by a well-timed neural intervention that exploits the stable modes embedded in the unstable dynamics.

  9. The fractal architecture of cytoplasmic organization: scaling, kinetics and emergence in metabolic networks.

    PubMed

    Aon, Miguel Antonio; O'Rourke, Brian; Cortassa, Sonia

    2004-01-01

    In this work, we highlight the links between fractals and scaling in cells and explore the kinetic consequences for biochemical reactions operating in fractal media. Based on the proposal that the cytoskeletal architecture is organized as a percolation lattice, with clusters emerging as fractal forms, the analysis of kinetics in percolation clusters is especially emphasized. A key consequence of this spatiotemporal cytoplasmic organization is that enzyme reactions following Michaelis-Menten or allosteric type kinetics exhibit higher rates in fractal media (for short times and at lower substrate concentrations) at the percolation threshold than in Euclidean media. As a result, considerably faster and higher amplification of enzymatic activity is obtained. Finally, we describe some of the properties bestowed by cytoskeletal organization and dynamics on metabolic networks.

  10. Fractals in geology and geophysics

    NASA Technical Reports Server (NTRS)

    Turcotte, Donald L.

    1989-01-01

    The definition of a fractal distribution is that the number of objects N with a characteristic size greater than r scales with the relation N of about r exp -D. The frequency-size distributions for islands, earthquakes, fragments, ore deposits, and oil fields often satisfy this relation. This application illustrates a fundamental aspect of fractal distributions, scale invariance. The requirement of an object to define a scale in photograhs of many geological features is one indication of the wide applicability of scale invariance to geological problems; scale invariance can lead to fractal clustering. Geophysical spectra can also be related to fractals; these are self-affine fractals rather than self-similar fractals. Examples include the earth's topography and geoid.

  11. Fractals in the Classroom

    ERIC Educational Resources Information Center

    Fraboni, Michael; Moller, Trisha

    2008-01-01

    Fractal geometry offers teachers great flexibility: It can be adapted to the level of the audience or to time constraints. Although easily explained, fractal geometry leads to rich and interesting mathematical complexities. In this article, the authors describe fractal geometry, explain the process of iteration, and provide a sample exercise.…

  12. Quantitative Assessment of Heart Rate Dynamics during Meditation: An ECG Based Study with Multi-Fractality and Visibility Graph

    PubMed Central

    Bhaduri, Anirban; Ghosh, Dipak

    2016-01-01

    The cardiac dynamics during meditation is explored quantitatively with two chaos-based non-linear techniques viz. multi-fractal detrended fluctuation analysis and visibility network analysis techniques. The data used are the instantaneous heart rate (in beats/minute) of subjects performing Kundalini Yoga and Chi meditation from PhysioNet. The results show consistent differences between the quantitative parameters obtained by both the analysis techniques. This indicates an interesting phenomenon of change in the complexity of the cardiac dynamics during meditation supported with quantitative parameters. The results also produce a preliminary evidence that these techniques can be used as a measure of physiological impact on subjects performing meditation. PMID:26909045

  13. Quantitative Assessment of Heart Rate Dynamics during Meditation: An ECG Based Study with Multi-Fractality and Visibility Graph.

    PubMed

    Bhaduri, Anirban; Ghosh, Dipak

    2016-01-01

    The cardiac dynamics during meditation is explored quantitatively with two chaos-based non-linear techniques viz. multi-fractal detrended fluctuation analysis and visibility network analysis techniques. The data used are the instantaneous heart rate (in beats/minute) of subjects performing Kundalini Yoga and Chi meditation from PhysioNet. The results show consistent differences between the quantitative parameters obtained by both the analysis techniques. This indicates an interesting phenomenon of change in the complexity of the cardiac dynamics during meditation supported with quantitative parameters. The results also produce a preliminary evidence that these techniques can be used as a measure of physiological impact on subjects performing meditation.

  14. Fractal mechanisms in the electrophysiology of the heart

    NASA Technical Reports Server (NTRS)

    Goldberger, A. L.

    1992-01-01

    The mathematical concept of fractals provides insights into complex anatomic branching structures that lack a characteristic (single) length scale, and certain complex physiologic processes, such as heart rate regulation, that lack a single time scale. Heart rate control is perturbed by alterations in neuro-autonomic function in a number of important clinical syndromes, including sudden cardiac death, congestive failure, cocaine intoxication, fetal distress, space sickness and physiologic aging. These conditions are associated with a loss of the normal fractal complexity of interbeat interval dynamics. Such changes, which may not be detectable using conventional statistics, can be quantified using new methods derived from "chaos theory.".

  15. Capability of 2 gait measures for detecting response to gait training in stroke survivors: Gait Assessment and Intervention Tool and the Tinetti Gait Scale.

    PubMed

    Zimbelman, Janice; Daly, Janis J; Roenigk, Kristen L; Butler, Kristi; Burdsall, Richard; Holcomb, John P

    2012-01-01

    To characterize the performance of 2 observational gait measures, the Tinetti Gait Scale (TGS) and the Gait Assessment and Intervention Tool (G.A.I.T.), in identifying improvement in gait in response to gait training. In secondary analysis from a larger study of multimodal gait training for stroke survivors, we measured gait at pre-, mid-, and posttreatment according to G.A.I.T. and TGS, assessing their capability to capture recovery of coordinated gait components. Large medical center. Cohort of stroke survivors (N=44) greater than 6 months after stroke. All subjects received 48 sessions of a multimodal gait-training protocol. Treatment consisted of 1.5 hours per session, 4 sessions per week for 12 weeks, receiving these 3 treatment aspects: (1) coordination exercise, (2) body weight-supported treadmill training, and (3) overground gait training, with 46% of subjects receiving functional electrical stimulation. All subjects were evaluated with the G.A.I.T. and TGS before and after completing the 48-session intervention. An additional evaluation was performed at midtreatment (after session 24). For the total subject sample, there were significant pre-/post-, pre-/mid-, and mid-/posttreatment gains for both the G.A.I.T. and the TGS. According to the G.A.I.T., 40 subjects (91%) showed improved scores, 2 (4%) no change, and 2 (4%) a worsening score. According to the TGS, only 26 subjects (59%) showed improved scores, 16 (36%) no change, and 1 (2%) a worsening score. For 1 treatment group of chronic stroke survivors, the TGS failed to identify a significant treatment response to gait training, whereas the G.A.I.T. measure was successful. The G.A.I.T. is more sensitive than the TGS for individual patients and group treatment response in identifying recovery of volitional control of gait components in response to gait training. Copyright © 2012 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

  16. The Novel Quantitative Technique for Assessment of Gait Symmetry Using Advanced Statistical Learning Algorithm

    PubMed Central

    Wu, Jianning; Wu, Bin

    2015-01-01

    The accurate identification of gait asymmetry is very beneficial to the assessment of at-risk gait in the clinical applications. This paper investigated the application of classification method based on statistical learning algorithm to quantify gait symmetry based on the assumption that the degree of intrinsic change in dynamical system of gait is associated with the different statistical distributions between gait variables from left-right side of lower limbs; that is, the discrimination of small difference of similarity between lower limbs is considered the reorganization of their different probability distribution. The kinetic gait data of 60 participants were recorded using a strain gauge force platform during normal walking. The classification method is designed based on advanced statistical learning algorithm such as support vector machine algorithm for binary classification and is adopted to quantitatively evaluate gait symmetry. The experiment results showed that the proposed method could capture more intrinsic dynamic information hidden in gait variables and recognize the right-left gait patterns with superior generalization performance. Moreover, our proposed techniques could identify the small significant difference between lower limbs when compared to the traditional symmetry index method for gait. The proposed algorithm would become an effective tool for early identification of the elderly gait asymmetry in the clinical diagnosis. PMID:25705672

  17. The novel quantitative technique for assessment of gait symmetry using advanced statistical learning algorithm.

    PubMed

    Wu, Jianning; Wu, Bin

    2015-01-01

    The accurate identification of gait asymmetry is very beneficial to the assessment of at-risk gait in the clinical applications. This paper investigated the application of classification method based on statistical learning algorithm to quantify gait symmetry based on the assumption that the degree of intrinsic change in dynamical system of gait is associated with the different statistical distributions between gait variables from left-right side of lower limbs; that is, the discrimination of small difference of similarity between lower limbs is considered the reorganization of their different probability distribution. The kinetic gait data of 60 participants were recorded using a strain gauge force platform during normal walking. The classification method is designed based on advanced statistical learning algorithm such as support vector machine algorithm for binary classification and is adopted to quantitatively evaluate gait symmetry. The experiment results showed that the proposed method could capture more intrinsic dynamic information hidden in gait variables and recognize the right-left gait patterns with superior generalization performance. Moreover, our proposed techniques could identify the small significant difference between lower limbs when compared to the traditional symmetry index method for gait. The proposed algorithm would become an effective tool for early identification of the elderly gait asymmetry in the clinical diagnosis.

  18. Fundamental Fractal Antenna Design Process

    NASA Astrophysics Data System (ADS)

    Zhu, L. P.; Kim, T. C.; Kakas, G. D.

    2017-12-01

    Antenna designers are always looking to come up with new ideas to push the envelope for new antennas, using a smaller volume while striving for higher bandwidth, wider bandwidth, and antenna gain. One proposed method of increasing bandwidth or shrinking antenna size is via the use of fractal geometry, which gives rise to fractal antennas. Fractals are those fun shapes that if one zooms in or zoom out, the structure is always the same. Design a new type of antenna based on fractal antenna design by utilize the Design of Experiment (DOE) will be shown in fractal antenna design process. Investigate conformal fractal antenna design for patterns, dimensions, and size, of the antenna but maintaining or improving the antenna performance. Research shows an antenna designer how to create basic requirements of the fractal antenna through a step by step process, and provides how to optimize the antenna design with the model prediction, lab measurement, and actual results from the compact range measurement on the antenna patterns.

  19. Changes in frontal plane dynamics and the loading response phase of the gait cycle are characteristic of severe knee osteoarthritis application of a multidimensional analysis technique.

    PubMed

    Astephen, J L; Deluzio, K J

    2005-02-01

    Osteoarthritis of the knee is related to many correlated mechanical factors that can be measured with gait analysis. Gait analysis results in large data sets. The analysis of these data is difficult due to the correlated, multidimensional nature of the measures. A multidimensional model that uses two multivariate statistical techniques, principal component analysis and discriminant analysis, was used to discriminate between the gait patterns of the normal subject group and the osteoarthritis subject group. Nine time varying gait measures and eight discrete measures were included in the analysis. All interrelationships between and within the measures were retained in the analysis. The multidimensional analysis technique successfully separated the gait patterns of normal and knee osteoarthritis subjects with a misclassification error rate of <6%. The most discriminatory feature described a static and dynamic alignment factor. The second most discriminatory feature described a gait pattern change during the loading response phase of the gait cycle. The interrelationships between gait measures and between the time instants of the gait cycle can provide insight into the mechanical mechanisms of pathologies such as knee osteoarthritis. These results suggest that changes in frontal plane loading and alignment and the loading response phase of the gait cycle are characteristic of severe knee osteoarthritis gait patterns. Subsequent investigations earlier in the disease process may suggest the importance of these factors to the progression of knee osteoarthritis.

  20. Preferred gait and walk-run transition speeds in ostriches measured using GPS-IMU sensors.

    PubMed

    Daley, Monica A; Channon, Anthony J; Nolan, Grant S; Hall, Jade

    2016-10-15

    The ostrich (Struthio camelus) is widely appreciated as a fast and agile bipedal athlete, and is a useful comparative bipedal model for human locomotion. Here, we used GPS-IMU sensors to measure naturally selected gait dynamics of ostriches roaming freely over a wide range of speeds in an open field and developed a quantitative method for distinguishing walking and running using accelerometry. We compared freely selected gait-speed distributions with previous laboratory measures of gait dynamics and energetics. We also measured the walk-run and run-walk transition speeds and compared them with those reported for humans. We found that ostriches prefer to walk remarkably slowly, with a narrow walking speed distribution consistent with minimizing cost of transport (CoT) according to a rigid-legged walking model. The dimensionless speeds of the walk-run and run-walk transitions are slower than those observed in humans. Unlike humans, ostriches transition to a run well below the mechanical limit necessitating an aerial phase, as predicted by a compass-gait walking model. When running, ostriches use a broad speed distribution, consistent with previous observations that ostriches are relatively economical runners and have a flat curve for CoT against speed. In contrast, horses exhibit U-shaped curves for CoT against speed, with a narrow speed range within each gait for minimizing CoT. Overall, the gait dynamics of ostriches moving freely over natural terrain are consistent with previous lab-based measures of locomotion. Nonetheless, ostriches, like humans, exhibit a gait-transition hysteresis that is not explained by steady-state locomotor dynamics and energetics. Further study is required to understand the dynamics of gait transitions. © 2016. Published by The Company of Biologists Ltd.

  1. Fractals: To Know, to Do, to Simulate.

    ERIC Educational Resources Information Center

    Talanquer, Vicente; Irazoque, Glinda

    1993-01-01

    Discusses the development of fractal theory and suggests fractal aggregates as an attractive alternative for introducing fractal concepts. Describes methods for producing metallic fractals and a computer simulation for drawing fractals. (MVL)

  2. Is the co-seismic slip distribution fractal?

    NASA Astrophysics Data System (ADS)

    Milliner, Christopher; Sammis, Charles; Allam, Amir; Dolan, James

    2015-04-01

    Co-seismic along-strike slip heterogeneity is widely observed for many surface-rupturing earthquakes as revealed by field and high-resolution geodetic methods. However, this co-seismic slip variability is currently a poorly understood phenomenon. Key unanswered questions include: What are the characteristics and underlying causes of along-strike slip variability? Do the properties of slip variability change from fault-to-fault, along-strike or at different scales? We cross-correlate optical, pre- and post-event air photos using the program COSI-Corr to measure the near-field, surface deformation pattern of the 1992 Mw 7.3 Landers and 1999 Mw 7.1 Hector Mine earthquakes in high-resolution. We produce the co-seismic slip profiles of both events from over 1,000 displacement measurements and observe consistent along-strike slip variability. Although the observed slip heterogeneity seems apparently complex and disordered, a spectral analysis reveals that the slip distributions are indeed self-affine fractal i.e., slip exhibits a consistent degree of irregularity at all observable length scales, with a 'short-memory' and is not random. We find a fractal dimension of 1.58 and 1.75 for the Landers and Hector Mine earthquakes, respectively, indicating that slip is more heterogeneous for the Hector Mine event. Fractal slip is consistent with both dynamic and quasi-static numerical simulations that use non-planar faults, which in turn causes heterogeneous along-strike stress, and we attribute the observed fractal slip to fault surfaces of fractal roughness. As fault surfaces are known to smooth over geologic time due to abrasional wear and fracturing, we also test whether the fractal properties of slip distributions alters between earthquakes from immature to mature fault systems. We will present results that test this hypothesis by using the optical image correlation technique to measure historic, co-seismic slip distributions of earthquakes from structurally mature, large

  3. Neurotomy of the rectus femoris nerve: Short-term effectiveness for spastic stiff knee gait: Clinical assessment and quantitative gait analysis.

    PubMed

    Gross, R; Robertson, J; Leboeuf, F; Hamel, O; Brochard, S; Perrouin-Verbe, B

    2017-02-01

    Stiff knee gait is a troublesome gait disturbance related to spastic paresis, frequently associated with overactivity of the rectus femoris muscle in the swing phase of gait. The aim of this study was to assess the short-term effects of rectus femoris neurotomy for the treatment of spastic stiff-knee gait in patients with hemiparesis. An Intervention study (before-after trial) with an observational design was carried out in a university hospital. Seven ambulatory patients with hemiparesis of spinal or cerebral origin and spastic stiff-knee gait, which had previously been improved by botulinum toxin injections, were proposed a selective neurotomy of the rectus femoris muscle. A functional evaluation (Functional Ambulation Classification and maximal walking distance), clinical evaluation (spasticity - Ashworth scale and Duncan-Ely test, muscle strength - Medical Research Council scale), and quantitative gait analysis (spatiotemporal parameters, stiff knee gait-related kinematic and kinetic parameters, and dynamic electromyography of rectus femoris) were performed as outcome measures, before and 3 months after rectus femoris neurotomy. Compared with preoperative values, there was a significant increase in maximal walking distance, gait speed, and stride length at 3 months. All kinematic parameters improved, and the average early swing phase knee extension moment decreased. The duration of the rectus femoris burst decreased post-op. This study is the first to show that rectus femoris neurotomy helps to normalise muscle activity during gait, and results in improvements in kinetic, kinematic, and functional parameters in patients with spastic stiff knee gait. Copyright © 2016 Elsevier B.V. All rights reserved.

  4. Electromagnetism on anisotropic fractal media

    NASA Astrophysics Data System (ADS)

    Ostoja-Starzewski, Martin

    2013-04-01

    Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.

  5. One month of contemporary dance modulates fractal posture in aging

    PubMed Central

    Coubard, Olivier A.; Ferrufino, Lena; Nonaka, Tetsushi; Zelada, Oscar; Bril, Blandine; Dietrich, Gilles

    2013-01-01

    Understanding the human aging of postural control and how physical or motor activity improves balance and gait is challenging for both clinicians and researchers. Previous studies have evidenced that physical and sporting activity focusing on cardiovascular and strength conditioning help older adults develop their balance and gait and/or decrease their frequency of falls. Motor activity based on motor-skill learning has also been put forward as an alternative to develop balance and/or prevent falls in aging. Specifically dance has been advocated as a promising program to boost motor control. In this study, we examined the effects of contemporary dance (CD) on postural control of older adults. Upright stance posturography was performed in 38 participants aged 54–89 years before and after the intervention period, during which one half of the randomly assigned participants was trained to CD and the other half was not trained at all (no dance, ND). CD training lasted 4 weeks, 3 times a week. We performed classical statistic scores of postural signal and dynamic analyses, namely signal diffusion analysis (SDA), recurrence quantification analysis (RQA), and detrended fluctuation analysis (DFA). CD modulated postural control in older trainees, as revealed in the eyes closed condition by a decrease in fractal dimension and an increase in DFA alpha component in the mediolateral plane. The ND group showed an increase in length and mean velocity of postural signal, and the eyes open a decrease in RQA maximal diagonal line in the anteroposterior plane and an increase in DFA alpha component in the mediolateral plane. No change was found in SDA in either group. We suggest that such a massed practice of CD reduced the quantity of exchange between the subject and the environment by increasing their postural confidence. Since CD has low-physical but high-motor impact, we conclude that it may be recommended as a useful program to rehabilitate posture in aging. PMID:24611047

  6. Changes in Dimensionality and Fractal Scaling Suggest Soft-Assembled Dynamics in Human EEG

    PubMed Central

    Wiltshire, Travis J.; Euler, Matthew J.; McKinney, Ty L.; Butner, Jonathan E.

    2017-01-01

    Humans are high-dimensional, complex systems consisting of many components that must coordinate in order to perform even the simplest of activities. Many behavioral studies, especially in the movement sciences, have advanced the notion of soft-assembly to describe how systems with many components coordinate to perform specific functions while also exhibiting the potential to re-structure and then perform other functions as task demands change. Consistent with this notion, within cognitive neuroscience it is increasingly accepted that the brain flexibly coordinates the networks needed to cope with changing task demands. However, evaluation of various indices of soft-assembly has so far been absent from neurophysiological research. To begin addressing this gap, we investigated task-related changes in two distinct indices of soft-assembly using the established phenomenon of EEG repetition suppression. In a repetition priming task, we assessed evidence for changes in the correlation dimension and fractal scaling exponents during stimulus-locked event-related potentials, as a function of stimulus onset and familiarity, and relative to spontaneous non-task-related activity. Consistent with predictions derived from soft-assembly, results indicated decreases in dimensionality and increases in fractal scaling exponents from resting to pre-stimulus states and following stimulus onset. However, contrary to predictions, familiarity tended to increase dimensionality estimates. Overall, the findings support the view from soft-assembly that neural dynamics should become increasingly ordered as external task demands increase, and support the broader application of soft-assembly logic in understanding human behavior and electrophysiology. PMID:28919862

  7. Diagnostics of multi-fractality of magnetized plasma inside coronal holes and quiet sun areas

    NASA Astrophysics Data System (ADS)

    Abramenko, Valentyna

    Turbulent and multi-fractal properties of magnetized plasma in solar Coronal Holes (CHs) and Quiet Sun (QS) photosphere were explored using high-resolution magnetograms measured with the New Solar Telescope (NST) at the Big Bear Solar Observatory (BBSO, USA), Hinode/SOT and SDO/HMI instruments. Distribution functions of size and magnetic flux measured for small-scale magnetic elements follow the log-normal law, which implies multi-fractal organization of the magnetic field and the absence of a unique power law for all scales. The magnetograms show multi-fractality in CHs on scales 400 - 10000 km, which becomes better pronounced as the spatial resolution of data improves. Photospheric granulation measured with NST exhibits multi-fractal properties on very small scales of 50 - 600 km. While multi-fractal nature of solar active regions is well known, newly established multi-fractality of weakest magnetic fields on the solar surface, i.e., in CHs and QS, leads us to a conclusion that the entire variety of solar magnetic fields is generated by a unique nonlinear dynamical process.

  8. A mechanized gait trainer for restoration of gait.

    PubMed

    Hesse, S; Uhlenbrock, D

    2000-01-01

    The newly developed gait trainer allows wheel-chair-bound subjects the repetitive practice of a gait-like movement without overstressing therapists. The device simulates the phases of gait, supports the subjects according to their abilities, and controls the center of mass (CoM) in the vertical and horizontal directions. The patterns of sagittal lower limb joint kinematics and of muscle activation for a normal subject were similar when using the mechanized trainer and when walking on a treadmill. A non-ambulatory hemiparetic subject required little help from one therapist on the gait trainer, while two therapists were required to support treadmill walking. Gait movements on the trainer were highly symmetrical, impact free, and less spastic. The vertical displacement of the CoM was bi-phasic instead of mono-phasic during each gait cycle on the new device. Two cases of non-ambulatory patients, who regained their walking ability after 4 weeks of daily training on the gait trainer, are reported.

  9. Fractal analysis of heart rate dynamics as a predictor of mortality in patients with depressed left ventricular function after acute myocardial infarction. TRACE Investigators. TRAndolapril Cardiac Evaluation

    NASA Technical Reports Server (NTRS)

    Makikallio, T. H.; Hoiber, S.; Kober, L.; Torp-Pedersen, C.; Peng, C. K.; Goldberger, A. L.; Huikuri, H. V.

    1999-01-01

    A number of new methods have been recently developed to quantify complex heart rate (HR) dynamics based on nonlinear and fractal analysis, but their value in risk stratification has not been evaluated. This study was designed to determine whether selected new dynamic analysis methods of HR variability predict mortality in patients with depressed left ventricular (LV) function after acute myocardial infarction (AMI). Traditional time- and frequency-domain HR variability indexes along with short-term fractal-like correlation properties of RR intervals (exponent alpha) and power-law scaling (exponent beta) were studied in 159 patients with depressed LV function (ejection fraction <35%) after an AMI. By the end of 4-year follow-up, 72 patients (45%) had died and 87 (55%) were still alive. Short-term scaling exponent alpha (1.07 +/- 0.26 vs 0.90 +/- 0.26, p <0.001) and power-law slope beta (-1.35 +/- 0.23 vs -1.44 +/- 0.25, p <0.05) differed between survivors and those who died, but none of the traditional HR variability measures differed between these groups. Among all analyzed variables, reduced scaling exponent alpha (<0.85) was the best univariable predictor of mortality (relative risk 3.17, 95% confidence interval 1.96 to 5.15, p <0.0001), with positive and negative predictive accuracies of 65% and 86%, respectively. In the multivariable Cox proportional hazards analysis, mortality was independently predicted by the reduced exponent alpha (p <0.001) after adjustment for several clinical variables and LV function. A short-term fractal-like scaling exponent was the most powerful HR variability index in predicting mortality in patients with depressed LV function. Reduction in fractal correlation properties implies more random short-term HR dynamics in patients with increased risk of death after AMI.

  10. The effect of gait training with shoe inserts on the improvement of pain and gait in sacroiliac joint patients.

    PubMed

    Cho, Byung-Yun; Yoon, Jung-Gyu

    2015-08-01

    [Purpose] The purpose of the current research was to identify how gait training with shoe inserts affects the pain and gait of sacroiliac joint dysfunction patients. [Subjects and Methods] Thirty subjects were randomly selected and assigned to be either the experimental group (gait training with shoe insert group) or control group. Each group consisted of 15 patients. Pain was measured by Visual Analogue Scale, and foot pressure in a standing position and during gait was measured with a Gateview AFA-50 system (Alpus, Seoul, Republic of Korea). A paired sample t-test was used to compare the pain and gait of the sacroiliac joint before and after the intervention. Correlation between pain and walking after gait training with shoe inserts was examined by Pearson test. The level of significance was set at α=0.05. [Results] It was found that application of the intervention to the experimental group resulted in a significant decrease in sacroiliac joint pain. It was also found that there was a significant correlation between Visual Analogue Scale score and dynamic asymmetric index (r= 0.796) and that there was a negative correlation between Visual Analogue Scale score and forefoot/rear foot peak pressure ratio (r=-0.728). [Conclusion] The results of our analysis lead us to conclude that the intervention with shoe inserts had a significant influence on the pain and gait of sacroiliac joint patients.

  11. The effects of plantar flexor static stretching and dynamic stretching using an aero-step on foot pressure during gait in healthy adults: a preliminary study.

    PubMed

    Shim, Je-Myung; Jung, Ju-Hyeon; Kim, Hwan-Hee

    2015-07-01

    [Purpose] The aim of this study was to examine whether plantar flexor static stretching and dynamic stretching using an Aero-Step results in changes in foot pressure during gait in healthy adults. [Subjects] Eighteen normal adults were randomly allocated to either a dynamic stretching using an Aero-Step group (DSUAS) group (n = 8) or a static stretching (SS) group (n = 10). [Methods] The DSUAS and SS participants took part in an exercise program for 15 minutes. Outcome measures were foot plantar pressure, which was measured during the subject's gait stance phase; the asymmetric ratio of foot pressure for both feet; and the visual analogue scale (VAS) measured during the interventions. [Results] There were significant differences in the asymmetric ratio of foot pressure for both feet and VAS between the two groups after intervention. However, there were no significant differences in foot plantar pressure during the gait stance phase within both groups. [Conclusion] DSUSAS is an effective stretching method, as pain during it is lower than that with SS, which can minimize the asymmetric ratio of foot pressure for both feet during gait due to asymmetric postural alignment.

  12. The fractal geometry of life.

    PubMed

    Losa, Gabriele A

    2009-01-01

    The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms (Weibel [1991]). Fractals fulfil a certain number of theoretical and methodological criteria including a high level of organization, shape irregularity, functional and morphological self-similarity, scale invariance, iterative pathways and a peculiar non-integer fractal dimension [FD]. Whereas mathematical objects are deterministic invariant or self-similar over an unlimited range of scales, biological components are statistically self-similar only within a fractal domain defined by upper and lower limits, called scaling window, in which the relationship between the scale of observation and the measured size or length of the object can be established (Losa and Nonnenmacher [1996]). Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also to show why the application of the fractal principle is valuable for measuring dimensional, geometrical and functional parameters of cells, tissues and organs occurring within the vegetal and animal realms. If the criteria for a strict description of natural fractals are met, then it follows that a Fractal Geometry of Life may be envisaged and all natural objects and biological systems exhibiting self-similar patterns and scaling properties may be considered as belonging to the new subdiscipline of "fractalomics".

  13. TauG-guidance of dynamic balance control during gait initiation in patients with chronic fatigue syndrome and fibromyalgia.

    PubMed

    Rasouli, Omid; Stensdotter, Ann-Katrin; Van der Meer, Audrey L H

    2016-08-01

    Impaired postural control has been reported in static conditions in chronic fatigue syndrome and fibromyalgia, but postural control in dynamic tasks have not yet been investigated. Thus, we investigated measurements from a force plate to evaluate dynamic balance control during gait initiation in patients with chronic fatigue syndrome and fibromyalgia compared to matched healthy controls. Thirty female participants (10 per group) performed five trials of gait initiation. Center of pressure (CoP) trajectory of the initial weight shift onto the supporting foot in the mediolateral direction (CoPX) was analyzed using General Tau Theory. We investigated the hypothesis that tau of the CoPX motion-gap (τCoPx) is coupled onto an intrinsic tauG-guide (τG) by keeping the relation τCoPx=KτG, where K is a scaling factor that determines the relevant kinematics of a movement. Mean K values were 0.57, 0.55, and 0.50 in fibromyalgia, chronic fatigue syndrome, and healthy controls, respectively. Both patient groups showed K values significantly higher than 0.50 (P<0.05), indicating that patients showed poorer dynamic balance control, CoPX colliding with the boundaries of the base of support (K>0.5). The findings revealed a lower level of dynamic postural control in both fibromyalgia and chronic fatigue syndrome compared to controls. Copyright © 2016 Elsevier Ltd. All rights reserved.

  14. Fractal correlation properties of R-R interval dynamics and mortality in patients with depressed left ventricular function after an acute myocardial infarction

    NASA Technical Reports Server (NTRS)

    Huikuri, H. V.; Makikallio, T. H.; Peng, C. K.; Goldberger, A. L.; Hintze, U.; Moller, M.

    2000-01-01

    BACKGROUND: Preliminary data suggest that the analysis of R-R interval variability by fractal analysis methods may provide clinically useful information on patients with heart failure. The purpose of this study was to compare the prognostic power of new fractal and traditional measures of R-R interval variability as predictors of death after acute myocardial infarction. METHODS AND RESULTS: Time and frequency domain heart rate (HR) variability measures, along with short- and long-term correlation (fractal) properties of R-R intervals (exponents alpha(1) and alpha(2)) and power-law scaling of the power spectra (exponent beta), were assessed from 24-hour Holter recordings in 446 survivors of acute myocardial infarction with a depressed left ventricular function (ejection fraction fractal measures of R-R interval variability were significant univariate predictors of all-cause mortality. Reduced short-term scaling exponent alpha(1) was the most powerful R-R interval variability measure as a predictor of all-cause mortality (alpha(1) <0.75, relative risk 3.0, 95% confidence interval 2.5 to 4.2, P<0.001). It remained an independent predictor of death (P<0.001) after adjustment for other postinfarction risk markers, such as age, ejection fraction, NYHA class, and medication. Reduced alpha(1) predicted both arrhythmic death (P<0.001) and nonarrhythmic cardiac death (P<0.001). CONCLUSIONS: Analysis of the fractal characteristics of short-term R-R interval dynamics yields more powerful prognostic information than the traditional measures of HR variability among patients with depressed left ventricular function after an acute myocardial infarction.

  15. Dual gait generative models for human motion estimation from a single camera.

    PubMed

    Zhang, Xin; Fan, Guoliang

    2010-08-01

    This paper presents a general gait representation framework for video-based human motion estimation. Specifically, we want to estimate the kinematics of an unknown gait from image sequences taken by a single camera. This approach involves two generative models, called the kinematic gait generative model (KGGM) and the visual gait generative model (VGGM), which represent the kinematics and appearances of a gait by a few latent variables, respectively. The concept of gait manifold is proposed to capture the gait variability among different individuals by which KGGM and VGGM can be integrated together, so that a new gait with unknown kinematics can be inferred from gait appearances via KGGM and VGGM. Moreover, a new particle-filtering algorithm is proposed for dynamic gait estimation, which is embedded with a segmental jump-diffusion Markov Chain Monte Carlo scheme to accommodate the gait variability in a long observed sequence. The proposed algorithm is trained from the Carnegie Mellon University (CMU) Mocap data and tested on the Brown University HumanEva data with promising results.

  16. Fractal growth of platinum electrodeposits revealed by in situ electron microscopy.

    PubMed

    Wang, Lifen; Wen, Jianguo; Sheng, Huaping; Miller, Dean J

    2016-10-06

    Fractals are commonly observed in nature and elucidating the mechanisms of fractal-related growth is a compelling issue for both fundamental science and technology. Here we report an in situ electron microscopy study of dynamic fractal growth of platinum during electrodeposition in a miniaturized electrochemical cell at varying growth conditions. Highly dendritic growth - either dense branching or ramified islands - are formed at the solid-electrolyte interface. We show how the diffusion length of ions in the electrolyte influences morphology selection and how instability induced by initial surface roughness, combined with local enhancement of electric field, gives rise to non-uniform branched deposition as a result of nucleation/growth at preferred locations. Comparing the growth behavior under these different conditions provides new insight into the fundamental mechanisms of platinum nucleation.

  17. Comparison of two fractal interpolation methods

    NASA Astrophysics Data System (ADS)

    Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo

    2017-03-01

    As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has

  18. Dynamic simulation of knee-joint loading during gait using force-feedback control and surrogate contact modelling.

    PubMed

    Walter, Jonathan P; Pandy, Marcus G

    2017-10-01

    The aim of this study was to perform multi-body, muscle-driven, forward-dynamics simulations of human gait using a 6-degree-of-freedom (6-DOF) model of the knee in tandem with a surrogate model of articular contact and force control. A forward-dynamics simulation incorporating position, velocity and contact force-feedback control (FFC) was used to track full-body motion capture data recorded for multiple trials of level walking and stair descent performed by two individuals with instrumented knee implants. Tibiofemoral contact force errors for FFC were compared against those obtained from a standard computed muscle control algorithm (CMC) with a 6-DOF knee contact model (CMC6); CMC with a 1-DOF translating hinge-knee model (CMC1); and static optimization with a 1-DOF translating hinge-knee model (SO). Tibiofemoral joint loads predicted by FFC and CMC6 were comparable for level walking, however FFC produced more accurate results for stair descent. SO yielded reasonable predictions of joint contact loading for level walking but significant differences between model and experiment were observed for stair descent. CMC1 produced the least accurate predictions of tibiofemoral contact loads for both tasks. Our findings suggest that reliable estimates of knee-joint loading may be obtained by incorporating position, velocity and force-feedback control with a multi-DOF model of joint contact in a forward-dynamics simulation of gait. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

  19. Gait Characteristic Analysis and Identification Based on the iPhone's Accelerometer and Gyrometer

    PubMed Central

    Sun, Bing; Wang, Yang; Banda, Jacob

    2014-01-01

    Gait identification is a valuable approach to identify humans at a distance. In this paper, gait characteristics are analyzed based on an iPhone's accelerometer and gyrometer, and a new approach is proposed for gait identification. Specifically, gait datasets are collected by the triaxial accelerometer and gyrometer embedded in an iPhone. Then, the datasets are processed to extract gait characteristic parameters which include gait frequency, symmetry coefficient, dynamic range and similarity coefficient of characteristic curves. Finally, a weighted voting scheme dependent upon the gait characteristic parameters is proposed for gait identification. Four experiments are implemented to validate the proposed scheme. The attitude and acceleration solutions are verified by simulation. Then the gait characteristics are analyzed by comparing two sets of actual data, and the performance of the weighted voting identification scheme is verified by 40 datasets of 10 subjects. PMID:25222034

  20. Fractality of sensations and the brain health: the theory linking neurodegenerative disorder with distortion of spatial and temporal scale-invariance and fractal complexity of the visible world

    PubMed Central

    Zueva, Marina V.

    2015-01-01

    The theory that ties normal functioning and pathology of the brain and visual system with the spatial–temporal structure of the visual and other sensory stimuli is described for the first time in the present study. The deficit of fractal complexity of environmental influences can lead to the distortion of fractal complexity in the visual pathways of the brain and abnormalities of development or aging. The use of fractal light stimuli and fractal stimuli of other modalities can help to restore the functions of the brain, particularly in the elderly and in patients with neurodegenerative disorders or amblyopia. Non-linear dynamics of these physiological processes have a strong base of evidence, which is seen in the impaired fractal regulation of rhythmic activity in aged and diseased brains. From birth to old age, we live in a non-linear world, in which objects and processes with the properties of fractality and non-linearity surround us. Against this background, the evolution of man took place and all periods of life unfolded. Works of art created by man may also have fractal properties. The positive influence of music on cognitive functions is well-known. Insufficiency of sensory experience is believed to play a crucial role in the pathogenesis of amblyopia and age-dependent diseases. The brain is very plastic in its early development, and the plasticity decreases throughout life. However, several studies showed the possibility to reactivate the adult’s neuroplasticity in a variety of ways. We propose that a non-linear structure of sensory information on many spatial and temporal scales is crucial to the brain health and fractal regulation of physiological rhythms. Theoretical substantiation of the author’s theory is presented. Possible applications and the future research that can experimentally confirm or refute the theoretical concept are considered. PMID:26236232

  1. Fractal model of polarization switching kinetics in ferroelectrics under nonequilibrium conditions of electron irradiation

    NASA Astrophysics Data System (ADS)

    Maslovskaya, A. G.; Barabash, T. K.

    2018-03-01

    The paper presents the results of the fractal and multifractal analysis of polarization switching current in ferroelectrics under electron irradiation, which allows statistical memory effects to be estimated at dynamics of domain structure. The mathematical model of formation of electron beam-induced polarization current in ferroelectrics was suggested taking into account the fractal nature of domain structure dynamics. In order to realize the model the computational scheme was constructed using the numerical solution approximation of fractional differential equation. Evidences of electron beam-induced polarization switching process in ferroelectrics were specified at a variation of control model parameters.

  2. Turbulence Enhancement by Fractal Square Grids: Effects of the Number of Fractal Scales

    NASA Astrophysics Data System (ADS)

    Omilion, Alexis; Ibrahim, Mounir; Zhang, Wei

    2017-11-01

    Fractal square grids offer a unique solution for passive flow control as they can produce wakes with a distinct turbulence intensity peak and a prolonged turbulence decay region at the expense of only minimal pressure drop. While previous studies have solidified this characteristic of fractal square grids, how the number of scales (or fractal iterations N) affect turbulence production and decay of the induced wake is still not well understood. The focus of this research is to determine the relationship between the fractal iteration N and the turbulence produced in the wake flow using well-controlled water-tunnel experiments. Particle Image Velocimetry (PIV) is used to measure the instantaneous velocity fields downstream of four different fractal grids with increasing number of scales (N = 1, 2, 3, and 4) and a conventional single-scale grid. By comparing the turbulent scales and statistics of the wake, we are able to determine how each iteration affects the peak turbulence intensity and the production/decay of turbulence from the grid. In light of the ability of these fractal grids to increase turbulence intensity with low pressure drop, this work can potentially benefit a wide variety of applications where energy efficient mixing or convective heat transfer is a key process.

  3. Nontrivial paths and periodic orbits of the T-fractal billiard table

    NASA Astrophysics Data System (ADS)

    Lapidus, Michel L.; Miller, Robyn L.; Niemeyer, Robert G.

    2016-07-01

    We introduce and prove numerous new results about the orbits of the T-fractal billiard. Specifically, in section 3, we give a variety of sufficient conditions for the existence of a sequence of compatible periodic orbits. In section 4, we examine the limiting behavior of particular sequences of compatible periodic orbits. Additionally, sufficient conditions for the existence of particular nontrivial paths are given in section 4. The proofs of two results of Lapidus and Niemeyer (2013 The current state of fractal billiards Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics (Contemporary Mathematics vol 601) ed D Carfi et al (Providence, RI: American Mathematical Society) pp 251-88 (e-print: arXiv:math.DS.1210.0282v2, 2013) appear here for the first time, as well. In section 5, an orbit with an irrational initial direction reaches an elusive point in a way that yields a nontrivial path of finite length, yet, by our convention, constitutes a singular orbit of the fractal billiard table. The existence of such an orbit seems to indicate that the classification of orbits may not be so straightforward. A discussion of our results and directions for future research is then given in section 6.

  4. Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

    NASA Astrophysics Data System (ADS)

    Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael

    2016-02-01

    One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.

  5. Order-fractal transitions in abstract paintings

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Calleja, E.M. de la, E-mail: elsama79@gmail.com; Cervantes, F.; Calleja, J. de la

    2016-08-15

    In this study, we determined the degree of order for 22 Jackson Pollock paintings using the Hausdorff–Besicovitch fractal dimension. Based on the maximum value of each multi-fractal spectrum, the artworks were classified according to the year in which they were painted. It has been reported that Pollock’s paintings are fractal and that this feature was more evident in his later works. However, our results show that the fractal dimension of these paintings ranges among values close to two. We characterize this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-ordermore » transition via the dark paint strokes in Pollock’s paintings as structured lines that follow a power law measured by the fractal dimension. We determined self-similarity in specific paintings, thereby demonstrating an important dependence on the scale of observations. We also characterized the fractal spectrum for the painting entitled Teri’s Find. We obtained similar spectra for Teri’s Find and Number 5, thereby suggesting that the fractal dimension cannot be rejected completely as a quantitative parameter for authenticating these artworks. -- Highlights: •We determined the degree of order in Jackson Pollock paintings using the Hausdorff–Besicovitch dimension. •We detected a fractal-order transition from Pollock’s paintings between 1947 and 1951. •We suggest that Jackson Pollock could have painted Teri’s Find.« less

  6. Optimality Principles for Model-Based Prediction of Human Gait

    PubMed Central

    Ackermann, Marko; van den Bogert, Antonie J.

    2010-01-01

    Although humans have a large repertoire of potential movements, gait patterns tend to be stereotypical and appear to be selected according to optimality principles such as minimal energy. When applied to dynamic musculoskeletal models such optimality principles might be used to predict how a patient’s gait adapts to mechanical interventions such as prosthetic devices or surgery. In this paper we study the effects of different performance criteria on predicted gait patterns using a 2D musculoskeletal model. The associated optimal control problem for a family of different cost functions was solved utilizing the direct collocation method. It was found that fatigue-like cost functions produced realistic gait, with stance phase knee flexion, as opposed to energy-related cost functions which avoided knee flexion during the stance phase. We conclude that fatigue minimization may be one of the primary optimality principles governing human gait. PMID:20074736

  7. The effect of gait training with shoe inserts on the improvement of pain and gait in sacroiliac joint patients

    PubMed Central

    Cho, Byung-Yun; Yoon, Jung-Gyu

    2015-01-01

    [Purpose] The purpose of the current research was to identify how gait training with shoe inserts affects the pain and gait of sacroiliac joint dysfunction patients. [Subjects and Methods] Thirty subjects were randomly selected and assigned to be either the experimental group (gait training with shoe insert group) or control group. Each group consisted of 15 patients. Pain was measured by Visual Analogue Scale, and foot pressure in a standing position and during gait was measured with a Gateview AFA-50 system (Alpus, Seoul, Republic of Korea). A paired sample t-test was used to compare the pain and gait of the sacroiliac joint before and after the intervention. Correlation between pain and walking after gait training with shoe inserts was examined by Pearson test. The level of significance was set at α=0.05. [Results] It was found that application of the intervention to the experimental group resulted in a significant decrease in sacroiliac joint pain. It was also found that there was a significant correlation between Visual Analogue Scale score and dynamic asymmetric index (r= 0.796) and that there was a negative correlation between Visual Analogue Scale score and forefoot/rear foot peak pressure ratio (r=-0.728). [Conclusion] The results of our analysis lead us to conclude that the intervention with shoe inserts had a significant influence on the pain and gait of sacroiliac joint patients. PMID:26357428

  8. Contour fractal analysis of grains

    NASA Astrophysics Data System (ADS)

    Guida, Giulia; Casini, Francesca; Viggiani, Giulia MB

    2017-06-01

    Fractal analysis has been shown to be useful in image processing to characterise the shape and the grey-scale complexity in different applications spanning from electronic to medical engineering (e.g. [1]). Fractal analysis consists of several methods to assign a dimension and other fractal characteristics to a dataset describing geometric objects. Limited studies have been conducted on the application of fractal analysis to the classification of the shape characteristics of soil grains. The main objective of the work described in this paper is to obtain, from the results of systematic fractal analysis of artificial simple shapes, the characterization of the particle morphology at different scales. The long term objective of the research is to link the microscopic features of granular media with the mechanical behaviour observed in the laboratory and in situ.

  9. Morphological computation of multi-gaited robot locomotion based on free vibration.

    PubMed

    Reis, Murat; Yu, Xiaoxiang; Maheshwari, Nandan; Iida, Fumiya

    2013-01-01

    In recent years, there has been increasing interest in the study of gait patterns in both animals and robots, because it allows us to systematically investigate the underlying mechanisms of energetics, dexterity, and autonomy of adaptive systems. In particular, for morphological computation research, the control of dynamic legged robots and their gait transitions provides additional insights into the guiding principles from a synthetic viewpoint for the emergence of sensible self-organizing behaviors in more-degrees-of-freedom systems. This article presents a novel approach to the study of gait patterns, which makes use of the intrinsic mechanical dynamics of robotic systems. Each of the robots consists of a U-shaped elastic beam and exploits free vibration to generate different locomotion patterns. We developed a simplified physics model of these robots, and through experiments in simulation and real-world robotic platforms, we show three distinctive mechanisms for generating different gait patterns in these robots.

  10. Kinematic and dynamic gait compensations in a rat model of lumbar radiculopathy and the effects of tumor necrosis factor-alpha antagonism

    PubMed Central

    2011-01-01

    Introduction Tumor necrosis factor-α (TNFα) has received significant attention as a mediator of lumbar radiculopathy, with interest in TNF antagonism to treat radiculopathy. Prior studies have demonstrated that TNF antagonists can attenuate heightened nociception resulting from lumbar radiculopathy in the preclinical model. Less is known about the potential impact of TNF antagonism on gait compensations, despite being of clinical relevance. In this study, we expand on previous descriptions of gait compensations resulting from lumbar radiculopathy in the rat and describe the ability of local TNF antagonism to prevent the development of gait compensations, altered weight bearing, and heightened nociception. Methods Eighteen male Sprague-Dawley rats were investigated for mechanical sensitivity, weight-bearing, and gait pre- and post-operatively. For surgery, tail nucleus pulposus (NP) tissue was collected and the right L5 dorsal root ganglion (DRG) was exposed (Day 0). In sham animals, NP tissue was discarded (n = 6); for experimental animals, autologous NP was placed on the DRG with or without 20 μg of soluble TNF receptor type II (sTNFRII, n = 6 per group). Spatiotemporal gait characteristics (open arena) and mechanical sensitivity (von Frey filaments) were assessed on post-operative Day 5; gait dynamics (force plate arena) and weight-bearing (incapacitance meter) were assessed on post-operative Day 6. Results High-speed gait characterization revealed animals with NP alone had a 5% decrease in stance time on their affected limbs on Day 5 (P ≤0.032). Ground reaction force analysis on Day 6 aligned with temporal changes observed on Day 5, with vertical impulse reduced in the affected limb of animals with NP alone (area under the vertical force-time curve, P <0.02). Concordant with gait, animals with NP alone also had some evidence of affected limb mechanical allodynia on Day 5 (P = 0.08) and reduced weight-bearing on the affected limb on Day 6 (P <0.05). Delivery

  11. Challenging Gait Conditions Predict 1-Year Decline in Gait Speed in Older Adults With Apparently Normal Gait

    PubMed Central

    Perera, Subashan; VanSwearingen, Jessie M.; Hile, Elizabeth S.; Wert, David M.; Studenski, Stephanie A.

    2011-01-01

    Background Mobility often is tested under a low challenge condition (ie, over a straight, uncluttered path), which often fails to identify early mobility difficulty. Tests of walking during challenging conditions may uncover mobility difficulty that is not identified with usual gait testing. Objective The purpose of this study was to determine whether gait during challenging conditions predicts decline in gait speed over 1 year in older people with apparently normal gait (ie, gait speed of ≥1.0 m/s). Design This was a prospective cohort study. Methods Seventy-one older adults (mean age=75.9 years) with a usual gait speed of ≥1.0 m/s participated. Gait was tested at baseline under 4 challenging conditions: (1) narrow walk (15 cm wide), (2) stepping over obstacles (15.24 cm [6 in] and 30.48 cm [12 in]), (3) simple walking while talking (WWT), and (4) complex WWT. Usual gait speed was recorded over a 4-m course at baseline and 1 year later. A 1-year change in gait speed was calculated, and participants were classified as declined (decreased ≥0.10 m/s, n=18), stable (changed <0.10 m/s, n=43), or improved (increased ≥0.10 m/s, n=10). Analysis of variance was used to compare challenging condition cost (usual − challenging condition gait speed difference) among the 3 groups. Results Participants who declined in the ensuing year had a greater narrow walk and obstacle walk cost than those who were stable or who improved in gait speed (narrow walk cost=0.43 versus 0.33 versus 0.22 m/s and obstacle walk cost=0.35 versus 0.26 versus 0.13 m/s). Simple and complex WWT cost did not differ among the groups. Limitations The participants who declined in gait speed over time walked the fastest, and those who improved walked the slowest at baseline; thus, the potential contribution of regression to the mean to the findings should not be overlooked. Conclusions In older adults with apparently normal gait, the assessment of gait during challenging conditions appears to uncover

  12. Reengineering through natural structures: the fractal factory

    NASA Astrophysics Data System (ADS)

    Sihn, Wilfried

    1995-08-01

    Many branches of European industry have had to recognize that their lead in the world market has been caught up with, particularly through Asian competition. In many cases a deficit of up to 30% in costs and productivity already exists. The reasons are rigid, Tayloristic company structures. The companies are not in a position to react flexibly to constantly changing environmental conditions. This article illustrates the methods of the `fractal company' which are necessary to solve the structure crisis. The fractal company distinguishes itself through its dynamics and its vitality, as well as its independent reaction to the changing circumstances. The developed methods, procedures, and framework conditions such as company structuring, human networking, hierarchy formation, and models for renumeration and working time are explained. They are based on practical examples from IPA's work with the automobile industry, their suppliers, and the engineering industry.

  13. Breathing of voltage dependent anion channel as revealed by the fractal property of its gating

    NASA Astrophysics Data System (ADS)

    Manna, Smarajit; Banerjee, Jyotirmoy; Ghosh, Subhendu

    2007-12-01

    The gating of voltage dependent anion channel (VDAC) depends on the movement of voltage sensors in the transmembrane region, but the actual mechanism is still not well understood. With a view to understand the phenomenon we have analyzed the current recordings of VDAC in lipid bilayer membrane (BLM) and found that the data show self-similarity and fractal characteristics. We look for the microscopic and molecular basis of fractal behavior of gating of VDAC. A model describing the oscillatory dynamics of voltage sensors of VDAC in the transmembrane region under applied potential has been proposed which gives rise to the aforesaid fractal behavior.

  14. Fractal reaction kinetics.

    PubMed

    Kopelman, R

    1988-09-23

    Classical reaction kinetics has been found to be unsatisfactory when the reactants are spatially constrained on the microscopic level by either walls, phase boundaries, or force fields. Recently discovered theories of heterogeneous reaction kinetics have dramatic consequences, such as fractal orders for elementary reactions, self-ordering and self-unmixing of reactants, and rate coefficients with temporal "memories." The new theories were needed to explain the results of experiments and supercomputer simulations of reactions that were confined to low dimensions or fractal dimensions or both. Among the practical examples of "fractal-like kinetics" are chemical reactions in pores of membranes, excitation trapping in molecular aggregates, exciton fusion in composite materials, and charge recombination in colloids and clouds.

  15. Low Power Shoe Integrated Intelligent Wireless Gait Measurement System

    NASA Astrophysics Data System (ADS)

    Wahab, Y.; Mazalan, M.; Bakar, N. A.; Anuar, A. F.; Zainol, M. Z.; Hamzah, F.

    2014-04-01

    Gait analysis measurement is a method to assess and identify gait events and the measurements of dynamic, motion and pressure parameters involving the lowest part of the body. This significant analysis is widely used in sports, rehabilitation as well as other health diagnostic towards improving the quality of life. This paper presents a new system empowered by Inertia Measurement Unit (IMU), ultrasonic sensors, piezoceramic sensors array, XBee wireless modules and Arduino processing unit. This research focuses on the design and development of a low power ultra-portable shoe integrated wireless intelligent gait measurement using MEMS and recent microelectronic devices for foot clearance, orientation, error correction, gait events and pressure measurement system. It is developed to be cheap, low power, wireless, real time and suitable for real life in-door and out-door environment.

  16. Fractality of pulsatile flow in speckle images

    NASA Astrophysics Data System (ADS)

    Nemati, M.; Kenjeres, S.; Urbach, H. P.; Bhattacharya, N.

    2016-05-01

    The scattering of coherent light from a system with underlying flow can be used to yield essential information about dynamics of the process. In the case of pulsatile flow, there is a rapid change in the properties of the speckle images. This can be studied using the standard laser speckle contrast and also the fractality of images. In this paper, we report the results of experiments performed to study pulsatile flow with speckle images, under different experimental configurations to verify the robustness of the techniques for applications. In order to study flow under various levels of complexity, the measurements were done for three in-vitro phantoms and two in-vivo situations. The pumping mechanisms were varied ranging from mechanical pumps to the human heart for the in vivo case. The speckle images were analyzed using the techniques of fractal dimension and speckle contrast analysis. The results of these techniques for the various experimental scenarios were compared. The fractal dimension is a more sensitive measure to capture the complexity of the signal though it was observed that it is also extremely sensitive to the properties of the scattering medium and cannot recover the signal for thicker diffusers in comparison to speckle contrast.

  17. Improved visibility graph fractality with application for the diagnosis of Autism Spectrum Disorder

    NASA Astrophysics Data System (ADS)

    Ahmadlou, Mehran; Adeli, Hojjat; Adeli, Amir

    2012-10-01

    Recently, the visibility graph (VG) algorithm was proposed for mapping a time series to a graph to study complexity and fractality of the time series through investigation of the complexity of its graph. The visibility graph algorithm converts a fractal time series to a scale-free graph. VG has been used for the investigation of fractality in the dynamic behavior of both artificial and natural complex systems. However, robustness and performance of the power of scale-freeness of VG (PSVG) as an effective method for measuring fractality has not been investigated. Since noise is unavoidable in real life time series, the robustness of a fractality measure is of paramount importance. To improve the accuracy and robustness of PSVG to noise for measurement of fractality of time series in biological time-series, an improved PSVG is presented in this paper. The proposed method is evaluated using two examples: a synthetic benchmark time series and a complicated real life Electroencephalograms (EEG)-based diagnostic problem, that is distinguishing autistic children from non-autistic children. It is shown that the proposed improved PSVG is less sensitive to noise and therefore more robust compared with PSVG. Further, it is shown that using improved PSVG in the wavelet-chaos neural network model of Adeli and c-workers in place of the Katz fractality dimension results in a more accurate diagnosis of autism, a complicated neurological and psychiatric disorder.

  18. Harmony as a convergence attractor that minimizes the energy expenditure and variability in physiological gait and the loss of harmony in cerebellar ataxia.

    PubMed

    Serrao, Mariano; Chini, Giorgia; Iosa, Marco; Casali, Carlo; Morone, Giovanni; Conte, Carmela; Bini, Fabiano; Marinozzi, Franco; Coppola, Gianluca; Pierelli, Francesco; Draicchio, Francesco; Ranavolo, Alberto

    2017-10-01

    The harmony of the human gait was recently found to be related to the golden ratio value (ϕ). The ratio between the duration of the stance and that of the swing phases of a gait cycle was in fact found to be close to ϕ, which implies that, because of the fractal property of autosimilarity of that number, the gait ratios stride/stance, stance/swing, swing/double support, were not significantly different from one another. We studied a group of patients with cerebellar ataxia to investigate how the differences between their gait ratios and the golden ratio are related to efficiency and stability of their gait, assessed by energy expenditure and stride-to-stride variability, respectively. The gait of 28 patients who were affected by degenerative cerebellar ataxia and of 28 healthy controls was studied using a stereophotogrammetric system. The above mentioned gait ratios, the energy expenditure estimated using the pelvis reconstructed method and the gait variability in terms of the stride length were computed, and their relationships were analyzed. Matching procedures have also been used to avoid multicollinearity biases. The gait ratio values of the patients were farther from the controls (and hence from ϕ), even in speed matched conditions (P=0.011, Cohen's D=0.76), but not when the variability and energy expenditure were matched between the two groups (Cohen's D=0.49). In patients with cerebellar ataxia, the farther the stance-swing ratio was from ϕ, the larger the total mechanical work (R 2 adj =0.64). Further, a significant positive correlation was observed between the difference of the gait ratio from the golden ratio and the severity of the disease (R=0.421, P=0.026). Harmony of gait appears to be a benchmark of physiological gait leading to physiological energy recovery and gait reliability. Neurorehabilitation of patients with ataxia might benefit from the restoration of harmony of their locomotor patterns. Copyright © 2017. Published by Elsevier Ltd.

  19. Recurrence Quantification of Fractal Structures

    PubMed Central

    Webber, Charles L.

    2012-01-01

    By definition, fractal structures possess recurrent patterns. At different levels repeating patterns can be visualized at higher magnifications. The purpose of this chapter is threefold. First, general characteristics of dynamical systems are addressed from a theoretical mathematical perspective. Second, qualitative and quantitative recurrence analyses are reviewed in brief, but the reader is directed to other sources for explicit details. Third, example mathematical systems that generate strange attractors are explicitly defined, giving the reader the ability to reproduce the rich dynamics of continuous chaotic flows or discrete chaotic iterations. The challenge is then posited for the reader to study for themselves the recurrent structuring of these different dynamics. With a firm appreciation of the power of recurrence analysis, the reader will be prepared to turn their sights on real-world systems (physiological, psychological, mechanical, etc.). PMID:23060808

  20. Chaos, Fractals, and Polynomials.

    ERIC Educational Resources Information Center

    Tylee, J. Louis; Tylee, Thomas B.

    1996-01-01

    Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

  1. Threshold of coexistence and critical behavior of a predator-prey stochastic model in a fractal landscape

    NASA Astrophysics Data System (ADS)

    Argolo, C.; Barros, P.; Tomé, T.; Arashiro, E.; Gleria, Iram; Lyra, M. L.

    2016-08-01

    We investigate a stochastic lattice model describing a predator-prey system in a fractal scale-free landscape, mimicked by the fractal Sierpinski carpet. We determine the threshold of species coexistence, that is, the critical phase boundary related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. We show that the predators must live longer in order to persist in a fractal habitat. We further performed a finite-size scaling analysis in the vicinity of the absorbing-state phase transition to compute a set of stationary and dynamical critical exponents. Our results indicate that the transition belongs to the directed percolation universality class exhibited by the usual contact process model on the same fractal landscape.

  2. How doing a dynamical analysis of gait movement may provide information about Autism

    NASA Astrophysics Data System (ADS)

    Wu, D.; Torres, E.; Nguyen, J.; Mistry, S.; Whyatt, C.; Kalampratsidou, V.; Kolevzon, A.; Jose, J.

    Individuals with Autism Spectrum Disorder (ASD) are known to have deficits in language and social skills. They also have deficits on how they move. Why individuals get ASD? It is not generally known. There is, however, one particular group of children with a SHANK3 gene deficiency (Phelan-McDermid Syndrome (PMDS)) that present symptoms similar to ASD. We have been searching for universal mechanism in ASD going beyond the usual heterogeneous ASD symptoms. We studied motions in gaits for both PMDS patients and idiopathic ASD. We have examined their motions continuously at milliseconds time scale, away from naked eye detection. Gait is a complex process, requiring a complex integration and coordination of different joints' motions. Significant information about the development and/or deficits in the sensory system is hidden in our gaits. We discovered that the speed smoothness in feet motion during gaits is a critical feature that provides a significant distinction between subjects with ASD and typical controls. The differences in appearance of the speed fluctuations suggested a different coordination mechanism in subjects with disorders. Our work provides a very important feature in gait motion that has significant physiological information.

  3. Stimulation of the mesencephalic locomotor region for gait recovery after stroke.

    PubMed

    Fluri, Felix; Malzahn, Uwe; Homola, György A; Schuhmann, Michael K; Kleinschnitz, Christoph; Volkmann, Jens

    2017-11-01

    One-third of all stroke survivors are unable to walk, even after intensive physiotherapy. Thus, other concepts to restore walking are needed. Because electrical stimulation of the mesencephalic locomotor region (MLR) is known to elicit gait movements, this area might be a promising target for restorative neurostimulation in stroke patients with gait disability. The present study aims to delineate the effect of high-frequency stimulation of the MLR (MLR-HFS) on gait impairment in a rodent stroke model. Male Wistar rats underwent photothrombotic stroke of the right sensorimotor cortex and chronic implantation of a stimulating electrode into the right MLR. Gait was assessed using clinical scoring of the beam-walking test and video-kinematic analysis (CatWalk) at baseline and on days 3 and 4 after experimental stroke with and without MLR-HFS. Kinematic analysis revealed significant changes in several dynamic and static gait parameters resulting in overall reduced gait velocity. All rats exhibited major coordination deficits during the beam-walking challenge and were unable to cross the beam. Simultaneous to the onset of MLR-HFS, a significantly higher walking speed and improvements in several dynamic gait parameters were detected by the CatWalk system. Rats regained the ability to cross the beam unassisted, showing a reduced number of paw slips and misses. MLR-HFS can improve disordered locomotor function in a rodent stroke model. It may act by shielding brainstem and spinal locomotor centers from abnormal cortical input after stroke, thus allowing for compensatory and independent action of these circuits. Ann Neurol 2017;82:828-840. © 2017 American Neurological Association.

  4. Fractal-Based Image Analysis In Radiological Applications

    NASA Astrophysics Data System (ADS)

    Dellepiane, S.; Serpico, S. B.; Vernazza, G.; Viviani, R.

    1987-10-01

    We present some preliminary results of a study aimed to assess the actual effectiveness of fractal theory and to define its limitations in the area of medical image analysis for texture description, in particular, in radiological applications. A general analysis to select appropriate parameters (mask size, tolerance on fractal dimension estimation, etc.) has been performed on synthetically generated images of known fractal dimensions. Moreover, we analyzed some radiological images of human organs in which pathological areas can be observed. Input images were subdivided into blocks of 6x6 pixels; then, for each block, the fractal dimension was computed in order to create fractal images whose intensity was related to the D value, i.e., texture behaviour. Results revealed that the fractal images could point out the differences between normal and pathological tissues. By applying histogram-splitting segmentation to the fractal images, pathological areas were isolated. Two different techniques (i.e., the method developed by Pentland and the "blanket" method) were employed to obtain fractal dimension values, and the results were compared; in both cases, the appropriateness of the fractal description of the original images was verified.

  5. Langevin Equation on Fractal Curves

    NASA Astrophysics Data System (ADS)

    Satin, Seema; Gangal, A. D.

    2016-07-01

    We analyze random motion of a particle on a fractal curve, using Langevin approach. This involves defining a new velocity in terms of mass of the fractal curve, as defined in recent work. The geometry of the fractal curve, plays an important role in this analysis. A Langevin equation with a particular model of noise is proposed and solved using techniques of the Fα-Calculus.

  6. Frequency-velocity mismatch: a fundamental abnormality in parkinsonian gait.

    PubMed

    Cho, Catherine; Kunin, Mikhail; Kudo, Koji; Osaki, Yasuhiro; Olanow, C Warren; Cohen, Bernard; Raphan, Theodore

    2010-03-01

    Gait dysfunction and falling are major sources of disability for patients with advanced Parkinson's disease (PD). It is presently thought that the fundamental defect is an inability to generate normal stride length. Our data suggest, however, that the basic problem in PD gait is an impaired ability to match step frequency to walking velocity. In this study, foot movements of PD and normal subjects were monitored with an OPTOTRAK motion-detection system while they walked on a treadmill at different velocities. PD subjects were also paced with auditory stimuli at different frequencies. PD gait was characterized by step frequencies that were faster and stride lengths that were shorter than those of normal controls. At low walking velocities, PD stepping had a reduced or absent terminal toe lift, which truncated swing phases, producing shortened steps. Auditory pacing was not able to normalize step frequency at these lower velocities. Peak forward toe velocities increased with walking velocity and PD subjects could initiate appropriate foot dynamics during initial phases of the swing. They could not control the foot appropriately in terminal phases, however. Increased treadmill velocity, which matched the natural PD step frequency, generated a second toe lift, normalizing step size. Levodopa increased the bandwidth of step frequencies, but was not as effective as increases in walking velocity in normalizing gait. We postulate that the inability to control step frequency and adjust swing phase dynamics to slower walking velocities are major causes for the gait impairment in PD.

  7. Frequency-Velocity Mismatch: A Fundamental Abnormality in Parkinsonian Gait

    PubMed Central

    Kunin, Mikhail; Kudo, Koji; Osaki, Yasuhiro; Olanow, C. Warren; Cohen, Bernard; Raphan, Theodore

    2010-01-01

    Gait dysfunction and falling are major sources of disability for patients with advanced Parkinson's disease (PD). It is presently thought that the fundamental defect is an inability to generate normal stride length. Our data suggest, however, that the basic problem in PD gait is an impaired ability to match step frequency to walking velocity. In this study, foot movements of PD and normal subjects were monitored with an OPTOTRAK motion-detection system while they walked on a treadmill at different velocities. PD subjects were also paced with auditory stimuli at different frequencies. PD gait was characterized by step frequencies that were faster and stride lengths that were shorter than those of normal controls. At low walking velocities, PD stepping had a reduced or absent terminal toe lift, which truncated swing phases, producing shortened steps. Auditory pacing was not able to normalize step frequency at these lower velocities. Peak forward toe velocities increased with walking velocity and PD subjects could initiate appropriate foot dynamics during initial phases of the swing. They could not control the foot appropriately in terminal phases, however. Increased treadmill velocity, which matched the natural PD step frequency, generated a second toe lift, normalizing step size. Levodopa increased the bandwidth of step frequencies, but was not as effective as increases in walking velocity in normalizing gait. We postulate that the inability to control step frequency and adjust swing phase dynamics to slower walking velocities are major causes for the gait impairment in PD. PMID:20042701

  8. The effect of modified trampoline training on balance, gait, and falls efficacy of stroke patients

    PubMed Central

    Hahn, Joohee; Shin, Seonhae; Lee, Wanhee

    2015-01-01

    [Purpose] This research was conducted to investigate the effects of modified trampoline training on the balance, gait, and falls efficacy of stroke patients. [Subjects] Twenty-four stroke patients participated in this study. The subjects were randomly allocated to one of two groups: the trampoline group (n=12) or the control group (n=12). [Methods] Both groups participated in conventional physical therapy for thirty minutes per day, three times a week for six weeks. The trampoline group also took part in trampoline training for thirty minutes per day, three times a week for six weeks. We evaluated balance (Berg balance scale, timed up and go test), gait (dynamic gait index), and falls efficacy (falls efficacy scale-K) to confirm the effects of the intervention. [Results] Both the trampoline and the control group showed significant improvements in balance, gait, and falls efficacy compared to before the intervention, and the improvements were significantly greater in the trampoline group than in the control group. [Conclusion] Modified trampoline training resulted in significantly improved balance, dynamic gait, and falls efficacy of stroke patients compared to the control group. These results suggest that modified trampoline training is feasible and effective at improving balance, dynamic gait, and falls efficacy after stroke. PMID:26696696

  9. The effect of modified trampoline training on balance, gait, and falls efficacy of stroke patients.

    PubMed

    Hahn, Joohee; Shin, Seonhae; Lee, Wanhee

    2015-11-01

    [Purpose] This research was conducted to investigate the effects of modified trampoline training on the balance, gait, and falls efficacy of stroke patients. [Subjects] Twenty-four stroke patients participated in this study. The subjects were randomly allocated to one of two groups: the trampoline group (n=12) or the control group (n=12). [Methods] Both groups participated in conventional physical therapy for thirty minutes per day, three times a week for six weeks. The trampoline group also took part in trampoline training for thirty minutes per day, three times a week for six weeks. We evaluated balance (Berg balance scale, timed up and go test), gait (dynamic gait index), and falls efficacy (falls efficacy scale-K) to confirm the effects of the intervention. [Results] Both the trampoline and the control group showed significant improvements in balance, gait, and falls efficacy compared to before the intervention, and the improvements were significantly greater in the trampoline group than in the control group. [Conclusion] Modified trampoline training resulted in significantly improved balance, dynamic gait, and falls efficacy of stroke patients compared to the control group. These results suggest that modified trampoline training is feasible and effective at improving balance, dynamic gait, and falls efficacy after stroke.

  10. The Twinkling Fractal Theory of the Glass Transition: Applications to Soft Matter

    NASA Astrophysics Data System (ADS)

    Wool, Richard

    2012-02-01

    The Twinkling Fractal Theory (TFT) of the glass transition has recently been demonstrated experimentally [J.F. Stanzione et al., J. Non Cryst. Sol., (2011, 357,311]. The hard to-soft matter transition is characterized by the presence of solid fractal clusters with liquid-like pools that are dynamically interchanging via their anharmonic intermolecular potentials with Boltzmann energy populations with a characteristic temperature dependent vibrational density of states g(φ) ˜ φ^df . The twinkling fractal frequencies φ cover a range of 10^12 Hz to 10-10Hz and the fractal solid clusters of size R have a lifetime τ ˜ R^Df/df, where the fractal dimension Df 2.4 and the fracton dimension df = 4/3. Here we explore its application to a number of soft matter issues. These include (a) Confinement effects on Tg reduction in thin films of thickness h, where by virtue of large cluster exclusion, δTg ˜ 1/h^Df/df; (b) Tg gradients near bulk surfaces, where the smaller clusters on the surface have a faster relaxation time; (c) Effect of twinkling surfaces on cell growth, where at T Tg + 20 C, there exists a twinkling fractal range that leads to bell-shaped enhancement of cell growth and chemical up-regulation via the twinkling surfaces ``communicating `` with the cells through their vibrations; and (d) adhesion above and below Tg where topological fluctuations associated with g(φ) promotes the development of nano-nails at the interface.

  11. Gait performance of children and adolescents with sensorineural hearing loss.

    PubMed

    Melo, Renato de Souza

    2017-09-01

    Several studies have demonstrated that children with sensorineural hearing loss (SNHL) may exhibit balance disorders, which can compromise the gait performance of this population. Compare the gait performance of normal hearing (NH) children and those with SNHL, considering the sex and age range of the sample, and analyze gait performance according to degrees of hearing loss and etiological factors in the latter group. This is a cross-sectional study that assessed 96 students, 48 NH and 48 with SNHL, aged between 7 and 18 years. The Brazilian version of the Dynamic Gait Index (DGI) was used to analyze gait and the Mann-Whitney test for statistical analysis. The group with SNHL obtained lower average gait performance compared to NH subjects (p=0.000). This was also observed when the children were grouped by sex female and male (p=0.000). The same difference occurred when the children were stratified by age group: 7-18 years (p=0.000). The group with severe and profound hearing loss exhibited worse gait performance than those with mild and moderate loss (p=0.048) and children with prematurity as an etiological factor demonstrated the worst gait performance. The children with SNHL showed worse gait performance compared to NH of the same sex and age group. Those with severe and profound hearing loss and prematurity as an etiological factor demonstrated the worst gait performances. Copyright © 2017 Elsevier B.V. All rights reserved.

  12. Computational evaluation of load carriage effects on gait balance stability.

    PubMed

    Mummolo, Carlotta; Park, Sukyung; Mangialardi, Luigi; Kim, Joo H

    2016-01-01

    Evaluating the effects of load carriage on gait balance stability is important in various applications. However, their quantification has not been rigorously addressed in the current literature, partially due to the lack of relevant computational indices. The novel Dynamic Gait Measure (DGM) characterizes gait balance stability by quantifying the relative effects of inertia in terms of zero-moment point, ground projection of center of mass, and time-varying foot support region. In this study, the DGM is formulated in terms of the gait parameters that explicitly reflect the gait strategy of a given walking pattern and is used for computational evaluation of the distinct balance stability of loaded walking. The observed gait adaptations caused by load carriage (decreased single support duration, inertia effects, and step length) result in decreased DGM values (p < 0.0001), which indicate that loaded walking motions are more statically stable compared with the unloaded normal walking. Comparison of the DGM with other common gait stability indices (the maximum Floquet multiplier and the margin of stability) validates the unique characterization capability of the DGM, which is consistently informative of the presence of the added load.

  13. Scrunching: a novel escape gait in planarians

    NASA Astrophysics Data System (ADS)

    Cochet-Escartin, Olivier; Mickolajczyk, Keith J.; Collins, Eva-Maria S.

    2015-10-01

    The ability to escape a predator or other life-threatening situations is central to animal survival. Different species have evolved unique strategies under anatomical and environmental constraints. In this study, we describe a novel musculature-driven escape gait in planarians, ‘scrunching’, which is quantitatively different from other planarian gaits, such as gliding and peristalsis. We show that scrunching is a conserved gait among different flatworm species, underlying its importance as an escape mechanism. We further demonstrate that it can be induced by a variety of physical stimuli, including amputation, high temperature, electric shock and low pH. We discuss the functional basis for scrunching as the preferential gait when gliding is impaired due to a disruption of mucus production. Finally, we show that the key mechanical features of scrunching are adequately captured by a simple biomechanical model that is solely based on experimental data from traction force microscopy and tissue rheology without fit parameters. Together, our results form a complete description of this novel form of planarian locomotion. Because scrunching has distinct dynamics, this gait can serve as a robust behavioral readout for studies of motor neuron and muscular functions in planarians and in particular the restoration of these functions during regeneration.

  14. Simultaneous estimation of deterministic and fractal stochastic components in non-stationary time series

    NASA Astrophysics Data System (ADS)

    García, Constantino A.; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G.

    2018-07-01

    In the past few decades, it has been recognized that 1 / f fluctuations are ubiquitous in nature. The most widely used mathematical models to capture the long-term memory properties of 1 / f fluctuations have been stochastic fractal models. However, physical systems do not usually consist of just stochastic fractal dynamics, but they often also show some degree of deterministic behavior. The present paper proposes a model based on fractal stochastic and deterministic components that can provide a valuable basis for the study of complex systems with long-term correlations. The fractal stochastic component is assumed to be a fractional Brownian motion process and the deterministic component is assumed to be a band-limited signal. We also provide a method that, under the assumptions of this model, is able to characterize the fractal stochastic component and to provide an estimate of the deterministic components present in a given time series. The method is based on a Bayesian wavelet shrinkage procedure that exploits the self-similar properties of the fractal processes in the wavelet domain. This method has been validated over simulated signals and over real signals with economical and biological origin. Real examples illustrate how our model may be useful for exploring the deterministic-stochastic duality of complex systems, and uncovering interesting patterns present in time series.

  15. Relationships among measures of balance, gait, and community integration in people with brain injury.

    PubMed

    Perry, Susan B; Woollard, Jason; Little, Susan; Shroyer, Kathleen

    2014-01-01

    To examine the relationship among measures of gait, balance, and community integration in adults with brain injury. Two rehabilitation hospitals. Thirty-four community-dwelling individuals with brain injury, aged 18 to 61 years (mean = 32 years), who were able to walk at least 12 m independently or with supervision. Mean time post-brain injury was 52 ± 44 months. Cross-sectional study. Community Balance and Mobility Scale, Dynamic Gait Index, Ten-Meter Walk Test for gait speed, and the Community Integration Questionnaire (CIQ). Mean balance and gait scores were as follows: 54 ± 26 of 96 on the Community Balance and Mobility Scale; 19 ± 5 of 24 on the Dynamic Gait Index; and gait speed of 1.36 ± 0.88 m/s. Mean score on the CIQ was 16 ± 5 of 29. Correlations between the balance/gait measures and the total CIQ score ranged from 0.21 to 0.30 and were not significant. All 3 balance/gait measures correlated significantly with the CIQ Productivity subscale (range = 0.38-0.52). The ability of people with brain injury to engage in work/school/volunteer activity may be reduced by impairments in balance and mobility. Future research should explore this relationship and determine whether interventions that improve balance and mobility result in improved community productivity.

  16. Some problems in fractal differential equations

    NASA Astrophysics Data System (ADS)

    Su, Weiyi

    2016-06-01

    Based upon the fractal calculus on local fields, or p-type calculus, or Gibbs-Butzer calculus ([1],[2]), we suggest a constructive idea for "fractal differential equations", beginning from some special examples to a general theory. However, this is just an original idea, it needs lots of later work to support. In [3], we show example "two dimension wave equations with fractal boundaries", and in this note, other examples, as well as an idea to construct fractal differential equations are shown.

  17. Quantitative characterization of the regressive ecological succession by fractal analysis of plant spatial patterns

    USGS Publications Warehouse

    Alados, C.L.; Pueyo, Y.; Giner, M.L.; Navarro, T.; Escos, J.; Barroso, F.; Cabezudo, B.; Emlen, J.M.

    2003-01-01

    We studied the effect of grazing on the degree of regression of successional vegetation dynamic in a semi-arid Mediterranean matorral. We quantified the spatial distribution patterns of the vegetation by fractal analyses, using the fractal information dimension and spatial autocorrelation measured by detrended fluctuation analyses (DFA). It is the first time that fractal analysis of plant spatial patterns has been used to characterize the regressive ecological succession. Plant spatial patterns were compared over a long-term grazing gradient (low, medium and heavy grazing pressure) and on ungrazed sites for two different plant communities: A middle dense matorral of Chamaerops and Periploca at Sabinar-Romeral and a middle dense matorral of Chamaerops, Rhamnus and Ulex at Requena-Montano. The two communities differed also in the microclimatic characteristics (sea oriented at the Sabinar-Romeral site and inland oriented at the Requena-Montano site). The information fractal dimension increased as we moved from a middle dense matorral to discontinuous and scattered matorral and, finally to the late regressive succession, at Stipa steppe stage. At this stage a drastic change in the fractal dimension revealed a change in the vegetation structure, accurately indicating end successional vegetation stages. Long-term correlation analysis (DFA) revealed that an increase in grazing pressure leads to unpredictability (randomness) in species distributions, a reduction in diversity, and an increase in cover of the regressive successional species, e.g. Stipa tenacissima L. These comparisons provide a quantitative characterization of the successional dynamic of plant spatial patterns in response to grazing perturbation gradient. ?? 2002 Elsevier Science B.V. All rights reserved.

  18. Kinematic measures for assessing gait stability in elderly individuals: a systematic review

    PubMed Central

    Hamacher, D.; Singh, N.B.; Van Dieën, J.H.; Heller, M.O.; Taylor, W.R.

    2011-01-01

    Falls not only present a considerable health threat, but the resulting treatment and loss of working days also place a heavy economic burden on society. Gait instability is a major fall risk factor, particularly in geriatric patients, and walking is one of the most frequent dynamic activities of daily living. To allow preventive strategies to become effective, it is therefore imperative to identify individuals with an unstable gait. Assessment of dynamic stability and gait variability via biomechanical measures of foot kinematics provides a viable option for quantitative evaluation of gait stability, but the ability of these methods to predict falls has generally not been assessed. Although various methods for assessing gait stability exist, their sensitivity and applicability in a clinical setting, as well as their cost-effectiveness, need verification. The objective of this systematic review was therefore to evaluate the sensitivity of biomechanical measures that quantify gait stability among elderly individuals and to evaluate the cost of measurement instrumentation required for application in a clinical setting. To assess gait stability, a comparative effect size (Cohen's d) analysis of variability and dynamic stability of foot trajectories during level walking was performed on 29 of an initial yield of 9889 articles from four electronic databases. The results of this survey demonstrate that linear variability of temporal measures of swing and stance was most capable of distinguishing between fallers and non-fallers, whereas step width and stride velocity prove more capable of discriminating between old versus young (OY) adults. In addition, while orbital stability measures (Floquet multipliers) applied to gait have been shown to distinguish between both elderly fallers and non-fallers as well as between young and old adults, local stability measures (λs) have been able to distinguish between young and old adults. Both linear and nonlinear measures of foot

  19. Kinematic measures for assessing gait stability in elderly individuals: a systematic review.

    PubMed

    Hamacher, D; Singh, N B; Van Dieën, J H; Heller, M O; Taylor, W R

    2011-12-07

    Falls not only present a considerable health threat, but the resulting treatment and loss of working days also place a heavy economic burden on society. Gait instability is a major fall risk factor, particularly in geriatric patients, and walking is one of the most frequent dynamic activities of daily living. To allow preventive strategies to become effective, it is therefore imperative to identify individuals with an unstable gait. Assessment of dynamic stability and gait variability via biomechanical measures of foot kinematics provides a viable option for quantitative evaluation of gait stability, but the ability of these methods to predict falls has generally not been assessed. Although various methods for assessing gait stability exist, their sensitivity and applicability in a clinical setting, as well as their cost-effectiveness, need verification. The objective of this systematic review was therefore to evaluate the sensitivity of biomechanical measures that quantify gait stability among elderly individuals and to evaluate the cost of measurement instrumentation required for application in a clinical setting. To assess gait stability, a comparative effect size (Cohen's d) analysis of variability and dynamic stability of foot trajectories during level walking was performed on 29 of an initial yield of 9889 articles from four electronic databases. The results of this survey demonstrate that linear variability of temporal measures of swing and stance was most capable of distinguishing between fallers and non-fallers, whereas step width and stride velocity prove more capable of discriminating between old versus young (OY) adults. In addition, while orbital stability measures (Floquet multipliers) applied to gait have been shown to distinguish between both elderly fallers and non-fallers as well as between young and old adults, local stability measures (λs) have been able to distinguish between young and old adults. Both linear and nonlinear measures of foot

  20. Thermodynamics of photons on fractals.

    PubMed

    Akkermans, Eric; Dunne, Gerald V; Teplyaev, Alexander

    2010-12-03

    A thermodynamical treatment of a massless scalar field (a photon) confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, PV(s) = U/d(s), where d(s) is the spectral dimension and V(s) defines the "spectral volume." For regular manifolds, V(s) coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. This is further evidence that on a fractal, momentum space can have a different dimension than position space. Our analysis also provides a natural definition of the vacuum (Casimir) energy of a fractal. We suggest ways that these unusual properties might be probed experimentally.

  1. Assessment of the spatial pattern of colorectal tumour perfusion estimated at perfusion CT using two-dimensional fractal analysis.

    PubMed

    Goh, Vicky; Sanghera, Bal; Wellsted, David M; Sundin, Josefin; Halligan, Steve

    2009-06-01

    The aim was to evaluate the feasibility of fractal analysis for assessing the spatial pattern of colorectal tumour perfusion at dynamic contrast-enhanced CT (perfusion CT). Twenty patients with colorectal adenocarcinoma underwent a 65-s perfusion CT study from which a perfusion parametric map was generated using validated commercial software. The tumour was identified by an experienced radiologist, segmented via thresholding and fractal analysis applied using in-house software: fractal dimension, abundance and lacunarity were assessed for the entire outlined tumour and for selected representative areas within the tumour of low and high perfusion. Comparison was made with ten patients with normal colons, processed in a similar manner, using two-way mixed analysis of variance with statistical significance at the 5% level. Fractal values were higher in cancer than normal colon (p < or = 0.001): mean (SD) 1.71 (0.07) versus 1.61 (0.07) for fractal dimension and 7.82 (0.62) and 6.89 (0.47) for fractal abundance. Fractal values were lower in 'high' than 'low' perfusion areas. Lacunarity curves were shifted to the right for cancer compared with normal colon. In conclusion, colorectal cancer mapped by perfusion CT demonstrates fractal properties. Fractal analysis is feasible, potentially providing a quantitative measure of the spatial pattern of tumour perfusion.

  2. Dynamic fractal signature dissimilarity analysis for therapeutic response assessment using dynamic contrast-enhanced MRI

    PubMed Central

    Wang, Chunhao; Subashi, Ergys; Yin, Fang-Fang; Chang, Zheng

    2016-01-01

    Purpose: To develop a dynamic fractal signature dissimilarity (FSD) method as a novel image texture analysis technique for the quantification of tumor heterogeneity information for better therapeutic response assessment with dynamic contrast-enhanced (DCE)-MRI. Methods: A small animal antiangiogenesis drug treatment experiment was used to demonstrate the proposed method. Sixteen LS-174T implanted mice were randomly assigned into treatment and control groups (n = 8/group). All mice received bevacizumab (treatment) or saline (control) three times in two weeks, and one pretreatment and two post-treatment DCE-MRI scans were performed. In the proposed dynamic FSD method, a dynamic FSD curve was generated to characterize the heterogeneity evolution during the contrast agent uptake, and the area under FSD curve (AUCFSD) and the maximum enhancement (MEFSD) were selected as representative parameters. As for comparison, the pharmacokinetic parameter Ktrans map and area under MR intensity enhancement curve AUCMR map were calculated. Besides the tumor’s mean value and coefficient of variation, the kurtosis, skewness, and classic Rényi dimensions d1 and d2 of Ktrans and AUCMR maps were evaluated for heterogeneity assessment for comparison. For post-treatment scans, the Mann–Whitney U-test was used to assess the differences of the investigated parameters between treatment/control groups. The support vector machine (SVM) was applied to classify treatment/control groups using the investigated parameters at each post-treatment scan day. Results: The tumor mean Ktrans and its heterogeneity measurements d1 and d2 values showed significant differences between treatment/control groups in the second post-treatment scan. In contrast, the relative values (in reference to the pretreatment value) of AUCFSD and MEFSD in both post-treatment scans showed significant differences between treatment/control groups. When using AUCFSD and MEFSD as SVM input for treatment/control classification

  3. Walking dynamics of the passive compass-gait model under OGY-based control: Emergence of bifurcations and chaos

    NASA Astrophysics Data System (ADS)

    Gritli, Hassène; Belghith, Safya

    2017-06-01

    An analysis of the passive dynamic walking of a compass-gait biped model under the OGY-based control approach using the impulsive hybrid nonlinear dynamics is presented in this paper. We describe our strategy for the development of a simplified analytical expression of a controlled hybrid Poincaré map and then for the design of a state-feedback control. Our control methodology is based mainly on the linearization of the impulsive hybrid nonlinear dynamics around a desired nominal one-periodic hybrid limit cycle. Our analysis of the controlled walking dynamics is achieved by means of bifurcation diagrams. Some interesting nonlinear phenomena are displayed, such as the period-doubling bifurcation, the cyclic-fold bifurcation, the period remerging, the period bubbling and chaos. A comparison between the raised phenomena in the impulsive hybrid nonlinear dynamics and the hybrid Poincaré map under control was also presented.

  4. [Gait disorders in geriatric patients. Classification and therapy].

    PubMed

    Jahn, K; Heinze, C; Selge, C; Heßelbarth, K; Schniepp, R

    2015-04-01

    Slow walking with reduced body dynamics is a characteristic feature of locomotion in the elderly. Impaired mobility and falls associated with gait disorders significantly contribute to a reduced quality of life in the elderly. A gait disorder is not an inevitable consequence of aging. This article shows that it is worth recognizing specific deficits and differentiating specific aspects in multifactorial disorders because many causes can be well treated. Also provided are the bases for clinical classification and therapeutic principles. Review of recent literature and clinical review based on own experience and own scientific results. Common causes of disturbed gait in the elderly are neurological deficits, including sensory deficits (e.g. peripheral neuropathy and vestibulopathy), neurodegeneration (e.g. cerebellar ataxia and parkinsonian syndromes, cognitive impairment (e.g. degenerative dementia), degeneration of joints (e.g. coxarthrosis) and general loss of muscle mass (sarcopenia). Furthermore, a fear of falling also contributes to the gait disorder. Multimodal therapies are often necessary and the principles are presented. Identification of deficits is a prerequisite for specific therapy. As physical activity protects against cognitive impairment, reduces the risk of falling and improves overall quality of life, a structured assessment of causes for gait impairment is crucial.

  5. Statistical Analysis of the Fractal Gating Motions of the Enzyme Acetylcholinesterase

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Shen, T Y.; Tai, Kaihsu; Mccammon, Andy

    The enzyme acetylcholinesterase has an active site that is accessible only by a gorge or main channel from the surface, and perhaps by secondary channels such as the back door. Molecular-dynamics simulations show that these channels are too narrow most of the time to admit substrate or other small molecules. Binding of substrates is therefore gated by structural fluctuations of the enzyme. Here, we analyze the fluctuations of these possible channels, as observed in the 10.8-ns trajectory of the simulation. The probability density function of the gorge proper radius (defined in the text) was calculated. A double-peak feature of themore » function was discovered and therefore two states with a threshold were identified. The relaxation (transition probability) functions of these two states were also calculated. The results revealed a power-law decay trend and an oscillation around it, which show properties of fractal dynamics with a complex exponent. The cross correlation of potential energy versus proper radius was also investigated. We discuss possible physical models behind the fractal protein dynamics; the dynamic hierarchical model for glassy systems is evaluated in detail.« less

  6. Fractal structures and fractal functions as disease indicators

    USGS Publications Warehouse

    Escos, J.M; Alados, C.L.; Emlen, J.M.

    1995-01-01

    Developmental instability is an early indicator of stress, and has been used to monitor the impacts of human disturbance on natural ecosystems. Here we investigate the use of different measures of developmental instability on two species, green peppers (Capsicum annuum), a plant, and Spanish ibex (Capra pyrenaica), an animal. For green peppers we compared the variance in allometric relationship between control plants, and a treatment group infected with the tomato spotted wilt virus. The results show that infected plants have a greater variance about the allometric regression line than the control plants. We also observed a reduction in complexity of branch structure in green pepper with a viral infection. Box-counting fractal dimension of branch architecture declined under stress infection. We also tested the reduction in complexity of behavioral patterns under stress situations in Spanish ibex (Capra pyrenaica). Fractal dimension of head-lift frequency distribution measures predator detection efficiency. This dimension decreased under stressful conditions, such as advanced pregnancy and parasitic infection. Feeding distribution activities reflect food searching efficiency. Power spectral analysis proves to be the most powerful tool for character- izing fractal behavior, revealing a reduction in complexity of time distribution activity under parasitic infection.

  7. Holographic Characterization of Colloidal Fractal Aggregates

    NASA Astrophysics Data System (ADS)

    Wang, Chen; Cheong, Fook Chiong; Ruffner, David B.; Zhong, Xiao; Ward, Michael D.; Grier, David G.

    In-line holographic microscopy images of micrometer-scale fractal aggregates can be interpreted with the Lorenz-Mie theory of light scattering and an effective-sphere model to obtain each aggregate's size and the population-averaged fractal dimension. We demonstrate this technique experimentally using model fractal clusters of polystyrene nanoparticles and fractal protein aggregates composed of bovine serum albumin and bovine pancreas insulin. This technique can characterize several thousand aggregates in ten minutes and naturally distinguishes aggregates from contaminants such as silicone oil droplets. Work supported by the SBIR program of the NSF.

  8. Fractal analysis of time varying data

    DOEpatents

    Vo-Dinh, Tuan; Sadana, Ajit

    2002-01-01

    Characteristics of time varying data, such as an electrical signal, are analyzed by converting the data from a temporal domain into a spatial domain pattern. Fractal analysis is performed on the spatial domain pattern, thereby producing a fractal dimension D.sub.F. The fractal dimension indicates the regularity of the time varying data.

  9. Fractal electrodynamics via non-integer dimensional space approach

    NASA Astrophysics Data System (ADS)

    Tarasov, Vasily E.

    2015-09-01

    Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.

  10. Comparison of the Classifier Oriented Gait Score and the Gait Profile Score based on imitated gait impairments.

    PubMed

    Christian, Josef; Kröll, Josef; Schwameder, Hermann

    2017-06-01

    Common summary measures of gait quality such as the Gait Profile Score (GPS) are based on the principle of measuring a distance from the mean pattern of a healthy reference group in a gait pattern vector space. The recently introduced Classifier Oriented Gait Score (COGS) is a pathology specific score that measures this distance in a unique direction, which is indicated by a linear classifier. This approach has potentially improved the discriminatory power to detect subtle changes in gait patterns but does not incorporate a profile of interpretable sub-scores like the GPS. The main aims of this study were to extend the COGS by decomposing it into interpretable sub-scores as realized in the GPS and to compare the discriminative power of the GPS and COGS. Two types of gait impairments were imitated to enable a high level of control of the gait patterns. Imitated impairments were realized by restricting knee extension and inducing leg length discrepancy. The results showed increased discriminatory power of the COGS for differentiating diverse levels of impairment. Comparison of the GPS and COGS sub-scores and their ability to indicate changes in specific variables supports the validity of both scores. The COGS is an overall measure of gait quality with increased power to detect subtle changes in gait patterns and might be well suited for tracing the effect of a therapeutic treatment over time. The newly introduced sub-scores improved the interpretability of the COGS, which is helpful for practical applications. Copyright © 2017 Elsevier B.V. All rights reserved.

  11. Roughness Perception of Haptically Displayed Fractal Surfaces

    NASA Technical Reports Server (NTRS)

    Costa, Michael A.; Cutkosky, Mark R.; Lau, Sonie (Technical Monitor)

    2000-01-01

    Surface profiles were generated by a fractal algorithm and haptically rendered on a force feedback joystick, Subjects were asked to use the joystick to explore pairs of surfaces and report to the experimenter which of the surfaces they felt was rougher. Surfaces were characterized by their root mean square (RMS) amplitude and their fractal dimension. The most important factor affecting the perceived roughness of the fractal surfaces was the RMS amplitude of the surface. When comparing surfaces of fractal dimension 1.2-1.35 it was found that the fractal dimension was negatively correlated with perceived roughness.

  12. A Double-Minded Fractal

    ERIC Educational Resources Information Center

    Simoson, Andrew J.

    2009-01-01

    This article presents a fun activity of generating a double-minded fractal image for a linear algebra class once the idea of rotation and scaling matrices are introduced. In particular the fractal flip-flops between two words, depending on the level at which the image is viewed. (Contains 5 figures.)

  13. Prospective dynamic functional evaluation of gait and spinal balance following spinal fusion in adolescent idiopathic scoliosis.

    PubMed

    Lenke, L G; Engsberg, J R; Ross, S A; Reitenbach, A; Blanke, K; Bridwell, K H

    2001-07-15

    Prospective evaluation of gait and spinal-pelvic balance parameters in patients with adolescent idiopathic scoliosis undergoing a spinal fusion. To evaluate changes in gait and three-dimensional alignment and balance of the spine relative to the pelvis as a consequence of spinal fusion. Preoperative and postoperative spinal radiographs have been the major forms of outcome analysis of adolescent idiopathic scoliosis fusions. The use of optoelectronic analysis for posture and gait has gained acceptance recently. However, there is a paucity of data quantifying, comparing, and correlating structural and functional changes in patients undergoing scoliosis fusion surgery including upright posture and gait. Thirty patients with adolescent idiopathic scoliosis undergoing an instrumented spinal fusion were prospectively evaluated. Coronal and sagittal vertical alignment was evaluated on radiographs (CVA-R, SVA-R), during upright posture (CVA-P and SVA-P), and during gait (CVA-G, SVA-G). Transverse plane alignment was evaluated by the acromion-pelvis angle during gait. Gait speed was significantly decreased (P < 0.05) between preoperative (129 +/- 16 cm/sec) and 2-year postoperative (119 +/- 16 cm/sec) testing sessions. Decreasing gait speed was the result of significantly reduced cadence and decreased stride length. There were no significant differences for lower extremity kinematics over the entire gait cycle. Spinal-pelvic balance parameters showed significant improvement in mean CVA-R, CVA-G (P < 0.05), then unchanged CVA-P at 2 years postoperation. CVA-P was relatively unchanged while the mean CVA-G also showed significant improvement from preoperation (2.2 +/- 2.4 cm) to 2 years postoperation (1.3 +/- 1.3 cm)(P < 0.05). The mean SVA-R, SVA-P, and SVA-G were unchanged at 2 years postoperation (P > 0.05). The acromion-pelvis angle during gait at maximum shoulder rotation was statistically improved at 1 year (P = 0.002) and 2 years (P = 0.001) after surgery. Importantly

  14. Fractal structures in centrifugal flywheel governor system

    NASA Astrophysics Data System (ADS)

    Rao, Xiao-Bo; Chu, Yan-Dong; Lu-Xu; Chang, Ying-Xiang; Zhang, Jian-Gang

    2017-09-01

    The global structure of nonlinear response of mechanical centrifugal governor, forming in two-dimensional parameter space, is studied in this paper. By using three kinds of phases, we describe how responses of periodicity, quasi-periodicity and chaos organize some self-similarity structures with parameters varying. For several parameter combinations, the regular vibration shows fractal characteristic, that is, the comb-shaped self-similarity structure is generated by alternating periodic response with intermittent chaos, and Arnold's tongues embedded in quasi-periodic response are organized according to Stern-Brocot tree. In particular, a new type of mixed-mode oscillations (MMOs) is found in the periodic response. These unique structures reveal the natural connection of various responses between part and part, part and the whole in parameter space based on self-similarity of fractal. Meanwhile, the remarkable and unexpected results are to contribute a valid dynamic reference for practical applications with respect to mechanical centrifugal governor.

  15. Fractal and chaotic laws on seismic dissipated energy in an energy system of engineering structures

    NASA Astrophysics Data System (ADS)

    Cui, Yu-Hong; Nie, Yong-An; Yan, Zong-Da; Wu, Guo-You

    1998-09-01

    Fractal and chaotic laws of engineering structures are discussed in this paper, it means that the intrinsic essences and laws on dynamic systems which are made from seismic dissipated energy intensity E d and intensity of seismic dissipated energy moment I e are analyzed. Based on the intrinsic characters of chaotic and fractal dynamic system of E d and I e, three kinds of approximate dynamic models are rebuilt one by one: index autoregressive model, threshold autoregressive model and local-approximate autoregressive model. The innate laws, essences and systematic error of evolutional behavior I e are explained over all, the short-term behavior predictability and long-term behavior probability of which are analyzed in the end. That may be valuable for earthquake-resistant theory and analysis method in practical engineering structures.

  16. Collisions of ideal gas molecules with a rough/fractal surface. A computational study.

    PubMed

    Panczyk, Tomasz

    2007-02-01

    The frequency of collisions of ideal gas molecules (argon) with a rough surface has been studied. The rough/fractal surface was created using random deposition technique. By applying various depositions, the roughness of the surface was controlled and, as a measure of the irregularity, the fractal dimensions of the surfaces were determined. The surfaces were next immersed in argon (under pressures 2 x 10(3) to 2 x 10(5) Pa) and the numbers of collisions with these surfaces were counted. The calculations were carried out using a simplified molecular dynamics simulation technique (only hard core repulsions were assumed). As a result, it was stated that the frequency of collisions is a linear function of pressure for all fractal dimensions studied (D = 2, ..., 2.5). The frequency per unit pressure is quite complex function of the fractal dimension; however, the changes of that frequency with the fractal dimension are not strong. It was found that the frequency of collisions is controlled by the number of weakly folded sites on the surfaces and there is some mapping between the shape of adsorption energy distribution functions and this number of weakly folded sites. The results for the rough/fractal surfaces were compared with the prediction given by the Langmuir-Hertz equation (valid for smooth surface), generally the departure from the Langmuir-Hertz equation is not higher than 48% for the studied systems (i.e. for the surfaces created using the random deposition technique).

  17. A physically based connection between fractional calculus and fractal geometry

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Butera, Salvatore, E-mail: sg.butera@gmail.com; Di Paola, Mario, E-mail: mario.dipaola@unipa.it

    2014-11-15

    We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalousmore » dimension of such geometry, as well as to the model used to describe the physics involved. By linearizing the non linear dependence of the response of the system at hand to a proper forcing action then, exploiting the Boltzmann superposition principle, a fractional differential equation is found, describing the dynamics of the system itself. The order of such equation is again related to the anomalous dimension of the underlying geometry.« less

  18. Definition of fractal topography to essential understanding of scale-invariance

    NASA Astrophysics Data System (ADS)

    Jin, Yi; Wu, Ying; Li, Hui; Zhao, Mengyu; Pan, Jienan

    2017-04-01

    Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter Hxy, a general Hurst exponent, which is analytically expressed by Hxy = log Px/log Py where Px and Py are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which . Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.

  19. Fractal dimension of turbulent black holes

    NASA Astrophysics Data System (ADS)

    Westernacher-Schneider, John Ryan

    2017-11-01

    We present measurements of the fractal dimension of a turbulent asymptotically anti-de Sitter black brane reconstructed from simulated boundary fluid data at the perfect fluid order using the fluid-gravity duality. We argue that the boundary fluid energy spectrum scaling as E (k )˜k-2 is a more natural setting for the fluid-gravity duality than the Kraichnan-Kolmogorov scaling of E (k )˜k-5 /3, but we obtain fractal dimensions D for spatial sections of the horizon H ∩Σ in both cases: D =2.584 (1 ) and D =2.645 (4 ), respectively. These results are consistent with the upper bound of D =3 , thereby resolving the tension with the recent claim in Adams et al. [Phys. Rev. Lett. 112, 151602 (2014), 10.1103/PhysRevLett.112.151602] that D =3 +1 /3 . We offer a critical examination of the calculation which led to their result, and show that their proposed definition of the fractal dimension performs poorly as a fractal dimension estimator on one-dimensional curves with known fractal dimension. Finally, we describe how to define and in principle calculate the fractal dimension of spatial sections of the horizon H ∩Σ in a covariant manner, and we speculate on assigning a "bootstrapped" value of fractal dimension to the entire horizon H when it is in a statistically quasisteady turbulent state.

  20. Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model.

    PubMed

    Gao, Xu-Zhen; Pan, Yue; Zhao, Meng-Dan; Zhang, Guan-Lin; Zhang, Yu; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

    2018-01-22

    We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.

  1. Pre-Service Teachers' Concept Images on Fractal Dimension

    ERIC Educational Resources Information Center

    Karakus, Fatih

    2016-01-01

    The analysis of pre-service teachers' concept images can provide information about their mental schema of fractal dimension. There is limited research on students' understanding of fractal and fractal dimension. Therefore, this study aimed to investigate the pre-service teachers' understandings of fractal dimension based on concept image. The…

  2. Gait bradykinesia in Parkinson's disease: a change in the motor program which controls the synergy of gait.

    PubMed

    Warabi, Tateo; Furuyama, Hiroyasu; Sugai, Eri; Kato, Masamichi; Yanagisawa, Nobuo

    2018-01-01

    This study examined how gait bradykinesia is changed by the motor programming in Parkinson's disease. Thirty-five idiopathic Parkinson's disease patients and nine age-matched healthy subjects participated in this study. After the patients fixated on a visual-fixation target (conditioning-stimulus), the voluntary-gait was triggered by a visual on-stimulus. While the subject walked on a level floor, soleus, tibialis anterior EMG latencies, and the y-axis-vector of the sole-floor reaction force were examined. Three paradigms were used to distinguish between the off-/on-latencies. The gap-task: the visual-fixation target was turned off; 200 ms before the on-stimulus was engaged (resulting in a 200 ms-gap). EMG latency was not influenced by the visual-fixation target. The overlap-task: the on-stimulus was turned on during the visual-fixation target presentation (200 ms-overlap). The no-gap-task: the fixation target was turned off and the on-stimulus was turned on simultaneously. The onset of EMG pause following the tonic soleus EMG was defined as the off-latency of posture (termination). The onset of the tibialis anterior EMG burst was defined as the on-latency of gait (initiation). In the gap-task, the on-latency was unchanged in all of the subjects. In Parkinson's disease, the visual-fixation target prolonged both the off-/on-latencies in the overlap-task. In all tasks, the off-latency was prolonged and the off-/on-latencies were unsynchronized, which changed the synergic movement to a slow, short-step-gait. The synergy of gait was regulated by two independent sensory-motor programs of the off- and on-latency levels. In Parkinson's disease, the delayed gait initiation was due to the difficulty in terminating the sensory-motor program which controls the subject's fixation. The dynamic gait bradykinesia was involved in the difficulty (long off-latency) in terminating the motor program of the prior posture/movement.

  3. Influence of altered gait patterns on the hip joint contact forces.

    PubMed

    Carriero, Alessandra; Zavatsky, Amy; Stebbins, Julie; Theologis, Tim; Lenaerts, Gerlinde; Jonkers, Ilse; Shefelbine, Sandra J

    2014-01-01

    Children who exhibit gait deviations often present a range of bone deformities, particularly at the proximal femur. Altered gait may affect bone growth and lead to deformities by exerting abnormal stresses on the developing bones. The objective of this study was to calculate variations in the hip joint contact forces with different gait patterns. Muscle and hip joint contact forces of four children with different walking characteristics were calculated using an inverse dynamic analysis and a static optimisation algorithm. Kinematic and kinetic analyses were based on a generic musculoskeletal model scaled down to accommodate the dimensions of each child. Results showed that for all the children with altered gaits both the orientation and magnitude of the hip joint contact force deviated from normal. The child with the most severe gait deviations had hip joint contact forces 30% greater than normal, most likely due to the increase in muscle forces required to sustain his crouched stance. Determining how altered gait affects joint loading may help in planning treatment strategies to preserve correct loading on the bone from a young age.

  4. Effects of Anisotropy on Scalar Field Ghost Dark Energy and the Non-Equilibrium Thermodynamics in Fractal Cosmology

    NASA Astrophysics Data System (ADS)

    Najafi, A.; Hossienkhani, H.

    2017-10-01

    Since the fractal cosmology has been created in early universe, therefore their models were mostly isotropic. The majority of previous studies had been based on FRW universe, while in the early universe, the best model for describing fractal cosmology is actually the anisotropic universe. Therefore in this work, by assuming the anisotropic universe, the cosmological implications of ghost and generalized ghost dark energy models with dark matter in fractal cosmology has been discussed. Moreover, the different kinds of dark energy models such as quintessence and tachyon field, with the generalized ghost dark energy in fractal universe has been investigated. In addition, we have reconstructed the Hubble parameter, H, the energy density, ρ, the deceleration parameter, q, the equations of state parameter, {ω }{{}D}, for both ghost and generalized ghost dark energy models. This correspondence allows us to reconstruct the potential and the dynamics of a fractal canonical scalar field according to the evolution of generalized ghost dark energy density. Eventually, thermodynamics of the cosmological apparent horizon in fractal cosmology was investigated and the validity of the Generalized second law of thermodynamics (GSLT) have been examined in an anisotropic universe. The results show the influence of the anisotropy on the GSLT of thermodynamics in a fractal cosmology.

  5. Fractal Analysis of Rock Joint Profiles

    NASA Astrophysics Data System (ADS)

    Audy, Ondřej; Ficker, Tomáš

    2017-10-01

    Surface reliefs of rock joints are analyzed in geotechnics when shear strength of rocky slopes is estimated. The rock joint profiles actually are self-affine fractal curves and computations of their fractal dimensions require special methods. Many papers devoted to the fractal properties of these profiles were published in the past but only a few of those papers employed a convenient computational method that would have guaranteed a sound value of that dimension. As a consequence, anomalously low dimensions were presented. This contribution deals with two computational modifications that lead to sound fractal dimensions of the self-affine rock joint profiles. These are the modified box-counting method and the modified yard-stick method sometimes called the compass method. Both these methods are frequently applied to self-similar fractal curves but the self-affine profile curves due to their self-affine nature require modified computational procedures implemented in computer programs.

  6. Aesthetic Responses to Exact Fractals Driven by Physical Complexity

    PubMed Central

    Bies, Alexander J.; Blanc-Goldhammer, Daryn R.; Boydston, Cooper R.; Taylor, Richard P.; Sereno, Margaret E.

    2016-01-01

    Fractals are physically complex due to their repetition of patterns at multiple size scales. Whereas the statistical characteristics of the patterns repeat for fractals found in natural objects, computers can generate patterns that repeat exactly. Are these exact fractals processed differently, visually and aesthetically, than their statistical counterparts? We investigated the human aesthetic response to the complexity of exact fractals by manipulating fractal dimensionality, symmetry, recursion, and the number of segments in the generator. Across two studies, a variety of fractal patterns were visually presented to human participants to determine the typical response to exact fractals. In the first study, we found that preference ratings for exact midpoint displacement fractals can be described by a linear trend with preference increasing as fractal dimension increases. For the majority of individuals, preference increased with dimension. We replicated these results for other exact fractal patterns in a second study. In the second study, we also tested the effects of symmetry and recursion by presenting asymmetric dragon fractals, symmetric dragon fractals, and Sierpinski carpets and Koch snowflakes, which have radial and mirror symmetry. We found a strong interaction among recursion, symmetry and fractal dimension. Specifically, at low levels of recursion, the presence of symmetry was enough to drive high preference ratings for patterns with moderate to high levels of fractal dimension. Most individuals required a much higher level of recursion to recover this level of preference in a pattern that lacked mirror or radial symmetry, while others were less discriminating. This suggests that exact fractals are processed differently than their statistical counterparts. We propose a set of four factors that influence complexity and preference judgments in fractals that may extend to other patterns: fractal dimension, recursion, symmetry and the number of segments in a

  7. Evaluation of the performance of accelerometer-based gait event detection algorithms in different real-world scenarios using the MAREA gait database.

    PubMed

    Khandelwal, Siddhartha; Wickström, Nicholas

    2017-01-01

    Numerous gait event detection (GED) algorithms have been developed using accelerometers as they allow the possibility of long-term gait analysis in everyday life. However, almost all such existing algorithms have been developed and assessed using data collected in controlled indoor experiments with pre-defined paths and walking speeds. On the contrary, human gait is quite dynamic in the real-world, often involving varying gait speeds, changing surfaces and varying surface inclinations. Though portable wearable systems can be used to conduct experiments directly in the real-world, there is a lack of publicly available gait datasets or studies evaluating the performance of existing GED algorithms in various real-world settings. This paper presents a new gait database called MAREA (n=20 healthy subjects) that consists of walking and running in indoor and outdoor environments with accelerometers positioned on waist, wrist and both ankles. The study also evaluates the performance of six state-of-the-art accelerometer-based GED algorithms in different real-world scenarios, using the MAREA gait database. The results reveal that the performance of these algorithms is inconsistent and varies with changing environments and gait speeds. All algorithms demonstrated good performance for the scenario of steady walking in a controlled indoor environment with a combined median F1score of 0.98 for Heel-Strikes and 0.94 for Toe-Offs. However, they exhibited significantly decreased performance when evaluated in other lesser controlled scenarios such as walking and running in an outdoor street, with a combined median F1score of 0.82 for Heel-Strikes and 0.53 for Toe-Offs. Moreover, all GED algorithms displayed better performance for detecting Heel-Strikes as compared to Toe-Offs, when evaluated in different scenarios. Copyright © 2016 Elsevier B.V. All rights reserved.

  8. Fractal Patterns and Chaos Games

    ERIC Educational Resources Information Center

    Devaney, Robert L.

    2004-01-01

    Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.

  9. Dynamic leg length asymmetry during gait is not a valid method for estimating mild anatomic leg length discrepancy.

    PubMed

    Leporace, Gustavo; Batista, Luiz Alberto; Serra Cruz, Raphael; Zeitoune, Gabriel; Cavalin, Gabriel Armondi; Metsavaht, Leonardo

    2018-03-01

    The purpose of this study was to test the validity of dynamic leg length discrepancy (DLLD) during gait as a radiation-free screening method for measuring anatomic leg length discrepancy (ALLD). Thirty-three subjects with mild leg length discrepancy walked along a walkway and the dynamic leg length discrepancy (DLLD) was calculated using a motion analysis system. Pearson correlation and paired Student t -tests were applied to calculate the correlation and compare the differences between DLLD and ALLD (α = 0.05). The results of our study showed DLLD is not a valid method to predict ALLD in subjects with mild limb discrepancy.

  10. Fractal analysis: A new tool in transient volcanic ash plume characterization.

    NASA Astrophysics Data System (ADS)

    Tournigand, Pierre-Yves; Peña Fernandez, Juan Jose; Taddeucci, Jacopo; Perugini, Diego; Sesterhenn, Jörn

    2017-04-01

    Transient volcanic plumes are time-dependent features generated by unstable eruptive sources. They represent a threat to human health and infrastructures, and a challenge to characterize due to their intrinsic instability. Plumes have been investigated through physical (e.g. visible, thermal, UV, radar imagery), experimental and numerical studies in order to provide new insights about their dynamics and better anticipate their behavior. It has been shown experimentally that plume dynamics is strongly dependent to source conditions and that plume shape evolution holds key to retrieve these conditions. In this study, a shape evolution analysis is performed on thermal high-speed videos of volcanic plumes from three different volcanoes Sakurajima (Japan), Stromboli (Italy) and Fuego (Guatemala), recorded with a FLIR SC655 thermal camera during several field campaigns between 2012 and 2016. To complete this dataset, three numerical gas-jet simulations at different Reynolds number (2000, 5000 and 10000) have been used in order to set reference values to the natural cases. Turbulent flow shapes are well known to feature scale-invariant structures and a high degree of complexity. For this reason we characterized the bi-dimensional shape of natural and synthetic plumes by using a fractal descriptor. Such method has been applied in other studies on experimental turbulent jets as well as on atmospheric clouds and have shown promising results. At each time-step plume contour has been manually outlined and measured using the box-counting method. This method consists in covering the image with squares of variable sizes and counting the number of squares containing the plume outline. The negative slope of the number of squares in function of their size in a log-log plot gives the fractal dimension of the plume at a given time. Preliminary results show an increase over time of the fractal dimension for natural volcanic plume as well as for the numerically simulated ones, but at

  11. Band structures in fractal grading porous phononic crystals

    NASA Astrophysics Data System (ADS)

    Wang, Kai; Liu, Ying; Liang, Tianshu; Wang, Bin

    2018-05-01

    In this paper, a new grading porous structure is introduced based on a Sierpinski triangle routine, and wave propagation in this fractal grading porous phononic crystal is investigated. The influences of fractal hierarchy and porosity on the band structures in fractal graidng porous phononic crystals are clarified. Vibration modes of unit cell at absolute band gap edges are given to manifest formation mechanism of absolute band gaps. The results show that absolute band gaps are easy to form in fractal structures comparatively to the normal ones with the same porosity. Structures with higher fractal hierarchies benefit multiple wider absolute band gaps. This work provides useful guidance in design of fractal porous phononic crystals.

  12. The relationship between the Activities-specific Balance Confidence Scale and the Dynamic Gait Index in peripheral vestibular dysfunction.

    PubMed

    Legters, Kristine; Whitney, Susan L; Porter, Rebecca; Buczek, Frank

    2005-01-01

    People with vestibular dysfunction experience dizziness, vertigo and postural instability. The persistence of these symptoms may result in decreased balance confidence. The purpose of the present study was to examine the relationship between decreased balance confidence and gait dysfunction in patients with unilateral peripheral vestibular dysfunction. A retrospective review of 137 charts with the Activities-specific Balance Confidence (ABC) Scale and the Dynamic Gait Index (DGI) scores was completed. Spearman rank-order correlation analysis was performed of the total sample, by age group and by degree of vestibular weakness. A moderate correlation of r = 0.58 (p < 0.001) was found between the ABC Scale score and the DGI score in the total sample. Those with mild or moderate vestibular weakness had a correlation of r = 0.72 (p < 0.001) between the ABC Scale score and the DGI score, compared with a correlation of r = 0.48 in those with severe or total vestibular weakness. Decreased balance confidence and increased fall risk are critical issues for people with vestibular dysfunction. The effects of aging did not have a significant impact on the relationship. The correlation between balance confidence and gait dysfunction was stronger in those with mild or moderate vestibular weakness, although those with severe or total weakness were more disabled by their vestibular symptoms.

  13. Fractal mechanisms and heart rate dynamics. Long-range correlations and their breakdown with disease

    NASA Technical Reports Server (NTRS)

    Peng, C. K.; Havlin, S.; Hausdorff, J. M.; Mietus, J. E.; Stanley, H. E.; Goldberger, A. L.

    1995-01-01

    Under healthy conditions, the normal cardiac (sinus) interbeat interval fluctuates in a complex manner. Quantitative analysis using techniques adapted from statistical physics reveals the presence of long-range power-law correlations extending over thousands of heartbeats. This scale-invariant (fractal) behavior suggests that the regulatory system generating these fluctuations is operating far from equilibrium. In contrast, it is found that for subjects at high risk of sudden death (e.g., congestive heart failure patients), these long-range correlations break down. Application of fractal scaling analysis and related techniques provides new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as motivating development of novel physiologic models of systems that appear to be heterodynamic rather than homeostatic.

  14. Guidelines for Assessment of Gait and Reference Values for Spatiotemporal Gait Parameters in Older Adults: The Biomathics and Canadian Gait Consortiums Initiative

    PubMed Central

    Beauchet, Olivier; Allali, Gilles; Sekhon, Harmehr; Verghese, Joe; Guilain, Sylvie; Steinmetz, Jean-Paul; Kressig, Reto W.; Barden, John M.; Szturm, Tony; Launay, Cyrille P.; Grenier, Sébastien; Bherer, Louis; Liu-Ambrose, Teresa; Chester, Vicky L.; Callisaya, Michele L.; Srikanth, Velandai; Léonard, Guillaume; De Cock, Anne-Marie; Sawa, Ryuichi; Duque, Gustavo; Camicioli, Richard; Helbostad, Jorunn L.

    2017-01-01

    Background: Gait disorders, a highly prevalent condition in older adults, are associated with several adverse health consequences. Gait analysis allows qualitative and quantitative assessments of gait that improves the understanding of mechanisms of gait disorders and the choice of interventions. This manuscript aims (1) to give consensus guidance for clinical and spatiotemporal gait analysis based on the recorded footfalls in older adults aged 65 years and over, and (2) to provide reference values for spatiotemporal gait parameters based on the recorded footfalls in healthy older adults free of cognitive impairment and multi-morbidities. Methods: International experts working in a network of two different consortiums (i.e., Biomathics and Canadian Gait Consortium) participated in this initiative. First, they identified items of standardized information following the usual procedure of formulation of consensus findings. Second, they merged databases including spatiotemporal gait assessments with GAITRite® system and clinical information from the “Gait, cOgnitiOn & Decline” (GOOD) initiative and the Generation 100 (Gen 100) study. Only healthy—free of cognitive impairment and multi-morbidities (i.e., ≤ 3 therapeutics taken daily)—participants aged 65 and older were selected. Age, sex, body mass index, mean values, and coefficients of variation (CoV) of gait parameters were used for the analyses. Results: Standardized systematic assessment of three categories of items, which were demographics and clinical information, and gait characteristics (clinical and spatiotemporal gait analysis based on the recorded footfalls), were selected for the proposed guidelines. Two complementary sets of items were distinguished: a minimal data set and a full data set. In addition, a total of 954 participants (mean age 72.8 ± 4.8 years, 45.8% women) were recruited to establish the reference values. Performance of spatiotemporal gait parameters based on the recorded

  15. Aging effect on step adjustments and stability control in visually perturbed gait initiation.

    PubMed

    Sun, Ruopeng; Cui, Chuyi; Shea, John B

    2017-10-01

    Gait adaptability is essential for fall avoidance during locomotion. It requires the ability to rapidly inhibit original motor planning, select and execute alternative motor commands, while also maintaining the stability of locomotion. This study investigated the aging effect on gait adaptability and dynamic stability control during a visually perturbed gait initiation task. A novel approach was used such that the anticipatory postural adjustment (APA) during gait initiation were used to trigger the unpredictable relocation of a foot-size stepping target. Participants (10 young adults and 10 older adults) completed visually perturbed gait initiation in three adjustment timing conditions (early, intermediate, late; all extracted from the stereotypical APA pattern) and two adjustment direction conditions (medial, lateral). Stepping accuracy, foot rotation at landing, and Margin of Dynamic Stability (MDS) were analyzed and compared across test conditions and groups using a linear mixed model. Stepping accuracy decreased as a function of adjustment timing as well as stepping direction, with older subjects exhibited a significantly greater undershoot in foot placement to late lateral stepping. Late adjustment also elicited a reaching-like movement (i.e. foot rotation prior to landing in order to step on the target), regardless of stepping direction. MDS measures in the medial-lateral and anterior-posterior direction revealed both young and older adults exhibited reduced stability in the adjustment step and subsequent steps. However, young adults returned to stable gait faster than older adults. These findings could be useful for future study of screening deficits in gait adaptability and preventing falls. Copyright © 2017 Elsevier B.V. All rights reserved.

  16. Fractal Signals & Space-Time Cartoons

    NASA Astrophysics Data System (ADS)

    Oetama, H. C. Jakob; Maksoed, W. H.

    2016-03-01

    In ``Theory of Scale Relativity'', 1991- L. Nottale states whereas ``scale relativity is a geometrical & fractal space-time theory''. It took in comparisons to ``a unified, wavelet based framework for efficiently synthetizing, analyzing ∖7 processing several broad classes of fractal signals''-Gregory W. Wornell:``Signal Processing with Fractals'', 1995. Furthers, in Fig 1.1. a simple waveform from statistically scale-invariant random process [ibid.,h 3 ]. Accompanying RLE Technical Report 566 ``Synthesis, Analysis & Processing of Fractal Signals'' as well as from Wornell, Oct 1991 herewith intended to deducts =a Δt + (1 - β Δ t) ...in Petersen, et.al: ``Scale invariant properties of public debt growth'',2010 h. 38006p2 to [1/{1- (2 α (λ) /3 π) ln (λ/r)}depicts in Laurent Nottale,1991, h 24. Acknowledgment devotes to theLates HE. Mr. BrigadierGeneral-TNI[rtd].Prof. Ir. HANDOJO.

  17. A fractal derivative model for the characterization of anomalous diffusion in magnetic resonance imaging

    NASA Astrophysics Data System (ADS)

    Liang, Yingjie; Ye, Allen Q.; Chen, Wen; Gatto, Rodolfo G.; Colon-Perez, Luis; Mareci, Thomas H.; Magin, Richard L.

    2016-10-01

    Non-Gaussian (anomalous) diffusion is wide spread in biological tissues where its effects modulate chemical reactions and membrane transport. When viewed using magnetic resonance imaging (MRI), anomalous diffusion is characterized by a persistent or 'long tail' behavior in the decay of the diffusion signal. Recent MRI studies have used the fractional derivative to describe diffusion dynamics in normal and post-mortem tissue by connecting the order of the derivative with changes in tissue composition, structure and complexity. In this study we consider an alternative approach by introducing fractal time and space derivatives into Fick's second law of diffusion. This provides a more natural way to link sub-voxel tissue composition with the observed MRI diffusion signal decay following the application of a diffusion-sensitive pulse sequence. Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. Furthermore, the results are readily expressed in terms of spectral entropy, which provides a quantitative measure of the overall complexity of the heterogeneous and multi-scale structure of biological tissues. As an example, we apply this new model for the characterization of diffusion in fixed samples of the mouse brain. These results are compared with those obtained using the mono-exponential, the stretched exponential, the fractional derivative, and the diffusion kurtosis models. Overall, we find that the order of the fractal time derivative, the diffusion coefficient, and the spectral entropy are potential biomarkers to differentiate between the microstructure of white and gray matter. In addition, we note that the fractal derivative model has practical advantages over the existing models from the

  18. The Calculation of Fractal Dimension in the Presence of Non-Fractal Clutter

    NASA Technical Reports Server (NTRS)

    Herren, Kenneth A.; Gregory, Don A.

    1999-01-01

    The area of information processing has grown dramatically over the last 50 years. In the areas of image processing and information storage the technology requirements have far outpaced the ability of the community to meet demands. The need for faster recognition algorithms and more efficient storage of large quantities of data has forced the user to accept less than lossless retrieval of that data for analysis. In addition to clutter that is not the object of interest in the data set, often the throughput requirements forces the user to accept "noisy" data and to tolerate the clutter inherent in that data. It has been shown that some of this clutter, both the intentional clutter (clouds, trees, etc) as well as the noise introduced on the data by processing requirements can be modeled as fractal or fractal-like. Traditional methods using Fourier deconvolution on these sources of noise in frequency space leads to loss of signal and can, in many cases, completely eliminate the target of interest. The parameters that characterize fractal-like noise (predominately the fractal dimension) have been investigated and a technique to reduce or eliminate noise from real scenes has been developed. Examples of clutter reduced images are presented.

  19. Altering length and velocity feedback during a neuro-musculoskeletal simulation of normal gait contributes to hemiparetic gait characteristics.

    PubMed

    Jansen, Karen; De Groote, Friedl; Aerts, Wouter; De Schutter, Joris; Duysens, Jacques; Jonkers, Ilse

    2014-04-30

    Spasticity is an important complication after stroke, especially in the anti-gravity muscles, i.e. lower limb extensors. However the contribution of hyperexcitable muscle spindle reflex loops to gait impairments after stroke is often disputed. In this study a neuro-musculoskeletal model was developed to investigate the contribution of an increased length and velocity feedback and altered reflex modulation patterns to hemiparetic gait deficits. A musculoskeletal model was extended with a muscle spindle model providing real-time length and velocity feedback of gastrocnemius, soleus, vasti and rectus femoris during a forward dynamic simulation (neural control model). By using a healthy subject's base muscle excitations, in combination with increased feedback gains and altered reflex modulation patterns, the effect on kinematics was simulated. A foot-ground contact model was added to account for the interaction effect between the changed kinematics and the ground. The qualitative effect i.e. the directional effect and the specific gait phases where the effect is present, on the joint kinematics was then compared with hemiparetic gait deviations reported in the literature. Our results show that increased feedback in combination with altered reflex modulation patterns of soleus, vasti and rectus femoris muscle can contribute to excessive ankle plantarflexion/inadequate dorsiflexion, knee hyperextension/inadequate flexion and increased hip extension/inadequate flexion during dedicated gait cycle phases. Increased feedback of gastrocnemius can also contribute to excessive plantarflexion/inadequate dorsiflexion, however in combination with excessive knee and hip flexion. Increased length/velocity feedback can therefore contribute to two types of gait deviations, which are both in accordance with previously reported gait deviations in hemiparetic patients. Furthermore altered modulation patterns, in particular the reduced suppression of the muscle spindle feedback during

  20. Fractal characteristic in the wearing of cutting tool

    NASA Astrophysics Data System (ADS)

    Mei, Anhua; Wang, Jinghui

    1995-11-01

    This paper studies the cutting tool wear with fractal geometry. The wearing image of the flank has been collected by machine vision which consists of CCD camera and personal computer. After being processed by means of preserving smoothing, binary making and edge extracting, the clear boundary enclosing the worn area has been obtained. The fractal dimension of the worn surface is calculated by the methods called `Slit Island' and `Profile'. The experiments and calciating give the conclusion that the worn surface is enclosed by a irregular boundary curve with some fractal dimension and characteristics of self-similarity. Furthermore, the relation between the cutting velocity and the fractal dimension of the worn region has been submitted. This paper presents a series of methods for processing and analyzing the fractal information in the blank wear, which can be applied to research the projective relation between the fractal structure and the wear state, and establish the fractal model of the cutting tool wear.

  1. Fractal-based wideband invisibility cloak

    NASA Astrophysics Data System (ADS)

    Cohen, Nathan; Okoro, Obinna; Earle, Dan; Salkind, Phil; Unger, Barry; Yen, Sean; McHugh, Daniel; Polterzycki, Stefan; Shelman-Cohen, A. J.

    2015-03-01

    A wideband invisibility cloak (IC) at microwave frequencies is described. Using fractal resonators in closely spaced (sub wavelength) arrays as a minimal number of cylindrical layers (rings), the IC demonstrates that it is physically possible to attain a `see through' cloaking device with: (a) wideband coverage; (b) simple and attainable fabrication; (c) high fidelity emulation of the free path; (d) minimal side scattering; (d) a near absence of shadowing in the scattering. Although not a practical device, this fractal-enabled technology demonstrator opens up new opportunities for diverted-image (DI) technology and use of fractals in wideband optical, infrared, and microwave applications.

  2. Higher heritabilities for gait components than for overall gait scores may improve mobility in ducks.

    PubMed

    Duggan, Brendan M; Rae, Anne M; Clements, Dylan N; Hocking, Paul M

    2017-05-02

    Genetic progress in selection for greater body mass and meat yield in poultry has been associated with an increase in gait problems which are detrimental to productivity and welfare. The incidence of suboptimal gait in breeding flocks is controlled through the use of a visual gait score, which is a subjective assessment of walking ability of each bird. The subjective nature of the visual gait score has led to concerns over its effectiveness in reducing the incidence of suboptimal gait in poultry through breeding. The aims of this study were to assess the reliability of the current visual gait scoring system in ducks and to develop a more objective method to select for better gait. Experienced gait scorers assessed short video clips of walking ducks to estimate the reliability of the current visual gait scoring system. Kendall's coefficients of concordance between and within observers were estimated at 0.49 and 0.75, respectively. In order to develop a more objective scoring system, gait components were visually scored on more than 4000 pedigreed Pekin ducks and genetic parameters were estimated for these components. Gait components, which are a more objective measure, had heritabilities that were as good as, or better than, those of the overall visual gait score. Measurement of gait components is simpler and therefore more objective than the standard visual gait score. The recording of gait components can potentially be automated, which may increase accuracy further and may improve heritability estimates. Genetic correlations were generally low, which suggests that it is possible to use gait components to select for an overall improvement in both economic traits and gait as part of a balanced breeding programme.

  3. Power dissipation in fractal AC circuits

    NASA Astrophysics Data System (ADS)

    Chen, Joe P.; Rogers, Luke G.; Anderson, Loren; Andrews, Ulysses; Brzoska, Antoni; Coffey, Aubrey; Davis, Hannah; Fisher, Lee; Hansalik, Madeline; Loew, Stephen; Teplyaev, Alexander

    2017-08-01

    We extend Feynman’s analysis of an infinite ladder circuit to fractal circuits, providing examples in which fractal circuits constructed with purely imaginary impedances can have characteristic impedances with positive real part. Using (weak) self-similarity of our fractal structures, we provide algorithms for studying the equilibrium distribution of energy on these circuits. This extends the analysis of self-similar resistance networks introduced by Fukushima, Kigami, Kusuoka, and more recently studied by Strichartz et al.

  4. Gait performance and foot pressure distribution during wearable robot-assisted gait in elderly adults.

    PubMed

    Lee, Su-Hyun; Lee, Hwang-Jae; Chang, Won Hyuk; Choi, Byung-Ok; Lee, Jusuk; Kim, Jeonghun; Ryu, Gyu-Ha; Kim, Yun-Hee

    2017-11-28

    A robotic exoskeleton device is an intelligent system designed to improve gait performance and quality of life for the wearer. Robotic technology has developed rapidly in recent years, and several robot-assisted gait devices were developed to enhance gait function and activities of daily living in elderly adults and patients with gait disorders. In this study, we investigated the effects of the Gait-enhancing Mechatronic System (GEMS), a new wearable robotic hip-assist device developed by Samsung Electronics Co, Ltd., Korea, on gait performance and foot pressure distribution in elderly adults. Thirty elderly adults who had no neurological or musculoskeletal abnormalities affecting gait participated in this study. A three-dimensional (3D) motion capture system, surface electromyography and the F-Scan system were used to collect data on spatiotemporal gait parameters, muscle activity and foot pressure distribution under three conditions: free gait without robot assistance (FG), robot-assisted gait with zero torque (RAG-Z) and robot-assisted gait (RAG). We found increased gait speed, cadence, stride length and single support time in the RAG condition. Reduced rectus femoris and medial gastrocnemius muscle activity throughout the terminal stance phase and reduced effort of the medial gastrocnemius muscle throughout the pre-swing phase were also observed in the RAG condition. In addition, walking with the assistance of GEMS resulted in a significant increase in foot pressure distribution, specifically in maximum force and peak pressure of the total foot, medial masks, anterior masks and posterior masks. The results of the present study reveal that GEMS may present an alternative way of restoring age-related changes in gait such as gait instability with muscle weakness, reduced step force and lower foot pressure in elderly adults. In addition, GEMS improved gait performance by improving push-off power and walking speed and reducing muscle activity in the lower

  5. Shedding light on walking in the dark: the effects of reduced lighting on the gait of older adults with a higher-level gait disorder and controls.

    PubMed

    Kesler, Anat; Leibovich, Gregory; Herman, Talia; Gruendlinger, Leor; Giladi, Nir; Hausdorff, Jeffrey M

    2005-08-28

    To study the effects of reduced lighting on the gait of older adults with a high level gait disorder (HLGD) and to compare their response to that of healthy elderly controls. 22 patients with a HLGD and 20 age-matched healthy controls were studied under usual lighting conditions (1000 lumens) and in near darkness (5 lumens). Gait speed and gait dynamics were measured under both conditions. Cognitive function, co-morbidities, depressive symptoms, and vision were also evaluated. Under usual lighting conditions, patients walked more slowly, with reduced swing times, and increased stride-to-stride variability, compared to controls. When walking under near darkness conditions, both groups slowed their gait. All other measures of gait were not affected by lighting in the controls. In contrast, patients further reduced their swing times and increased their stride-to-stride variability, both stride time variability and swing time variability. The unique response of the patients was not explained by vision, mental status, co-morbidities, or the values of walking under usual lighting conditions. Walking with reduced lighting does not affect the gait of healthy elderly subjects, except for a reduction in speed. On the other hand, the gait of older adults with a HLGD becomes more variable and unsteady when they walk in near darkness, despite adapting a slow and cautious gait. Further work is needed to identify the causes of the maladaptive response among patients with a HLGD and the potential connection between this behavior and the increased fall risk observed in these patients.

  6. The fractal dimension of cell membrane correlates with its capacitance: A new fractal single-shell model

    PubMed Central

    Wang, Xujing; Becker, Frederick F.; Gascoyne, Peter R. C.

    2010-01-01

    The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski–Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM. PMID:21198103

  7. Spectral analysis for weighted tree-like fractals

    NASA Astrophysics Data System (ADS)

    Dai, Meifeng; Chen, Yufei; Wang, Xiaoqian; Sun, Yu; Su, Weiyi

    2018-02-01

    Much information about the structural properties and dynamical aspects of a network is measured by the eigenvalues of its normalized Laplacian matrix. In this paper, we aim to present a study on the spectra of the normalized Laplacian of weighted tree-like fractals. We analytically obtain the relationship between the eigenvalues and their multiplicities for two successive generations. As an example of application of these results, we then derive closed-form expressions for their multiplicative Kirchhoff index and Kemeny's constant.

  8. Modeling fractal cities using the correlated percolation model.

    NASA Astrophysics Data System (ADS)

    Makse, Hernán A.; Havlin, Shlomo; Stanley, H. Eugene

    1996-03-01

    Cities grow in a way that might be expected to resemble the growth of two-dimensional aggregates of particles, and this has led to recent attempts to model urban growth using ideas from the statistical physics of clusters. In particular, the model of diffusion limited aggregation (DLA) has been invoked to rationalize the apparently fractal nature of urban morphologies(M. Batty and P. Longley, Fractal Cities) (Academic, San Diego, 1994). The DLA model predicts that there should exist only one large fractal cluster, which is almost perfectly screened from incoming 'development units' (representing, for example, people, capital or resources), so that almost all of the cluster growth takes place at the tips of the cluster's branches. We show that an alternative model(H. A. Makse, S. Havlin, H. E. Stanley, Nature 377), 608 (1995), in which development units are correlated rather than being added to the cluster at random, is better able to reproduce the observed morphology of cities and the area distribution of sub-clusters ('towns') in an urban system, and can also describe urban growth dynamics. Our physical model, which corresponds to the correlated percolation model in the presence of a density gradient, is motivated by the fact that in urban areas development attracts further development. The model offers the possibility of predicting the global properties (such as scaling behavior) of urban morphologies.

  9. Poiseuille equation for steady flow of fractal fluid

    NASA Astrophysics Data System (ADS)

    Tarasov, Vasily E.

    2016-07-01

    Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.

  10. Analysis of Modification Mechanism of Gait with Rhythmic Cueing Training Paradigm

    NASA Astrophysics Data System (ADS)

    Muto, Takeshi; Kanai, Tetsuya; Sakuta, Hiroshi; Miyake, Yoshihiro

    In this research, we applied the gait training method which takes in the rhythmic auditory stimulation as a pace maker to the assistance of gait motion, and analyzed the dynamical stability of the period and trajectory of the lower limbs' motions. As the result, it was clarified that, in the training style which presents a constant rhythm, trajectory of ankles was modified as the stable state which has the historical property, but the period of footsteps was not modified but susceptible to the external environment. This result suggests that the hierarchical modification mechanism of motor schema of gait is realized by the connection between the immediate and historical modification system.

  11. Modelling gait transition in two-legged animals

    NASA Astrophysics Data System (ADS)

    Pinto, Carla M. A.; Santos, Alexandra P.

    2011-12-01

    The study of locomotor patterns has been a major research goal in the last decades. Understanding how intralimb and interlimb coordination works out so well in animals' locomotion is a hard and challenging task. Many models have been proposed to model animal's rhythms. These models have also been applied to the control of rhythmic movements of adaptive legged robots, namely biped, quadruped and other designs. In this paper we study gait transition in a central pattern generator (CPG) model for bipeds, the 4-cells model. This model is proposed by Golubitsky, Stewart, Buono and Collins and is studied further by Pinto and Golubitsky. We briefly resume the work done by Pinto and Golubitsky. We compute numerically gait transition in the 4-cells CPG model for bipeds. We use Morris-Lecar equations and Wilson-Cowan equations as the internal dynamics for each cell. We also consider two types of coupling between the cells: diffusive and synaptic. We obtain secondary gaits by bifurcation of primary gaits, by varying the coupling strengths. Nevertheless, some bifurcating branches could not be obtained, emphasizing the fact that despite analytically those bifurcations exist, finding them is a hard task and requires variation of other parameters of the equations. We note that the type of coupling did not influence the results.

  12. An electromechanical gait trainer for restoration of gait in hemiparetic stroke patients: preliminary results.

    PubMed

    Hesse, S; Werner, C; Uhlenbrock, D; von Frankenberg, S; Bardeleben, A; Brandl-Hesse, B

    2001-01-01

    Modern concepts of gait rehabilitation after stroke favor a task-specific repetitive approach. In practice, the required physical effort of the therapists limits the realization of this approach. Therefore, a mechanized gait trainer enabling nonambulatory patients to have the repetitive practice of a gait-like movement without overstraining therapists was constructed. This preliminary study investigated whether an additional 4-week daily therapy on the gait trainer could improve gait ability in 14 chronic wheelchair-bound hemiparetic subjects. The 4 weeks of physiotherapy and gait-trainer therapy resulted in a relevant improvement of gait ability in all subjects. Velocity, cadence, and stride length improved significantly (p < 0.01). The kinesiologic electromyogram of selected lower-limb muscles revealed a more physiologic pattern. The confounding influence of spontaneous recovery, the lack of a control group, and the double amount of therapy limit the clinical relevance of this study. Nevertheless, the gait trainer seems feasible as an adjunctive tool in gait rehabilitation after stroke; further studies are needed.

  13. Prediction of human gait trajectories during the SSP using a neuromusculoskeletal modeling: A challenge for parametric optimization.

    PubMed

    Seyed, Mohammadali Rahmati; Mostafa, Rostami; Borhan, Beigzadeh

    2018-04-27

    The parametric optimization techniques have been widely employed to predict human gait trajectories; however, their applications to reveal the other aspects of gait are questionable. The aim of this study is to investigate whether or not the gait prediction model is able to justify the movement trajectories for the higher average velocities. A planar, seven-segment model with sixteen muscle groups was used to represent human neuro-musculoskeletal dynamics. At first, the joint angles, ground reaction forces (GRFs) and muscle activations were predicted and validated for normal average velocity (1.55 m/s) in the single support phase (SSP) by minimizing energy expenditure, which is subject to the non-linear constraints of the gait. The unconstrained system dynamics of extended inverse dynamics (USDEID) approach was used to estimate muscle activations. Then by scaling time and applying the same procedure, the movement trajectories were predicted for higher average velocities (from 2.07 m/s to 4.07 m/s) and compared to the pattern of movement with fast walking speed. The comparison indicated a high level of compatibility between the experimental and predicted results, except for the vertical position of the center of gravity (COG). It was concluded that the gait prediction model can be effectively used to predict gait trajectories for higher average velocities.

  14. Fractal diffusion in high temperature polymer electrolyte fuel cell membranes

    NASA Astrophysics Data System (ADS)

    Hopfenmüller, Bernhard; Zorn, Reiner; Holderer, Olaf; Ivanova, Oxana; Lehnert, Werner; Lüke, Wiebke; Ehlers, Georg; Jalarvo, Niina; Schneider, Gerald J.; Monkenbusch, Michael; Richter, Dieter

    2018-05-01

    The performance of fuel cells depends largely on the proton diffusion in the proton conducting membrane, the core of a fuel cell. High temperature polymer electrolyte fuel cells are based on a polymer membrane swollen with phosphoric acid as the electrolyte, where proton conduction takes place. We studied the proton diffusion in such membranes with neutron scattering techniques which are especially sensitive to the proton contribution. Time of flight spectroscopy and backscattering spectroscopy have been combined to cover a broad dynamic range. In order to selectively observe the diffusion of protons potentially contributing to the ion conductivity, two samples were prepared, where in one of the samples the phosphoric acid was used with hydrogen replaced by deuterium. The scattering data from the two samples were subtracted in a suitable way after measurement. Thereby subdiffusive behavior of the proton diffusion has been observed and interpreted in terms of a model of fractal diffusion. For this purpose, a scattering function for fractal diffusion has been developed. The fractal diffusion dimension dw and the Hausdorff dimension df have been determined on the length scales covered in the neutron scattering experiments.

  15. Fractal diffusion in high temperature polymer electrolyte fuel cell membranes

    DOE PAGES

    Hopfenmuller, Bernhard; Zorn, Reiner; Holderer, Olaf; ...

    2018-05-29

    In this paper, the performance of fuel cells depends largely on the proton diffusion in the proton conducting membrane, the core of a fuel cell. High temperature polymer electrolyte fuel cells are based on a polymer membrane swollen with phosphoric acid as the electrolyte, where proton conduction takes place. We studied the proton diffusion in such membranes with neutron scattering techniques which are especially sensitive to the proton contribution. Time of flight spectroscopy and backscattering spectroscopy have been combined to cover a broad dynamic range. In order to selectively observe the diffusion of protons potentially contributing to the ion conductivity,more » two samples were prepared, where in one of the samples the phosphoric acid was used with hydrogen replaced by deuterium. The scattering data from the two samples were subtracted in a suitable way after measurement. Thereby subdiffusive behavior of the proton diffusion has been observed and interpreted in terms of a model of fractal diffusion. For this purpose, a scattering function for fractal diffusion has been developed. The fractal diffusion dimension d w and the Hausdorff dimension d f have been determined on the length scales covered in the neutron scattering experiments.« less

  16. Fractal diffusion in high temperature polymer electrolyte fuel cell membranes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hopfenmuller, Bernhard; Zorn, Reiner; Holderer, Olaf

    In this paper, the performance of fuel cells depends largely on the proton diffusion in the proton conducting membrane, the core of a fuel cell. High temperature polymer electrolyte fuel cells are based on a polymer membrane swollen with phosphoric acid as the electrolyte, where proton conduction takes place. We studied the proton diffusion in such membranes with neutron scattering techniques which are especially sensitive to the proton contribution. Time of flight spectroscopy and backscattering spectroscopy have been combined to cover a broad dynamic range. In order to selectively observe the diffusion of protons potentially contributing to the ion conductivity,more » two samples were prepared, where in one of the samples the phosphoric acid was used with hydrogen replaced by deuterium. The scattering data from the two samples were subtracted in a suitable way after measurement. Thereby subdiffusive behavior of the proton diffusion has been observed and interpreted in terms of a model of fractal diffusion. For this purpose, a scattering function for fractal diffusion has been developed. The fractal diffusion dimension d w and the Hausdorff dimension d f have been determined on the length scales covered in the neutron scattering experiments.« less

  17. Fractal Interrelationships in Field and Seismic Data

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Wilson, T.H.; Dominic, Jovita; Halverson, Joel

    1997-10-01

    Size scaling interrelationships are evaluated in this study using a fractal model. Fractal models of several geologic variables are examined and include fracture patterns, reflection travel times, structural relief, drainage, topographic relief and active fault patterns. The fractal properties of structural relief inferred from seismic data and structural cross sections provide a quantitative means to characterize and compare complex structural patterns. Studies were conducted using seismic data from the Granny Creek oil field in the Appalachian Plateau. Previous studies of the field reveal that subtle detached structures present on the limb of a larger structure are associated with enhanced productionmore » from the field. Vertical increases of fractal dimension across the zone of detachment provide a measure of the extent to which detachment has occurred. The increases of fractal dimension are greatest in the more productive areas of the field. A result with equally important ramifications is that fracture systems do not appear to be intrinsically fractal as is often suggested in the literature. While examples of nearly identical patterns can be found at different scales supporting the idea of self-similarity, these examples are often taken from different areas and from different lithologies. Examination of fracture systems at different scales in the Valley and Ridge Province suggest that their distribution become increasingly sparse with scale reduction, and therefore are dissimilar or non-fractal. Box counting data in all cases failed to yield a fractal regime. The results obtained from this analysis bring into question the general applicability of reservoir simulations employing fractal models of fracture distribution. The same conclusions were obtained from the analysis of 1D fracture patterns such as those that might appear in a horizontal well.« less

  18. Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

    NASA Astrophysics Data System (ADS)

    Besselink, R.; Stawski, T. M.; Van Driessche, A. E. S.; Benning, L. G.

    2016-12-01

    Densely packed surface fractal aggregates form in systems with high local volume fractions of particles with very short diffusion lengths, which effectively means that particles have little space to move. However, there are no prior mathematical models, which would describe scattering from such surface fractal aggregates and which would allow the subdivision between inter- and intraparticle interferences of such aggregates. Here, we show that by including a form factor function of the primary particles building the aggregate, a finite size of the surface fractal interfacial sub-surfaces can be derived from a structure factor term. This formalism allows us to define both a finite specific surface area for fractal aggregates and the fraction of particle interfacial sub-surfaces at the perimeter of an aggregate. The derived surface fractal model is validated by comparing it with an ab initio approach that involves the generation of a "brick-in-a-wall" von Koch type contour fractals. Moreover, we show that this approach explains observed scattering intensities from in situ experiments that followed gypsum (CaSO4 ṡ 2H2O) precipitation from highly supersaturated solutions. Our model of densely packed "brick-in-a-wall" surface fractal aggregates may well be the key precursor step in the formation of several types of mosaic- and meso-crystals.

  19. Determinants of gait stability while walking on a treadmill: A machine learning approach.

    PubMed

    Reynard, Fabienne; Terrier, Philippe

    2017-12-08

    Dynamic balance in human locomotion can be assessed through the local dynamic stability (LDS) method. Whereas gait LDS has been used successfully in many settings and applications, little is known about its sensitivity to individual characteristics of healthy adults. Therefore, we reanalyzed a large dataset of accelerometric data measured for 100 healthy adults from 20 to 70 years of age performing 10 min treadmill walking. We sought to assess the extent to which the variations of age, body mass and height, sex, and preferred walking speed (PWS) could influence gait LDS. The random forest (RF) and multiple adaptive regression splines (MARS) algorithms were selected for their good bias-variance tradeoff and their capabilities to handle nonlinear associations. First, through variable importance measure (VIM), we used RF to evaluate which individual characteristics had the highest influence on gait LDS. Second, we used MARS to detect potential interactions among individual characteristics that may influence LDS. The VIM and MARS results indicated that PWS and age correlated with LDS, whereas no associations were found for sex, body height, and body mass. Further, the MARS model detected an age by PWS interaction: on one hand, at high PWS, gait stability is constant across age while, on the other hand, at low PWS, gait instability increases substantially with age. We conclude that it is advisable to consider the participants' age as well as their PWS to avoid potential biases in evaluating dynamic balance through LDS. Copyright © 2017 Elsevier Ltd. All rights reserved.

  20. Application to recognition of ferrography image with fractal neural network

    NASA Astrophysics Data System (ADS)

    Tian, Xianzhong; Hu, Tongsen; Zhang, Jian

    2005-10-01

    Because wear particles have fractal characteristics, it is necessary that adding fractal parameters to studying wear particles and diagnosing machine troubles. This paper discusses fractal parameters of wear particles, presents arithmetic calculating fractal dimension, and constructs a fractal neural network which can recognize wear particles image. It is proved by experiments that this fractal neural network can recognize some characteristics of wear particles image, and can also classify wear types.

  1. Fractal characterization of fracture surfaces in concrete

    USGS Publications Warehouse

    Saouma, V.E.; Barton, C.C.; Gamaleldin, N.A.

    1990-01-01

    Fractal geometry is used to characterize the roughness of cracked concrete surfaces through a specially built profilometer, and the fractal dimension is subsequently correlated to the fracture toughness and direction of crack propagation. Preliminary results indicate that the fracture surface is indeed fractal over two orders of magnitudes with a dimension of approximately 1.20. ?? 1990.

  2. Identification of mouse gaits using a novel force-sensing exercise wheel.

    PubMed

    Smith, Benjamin J H; Cullingford, Lottie; Usherwood, James R

    2015-09-15

    The gaits that animals use can provide information on neurological and musculoskeletal disorders, as well as the biomechanics of locomotion. Mice are a common research model in many fields; however, there is no consensus in the literature on how (and if) mouse gaits vary with speed. One of the challenges in studying mouse gaits is that mice tend to run intermittently on treadmills or overground; this paper attempts to overcome this issue with a novel exercise wheel that measures vertical ground reaction forces. Unlike previous instrumented wheels, this wheel is able to measure forces continuously and can therefore record data from consecutive strides. By concatenating the maximum limb force at each time point, a force trace can be constructed to quantify and identify gaits. The wheel was three dimensionally printed, allowing the design to be shared with other researchers. The kinematic parameters measured by the wheel were evaluated using high-speed video. Gaits were classified using a metric called "3S" (stride signal symmetry), which quantifies the half wave symmetry of the force trace peaks. Although mice are capable of using both symmetric and asymmetric gaits throughout their speed range, the continuum of gaits can be divided into regions based on the frequency of symmetric and asymmetric gaits; these divisions are further supported by the fact that mice run less frequently at speeds near the boundaries between regions. The boundary speeds correspond to gait transition speeds predicted by the hypothesis that mice move in a dynamically similar fashion to other legged animals. Copyright © 2015 the American Physiological Society.

  3. Identification of mouse gaits using a novel force-sensing exercise wheel

    PubMed Central

    Cullingford, Lottie; Usherwood, James R.

    2015-01-01

    The gaits that animals use can provide information on neurological and musculoskeletal disorders, as well as the biomechanics of locomotion. Mice are a common research model in many fields; however, there is no consensus in the literature on how (and if) mouse gaits vary with speed. One of the challenges in studying mouse gaits is that mice tend to run intermittently on treadmills or overground; this paper attempts to overcome this issue with a novel exercise wheel that measures vertical ground reaction forces. Unlike previous instrumented wheels, this wheel is able to measure forces continuously and can therefore record data from consecutive strides. By concatenating the maximum limb force at each time point, a force trace can be constructed to quantify and identify gaits. The wheel was three dimensionally printed, allowing the design to be shared with other researchers. The kinematic parameters measured by the wheel were evaluated using high-speed video. Gaits were classified using a metric called “3S” (stride signal symmetry), which quantifies the half wave symmetry of the force trace peaks. Although mice are capable of using both symmetric and asymmetric gaits throughout their speed range, the continuum of gaits can be divided into regions based on the frequency of symmetric and asymmetric gaits; these divisions are further supported by the fact that mice run less frequently at speeds near the boundaries between regions. The boundary speeds correspond to gait transition speeds predicted by the hypothesis that mice move in a dynamically similar fashion to other legged animals. PMID:26139220

  4. Fractal Theory and Field Cover Experiments: Implications for the Fractal Characteristics and Radon Diffusion Behavior of Soils and Rocks.

    PubMed

    Tan, Wanyu; Li, Yongmei; Tan, Kaixuan; Duan, Xianzhe; Liu, Dong; Liu, Zehua

    2016-12-01

    Radon diffusion and transport through different media is a complex process affected by many factors. In this study, the fractal theories and field covering experiments were used to study the fractal characteristics of particle size distribution (PSD) of six kinds of geotechnical materials (e.g., waste rock, sand, laterite, kaolin, mixture of sand and laterite, and mixture of waste rock and laterite) and their effects on radon diffusion. In addition, the radon diffusion coefficient and diffusion length were calculated. Moreover, new formulas for estimating diffusion coefficient and diffusion length functional of fractal dimension d of PSD were proposed. These results demonstrate the following points: (1) the fractal dimension d of the PSD can be used to characterize the property of soils and rocks in the studies of radon diffusion behavior; (2) the diffusion coefficient and diffusion length decrease with increasing fractal dimension of PSD; and (3) the effectiveness of final covers in reducing radon exhalation of uranium tailings impoundments can be evaluated on the basis of the fractal dimension of PSD of materials.

  5. Variability of fractal dimension of solar radio flux

    NASA Astrophysics Data System (ADS)

    Bhatt, Hitaishi; Sharma, Som Kumar; Trivedi, Rupal; Vats, Hari Om

    2018-04-01

    In the present communication, the variation of the fractal dimension of solar radio flux is reported. Solar radio flux observations on a day to day basis at 410, 1415, 2695, 4995, and 8800 MHz are used in this study. The data were recorded at Learmonth Solar Observatory, Australia from 1988 to 2009 covering an epoch of two solar activity cycles (22 yr). The fractal dimension is calculated for the listed frequencies for this period. The fractal dimension, being a measure of randomness, represents variability of solar radio flux at shorter time-scales. The contour plot of fractal dimension on a grid of years versus radio frequency suggests high correlation with solar activity. Fractal dimension increases with increasing frequency suggests randomness increases towards the inner corona. This study also shows that the low frequency is more affected by solar activity (at low frequency fractal dimension difference between solar maximum and solar minimum is 0.42) whereas, the higher frequency is less affected by solar activity (here fractal dimension difference between solar maximum and solar minimum is 0.07). A good positive correlation is found between fractal dimension averaged over all frequencies and yearly averaged sunspot number (Pearson's coefficient is 0.87).

  6. Fractal fluctuations in gaze speed visual search.

    PubMed

    Stephen, Damian G; Anastas, Jason

    2011-04-01

    Visual search involves a subtle coordination of visual memory and lower-order perceptual mechanisms. Specifically, the fluctuations in gaze may provide support for visual search above and beyond what may be attributed to memory. Prior research indicates that gaze during search exhibits fractal fluctuations, which allow for a wide sampling of the field of view. Fractal fluctuations constitute a case of fast diffusion that may provide an advantage in exploration. We present reanalyses of eye-tracking data collected by Stephen and Mirman (Cognition, 115, 154-165, 2010) for single-feature and conjunction search tasks. Fluctuations in gaze during these search tasks were indeed fractal. Furthermore, the degree of fractality predicted decreases in reaction time on a trial-by-trial basis. We propose that fractality may play a key role in explaining the efficacy of perceptual exploration.

  7. Measuring Gait Quality in Parkinson’s Disease through Real-Time Gait Phase Recognition

    PubMed Central

    Mileti, Ilaria; Germanotta, Marco; Di Sipio, Enrica; Imbimbo, Isabella; Pacilli, Alessandra; Erra, Carmen; Petracca, Martina; Del Prete, Zaccaria; Bentivoglio, Anna Rita; Padua, Luca

    2018-01-01

    Monitoring gait quality in daily activities through wearable sensors has the potential to improve medical assessment in Parkinson’s Disease (PD). In this study, four gait partitioning methods, two based on thresholds and two based on a machine learning approach, considering the four-phase model, were compared. The methods were tested on 26 PD patients, both in OFF and ON levodopa conditions, and 11 healthy subjects, during walking tasks. All subjects were equipped with inertial sensors placed on feet. Force resistive sensors were used to assess reference time sequence of gait phases. Goodness Index (G) was evaluated to assess accuracy in gait phases estimation. A novel synthetic index called Gait Phase Quality Index (GPQI) was proposed for gait quality assessment. Results revealed optimum performance (G < 0.25) for three tested methods and good performance (0.25 < G < 0.70) for one threshold method. The GPQI resulted significantly higher in PD patients than in healthy subjects, showing a moderate correlation with clinical scales score. Furthermore, in patients with severe gait impairment, GPQI was found higher in OFF than in ON state. Our results unveil the possibility of monitoring gait quality in PD through real-time gait partitioning based on wearable sensors. PMID:29558410

  8. Gait Analysis Using Wearable Sensors

    PubMed Central

    Tao, Weijun; Liu, Tao; Zheng, Rencheng; Feng, Hutian

    2012-01-01

    Gait analysis using wearable sensors is an inexpensive, convenient, and efficient manner of providing useful information for multiple health-related applications. As a clinical tool applied in the rehabilitation and diagnosis of medical conditions and sport activities, gait analysis using wearable sensors shows great prospects. The current paper reviews available wearable sensors and ambulatory gait analysis methods based on the various wearable sensors. After an introduction of the gait phases, the principles and features of wearable sensors used in gait analysis are provided. The gait analysis methods based on wearable sensors is divided into gait kinematics, gait kinetics, and electromyography. Studies on the current methods are reviewed, and applications in sports, rehabilitation, and clinical diagnosis are summarized separately. With the development of sensor technology and the analysis method, gait analysis using wearable sensors is expected to play an increasingly important role in clinical applications. PMID:22438763

  9. Gait recognition based on Gabor wavelets and modified gait energy image for human identification

    NASA Astrophysics Data System (ADS)

    Huang, Deng-Yuan; Lin, Ta-Wei; Hu, Wu-Chih; Cheng, Chih-Hsiang

    2013-10-01

    This paper proposes a method for recognizing human identity using gait features based on Gabor wavelets and modified gait energy images (GEIs). Identity recognition by gait generally involves gait representation, extraction, and classification. In this work, a modified GEI convolved with an ensemble of Gabor wavelets is proposed as a gait feature. Principal component analysis is then used to project the Gabor-wavelet-based gait features into a lower-dimension feature space for subsequent classification. Finally, support vector machine classifiers based on a radial basis function kernel are trained and utilized to recognize human identity. The major contributions of this paper are as follows: (1) the consideration of the shadow effect to yield a more complete segmentation of gait silhouettes; (2) the utilization of motion estimation to track people when walkers overlap; and (3) the derivation of modified GEIs to extract more useful gait information. Extensive performance evaluation shows a great improvement of recognition accuracy due to the use of shadow removal, motion estimation, and gait representation using the modified GEIs and Gabor wavelets.

  10. Biomechanics of normal and pathological gait: implications for understanding human locomotor control.

    PubMed

    Winter, D A

    1989-12-01

    The biomechanical (kinetic) analysis of human gait reveals the integrated and detailed motor patterns that are essential in pinpointing the abnormal patterns in pathological gait. In a similar manner, these motor patterns (moments, powers, and EMGs) can be used to identify synergies and to validate theories of CNS control. Based on kinetic and EMG patterns for a wide range of normal subjects and cadences, evidence is presented that both supports and negates the central pattern generator theory of locomotion. Adaptive motor patterns that are evident in peripheral gait pathologies reinforce a strong peripheral rather than a central control. Finally, a three-component subtask theory of human gait is presented and is supported by reference to the motor patterns seen in a normal gait. The identified subtasks are (a) support (against collapse during stance); (b) dynamic balance of the upper body, also during stance; and (c) feedforward control of the foot trajectory to achieve safe ground clearance and a gentle heel contact.

  11. Is Fractal 1/f Scaling in Stream Chemistry Universal?

    NASA Astrophysics Data System (ADS)

    Hrachowitz, M.

    2016-12-01

    Stream water chemistry data from catchments worldwide suggest that catchments act as filters that transform white noise, i.e. random input signals such as in precipitation, into 1/fαnoise whose slope in a power spectrum typically ranges between -0.5>α> -1.5. This previously lead to the hypothesis that catchments act as fractal filters, i.e. a slope of α=-1 may be a universal and intrinsic property of catchments. That would have considerable implications on the predictability of stream water chemistry, as both, temporal short- and long-range interdependence control the system response. While short memories and thus flatter slopes with α closer to 0 indicate poor short term but good long-term predictability, steeper slopes (α <<-1) indicate the opposite. In fractal systems, i.e. α=-1, this therefore leads to inherent problems of predicting both, short and long-term response patterns. The hypothesis of catchments acting as fractal filters remains to be tested more profoundly. It is not yet clear, if observed inter-catchment variations in α need to be interpreted as noise in the signal or if the variations underlie a systematic pattern and can be explained by some characteristic of catchment function. Here we will test the hypothesis that the spectral slope of stream water chemistry is not necessarily α=-1 and that catchments therefore do not inherently act as fractal filters. Further, it will be tested if closer links between the variations in spectral slope and hydrological function of catchments can be identified. The combined data-analysis and modelling study uses hydrochemical data (i.e. Cl-) from a wide range of catchments worldwide. The study catchments are physically contrasting, from distinct climate zones, and with distinct landscapes and vegetation. To identify patterns in the variations of α, firstly the power spectra of observed stream chemistry are compared with physical catchment characteristics using methods such as cluster analysis. In a

  12. Muscle Activation during Gait in Children with Duchenne Muscular Dystrophy.

    PubMed

    Ropars, Juliette; Lempereur, Mathieu; Vuillerot, Carole; Tiffreau, Vincent; Peudenier, Sylviane; Cuisset, Jean-Marie; Pereon, Yann; Leboeuf, Fabien; Delporte, Ludovic; Delpierre, Yannick; Gross, Raphaël; Brochard, Sylvain

    2016-01-01

    The aim of this prospective study was to investigate changes in muscle activity during gait in children with Duchenne muscular Dystrophy (DMD). Dynamic surface electromyography recordings (EMGs) of 16 children with DMD and pathological gait were compared with those of 15 control children. The activity of the rectus femoris (RF), vastus lateralis (VL), medial hamstrings (HS), tibialis anterior (TA) and gastrocnemius soleus (GAS) muscles was recorded and analysed quantitatively and qualitatively. The overall muscle activity in the children with DMD was significantly different from that of the control group. Percentage activation amplitudes of RF, HS and TA were greater throughout the gait cycle in the children with DMD and the timing of GAS activity differed from the control children. Significantly greater muscle coactivation was found in the children with DMD. There were no significant differences between sides. Since the motor command is normal in DMD, the hyper-activity and co-contractions likely compensate for gait instability and muscle weakness, however may have negative consequences on the muscles and may increase the energy cost of gait. Simple rehabilitative strategies such as targeted physical therapies may improve stability and thus the pattern of muscle activity.

  13. Verifying the Dependence of Fractal Coefficients on Different Spatial Distributions

    NASA Astrophysics Data System (ADS)

    Gospodinov, Dragomir; Marekova, Elisaveta; Marinov, Alexander

    2010-01-01

    A fractal distribution requires that the number of objects larger than a specific size r has a power-law dependence on the size N(r) = C/rD∝r-D where D is the fractal dimension. Usually the correlation integral is calculated to estimate the correlation fractal dimension of epicentres. A `box-counting' procedure could also be applied giving the `capacity' fractal dimension. The fractal dimension can be an integer and then it is equivalent to a Euclidean dimension (it is zero of a point, one of a segment, of a square is two and of a cube is three). In general the fractal dimension is not an integer but a fractional dimension and there comes the origin of the term `fractal'. The use of a power-law to statistically describe a set of events or phenomena reveals the lack of a characteristic length scale, that is fractal objects are scale invariant. Scaling invariance and chaotic behavior constitute the base of a lot of natural hazards phenomena. Many studies of earthquakes reveal that their occurrence exhibits scale-invariant properties, so the fractal dimension can characterize them. It has first been confirmed that both aftershock rate decay in time and earthquake size distribution follow a power law. Recently many other earthquake distributions have been found to be scale-invariant. The spatial distribution of both regional seismicity and aftershocks show some fractal features. Earthquake spatial distributions are considered fractal, but indirectly. There are two possible models, which result in fractal earthquake distributions. The first model considers that a fractal distribution of faults leads to a fractal distribution of earthquakes, because each earthquake is characteristic of the fault on which it occurs. The second assumes that each fault has a fractal distribution of earthquakes. Observations strongly favour the first hypothesis. The fractal coefficients analysis provides some important advantages in examining earthquake spatial distribution, which are

  14. Hardware Development and Locomotion Control Strategy for an Over-Ground Gait Trainer: NaTUre-Gaits.

    PubMed

    Luu, Trieu Phat; Low, Kin Huat; Qu, Xingda; Lim, Hup Boon; Hoon, Kay Hiang

    2014-01-01

    Therapist-assisted body weight supported (TABWS) gait rehabilitation was introduced two decades ago. The benefit of TABWS in functional recovery of walking in spinal cord injury and stroke patients has been demonstrated and reported. However, shortage of therapists, labor-intensiveness, and short duration of training are some limitations of this approach. To overcome these deficiencies, robotic-assisted gait rehabilitation systems have been suggested. These systems have gained attentions from researchers and clinical practitioner in recent years. To achieve the same objective, an over-ground gait rehabilitation system, NaTUre-gaits, was developed at the Nanyang Technological University. The design was based on a clinical approach to provide four main features, which are pelvic motion, body weight support, over-ground walking experience, and lower limb assistance. These features can be achieved by three main modules of NaTUre-gaits: 1) pelvic assistance mechanism, mobile platform, and robotic orthosis. Predefined gait patterns are required for a robotic assisted system to follow. In this paper, the gait pattern planning for NaTUre-gaits was accomplished by an individual-specific gait pattern prediction model. The model generates gait patterns that resemble natural gait patterns of the targeted subjects. The features of NaTUre-gaits have been demonstrated by walking trials with several subjects. The trials have been evaluated by therapists and doctors. The results show that 10-m walking trial with a reduction in manpower. The task-specific repetitive training approach and natural walking gait patterns were also successfully achieved.

  15. Multilayer Joint Gait-Pose Manifolds for Human Gait Motion Modeling.

    PubMed

    Ding, Meng; Fan, Guolian

    2015-11-01

    We present new multilayer joint gait-pose manifolds (multilayer JGPMs) for complex human gait motion modeling, where three latent variables are defined jointly in a low-dimensional manifold to represent a variety of body configurations. Specifically, the pose variable (along the pose manifold) denotes a specific stage in a walking cycle; the gait variable (along the gait manifold) represents different walking styles; and the linear scale variable characterizes the maximum stride in a walking cycle. We discuss two kinds of topological priors for coupling the pose and gait manifolds, i.e., cylindrical and toroidal, to examine their effectiveness and suitability for motion modeling. We resort to a topologically-constrained Gaussian process (GP) latent variable model to learn the multilayer JGPMs where two new techniques are introduced to facilitate model learning under limited training data. First is training data diversification that creates a set of simulated motion data with different strides. Second is the topology-aware local learning to speed up model learning by taking advantage of the local topological structure. The experimental results on the Carnegie Mellon University motion capture data demonstrate the advantages of our proposed multilayer models over several existing GP-based motion models in terms of the overall performance of human gait motion modeling.

  16. a Fractal Network Model for Fractured Porous Media

    NASA Astrophysics Data System (ADS)

    Xu, Peng; Li, Cuihong; Qiu, Shuxia; Sasmito, Agus Pulung

    2016-04-01

    The transport properties and mechanisms of fractured porous media are very important for oil and gas reservoir engineering, hydraulics, environmental science, chemical engineering, etc. In this paper, a fractal dual-porosity model is developed to estimate the equivalent hydraulic properties of fractured porous media, where a fractal tree-like network model is used to characterize the fracture system according to its fractal scaling laws and topological structures. The analytical expressions for the effective permeability of fracture system and fractured porous media, tortuosity, fracture density and fraction are derived. The proposed fractal model has been validated by comparisons with available experimental data and numerical simulation. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. The effective permeability of fracture system can be increased with the increase of fractal dimensions for fracture length and aperture, while it can be remarkably lowered by introducing tortuosity at large branching angle. Also, a scaling law between the fracture density and fractal dimension for fracture length has been found, where the scaling exponent depends on the fracture number. The present fractal dual-porosity model may shed light on the transport physics of fractured porous media and provide theoretical basis for oil and gas exploitation, underground water, nuclear waste disposal and geothermal energy extraction as well as chemical engineering, etc.

  17. The fractal nature of vacuum arc cathode spots

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Anders, Andre

    2005-05-27

    Cathode spot phenomena show many features of fractals, for example self-similar patterns in the emitted light and arc erosion traces. Although there have been hints on the fractal nature of cathode spots in the literature, the fractal approach to spot interpretation is underutilized. In this work, a brief review of spot properties is given, touching the differences between spot type 1 (on cathodes surfaces with dielectric layers) and spot type 2 (on metallic, clean surfaces) as well as the known spot fragment or cell structure. The basic properties of self-similarity, power laws, random colored noise, and fractals are introduced. Severalmore » points of evidence for the fractal nature of spots are provided. Specifically power laws are identified as signature of fractal properties, such as spectral power of noisy arc parameters (ion current, arc voltage, etc) obtained by fast Fourier transform. It is shown that fractal properties can be observed down to the cutoff by measurement resolution or occurrence of elementary steps in physical processes. Random walk models of cathode spot motion are well established: they go asymptotically to Brownian motion for infinitesimal step width. The power spectrum of the arc voltage noise falls as 1/f {sup 2}, where f is frequency, supporting a fractal spot model associated with Brownian motion.« less

  18. The Effect of Underwater Gait Training on Balance Ability of Stroke Patients

    PubMed Central

    Park, Seok Woo; Lee, Kyoung Jin; Shin, Doo Chul; Shin, Seung Ho; Lee, Myung Mo; Song, Chang Ho

    2014-01-01

    [Purpose] The purpose of this study was to investigate the effects of underwater treadmill gait training on the balance ability of stroke patients. [Subjects] Twenty-two patients with stroke were randomly assigned to an underwater treadmill group (n =11) or a control group (n =11). [Methods] Both groups received general rehabilitation for 30 min per session, 5 times per week, over a 4-week period. The underwater treadmill group received additional underwater gait training for 30 min per session, 5 times per week, over the same 4-week period. Static and dynamic balances were evaluated before and after the intervention. [Results] The means of static and dynamic balance ability increased significantly in both groups, but there was no significant difference between the two groups. [Conclusion] Compared to the general rehabilitation program, underwater treadmill gait training was not more effective at improving the balance ability of stroke patients than land-based training. PMID:25013292

  19. Gait-Event-Based Synchronization Method for Gait Rehabilitation Robots via a Bioinspired Adaptive Oscillator.

    PubMed

    Chen, Gong; Qi, Peng; Guo, Zhao; Yu, Haoyong

    2017-06-01

    In the field of gait rehabilitation robotics, achieving human-robot synchronization is very important. In this paper, a novel human-robot synchronization method using gait event information is proposed. This method includes two steps. First, seven gait events in one gait cycle are detected in real time with a hidden Markov model; second, an adaptive oscillator is utilized to estimate the stride percentage of human gait using any one of the gait events. Synchronous reference trajectories for the robot are then generated with the estimated stride percentage. This method is based on a bioinspired adaptive oscillator, which is a mathematical tool, first proposed to explain the phenomenon of synchronous flashing among fireflies. The proposed synchronization method is implemented in a portable knee-ankle-foot robot and tested in 15 healthy subjects. This method has the advantages of simple structure, flexible selection of gait events, and fast adaptation. Gait event is the only information needed, and hence the performance of synchronization holds when an abnormal gait pattern is involved. The results of the experiments reveal that our approach is efficient in achieving human-robot synchronization and feasible for rehabilitation robotics application.

  20. Hardware Development and Locomotion Control Strategy for an Over-Ground Gait Trainer: NaTUre-Gaits

    PubMed Central

    Low, Kin Huat; Qu, Xingda; Lim, Hup Boon; Hoon, Kay Hiang

    2014-01-01

    Therapist-assisted body weight supported (TABWS) gait rehabilitation was introduced two decades ago. The benefit of TABWS in functional recovery of walking in spinal cord injury and stroke patients has been demonstrated and reported. However, shortage of therapists, labor-intensiveness, and short duration of training are some limitations of this approach. To overcome these deficiencies, robotic-assisted gait rehabilitation systems have been suggested. These systems have gained attentions from researchers and clinical practitioner in recent years. To achieve the same objective, an over-ground gait rehabilitation system, NaTUre-gaits, was developed at the Nanyang Technological University. The design was based on a clinical approach to provide four main features, which are pelvic motion, body weight support, over-ground walking experience, and lower limb assistance. These features can be achieved by three main modules of NaTUre-gaits: 1) pelvic assistance mechanism, mobile platform, and robotic orthosis. Predefined gait patterns are required for a robotic assisted system to follow. In this paper, the gait pattern planning for NaTUre-gaits was accomplished by an individual-specific gait pattern prediction model. The model generates gait patterns that resemble natural gait patterns of the targeted subjects. The features of NaTUre-gaits have been demonstrated by walking trials with several subjects. The trials have been evaluated by therapists and doctors. The results show that 10-m walking trial with a reduction in manpower. The task-specific repetitive training approach and natural walking gait patterns were also successfully achieved. PMID:27170876

  1. Disturbances of automatic gait control mechanisms in higher level gait disorder.

    PubMed

    Danoudis, Mary; Ganesvaran, Ganga; Iansek, Robert

    2016-07-01

    The underlying mechanisms responsible for the gait changes in frontal gait disorder (FGD), a form of higher level gait disorders, are poorly understood. We investigated the relationship between stride length and cadence (SLCrel) in people with FGD (n=15) in comparison to healthy older adults (n=21) to improve our understanding of the changes to gait in FGD. Gait data was captured using an electronic walkway system as participants walked at five self-selected speed conditions: preferred, very slow, slow, fast and very fast. Linear regression was used to determine the strength of the relationship (R(2)), slope and intercept. In the FGD group 9 participants had a strong SLCrel (linear group) (R(2)>0.8) and 6 a weak relationship (R(2)<0.8) (nonlinear group). The linear FGD group did not differ to healthy control for slope (p>0.05) but did have a lower intercept (p<0.001). The linear FGD group modulated gait speed by adjusting stride length and cadence similar to controls whereas the nonlinear FGD participants adjusted stride length but not cadence similar to controls. The non-linear FGD group had greater disturbance to their gait, poorer postural control and greater fear of falling compared to the linear FGD group. Investigation of the SLCrel resulted in new insights into the underlying mechanisms responsible for the gait changes found in FGD. The findings suggest stride length regulation was disrupted in milder FGD but as the disorder worsened, cadence control also became disordered resulting in a break down in the relationship between stride length and cadence. Copyright © 2016 Elsevier B.V. All rights reserved.

  2. Scaling of avian bipedal locomotion reveals independent effects of body mass and leg posture on gait.

    PubMed

    Daley, Monica A; Birn-Jeffery, Aleksandra

    2018-05-22

    Birds provide an interesting opportunity to study the relationships between body size, limb morphology and bipedal locomotor function. Birds are ecologically diverse and span a large range of body size and limb proportions, yet all use their hindlimbs for bipedal terrestrial locomotion, for at least some part of their life history. Here, we review the scaling of avian striding bipedal gaits to explore how body mass and leg morphology influence walking and running. We collate literature data from 21 species, spanning a 2500× range in body mass from painted quail to ostriches. Using dynamic similarity theory to interpret scaling trends, we find evidence for independent effects of body mass, leg length and leg posture on gait. We find no evidence for scaling of duty factor with body size, suggesting that vertical forces scale with dynamic similarity. However, at dynamically similar speeds, large birds use relatively shorter stride lengths and higher stride frequencies compared with small birds. We also find that birds with long legs for their mass, such as the white stork and red-legged seriema, use longer strides and lower swing frequencies, consistent with the influence of high limb inertia on gait. We discuss the observed scaling of avian bipedal gait in relation to mechanical demands for force, work and power relative to muscle actuator capacity, muscle activation costs related to leg cycling frequency, and considerations of stability and agility. Many opportunities remain for future work to investigate how morphology influences gait dynamics among birds specialized for different habitats and locomotor behaviors. © 2018. Published by The Company of Biologists Ltd.

  3. GENERATING FRACTAL PATTERNS BY USING p-CIRCLE INVERSION

    NASA Astrophysics Data System (ADS)

    Ramírez, José L.; Rubiano, Gustavo N.; Zlobec, Borut Jurčič

    2015-10-01

    In this paper, we introduce the p-circle inversion which generalizes the classical inversion with respect to a circle (p = 2) and the taxicab inversion (p = 1). We study some basic properties and we also show the inversive images of some basic curves. We apply this new transformation to well-known fractals such as Sierpinski triangle, Koch curve, dragon curve, Fibonacci fractal, among others. Then we obtain new fractal patterns. Moreover, we generalize the method called circle inversion fractal be means of the p-circle inversion.

  4. Experimental investigation of the flow field and power consumption characteristics of regular and fractal blade impellers in a dynamic mixer

    NASA Astrophysics Data System (ADS)

    Steiros, K.; Bruce, P. J. K.; Buxton, O. R. H.; Vassilicos, J. C.

    2015-11-01

    Experiments have been performed in an octagonal un-baffled water tank, stirred by three radial turbines with different geometry impellers: (1) regular rectangular blades; (2) single-iteration fractal blades; (3) two-iteration fractal blades. Shaft torque was monitored and the power number calculated for each case. Both impellers with fractal geometry blades exhibited a decrease of turbine power number compared to the regular one (15% decrease for single-iteration and 19% for two iterations). Phase locked PIV in the discharge region of the blades revealed that the vortices emanating from the regular blades are more coherent, have higher kinetic energy, and advect faster towards the tank's walls where they are dissipated, compared to their fractal counterparts. This suggests a strong link between vortex production and behaviour and the energy input for the different impellers. Planar PIV measurements in the bulk of the tank showed an increase of turbulence intensity of over 20% for the fractal geometry blades, suggesting higher mixing efficiency. Experiments with pressure measurements on the different geometry blade surfaces are ongoing to investigate the distribution of forces, and calculate hydrodynamic centres of pressure. The authors would like to acknowledge the financial support given by European Union FP7 Marie Curie MULTISOLVE project (Grant Agreement No. 317269).

  5. Objective Biomarkers of Balance and Gait for Parkinson’s Disease using Body-worn Sensors

    PubMed Central

    Horak, Fay B; Mancini, Martina

    2014-01-01

    Balance and gait impairments characterize progression of Parkinson’s disease (PD), predict fall risk, and are important contributors to reduced quality of life. Advances in technology of small, body-worn inertial sensors have made it possible to develop quick, objective measures of balance and gait impairments in the clinic for research trials and clinical practice. Objective balance and gait metrics may eventually provide useful biomarkers for PD. In fact, objective balance and gait measures are already being used as surrogate end-points for demonstrating clinical efficacy of new treatments, in place of counting falls from diaries, using stop-watch measures of gait speed, or clinical balance rating scales. This review summarizes the types of objective measures available from body-worn sensors. We organize the metrics based on the neural control system for mobility affected by PD: postural stability in stance, postural responses, gait initiation, gait (temporal-spatial lower and upper body coordination and dynamic equilibrium), postural transitions, and freezing of gait. However, the explosion of metrics derived by wearable sensors during prescribed balance and gait tasks that are abnormal in people with PD do not yet qualify as behavioral biomarkers because many balance and gait impairments observed in PD are not specific to the disease, nor shown to be related to specific pathophysiologic biomarkers. In the future, the most useful balance and gait biomarkers for PD will be those that are sensitive and specific for early PD and related to the underlying disease process. PMID:24132842

  6. Evidence of end-effector based gait machines in gait rehabilitation after CNS lesion.

    PubMed

    Hesse, S; Schattat, N; Mehrholz, J; Werner, C

    2013-01-01

    A task-specific repetitive approach in gait rehabilitation after CNS lesion is well accepted nowadays. To ease the therapists' and patients' physical effort, the past two decades have seen the introduction of gait machines to intensify the amount of gait practice. Two principles have emerged, an exoskeleton- and an endeffector-based approach. Both systems share the harness and the body weight support. With the end-effector-based devices, the patients' feet are positioned on two foot plates, whose movements simulate stance and swing phase. This article provides an overview on the end-effector based machine's effectiveness regarding the restoration of gait. For the electromechanical gait trainer GT I, a meta analysis identified nine controlled trials (RCT) in stroke subjects (n = 568) and were analyzed to detect differences between end-effector-based locomotion + physiotherapy and physiotherapy alone. Patients practising with the machine effected in a superior gait ability (210 out of 319 patients, 65.8% vs. 96 out of 249 patients, 38.6%, respectively, Z = 2.29, p = 0.020), due to a larger training intensity. Only single RCTs have been reported for other devices and etiologies. The introduction of end-effector based gait machines has opened a new succesful chapter in gait rehabilitation after CNS lesion.

  7. Electro-chemical manifestation of nanoplasmonics in fractal media

    NASA Astrophysics Data System (ADS)

    Baskin, Emmanuel; Iomin, Alexander

    2013-06-01

    Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integrodifferentiation. The photoconductivity in the vicinity of the electrode-electrolyte fractal interface is studied. The methods of fractional calculus are employed to obtain an analytical expression for the giant local enhancement of the optical electric field inside the fractal composite structure at the condition of the surface plasmon excitation. This approach makes it possible to explain experimental data on photoconductivity in the nano-electrochemistry.

  8. FAST TRACK COMMUNICATION: Weyl law for fat fractals

    NASA Astrophysics Data System (ADS)

    Spina, María E.; García-Mata, Ignacio; Saraceno, Marcos

    2010-10-01

    It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.

  9. Effective degrees of freedom of a random walk on a fractal.

    PubMed

    Balankin, Alexander S

    2015-12-01

    We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν-dimensional space F(ν) equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν) and fractal dimensionalities is deduced. The intrinsic time of random walk in F(ν) is inferred. The Laplacian operator in F(ν) is constructed. This allows us to map physical problems on fractals into the corresponding problems in F(ν). In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

  10. Effective degrees of freedom of a random walk on a fractal

    NASA Astrophysics Data System (ADS)

    Balankin, Alexander S.

    2015-12-01

    We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

  11. The development and validity of the Salford Gait Tool: an observation-based clinical gait assessment tool.

    PubMed

    Toro, Brigitte; Nester, Christopher J; Farren, Pauline C

    2007-03-01

    To develop the construct, content, and criterion validity of the Salford Gait Tool (SF-GT) and to evaluate agreement between gait observations using the SF-GT and kinematic gait data. Tool development and comparative evaluation. University in the United Kingdom. For designing construct and content validity, convenience samples of 10 children with hemiplegic, diplegic, and quadriplegic cerebral palsy (CP) and 152 physical therapy students and 4 physical therapists were recruited. For developing criterion validity, kinematic gait data of 13 gait clusters containing 56 children with hemiplegic, diplegic, and quadriplegic CP and 11 neurologically intact children was used. For clinical evaluation, a convenience sample of 23 pediatric physical therapists participated. We developed a sagittal plane observational gait assessment tool through a series of design, test, and redesign iterations. The tool's grading system was calibrated using kinematic gait data of 13 gait clusters and was evaluated by comparing the agreement of gait observations using the SF-GT with kinematic gait data. Criterion standard kinematic gait data. There was 58% mean agreement based on grading categories and 80% mean agreement based on degree estimations evaluated with the least significant difference method. The new SF-GT has good concurrent criterion validity.

  12. Self-Similarity of Plasmon Edge Modes on Koch Fractal Antennas.

    PubMed

    Bellido, Edson P; Bernasconi, Gabriel D; Rossouw, David; Butet, Jérémy; Martin, Olivier J F; Botton, Gianluigi A

    2017-11-28

    We investigate the plasmonic behavior of Koch snowflake fractal geometries and their possible application as broadband optical antennas. Lithographically defined planar silver Koch fractal antennas were fabricated and characterized with high spatial and spectral resolution using electron energy loss spectroscopy. The experimental data are supported by numerical calculations carried out with a surface integral equation method. Multiple surface plasmon edge modes supported by the fractal structures have been imaged and analyzed. Furthermore, by isolating and reproducing self-similar features in long silver strip antennas, the edge modes present in the Koch snowflake fractals are identified. We demonstrate that the fractal response can be obtained by the sum of basic self-similar segments called characteristic edge units. Interestingly, the plasmon edge modes follow a fractal-scaling rule that depends on these self-similar segments formed in the structure after a fractal iteration. As the size of a fractal structure is reduced, coupling of the modes in the characteristic edge units becomes relevant, and the symmetry of the fractal affects the formation of hybrid modes. This analysis can be utilized not only to understand the edge modes in other planar structures but also in the design and fabrication of fractal structures for nanophotonic applications.

  13. Fractal dust constrains the collisional history of comets

    NASA Astrophysics Data System (ADS)

    Fulle, M.; Blum, J.

    2017-07-01

    The fractal dust particles observed by Rosetta cannot form in the physical conditions observed today in comet 67P/Churyumov-Gerasimenko (67P hereinafter), being instead consistent with models of the pristine dust aggregates coagulated in the solar nebula. Since bouncing collisions in the protoplanetary disc restructure fractals into compact aggregates (pebbles), the only way to preserve fractals in a comet is the gentle gravitational collapse of a mixture of pebbles and fractals, which must occur before their mutual collision speeds overcome ≈1 m s-1. This condition fixes the pebble radius to ≲1 cm, as confirmed by Comet Nucleus Infrared and Visible Analyser onboard Philae. Here, we show that the flux of fractal particles measured by Rosetta constrains the 67P nucleus in a random packing of cm-sized pebbles, with all the voids among them filled by fractal particles. This structure is inconsistent with any catastrophic collision, which would have compacted or dispersed most fractals, thus leaving empty most voids in the reassembled nucleus. Comets are less numerous than current estimates, as confirmed by lacking small craters on Pluto and Charon. Bilobate comets accreted at speeds <1 m s-1 from cometesimals born in the same disc stream.

  14. Single-task and dual-task tandem gait test performance after concussion.

    PubMed

    Howell, David R; Osternig, Louis R; Chou, Li-Shan

    2017-07-01

    To compare single-task and dual-task tandem gait test performance between athletes after concussion with controls on observer-timed, spatio-temporal, and center-of-mass (COM) balance control measurements. Ten participants (19.0±5.5years) were prospectively identified and completed a tandem gait test protocol within 72h of concussion and again 1 week, 2 weeks, 1 month, and 2 months post-injury. Seven uninjured controls (20.0±4.5years) completed the same protocol in similar time increments. Tandem gait test trials were performed with (dual-task) and without (single-task) concurrently performing a cognitive test as whole-body motion analysis was performed. Outcome variables included test completion time, average tandem gait velocity, cadence, and whole-body COM frontal plane displacement. Concussion participants took significantly longer to complete the dual-task tandem gait test than controls throughout the first 2 weeks post-injury (mean time=16.4 [95% CI: 13.4-19.4] vs. 10.1 [95% CI: 6.4-13.7] seconds; p=0.03). Single-task tandem gait times were significantly lower 72h post-injury (p=0.04). Dual-task cadence was significantly lower for concussion participants than controls (89.5 [95% CI: 68.6-110.4] vs. 127.0 [95% CI: 97.4-156.6] steps/minute; p=0.04). Moderately-high to high correlations between tandem gait test time and whole-body COM medial-lateral displacement were detected at each time point during dual-task gait (r s =0.70-0.93; p=0.03-0.001). Adding a cognitive task during the tandem gait test resulted in longer detectable deficits post-concussion compared to the traditional single-task tandem gait test. As a clinical tool to assess dynamic motor function, tandem gait may assist with return to sport decisions after concussion. Copyright © 2017 Sports Medicine Australia. Published by Elsevier Ltd. All rights reserved.

  15. Perceptual and Physiological Responses to Jackson Pollock's Fractals

    PubMed Central

    Taylor, Richard P.; Spehar, Branka; Van Donkelaar, Paul; Hagerhall, Caroline M.

    2011-01-01

    Fractals have been very successful in quantifying the visual complexity exhibited by many natural patterns, and have captured the imagination of scientists and artists alike. Our research has shown that the poured patterns of the American abstract painter Jackson Pollock are also fractal. This discovery raises an intriguing possibility – are the visual characteristics of fractals responsible for the long-term appeal of Pollock's work? To address this question, we have conducted 10 years of scientific investigation of human response to fractals and here we present, for the first time, a review of this research that examines the inter-relationship between the various results. The investigations include eye tracking, visual preference, skin conductance, and EEG measurement techniques. We discuss the artistic implications of the positive perceptual and physiological responses to fractal patterns. PMID:21734876

  16. A Fractal Dimension Survey of Active Region Complexity

    NASA Technical Reports Server (NTRS)

    McAteer, R. T. James; Gallagher, Peter; Ireland, Jack

    2005-01-01

    A new approach to quantifying the magnetic complexity of active regions using a fractal dimension measure is presented. This fully-automated approach uses full disc MDI magnetograms of active regions from a large data set (2742 days of the SoHO mission; 9342 active regions) to compare the calculated fractal dimension to both Mount Wilson classification and flare rate. The main Mount Wilson classes exhibit no distinct fractal dimension distribution, suggesting a self-similar nature of all active regions. Solar flare productivity exhibits an increase in both the frequency and GOES X-ray magnitude of flares from regions with higher fractal dimensions. Specifically a lower threshold fractal dimension of 1.2 and 1.25 exists as a necessary, but not sufficient, requirement for an active region to produce M- and X-class flares respectively .

  17. Approach for gait analysis in persons with limb loss including residuum and prosthesis socket dynamics.

    PubMed

    LaPrè, A K; Price, M A; Wedge, R D; Umberger, B R; Sup, Frank C

    2018-04-01

    Musculoskeletal modeling and marker-based motion capture techniques are commonly used to quantify the motions of body segments, and the forces acting on them during human gait. However, when these techniques are applied to analyze the gait of people with lower limb loss, the clinically relevant interaction between the residual limb and prosthesis socket is typically overlooked. It is known that there is considerable motion and loading at the residuum-socket interface, yet traditional gait analysis techniques do not account for these factors due to the inability to place tracking markers on the residual limb inside of the socket. In the present work, we used a global optimization technique and anatomical constraints to estimate the motion and loading at the residuum-socket interface as part of standard gait analysis procedures. We systematically evaluated a range of parameters related to the residuum-socket interface, such as the number of degrees of freedom, and determined the configuration that yields the best compromise between faithfully tracking experimental marker positions while yielding anatomically realistic residuum-socket kinematics and loads that agree with data from the literature. Application of the present model to gait analysis for people with lower limb loss will deepen our understanding of the biomechanics of walking with a prosthesis, which should facilitate the development of enhanced rehabilitation protocols and improved assistive devices. Copyright © 2017 John Wiley & Sons, Ltd.

  18. A mechanized gait trainer for restoring gait in nonambulatory subjects.

    PubMed

    Hesse, S; Uhlenbrock, D; Werner, C; Bardeleben, A

    2000-09-01

    To construct an advanced mechanized gait trainer to enable patients the repetitive practice of a gaitlike movement without overstraining therapists. DEVICE: Prototype gait trainer that simulates the phases of gait (by generating a ratio of 40% to 60% between swing and stance phases), supports the subjects according to their ability (lifts the foot during swing phase), and controls the center of mass in the vertical and horizontal directions. Two nonambulatory, hemiparetic patients who regained their walking ability after 4 weeks of daily training on the gait trainer, a 55-year-old woman and a 62-year-old man, both of whom had a first-time ischemic stroke. Four weeks of training, five times a week, each session 20 minutes long. Functional ambulation category (FAC, levels 0-5) to assess gait ability and ground level walking velocity. Rivermead motor assessment score (RMAS, 0-13) to assess gross motor function. Patient 1: At the end of treatment, she was able to walk independently on level ground with use of a walking stick. Her walking velocity had improved from .29m/sec to .59m/sec. Her RMAS score increased from 4 to 10, meaning she could walk at least 40 meters outside, pick up objects from floor, and climb stairs independently. Patient 2: At end of 4-week training, he could walk independently on even surfaces (FAC level 4), using an ankle-foot orthosis and a walking stick. His walking velocity improved from .14m/sec to .63m/sec. His RMAS increased from 3 to 10. The gait trainer enabled severely affected patients the repetitive practice of a gaitlike movement. Future studies may elucidate its value in gait rehabilitation of nonambulatory subjects.

  19. Balance control during gait initiation: State-of-the-art and research perspectives.

    PubMed

    Yiou, Eric; Caderby, Teddy; Delafontaine, Arnaud; Fourcade, Paul; Honeine, Jean-Louis

    2017-11-18

    It is well known that balance control is affected by aging, neurological and orthopedic conditions. Poor balance control during gait and postural maintenance are associated with disability, falls and increased mortality. Gait initiation - the transient period between the quiet standing posture and steady state walking - is a functional task that is classically used in the literature to investigate how the central nervous system (CNS) controls balance during a whole-body movement involving change in the base of support dimensions and center of mass progression. Understanding how the CNS in able-bodied subjects exerts this control during such a challenging task is a pre-requisite to identifying motor disorders in populations with specific impairments of the postural system. It may also provide clinicians with objective measures to assess the efficiency of rehabilitation programs and better target interventions according to individual impairments. The present review thus proposes a state-of-the-art analysis on: (1) the balance control mechanisms in play during gait initiation in able bodied subjects and in the case of some frail populations; and (2) the biomechanical parameters used in the literature to quantify dynamic stability during gait initiation. Balance control mechanisms reviewed in this article included anticipatory postural adjustments, stance leg stiffness, foot placement, lateral ankle strategy, swing foot strike pattern and vertical center of mass braking. Based on this review, the following viewpoints were put forward: (1) dynamic stability during gait initiation may share a principle of homeostatic regulation similar to most physiological variables, where separate mechanisms need to be coordinated to ensure stabilization of vital variables, and consequently; and (2) rehabilitation interventions which focus on separate or isolated components of posture, balance, or gait may limit the effectiveness of current clinical practices.

  20. Balance control during gait initiation: State-of-the-art and research perspectives

    PubMed Central

    Yiou, Eric; Caderby, Teddy; Delafontaine, Arnaud; Fourcade, Paul; Honeine, Jean-Louis

    2017-01-01

    It is well known that balance control is affected by aging, neurological and orthopedic conditions. Poor balance control during gait and postural maintenance are associated with disability, falls and increased mortality. Gait initiation - the transient period between the quiet standing posture and steady state walking - is a functional task that is classically used in the literature to investigate how the central nervous system (CNS) controls balance during a whole-body movement involving change in the base of support dimensions and center of mass progression. Understanding how the CNS in able-bodied subjects exerts this control during such a challenging task is a pre-requisite to identifying motor disorders in populations with specific impairments of the postural system. It may also provide clinicians with objective measures to assess the efficiency of rehabilitation programs and better target interventions according to individual impairments. The present review thus proposes a state-of-the-art analysis on: (1) the balance control mechanisms in play during gait initiation in able bodied subjects and in the case of some frail populations; and (2) the biomechanical parameters used in the literature to quantify dynamic stability during gait initiation. Balance control mechanisms reviewed in this article included anticipatory postural adjustments, stance leg stiffness, foot placement, lateral ankle strategy, swing foot strike pattern and vertical center of mass braking. Based on this review, the following viewpoints were put forward: (1) dynamic stability during gait initiation may share a principle of homeostatic regulation similar to most physiological variables, where separate mechanisms need to be coordinated to ensure stabilization of vital variables, and consequently; and (2) rehabilitation interventions which focus on separate or isolated components of posture, balance, or gait may limit the effectiveness of current clinical practices. PMID:29184756

  1. Pond fractals in a tidal flat.

    PubMed

    Cael, B B; Lambert, Bennett; Bisson, Kelsey

    2015-11-01

    Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces.

  2. Pond fractals in a tidal flat

    NASA Astrophysics Data System (ADS)

    Cael, B. B.; Lambert, Bennett; Bisson, Kelsey

    2015-11-01

    Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces.

  3. Adaptive changes in spatiotemporal gait characteristics in women during pregnancy.

    PubMed

    Błaszczyk, Janusz W; Opala-Berdzik, Agnieszka; Plewa, Michał

    2016-01-01

    Spatiotemporal gait cycle characteristics were assessed at early (P1), and late (P2) pregnancy, as well as at 2 months (PP1) and 6 months (PP2) postpartum. A substantial decrease in walking speed was observed throughout the pregnancy, with the slowest speed (1±0.2m/s) being during the third trimester. Walking at slower velocity resulted in complex adaptive adjustments to their spatiotemporal gait pattern, including a shorter step length and an increased duration of both their stance and double-support phases. Duration of the swing phase remained the least susceptible to changes. Habitual walking velocity (1.13±0.2m/s) and the optimal gait pattern were fully recovered 6 months after childbirth. Documented here adaptive changes in the preferred gait pattern seem to result mainly from the altered body anthropometry leading to temporary balance impairments. All the observed changes within stride cycle aimed to improve gait safety by focusing on its dynamic stability. The pregnant women preferred to walk at a slower velocity which allowed them to spend more time in double-support compared with their habitual pattern. Such changes provided pregnant women with a safer and more tentative ambulation that reduced the single-support period and, hence, the possibility of instability. As pregnancy progressed a significant increase in stance width and a decrease in step length was observed. Both factors allow also for gait stability improvement. Copyright © 2015 Elsevier B.V. All rights reserved.

  4. Transport properties of electrons in fractal magnetic-barrier structures

    NASA Astrophysics Data System (ADS)

    Sun, Lifeng; Fang, Chao; Guo, Yong

    2010-09-01

    Quantum transport properties in fractal magnetically modulated structures are studied by the transfer-matrix method. It is found that the transmission spectra depend sensitively not only on the incident energy and the direction of the wave vector but also on the stage of the fractal structures. Resonance splitting, enhancement, and position shift of the resonance peaks under different magnetic modulation are observed at four different fractal stages, and the relationship between the conductance in the fractal structure and magnetic modulation is also revealed. The results indicate the spectra of the transmission can be considered as fingerprints for the fractal structures, which show the subtle correspondence between magnetic structures and transport behaviors.

  5. Characterization of branch complexity by fractal analyses

    USGS Publications Warehouse

    Alados, C.L.; Escos, J.; Emlen, J.M.; Freeman, D.C.

    1999-01-01

    The comparison between complexity in the sense of space occupancy (box-counting fractal dimension D(c) and information dimension D1) and heterogeneity in the sense of space distribution (average evenness index f and evenness variation coefficient J(cv)) were investigated in mathematical fractal objects and natural branch structures. In general, increased fractal dimension was paired with low heterogeneity. Comparisons between branch architecture in Anthyllis cytisoides under different slope exposure and grazing impact revealed that branches were more complex and more homogeneously distributed for plants on northern exposures than southern, while grazing had no impact during a wet year. Developmental instability was also investigated by the statistical noise of the allometric relation between internode length and node order. In conclusion, our study demonstrated that fractal dimension of branch structure can be used to analyze the structural organization of plants, especially if we consider not only fractal dimension but also shoot distribution within the canopy (lacunarity). These indexes together with developmental instability analyses are good indicators of growth responses to the environment.

  6. Is fractal 1/f scaling in stream chemistry universal?

    NASA Astrophysics Data System (ADS)

    Hrachowitz, Markus

    2016-04-01

    Stream water chemistry data from catchments worldwide suggest that catchments act as filters that transform white noise, i.e. random, input signals such as in precipitation, into 1/f^α noise whose slope in a power spectrum typically ranges between -0.5>α>-1.5. This previously lead to the hypothesis that catchments act as fractal filters. In other words, it was posed that considering uncertainty, a slope of α=-1 may be a universal and intrinsic property of catchments. Such fractal scaling characteristics would have considerable implications on the predictability of stream water chemistry, as both, temporal short- and long-range interdependence and memory control the system response. While short memories and thus flatter slopes with α closer to 0 indicate poor short term but good long-term predictability, steeper slopes with values of α <<-1 indicate the opposite. In fractal systems, i.e. where α=-1, this therefore leads to inherent problems of robustly predicting both, short and long-term response patterns. The hypothesis of catchments acting as fractal filters (α=-1), however, remains to be tested more profoundly. It is, for example, not yet clear, if the observed inter-catchment variations in α indeed need to be interpreted as uncertainty and noise in the signal or if the variations underlie a systematic pattern and can be explained by some characteristic of catchment function, as was recently suggested in a modelling study based two experimental catchments (Hrachowitz et al., 2015). Here we will therefore further test the hypothesis that the spectral slope of stream water chemistry is not necessarily α=-1 and that catchments therefore do not inherently act as fractal filters. Further, it will be tested if closer links between the variations in spectral slope and hydrological function of catchments can be identified. The combined data-analysis and modelling study uses hydrochemical data (i.e. Cl- and O-18) from a wide range of catchments worldwide to

  7. Towards thermomechanics of fractal media

    NASA Astrophysics Data System (ADS)

    Ostoja-Starzewski, Martin

    2007-11-01

    Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.

  8. Undergraduate Experiment with Fractal Diffraction Gratings

    ERIC Educational Resources Information Center

    Monsoriu, Juan A.; Furlan, Walter D.; Pons, Amparo; Barreiro, Juan C.; Gimenez, Marcos H.

    2011-01-01

    We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics…

  9. Gait Phase Estimation Based on Noncontact Capacitive Sensing and Adaptive Oscillators.

    PubMed

    Zheng, Enhao; Manca, Silvia; Yan, Tingfang; Parri, Andrea; Vitiello, Nicola; Wang, Qining

    2017-10-01

    This paper presents a novel strategy aiming to acquire an accurate and walking-speed-adaptive estimation of the gait phase through noncontact capacitive sensing and adaptive oscillators (AOs). The capacitive sensing system is designed with two sensing cuffs that can measure the leg muscle shape changes during walking. The system can be dressed above the clothes and free human skin from contacting to electrodes. In order to track the capacitance signals, the gait phase estimator is designed based on the AO dynamic system due to its ability of synchronizing with quasi-periodic signals. After the implementation of the whole system, we first evaluated the offline estimation performance by experiments with 12 healthy subjects walking on a treadmill with changing speeds. The strategy achieved an accurate and consistent gait phase estimation with only one channel of capacitance signal. The average root-mean-square errors in one stride were 0.19 rad (3.0% of one gait cycle) for constant walking speeds and 0.31 rad (4.9% of one gait cycle) for speed transitions even after the subjects rewore the sensing cuffs. We then validated our strategy in a real-time gait phase estimation task with three subjects walking with changing speeds. Our study indicates that the strategy based on capacitive sensing and AOs is a promising alternative for the control of exoskeleton/orthosis.

  10. Instrumented gait analysis: a measure of gait improvement by a wheeled walker in hospitalized geriatric patients.

    PubMed

    Schülein, Samuel; Barth, Jens; Rampp, Alexander; Rupprecht, Roland; Eskofier, Björn M; Winkler, Jürgen; Gaßmann, Karl-Günter; Klucken, Jochen

    2017-02-27

    In an increasing aging society, reduced mobility is one of the most important factors limiting activities of daily living and overall quality of life. The ability to walk independently contributes to the mobility, but is increasingly restricted by numerous diseases that impair gait and balance. The aim of this cross-sectional observation study was to examine whether spatio-temporal gait parameters derived from mobile instrumented gait analysis can be used to measure the gait stabilizing effects of a wheeled walker (WW) and whether these gait parameters may serve as surrogate marker in hospitalized patients with multifactorial gait and balance impairment. One hundred six patients (ages 68-95) wearing inertial sensor equipped shoes passed an instrumented walkway with and without gait support from a WW. The walkway assessed the risk of falling associated gait parameters velocity, swing time, stride length, stride time- and double support time variability. Inertial sensor-equipped shoes measured heel strike and toe off angles, and foot clearance. The use of a WW improved the risk of spatio-temporal parameters velocity, swing time, stride length and the sagittal plane associated parameters heel strike and toe off angles in all patients. First-time users (FTUs) showed similar gait parameter improvement patterns as frequent WW users (FUs). However, FUs with higher levels of gait impairment improved more in velocity, stride length and toe off angle compared to the FTUs. The impact of a WW can be quantified objectively by instrumented gait assessment. Thus, objective gait parameters may serve as surrogate markers for the use of walking aids in patients with gait and balance impairments.

  11. Fractal dimension analysis of complexity in Ligeti piano pieces

    NASA Astrophysics Data System (ADS)

    Bader, Rolf

    2005-04-01

    Fractal correlation dimensional analysis has been performed with whole solo piano pieces by Gyrgy Ligeti at every 50ms interval of the pieces. The resulting curves of development of complexity represented by the fractal dimension showed up a very reasonable correlation with the perceptional density of events during these pieces. The seventh piece of Ligeti's ``Musica ricercata'' was used as a test case. Here, each new part of the piece was followed by an increase of the fractal dimension because of the increase of information at the part changes. The second piece ``Galamb borong,'' number seven of the piano Etudes was used, because Ligeti wrote these Etudes after studying fractal geometry. Although the piece is not fractal in the strict mathematical sense, the overall structure of the psychoacoustic event-density as well as the detailed event development is represented by the fractal dimension plot.

  12. Lack of maintenance of gait pattern as measured by instrumental methods suggests psychogenic gait.

    PubMed

    Merello, Marcelo; Ballesteros, Diego; Rossi, Malco; Arena, Julieta; Crespo, Marcos; Cervio, Andres; Cuello Oderiz, Carolina; Rivero, Alberto; Cerquetti, Daniel; Risk, Marcelo; Balej, Jorge

    2012-01-01

    Fluctuation is a common feature of all psychogenic gait disorder (PGD) patterns. Whether this fluctuation involves only the degree of impairment or whether it affects the gait pattern itself remains an interesting question. We hypothesize that, on repeated measurements, both normal and abnormal gait may present quantitative differences while maintaining their basic underlying pattern; conversely, in psychogenic gait, the basic pattern appears not to be preserved. Using an optoelectronic system, data acquired from 19 normal subjects and 66 patients were applied to train a neural network (NN) and subsequently classify gait patterns into four different groups (normal, ataxic, spastic-paraparetic and parkinsonian). Five patients who fulfilled clinical criteria for psychogenic gait and six controls were then prospectively evaluated on two separate occasions, three months apart. Normal controls and ataxic, parkinsonian or spastic patients were correctly identified by the NN, and categorized within the corresponding groups at baseline as well as at a three-month follow-up evaluation. NN analysis showed that after three months, no PGD patient preserved the gait pattern detected at baseline, even though this finding was not clinically apparent. Modification of gait pattern detected by repeated kinematic measurement and NN analysis could suggest the presence of PGD, particularly in difficult-to-diagnose cases.

  13. Quantitative assessment of early diabetic retinopathy using fractal analysis.

    PubMed

    Cheung, Ning; Donaghue, Kim C; Liew, Gerald; Rogers, Sophie L; Wang, Jie Jin; Lim, Shueh-Wen; Jenkins, Alicia J; Hsu, Wynne; Li Lee, Mong; Wong, Tien Y

    2009-01-01

    Fractal analysis can quantify the geometric complexity of the retinal vascular branching pattern and may therefore offer a new method to quantify early diabetic microvascular damage. In this study, we examined the relationship between retinal fractal dimension and retinopathy in young individuals with type 1 diabetes. We conducted a cross-sectional study of 729 patients with type 1 diabetes (aged 12-20 years) who had seven-field stereoscopic retinal photographs taken of both eyes. From these photographs, retinopathy was graded according to the modified Airlie House classification, and fractal dimension was quantified using a computer-based program following a standardized protocol. In this study, 137 patients (18.8%) had diabetic retinopathy signs; of these, 105 had mild retinopathy. Median (interquartile range) retinal fractal dimension was 1.46214 (1.45023-1.47217). After adjustment for age, sex, diabetes duration, A1C, blood pressure, and total cholesterol, increasing retinal vascular fractal dimension was significantly associated with increasing odds of retinopathy (odds ratio 3.92 [95% CI 2.02-7.61] for fourth versus first quartile of fractal dimension). In multivariate analysis, each 0.01 increase in retinal vascular fractal dimension was associated with a nearly 40% increased odds of retinopathy (1.37 [1.21-1.56]). This association remained after additional adjustment for retinal vascular caliber. Greater retinal fractal dimension, representing increased geometric complexity of the retinal vasculature, is independently associated with early diabetic retinopathy signs in type 1 diabetes. Fractal analysis of fundus photographs may allow quantitative measurement of early diabetic microvascular damage.

  14. The role of the circadian system in fractal neurophysiological control

    PubMed Central

    Pittman-Polletta, Benjamin R.; Scheer, Frank A.J.L.; Butler, Matthew P.; Shea, Steven A.; Hu, Kun

    2013-01-01

    Many neurophysiological variables such as heart rate, motor activity, and neural activity are known to exhibit intrinsic fractal fluctuations - similar temporal fluctuation patterns at different time scales. These fractal patterns contain information about health, as many pathological conditions are accompanied by their alteration or absence. In physical systems, such fluctuations are characteristic of critical states on the border between randomness and order, frequently arising from nonlinear feedback interactions between mechanisms operating on multiple scales. Thus, the existence of fractal fluctuations in physiology challenges traditional conceptions of health and disease, suggesting that high levels of integrity and adaptability are marked by complex variability, not constancy, and are properties of a neurophysiological network, not individual components. Despite the subject's theoretical and clinical interest, the neurophysiological mechanisms underlying fractal regulation remain largely unknown. The recent discovery that the circadian pacemaker (suprachiasmatic nucleus) plays a crucial role in generating fractal patterns in motor activity and heart rate sheds an entirely new light on both fractal control networks and the function of this master circadian clock, and builds a bridge between the fields of circadian biology and fractal physiology. In this review, we sketch the emerging picture of the developing interdisciplinary field of fractal neurophysiology by examining the circadian system’s role in fractal regulation. PMID:23573942

  15. Using Peano Curves to Construct Laplacians on Fractals

    NASA Astrophysics Data System (ADS)

    Molitor, Denali; Ott, Nadia; Strichartz, Robert

    2015-12-01

    We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions of the Laplacian by graphing the pullback to the circle. We study in detail three fractals: the pentagasket, the octagasket and the magic carpet. We also use the method for two nonfractal self-similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. In contrast to the many familiar pictures of approximations to standard Peano curves, that do no show self-intersections, our descriptions of approximations to the Peano curves have self-intersections that play a vital role in constructing graph approximations to the fractal with explicit graph Laplacians that give the fractal Laplacian in the limit.

  16. Bipedal gait model for precise gait recognition and optimal triggering in foot drop stimulator: a proof of concept.

    PubMed

    Shaikh, Muhammad Faraz; Salcic, Zoran; Wang, Kevin I-Kai; Hu, Aiguo Patrick

    2018-03-10

    Electrical stimulators are often prescribed to correct foot drop walking. However, commercial foot drop stimulators trigger inappropriately under certain non-gait scenarios. Past researches addressed this limitation by defining stimulation control based on automaton of a gait cycle executed by foot drop of affected limb/foot only. Since gait is a collaborative activity of both feet, this research highlights the role of normal foot for robust gait detection and stimulation triggering. A novel bipedal gait model is proposed where gait cycle is realized as an automaton based on concurrent gait sub-phases (states) from each foot. The input for state transition is fused information from feet-worn pressure and inertial sensors. Thereafter, a bipedal gait model-based stimulation control algorithm is developed. As a feasibility study, bipedal gait model and stimulation control are evaluated in real-time simulation manner on normal and simulated foot drop gait measurements from 16 able-bodied participants with three speed variations, under inappropriate triggering scenarios and with foot drop rehabilitation exercises. Also, the stimulation control employed in commercial foot drop stimulators and single foot gait-based foot drop stimulators are compared alongside. Gait detection accuracy (98.9%) and precise triggering under all investigations prove bipedal gait model reliability. This infers that gait detection leveraging bipedal periodicity is a promising strategy to rectify prevalent stimulation triggering deficiencies in commercial foot drop stimulators. Graphical abstract Bipedal information-based gait recognition and stimulation triggering.

  17. ABC of multi-fractal spacetimes and fractional sea turtles

    NASA Astrophysics Data System (ADS)

    Calcagni, Gianluca

    2016-04-01

    We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.

  18. Contribution of tibiofemoral joint contact to net loads at the knee in gait.

    PubMed

    Walter, Jonathan P; Korkmaz, Nuray; Fregly, Benjamin J; Pandy, Marcus G

    2015-07-01

    Inverse dynamics analysis is commonly used to estimate the net loads at a joint during human motion. Most lower-limb models of movement represent the knee as a simple hinge joint when calculating muscle forces. This approach is limited because it neglects the contributions from tibiofemoral joint contact forces and may therefore lead to errors in estimated muscle forces. The aim of this study was to quantify the contributions of tibiofemoral joint contact loads to the net knee loads calculated from inverse dynamics for multiple subjects and multiple gait patterns. Tibiofemoral joint contact loads were measured in four subjects with instrumented implants as each subject walked at their preferred speed (normal gait) and performed prescribed gait modifications designed to treat medial knee osteoarthritis. Tibiofemoral contact loads contributed substantially to the net knee extension and knee adduction moments in normal gait with mean values of 16% and 54%, respectively. These findings suggest that knee-contact kinematics and loads should be included in lower-limb models of movement for more accurate determination of muscle forces. The results of this study may be used to guide the development of more realistic lower-limb models that account for the effects of tibiofemoral joint contact at the knee. © 2015 Orthopaedic Research Society. Published by Wiley Periodicals, Inc.

  19. Effects of conventional overground gait training and a gait trainer with partial body weight support on spatiotemporal gait parameters of patients after stroke

    PubMed Central

    Park, Byoung-Sun; Kim, Mee-Young; Lee, Lim-Kyu; Yang, Seung-Min; Lee, Won-Deok; Noh, Ji-Woong; Shin, Yong-Sub; Kim, Ju-Hyun; Lee, Jeong-Uk; Kwak, Taek-Yong; Lee, Tae-Hyun; Kim, Ju-Young; Kim, Junghwan

    2015-01-01

    [Purpose] The purpose of this study was to confirm the effects of both conventional overground gait training (CGT) and a gait trainer with partial body weight support (GTBWS) on spatiotemporal gait parameters of patients with hemiparesis following chronic stroke. [Subjects and Methods] Thirty stroke patients were alternately assigned to one of two treatment groups, and both groups underwent CGT and GTBWS. [Results] The functional ambulation classification on the affected side improved significantly in the CGT and GTBWS groups. Walking speed also improved significantly in both groups. [Conclusion] These results suggest that the GTBWS in company with CGT may be, in part, an effective method of gait training for restoring gait ability in patients after a stroke. PMID:26157272

  20. Effects of conventional overground gait training and a gait trainer with partial body weight support on spatiotemporal gait parameters of patients after stroke.

    PubMed

    Park, Byoung-Sun; Kim, Mee-Young; Lee, Lim-Kyu; Yang, Seung-Min; Lee, Won-Deok; Noh, Ji-Woong; Shin, Yong-Sub; Kim, Ju-Hyun; Lee, Jeong-Uk; Kwak, Taek-Yong; Lee, Tae-Hyun; Kim, Ju-Young; Kim, Junghwan

    2015-05-01

    [Purpose] The purpose of this study was to confirm the effects of both conventional overground gait training (CGT) and a gait trainer with partial body weight support (GTBWS) on spatiotemporal gait parameters of patients with hemiparesis following chronic stroke. [Subjects and Methods] Thirty stroke patients were alternately assigned to one of two treatment groups, and both groups underwent CGT and GTBWS. [Results] The functional ambulation classification on the affected side improved significantly in the CGT and GTBWS groups. Walking speed also improved significantly in both groups. [Conclusion] These results suggest that the GTBWS in company with CGT may be, in part, an effective method of gait training for restoring gait ability in patients after a stroke.

  1. Fractal morphometry of cell complexity.

    PubMed

    Losa, Gabriele A

    2002-01-01

    Irregularity and self-similarity under scale changes are the main attributes of the morphological complexity of both normal and abnormal cells and tissues. In other words, the shape of a self-similar object does not change when the scale of measurement changes, because each part of it looks similar to the original object. However, the size and geometrical parameters of an irregular object do differ when it is examined at increasing resolution, which reveals more details. Significant progress has been made over the past three decades in understanding how irregular shapes and structures in the physical and biological sciences can be analysed. Dominant influences have been the discovery of a new practical geometry of Nature, now known as fractal geometry, and the continuous improvements in computation capabilities. Unlike conventional Euclidean geometry, which was developed to describe regular and ideal geometrical shapes which are practically unknown in nature, fractal geometry can be used to measure the fractal dimension, contour length, surface area and other dimension parameters of almost all irregular and complex biological tissues. We have used selected examples to illustrate the application of the fractal principle to measuring irregular and complex membrane ultrastructures of cells at specific functional and pathological stage.

  2. Gait and Cognition in Parkinson's Disease: Cognitive Impairment Is Inadequately Reflected by Gait Performance during Dual Task.

    PubMed

    Gaßner, Heiko; Marxreiter, Franz; Steib, Simon; Kohl, Zacharias; Schlachetzki, Johannes C M; Adler, Werner; Eskofier, Bjoern M; Pfeifer, Klaus; Winkler, Jürgen; Klucken, Jochen

    2017-01-01

    Cognitive and gait deficits are common symptoms in Parkinson's disease (PD). Motor-cognitive dual tasks (DTs) are used to explore the interplay between gait and cognition. However, it is unclear if DT gait performance is indicative for cognitive impairment. Therefore, the aim of this study was to investigate if cognitive deficits are reflected by DT costs of spatiotemporal gait parameters. Cognitive function, single task (ST) and DT gait performance were investigated in 67 PD patients. Cognition was assessed by the Montreal Cognitive Assessment (MoCA) followed by a standardized, sensor-based gait test and the identical gait test while subtracting serial 3's. Cognitive impairment was defined by a MoCA score <26. DT costs in gait parameters [(DT - ST)/ST × 100] were calculated as a measure of DT effect on gait. Correlation analysis was used to evaluate the association between MoCA performance and gait parameters. In a linear regression model, DT gait costs and clinical confounders (age, gender, disease duration, motor impairment, medication, and depression) were correlated to cognitive performance. In a subgroup analysis, we compared matched groups of cognitively impaired and unimpaired PD patients regarding differences in ST, DT, and DT gait costs. Correlation analysis revealed weak correlations between MoCA score and DT costs of gait parameters ( r / r Sp  ≤ 0.3). DT costs of stride length, swing time variability, and maximum toe clearance (| r / r Sp | > 0.2) were included in a regression analysis. The parameters only explain 8% of the cognitive variance. In combination with clinical confounders, regression analysis showed that these gait parameters explained 30% of MoCA performance. Group comparison revealed strong DT effects within both groups (large effect sizes), but significant between-group effects in DT gait costs were not observed. These findings suggest that DT gait performance is not indicative for cognitive impairment in PD. DT

  3. The effects of gait training with body weight support (BWS) with no body weight support (no-BWS) in stroke patients.

    PubMed

    Ullah, Muhammad Asad; Shafi, Hina; Khan, Ghazanfar Ali; Malik, Arshad Nawaz; Amjad, Imran

    2017-07-01

    The purpose of this study was to measure the clinical outcomes for patients with stroke after gait training with body weight support (BWS) and with no body weight support (no-BWS).Experimental group was trained to walk by a BWS system with overhead harness (BWS group), and Control group was trained with full weight bearing walk on their lower extremities. Treatment session comprised of six weeks training. Treatment outcomes were assessed on the basis of Timed 10 Meter Walk Test, Timed Get Up and Go Test and Dynamic Gait Index. There was a significant (P<0.05) difference in BWS and NBWS for Dynamic Gait Index, Timed Get Up and Go Test, Timed 10 Meter Walk Test (Self-Selected Velocity), and Timed 10 Meter Walk Test (Fast-Velocity). Training of gait in stroke patients while a percentage of their body weight supported by a harness, resulted in better walking abilities than the Training of gait while full weight was placed on patient's lower extremities.

  4. Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel

    PubMed Central

    Shanhua, Xu; Songbo, Ren; Youde, Wang

    2015-01-01

    To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel. PMID:26121468

  5. Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel.

    PubMed

    Shanhua, Xu; Songbo, Ren; Youde, Wang

    2015-01-01

    To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel.

  6. Gait characteristics after gait-oriented rehabilitation in chronic stroke.

    PubMed

    Peurala, Sinikka H; Titianova, Ekaterina B; Mateev, Plamen; Pitkänen, Kauko; Sivenius, Juhani; Tarkka, Ina M

    2005-01-01

    To assess the effects of rehabilitation in thirty-seven ambulatory patients with chronic stroke during three weeks in-patient rehabilitation period. In the intervention group, each patient received 75 min physiotherapy daily every workday including 20 minutes in the electromechanical gait trainer with body-weight support (BWS). In the control group, each patient participated in 45 min conventional physiotherapy daily. Motor ability was assessed with the first five items of the Modified Motor Assessment Scale (MMAS1-5) and ten meters walking speed. Spatio-temporal gait characteristics were recorded with an electrical walkway. The MMAS1-5 (p<0.0005 and p=0.005) and ten meters walking time (p<0.0005 and p=0.006) improved in both groups. The improvements in MMAS1-5 and ten meters walking time did not differ between the groups (p=0.217 and p=0.195). Specific gait characteristics improved only in the intervention group, as seen in increased Functional Ambulation Profile score (p=0.023), velocity (p=0.023), the step lengths (affected side, p=0.011, non-affected side p=0.040), the stride lengths (p=0.018, p=0.006) and decreased step-time differential (p=0.043). Furthermore, all gait characteristics and other motor abilities remained in the discharge level at the six months in the intervention group. It appears that BWS training gives a long-lasting benefit in gait qualities even in chronic stroke patients.

  7. Exploring fractal behaviour of blood oxygen saturation in preterm babies

    NASA Astrophysics Data System (ADS)

    Zahari, Marina; Hui, Tan Xin; Zainuri, Nuryazmin Ahmat; Darlow, Brian A.

    2017-04-01

    Recent evidence has been emerging that oxygenation instability in preterm babies could lead to an increased risk of retinal injury such as retinopathy of prematurity. There is a potential that disease severity could be better understood using nonlinear methods for time series data such as fractal theories [1]. Theories on fractal behaviours have been employed by researchers in various disciplines who were motivated to look into the behaviour or structure of irregular fluctuations in temporal data. In this study, an investigation was carried out to examine whether fractal behaviour could be detected in blood oxygen time series. Detection for the presence of fractals in oxygen data of preterm infants was performed using the methods of power spectrum, empirical probability distribution function and autocorrelation function. The results from these fractal identification methods indicate the possibility that these data exhibit fractal nature. Subsequently, a fractal framework for future research was suggested for oxygen time series.

  8. Hierarchical socioeconomic fractality: The rich, the poor, and the middle-class

    NASA Astrophysics Data System (ADS)

    Eliazar, Iddo; Cohen, Morrel H.

    2014-05-01

    Since the seminal work of the Italian economist Vilfredo Pareto, the study of wealth and income has been a topic of active scientific exploration engaging researches ranging from economics and political science to econophysics and complex systems. This paper investigates the intrinsic fractality of wealth and income. To that end we introduce and characterize three forms of socioeconomic scale-invariance-poor fractality, rich fractality, and middle-class fractality-and construct hierarchical fractal approximations of general wealth and income distributions, based on the stitching of these three forms of fractality. Intertwining the theoretical results with real-world empirical data we then establish that the three forms of socioeconomic fractality-amalgamated into a composite hierarchical structure-underlie the distributions of wealth and income in human societies. We further establish that the hierarchical socioeconomic fractality of wealth and income is also displayed by empirical rank distributions observed across the sciences.

  9. Arbitrary Symmetric Running Gait Generation for an Underactuated Biped Model.

    PubMed

    Dadashzadeh, Behnam; Esmaeili, Mohammad; Macnab, Chris

    2017-01-01

    This paper investigates generating symmetric trajectories for an underactuated biped during the stance phase of running. We use a point mass biped (PMB) model for gait analysis that consists of a prismatic force actuator on a massless leg. The significance of this model is its ability to generate more general and versatile running gaits than the spring-loaded inverted pendulum (SLIP) model, making it more suitable as a template for real robots. The algorithm plans the necessary leg actuator force to cause the robot center of mass to undergo arbitrary trajectories in stance with any arbitrary attack angle and velocity angle. The necessary actuator forces follow from the inverse kinematics and dynamics. Then these calculated forces become the control input to the dynamic model. We compare various center-of-mass trajectories, including a circular arc and polynomials of the degrees 2, 4 and 6. The cost of transport and maximum leg force are calculated for various attack angles and velocity angles. The results show that choosing the velocity angle as small as possible is beneficial, but the angle of attack has an optimum value. We also find a new result: there exist biped running gaits with double-hump ground reaction force profiles which result in less maximum leg force than single-hump profiles.

  10. Arbitrary Symmetric Running Gait Generation for an Underactuated Biped Model

    PubMed Central

    Esmaeili, Mohammad; Macnab, Chris

    2017-01-01

    This paper investigates generating symmetric trajectories for an underactuated biped during the stance phase of running. We use a point mass biped (PMB) model for gait analysis that consists of a prismatic force actuator on a massless leg. The significance of this model is its ability to generate more general and versatile running gaits than the spring-loaded inverted pendulum (SLIP) model, making it more suitable as a template for real robots. The algorithm plans the necessary leg actuator force to cause the robot center of mass to undergo arbitrary trajectories in stance with any arbitrary attack angle and velocity angle. The necessary actuator forces follow from the inverse kinematics and dynamics. Then these calculated forces become the control input to the dynamic model. We compare various center-of-mass trajectories, including a circular arc and polynomials of the degrees 2, 4 and 6. The cost of transport and maximum leg force are calculated for various attack angles and velocity angles. The results show that choosing the velocity angle as small as possible is beneficial, but the angle of attack has an optimum value. We also find a new result: there exist biped running gaits with double-hump ground reaction force profiles which result in less maximum leg force than single-hump profiles. PMID:28118401

  11. A Tutorial Review on Fractal Spacetime and Fractional Calculus

    NASA Astrophysics Data System (ADS)

    He, Ji-Huan

    2014-11-01

    This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

  12. Gait analysis and weight bearing in pre-clinical joint pain research.

    PubMed

    Ängeby Möller, Kristina; Svärd, Heta; Suominen, Anni; Immonen, Jarmo; Holappa, Johanna; Stenfors, Carina

    2018-04-15

    There is a need for better joint pain treatment, but development of new medication has not been successful. Pre-clinical models with readouts that better reflect the clinical situation are needed. In patients with joint pain, pain at rest and pain at walking are two major complaints. We describe a new way of calculating results from gait analysis using the CatWalk™ setup. Rats with monoarthritis induced by injection of Complete Freund's Adjuvant (CFA) intra-articularly into the ankle joint of one hind limb were used to assess gait and dynamic weight bearing. The results show that dynamic weight bearing was markedly reduced for the injected paw. Gait parameters such as amount of normal step sequences, walking speed and duration of step placement were also affected. Treatment with naproxen (an NSAID commonly used for inflammatory pain) attenuated the CFA-induced effects. Pregabalin, which is used for neuropathic pain, had no effect. Reduced dynamic weight bearing during locomotion, assessed and calculated in the way we present here, showed a dose-dependent and lasting normalization after naproxen treatment. In contrast, static weight bearing while standing (Incapacitance tester) showed a significant effect for a limited time only. Mechanical sensitivity (von Frey Optihairs) was completely normalized by naproxen, and the window for testing pharmacological effect disappeared. Objective and reproducible effects, with an endpoint showing face validity compared to pain while walking in patients with joint pain, are achieved by a new way of calculating dynamic weight bearing in monoarthritic rats. Copyright © 2017 Elsevier B.V. All rights reserved.

  13. Measurement instruments to assess posture, gait, and balance in Parkinson's disease: Critique and recommendations.

    PubMed

    Bloem, Bastiaan R; Marinus, Johan; Almeida, Quincy; Dibble, Lee; Nieuwboer, Alice; Post, Bart; Ruzicka, Evzen; Goetz, Christopher; Stebbins, Glenn; Martinez-Martin, Pablo; Schrag, Anette

    2016-09-01

    Disorders of posture, gait, and balance in Parkinson's disease (PD) are common and debilitating. This MDS-commissioned task force assessed clinimetric properties of existing rating scales, questionnaires, and timed tests that assess these features in PD. A literature review was conducted. Identified instruments were evaluated systematically and classified as "recommended," "suggested," or "listed." Inclusion of rating scales was restricted to those that could be used readily in clinical research and practice. One rating scale was classified as "recommended" (UPDRS-derived Postural Instability and Gait Difficulty score) and 2 as "suggested" (Tinetti Balance Scale, Rating Scale for Gait Evaluation). Three scales requiring equipment (Berg Balance Scale, Mini-BESTest, Dynamic Gait Index) also fulfilled criteria for "recommended" and 2 for "suggested" (FOG score, Gait and Balance Scale). Four questionnaires were "recommended" (Freezing of Gait Questionnaire, Activities-specific Balance Confidence Scale, Falls Efficacy Scale, Survey of Activities, and Fear of Falling in the Elderly-Modified). Four tests were classified as "recommended" (6-minute and 10-m walk tests, Timed Up-and-Go, Functional Reach). We identified several questionnaires that adequately assess freezing of gait and balance confidence in PD and a number of useful clinical tests. However, most clinical rating scales for gait, balance, and posture perform suboptimally or have been evaluated insufficiently. No instrument comprehensively and separately evaluates all relevant PD-specific gait characteristics with good clinimetric properties, and none provides separate balance and gait scores with adequate content validity for PD. We therefore recommend the development of such a PD-specific, easily administered, comprehensive gait and balance scale that separately assesses all relevant constructs. © 2016 International Parkinson and Movement Disorder Society. © 2016 International Parkinson and Movement Disorder

  14. Fractal analysis of scatter imaging signatures to distinguish breast pathologies

    NASA Astrophysics Data System (ADS)

    Eguizabal, Alma; Laughney, Ashley M.; Krishnaswamy, Venkataramanan; Wells, Wendy A.; Paulsen, Keith D.; Pogue, Brian W.; López-Higuera, José M.; Conde, Olga M.

    2013-02-01

    Fractal analysis combined with a label-free scattering technique is proposed for describing the pathological architecture of tumors. Clinicians and pathologists are conventionally trained to classify abnormal features such as structural irregularities or high indices of mitosis. The potential of fractal analysis lies in the fact of being a morphometric measure of the irregular structures providing a measure of the object's complexity and self-similarity. As cancer is characterized by disorder and irregularity in tissues, this measure could be related to tumor growth. Fractal analysis has been probed in the understanding of the tumor vasculature network. This work addresses the feasibility of applying fractal analysis to the scattering power map (as a physical modeling) and principal components (as a statistical modeling) provided by a localized reflectance spectroscopic system. Disorder, irregularity and cell size variation in tissue samples is translated into the scattering power and principal components magnitude and its fractal dimension is correlated with the pathologist assessment of the samples. The fractal dimension is computed applying the box-counting technique. Results show that fractal analysis of ex-vivo fresh tissue samples exhibits separated ranges of fractal dimension that could help classifier combining the fractal results with other morphological features. This contrast trend would help in the discrimination of tissues in the intraoperative context and may serve as a useful adjunct to surgeons.

  15. Subliminal gait initiation deficits in REM sleep behavior disorder: a harbinger of freezing of gait?

    PubMed Central

    Alibiglou, L.; Videnovic, A.; Planetta, P.J.; Vaillancourt, D.E.; MacKinnon, C.D.

    2016-01-01

    Background Muscle activity during REM sleep is markedly increased in people with REM sleep behavior disorder (RBD) and people with Parkinson’s disease (PD) who have freezing of gait. This study examined if individuals with RBD, who do not have a diagnosis of PD, show abnormalities in gait initiation that resemble the impairments observed in PD and whether there is a relationship between these deficits and the level of REM sleep without atonia. Methods Gait initiation and polysomnography studies were conducted in four groups of 10 subjects each: RBD, PD with and without freezing of gait and control subjects. Results Significant reductions were seen in the posterior shift of the center of pressure during the propulsive phase of gait initiation in the RBD and PD with freezing of gait groups compared with controls and PD non-freezers. These reductions negatively correlated with the amount of REM sleep without atonia. The duration of the initial dorsiflexor muscle burst during gait initiation was significantly reduced in both PD groups and the RBD cohort. Conclusions These results provide evidence that people with RBD, prior to a diagnosis of a degenerative neurologic disorder, show alterations in the coupling of posture and gait similar to those seen in PD. The correlation between increased REM sleep without atonia and deficits in forward propulsion during the push-off phase of gait initiation suggests that abnormities in the regulation of muscle tone during REM sleep may be related to the pathogenesis of freezing of gait. PMID:27250871

  16. Plasmon confinement in fractal quantum systems

    NASA Astrophysics Data System (ADS)

    Westerhout, Tom; van Veen, Edo; Katsnelson, Mikhail I.; Yuan, Shengjun

    2018-05-01

    Recent progress in the fabrication of materials has made it possible to create arbitrary nonperiodic two-dimensional structures in the quantum plasmon regime. This paves the way for exploring the quantum plasmonic properties of electron gases in complex geometries. In this work we study systems with a fractal dimension. We calculate the full dielectric functions of two prototypical fractals with different ramification numbers, namely the Sierpinski carpet and gasket. We show that the Sierpinski carpet has a dispersion comparable to a square lattice, but the Sierpinski gasket features highly localized plasmon modes with a flat dispersion. This strong plasmon confinement in finitely ramified fractals can provide a novel setting for manipulating light at the quantum level.

  17. Multi-Scale Fractal Analysis of Image Texture and Pattern

    NASA Technical Reports Server (NTRS)

    Emerson, Charles W.

    1998-01-01

    Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely independent of scale. Self-similarity is defined as a property of curves or surfaces where each part is indistinguishable from the whole, or where the form of the curve or surface is invariant with respect to scale. An ideal fractal (or monofractal) curve or surface has a constant dimension over all scales, although it may not be an integer value. This is in contrast to Euclidean or topological dimensions, where discrete one, two, and three dimensions describe curves, planes, and volumes. Theoretically, if the digital numbers of a remotely sensed image resemble an ideal fractal surface, then due to the self-similarity property, the fractal dimension of the image will not vary with scale and resolution. However, most geographical phenomena are not strictly self-similar at all scales, but they can often be modeled by a stochastic fractal in which the scaling and self-similarity properties of the fractal have inexact patterns that can be described by statistics. Stochastic fractal sets relax the monofractal self-similarity assumption and measure many scales and resolutions in order to represent the varying form of a phenomenon as a function of local variables across space. In image interpretation, pattern is defined as the overall spatial form of related features, and the repetition of certain forms is a characteristic pattern found in many cultural objects and some natural features. Texture is the visual impression of coarseness or smoothness caused by the variability or uniformity of image tone or color. A potential use of fractals concerns the analysis of image texture. In these situations it is commonly observed that the degree of roughness or inexactness in an image or surface is a function of scale and not of experimental technique. The fractal dimension of remote sensing data could yield quantitative insight on the spatial complexity and

  18. Investigation into How 8th Grade Students Define Fractals

    ERIC Educational Resources Information Center

    Karakus, Fatih

    2015-01-01

    The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…

  19. Balzac and human gait analysis.

    PubMed

    Collado-Vázquez, S; Carrillo, J M

    2015-05-01

    People have been interested in movement analysis in general, and gait analysis in particular, since ancient times. Aristotle, Hippocrates, Galen, Leonardo da Vinci and Honoré de Balzac all used observation to analyse the gait of human beings. The purpose of this study is to compare Honoré de Balzac's writings with a scientific analysis of human gait. Honoré de Balzac's Theory of walking and other works by that author referring to gait. Honoré de Balzac had an interest in gait analysis, as demonstrated by his descriptions of characters which often include references to their way of walking. He also wrote a treatise entitled Theory of walking (Théorie de la demarche) in which he employed his keen observation skills to define gait using a literary style. He stated that the walking process is divided into phases and listed the factors that influence gait, such as personality, mood, height, weight, profession and social class, and also provided a description of the correct way of walking. Balzac considered gait analysis to be very important and this is reflected in both his character descriptions and Theory of walking, his analytical observation of gait. In our own technology-dominated times, this serves as a reminder of the importance of observation. Copyright © 2011 Sociedad Española de Neurología. Published by Elsevier España, S.L.U. All rights reserved.

  20. Iterons, fractals and computations of automata

    NASA Astrophysics Data System (ADS)

    Siwak, Paweł

    1999-03-01

    Processing of strings by some automata, when viewed on space-time (ST) diagrams, reveals characteristic soliton-like coherent periodic objects. They are inherently associated with iterations of automata mappings thus we call them the iterons. In the paper we present two classes of one-dimensional iterons: particles and filtrons. The particles are typical for parallel (cellular) processing, while filtrons, introduced in (32) are specific for serial processing of strings. In general, the images of iterated automata mappings exhibit not only coherent entities but also the fractals, and quasi-periodic and chaotic dynamics. We show typical images of such computations: fractals, multiplication by a number, and addition of binary numbers defined by a Turing machine. Then, the particles are presented as iterons generated by cellular automata in three computations: B/U code conversion (13, 29), majority classification (9), and in discrete version of the FPU (Fermi-Pasta-Ulam) dynamics (7, 23). We disclose particles by a technique of combinational recoding of ST diagrams (as opposed to sequential recoding). Subsequently, we recall the recursive filters based on FCA (filter cellular automata) window operators, and considered by Park (26), Ablowitz (1), Fokas (11), Fuchssteiner (12), Bruschi (5) and Jiang (20). We present the automata equivalents to these filters (33). Some of them belong to the class of filter automata introduced in (30). We also define and illustrate some properties of filtrons. Contrary to particles, the filtrons interact nonlocally in the sense that distant symbols may influence one another. Thus their interactions are very unusual. Some examples have been given in (32). Here we show new examples of filtron phenomena: multifiltron solitonic collisions, attracting and repelling filtrons, trapped bouncing filtrons (which behave like a resonance cavity) and quasi filtrons.

  1. Gait analysis in children with cerebral palsy.

    PubMed

    Armand, Stéphane; Decoulon, Geraldo; Bonnefoy-Mazure, Alice

    2016-12-01

    Cerebral palsy (CP) children present complex and heterogeneous motor disorders that cause gait deviations.Clinical gait analysis (CGA) is needed to identify, understand and support the management of gait deviations in CP. CGA assesses a large amount of quantitative data concerning patients' gait characteristics, such as video, kinematics, kinetics, electromyography and plantar pressure data.Common gait deviations in CP can be grouped into the gait patterns of spastic hemiplegia (drop foot, equinus with different knee positions) and spastic diplegia (true equinus, jump, apparent equinus and crouch) to facilitate communication. However, gait deviations in CP tend to be a continuum of deviations rather than well delineated groups. To interpret CGA, it is necessary to link gait deviations to clinical impairments and to distinguish primary gait deviations from compensatory strategies.CGA does not tell us how to treat a CP patient, but can provide objective identification of gait deviations and further the understanding of gait deviations. Numerous treatment options are available to manage gait deviations in CP. Generally, treatments strive to limit secondary deformations, re-establish the lever arm function and preserve muscle strength.Additional roles of CGA are to better understand the effects of treatments on gait deviations. Cite this article: Armand S, Decoulon G, Bonnefoy-Mazure A. Gait analysis in children with cerebral palsy. EFORT Open Rev 2016;1:448-460. DOI: 10.1302/2058-5241.1.000052.

  2. Anomalous relaxation in fractal structures

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Fujiwara, S.; Yonezawa, F.

    1995-03-01

    For the purpose of studying some interesting properties of anomalous relaxation in fractal structures, we carry out Monte Carlo simulations of random walks on two-dimensional fractal structures (Sierpinski carpets with different cutouts and site-percolation clusters in a square lattice at the critical concentration). We find that the relaxation is of the Cole-Cole type [J. Chem. Phys. 9, 341 (1941)], which is one of the empirical laws of anomalous relaxation. Scaling properties are found in the relaxation function as well as in the particle density. We also find that, in strucures with almost the same fractal dimension, relaxation in structures withmore » dead ends is slower than that in structures without them. This paper ascertains that the essential aspects of the anomalous relaxation due to many-body effects can be explained in the framework of the one-body model.« less

  3. Pulse regime in formation of fractal fibers

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Smirnov, B. M., E-mail: bmsmirnov@gmail.com

    The pulse regime of vaporization of a bulk metal located in a buffer gas is analyzed as a method of generation of metal atoms under the action of a plasma torch or a laser beam. Subsequently these atoms are transformed into solid nanoclusters, fractal aggregates and then into fractal fibers if the growth process proceeds in an external electric field. We are guided by metals in which transitions between s and d-electrons of their atoms are possible, since these metals are used as catalysts and filters in interaction with gas flows. The resistance of metal fractal structures to a gasmore » flow is evaluated that allows one to find optimal parameters of a fractal structure for gas flow propagation through it. The thermal regime of interaction between a plasma pulse or a laser beam and a metal surface is analyzed. It is shown that the basic energy from an external source is consumed on a bulk metal heating, and the efficiency of atom evaporation from the metal surface, that is the ratio of energy fluxes for vaporization and heating, is 10{sup –3}–10{sup –4} for transient metals under consideration. A typical energy flux (~10{sup 6} W/cm{sup 2}), a typical surface temperature (~3000 K), and a typical pulse duration (~1 μs) provide a sufficient amount of evaporated atoms to generate fractal fibers such that each molecule of a gas flow collides with the skeleton of fractal fibers many times.« less

  4. Cognitive and motor dual task gait training improve dual task gait performance after stroke - A randomized controlled pilot trial.

    PubMed

    Liu, Yan-Ci; Yang, Yea-Ru; Tsai, Yun-An; Wang, Ray-Yau

    2017-06-22

    This study investigated effects of cognitive and motor dual task gait training on dual task gait performance in stroke. Participants (n = 28) were randomly assigned to cognitive dual task gait training (CDTT), motor dual task gait training (MDTT), or conventional physical therapy (CPT) group. Participants in CDTT or MDTT group practiced the cognitive or motor tasks respectively during walking. Participants in CPT group received strengthening, balance, and gait training. The intervention was 30 min/session, 3 sessions/week for 4 weeks. Three test conditions to evaluate the training effects were single walking, walking while performing cognitive task (serial subtraction), and walking while performing motor task (tray-carrying). Parameters included gait speed, dual task cost of gait speed (DTC-speed), cadence, stride time, and stride length. After CDTT, cognitive-motor dual task gait performance (stride length and DTC-speed) was improved (p = 0.021; p = 0.015). After MDTT, motor dual task gait performance (gait speed, stride length, and DTC-speed) was improved (p = 0.008; p = 0.008; p = 0.008 respectively). It seems that CDTT improved cognitive dual task gait performance and MDTT improved motor dual task gait performance although such improvements did not reach significant group difference. Therefore, different types of dual task gait training can be adopted to enhance different dual task gait performance in stroke.

  5. The Effect of Prior Concussion History on Dual-Task Gait following a Concussion.

    PubMed

    Howell, David R; Beasley, Michael; Vopat, Lisa; Meehan, William P

    2017-02-15

    Sustaining repeated concussions has been associated with worse outcomes after additional injuries. This effect has been identified using symptom inventories and neurocognitive tests; however, few investigations have examined how a prior concussion history affects gait soon after a subsequent concussion. We examined the gait characteristics of athletes with no documented concussion history (n = 31), athletes recovering from their first lifetime concussion (n = 15), and athletes recovering from their second or greater lifetime concussion (n = 22). All participants completed a single-task and dual-task gait examination, a medical history questionnaire, and a postconcussion symptom scale. Multivariate analyses of covariance (MANCOVA) models were used to evaluate mean gait differences among groups, and Spearman's ρ analyses were used to assess correlations between the number of lifetime concussions and gait characteristics. Patients reporting to the clinic with their second or greater lifetime concussion demonstrated smaller stride lengths than healthy control participants during dual-task walking (p = 0.01; d = 0.70). A moderate but insignificant correlation was detected between dual-task gait speed and the number of prior concussions (ρ = 0.41, p = 0.07). These results indicate that a cumulative effect of concussions across the lifetime may contribute to worsening dual-task dynamic motor function after concussion.

  6. Femoral anteversion assessment: Comparison of physical examination, gait analysis, and EOS biplanar radiography.

    PubMed

    Westberry, David E; Wack, Linda I; Davis, Roy B; Hardin, James W

    2018-05-01

    Multiple measurement methods are available to assess transverse plane alignment of the lower extremity. This study was performed to determine the extent of correlation between femoral anteversion assessment using simultaneous biplanar radiographs and three-dimensional modeling (EOS imaging), clinical hip rotation by physical examination, and dynamic hip rotation assessed by gait analysis. Seventy-seven patients with cerebral palsy (GMFCS Level I and II) and 33 neurologically typical children with torsional abnormalities completed a comprehensive gait analysis with same day biplanar anterior-posterior and lateral radiographs and three-dimensional transverse plane assessment of femoral anteversion. Correlations were determined between physical exam of hip rotation, EOS imaging of femoral anteversion, and transverse plane hip kinematics for this retrospective review study. Linear regression analysis revealed a weak relationship between physical examination measures of hip rotation and biplanar radiographic assessment of femoral anteversion. Similarly, poor correlation was found between clinical evaluation of femoral anteversion and motion assessment of dynamic hip rotation. Correlations were better in neurologically typical children with torsional abnormalities compared to children with gait dysfunction secondary to cerebral palsy. Dynamic hip rotation cannot be predicted by physical examination measures of hip range of motion or from three-dimensional assessment of femoral anteversion derived from biplanar radiographs. Copyright © 2018 Elsevier B.V. All rights reserved.

  7. Fractal tomography and its application in 3D vision

    NASA Astrophysics Data System (ADS)

    Trubochkina, N.

    2018-01-01

    A three-dimensional artistic fractal tomography method that implements a non-glasses 3D visualization of fractal worlds in layered media is proposed. It is designed for the glasses-free 3D vision of digital art objects and films containing fractal content. Prospects for the development of this method in art galleries and the film industry are considered.

  8. Wetting characteristics of 3-dimensional nanostructured fractal surfaces

    NASA Astrophysics Data System (ADS)

    Davis, Ethan; Liu, Ying; Jiang, Lijia; Lu, Yongfeng; Ndao, Sidy

    2017-01-01

    This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.

  9. Teaching about Fractals.

    ERIC Educational Resources Information Center

    Willson, Stephen J.

    1991-01-01

    Described is a course designed to teach students about fractals using various teaching methods including the computer. Discussed are why the course drew students, prerequisites, clientele, textbook, grading, computer usage, and the syllabus. (KR)

  10. Two-Dimensional Animal-Like Fractals in Thin Films

    NASA Astrophysics Data System (ADS)

    Gao, Hong-jun; Xue, Zeng-quan; Wu, Quan-de; Pang, Shi-jin

    1996-02-01

    We present a few unique animal-like fractal patterns in ionized-cluster-beam deposited fullerene-tetracyanoquinodimethane thin films. The fractal patterns consisting of animal-like aggregates such as "fishes" and "quasi-seahorses" have been characterized by transmission electron microscopy. The results indicate that the small aggregates of the animal-like body are composed of many single crystals whose crystalline directions are generally different. The formation of the fractal patterns can be attributed to the cluster-diffusion-limited aggregation.

  11. A Microsoft Kinect-Based Point-of-Care Gait Assessment Framework for Multiple Sclerosis Patients.

    PubMed

    Gholami, Farnood; Trojan, Daria A; Kovecses, Jozsef; Haddad, Wassim M; Gholami, Behnood

    2017-09-01

    Gait impairment is a prevalent and important difficulty for patients with multiple sclerosis (MS), a common neurological disorder. An easy to use tool to objectively evaluate gait in MS patients in a clinical setting can assist clinicians to perform an objective assessment. The overall objective of this study is to develop a framework to quantify gait abnormalities in MS patients using the Microsoft Kinect for the Windows sensor; an inexpensive, easy to use, portable camera. Specifically, we aim to evaluate its feasibility for utilization in a clinical setting, assess its reliability, evaluate the validity of gait indices obtained, and evaluate a novel set of gait indices based on the concept of dynamic time warping. In this study, ten ambulatory MS patients, and ten age and sex-matched normal controls were studied at one session in a clinical setting with gait assessment using a Kinect camera. The expanded disability status scale (EDSS) clinical ambulation score was calculated for the MS subjects, and patients completed the Multiple Sclerosis walking scale (MSWS). Based on this study, we established the potential feasibility of using a Microsoft Kinect camera in a clinical setting. Seven out of the eight gait indices obtained using the proposed method were reliable with intraclass correlation coefficients ranging from 0.61 to 0.99. All eight MS gait indices were significantly different from those of the controls (p-values less than 0.05). Finally, seven out of the eight MS gait indices were correlated with the objective and subjective gait measures (Pearson's correlation coefficients greater than 0.40). This study shows that the Kinect camera is an easy to use tool to assess gait in MS patients in a clinical setting.

  12. Inter- and intraobserver repeatability of the Salford Gait Tool: an observation-based clinical gait assessment tool.

    PubMed

    Toro, Brigitte; Nester, Christopher J; Farren, Pauline C

    2007-03-01

    To evaluate the inter- and intraobserver repeatability of the Salford Gait Tool (SF-GT), a new observation-based gait assessment tool for evaluating sagittal plane cerebral palsy (CP) gait. Masked comparative evaluation. University in the United Kingdom. A convenience sample of 23 pediatric physical therapists with varying degrees of clinical experience recruited from the Greater Manchester area. Participants viewed videotapes of the sagittal plane gait of 13 children and used the SF-GT to analyze their 13 different gait styles on 2 occasions. Eleven children had hemiplegic, diplegic, or quadriplegic CP and 2 were neurologically intact. Inter- and intraobserver repeatability of hip, knee, and ankle joint positions at 6 different phases of the gait cycle. The SF-GT demonstrated good interobserver (77%) and intraobserver (75%) repeatability. We have established that the SF-GT is a repeatable clinical assessment tool with which to guide the diagnosis, treatment planning, and evaluation of interventions by pediatric physical therapists of sagittal plane gait deviations in CP.

  13. Flat bands in fractal-like geometry

    NASA Astrophysics Data System (ADS)

    Pal, Biplab; Saha, Kush

    2018-05-01

    We report the presence of multiple flat bands in a class of two-dimensional lattices formed by Sierpinski gasket (SPG) fractal geometries as the basic unit cells. Solving the tight-binding Hamiltonian for such lattices with different generations of a SPG network, we find multiple degenerate and nondegenerate completely flat bands, depending on the configuration of parameters of the Hamiltonian. Moreover, we establish a generic formula to determine the number of such bands as a function of the generation index ℓ of the fractal geometry. We show that the flat bands and their neighboring dispersive bands have remarkable features, the most interesting one being the spin-1 conical-type spectrum at the band center without any staggered magnetic flux, in contrast to the kagome lattice. We furthermore investigate the effect of magnetic flux in these lattice settings and show that different combinations of fluxes through such fractal unit cells lead to a richer spectrum with a single isolated flat band or gapless electron- or holelike flat bands. Finally, we discuss a possible experimental setup to engineer such a fractal flat-band network using single-mode laser-induced photonic waveguides.

  14. Fractals and Transformations.

    ERIC Educational Resources Information Center

    Bannon, Thomas J.

    1991-01-01

    Discussed are several different transformations based on the generation of fractals including self-similar designs, the chaos game, the koch curve, and the Sierpinski Triangle. Three computer programs which illustrate these concepts are provided. (CW)

  15. Gait-Related Brain Activity in People with Parkinson Disease with Freezing of Gait

    PubMed Central

    Peterson, Daniel S.; Pickett, Kristen A.; Duncan, Ryan; Perlmutter, Joel; Earhart, Gammon M.

    2014-01-01

    Approximately 50% of people with Parkinson disease experience freezing of gait, described as a transient inability to produce effective stepping. Complex gait tasks such as turning typically elicit freezing more commonly than simple gait tasks, such as forward walking. Despite the frequency of this debilitating and dangerous symptom, the brain mechanisms underlying freezing remain unclear. Gait imagery during functional magnetic resonance imaging permits investigation of brain activity associated with locomotion. We used this approach to better understand neural function during gait-like tasks in people with Parkinson disease who experience freezing- “FoG+” and people who do not experience freezing- ”FoG−“. Nine FoG+ and nine FoG− imagined complex gait tasks (turning, backward walking), simple gait tasks (forward walking), and quiet standing during measurements of blood oxygen level dependent (BOLD) signal. Changes in BOLD signal (i.e. beta weights) during imagined walking and imagined standing were analyzed across FoG+ and FoG− groups in locomotor brain regions including supplementary motor area, globus pallidus, putamen, mesencephalic locomotor region, and cerebellar locomotor region. Beta weights in locomotor regions did not differ for complex tasks compared to simple tasks in either group. Across imagined gait tasks, FoG+ demonstrated significantly lower beta weights in the right globus pallidus with respect to FoG−. FoG+ also showed trends toward lower beta weights in other right-hemisphere locomotor regions (supplementary motor area, mesencephalic locomotor region). Finally, during imagined stand, FoG+ exhibited lower beta weights in the cerebellar locomotor region with respect to FoG−. These data support previous results suggesting FoG+ exhibit dysfunction in a number of cortical and subcortical regions, possibly with asymmetric dysfunction towards the right hemisphere. PMID:24595265

  16. Elasticity of fractal materials using the continuum model with non-integer dimensional space

    NASA Astrophysics Data System (ADS)

    Tarasov, Vasily E.

    2015-01-01

    Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.

  17. Quantitative assessment of the effects of 6 months of adapted physical activity on gait in people with multiple sclerosis: a randomized controlled trial.

    PubMed

    Pau, Massimiliano; Corona, Federica; Coghe, Giancarlo; Marongiu, Elisabetta; Loi, Andrea; Crisafulli, Antonio; Concu, Alberto; Galli, Manuela; Marrosu, Maria Giovanna; Cocco, Eleonora

    2018-01-01

    The purpose of this study is to quantitatively assess the effect of 6 months of supervised adapted physical activity (APA i.e. physical activity designed for people with special needs) on spatio-temporal and kinematic parameters of gait in persons with Multiple Sclerosis (pwMS). Twenty-two pwMS with Expanded Disability Status Scale scores ranging from 1.5 to 5.5 were randomly assigned either to the intervention group (APA, n = 11) or the control group (CG, n = 11). The former underwent 6 months of APA consisting of 3 weekly 60-min sessions of aerobic and strength training, while CG participants were engaged in no structured PA program. Gait patterns were analyzed before and after the training using three-dimensional gait analysis by calculating spatio-temporal parameters and concise indexes of gait kinematics (Gait Profile Score - GPS and Gait Variable Score - GVS) as well as dynamic Range of Motion (ROM) of hip, knee, and ankle joints. The training originated significant improvements in stride length, gait speed and cadence in the APA group, while GPS and GVS scores remained practically unchanged. A trend of improvement was also observed as regard the dynamic ROM of hip, knee, and ankle joints. No significant changes were observed in the CG for any of the parameters considered. The quantitative analysis of gait supplied mixed evidence about the actual impact of 6 months of APA on pwMS. Although some improvements have been observed, the substantial constancy of kinematic patterns of gait suggests that the full transferability of the administered training on the ambulation function may require more specific exercises. Implications for rehabilitation Adapted Physical Activity (APA) is effective in improving spatio-temporal parameters of gait, but not kinematics, in people with multiple sclerosis. Dynamic range of motion during gait is increased after APA. The full transferability of APA on the ambulation function may require specific exercises rather than

  18. Evaluation of a musculoskeletal model with prosthetic knee through six experimental gait trials.

    PubMed

    Kia, Mohammad; Stylianou, Antonis P; Guess, Trent M

    2014-03-01

    Knowledge of the forces acting on musculoskeletal joint tissues during movement benefits tissue engineering, artificial joint replacement, and our understanding of ligament and cartilage injury. Computational models can be used to predict these internal forces, but musculoskeletal models that simultaneously calculate muscle force and the resulting loading on joint structures are rare. This study used publicly available gait, skeletal geometry, and instrumented prosthetic knee loading data [1] to evaluate muscle driven forward dynamics simulations of walking. Inputs to the simulation were measured kinematics and outputs included muscle, ground reaction, ligament, and joint contact forces. A full body musculoskeletal model with subject specific lower extremity geometries was developed in the multibody framework. A compliant contact was defined between the prosthetic femoral component and tibia insert geometries. Ligament structures were modeled with a nonlinear force-strain relationship. The model included 45 muscles on the right lower leg. During forward dynamics simulations a feedback control scheme calculated muscle forces using the error signal between the current muscle lengths and the lengths recorded during inverse kinematics simulations. Predicted tibio-femoral contact force, ground reaction forces, and muscle forces were compared to experimental measurements for six different gait trials using three different gait types (normal, trunk sway, and medial thrust). The mean average deviation (MAD) and root mean square deviation (RMSD) over one gait cycle are reported. The muscle driven forward dynamics simulations were computationally efficient and consistently reproduced the inverse kinematics motion. The forward simulations also predicted total knee contact forces (166N

  19. Surface and mass fractals in vapor-phase aggregates

    NASA Astrophysics Data System (ADS)

    Hurd, Alan J.; Schaefer, Dale W.; Martin, James E.

    1987-03-01

    Several types of fumed-silica aggregates with differing surface areas were studied over a wide range of spatial resolution by employing both light and neutron scattering. At intermediate length scales, between 100 and 1000 Å, the aggregates are mass fractals with Dm~=1.7-2.0, in basic agreement with simulations of aggregating clusters. At short length scales below 100 Å where the nature of the surfaces of the primary particles dominates the scattering, some of the samples appear to be fractally rough. In particular, a higher surface area seems to be correlated not with smaller primary particles in the aggregates, as previously assumed, but with fractally rough surfaces having Ds as high as 2.5. These may be the first materials discovered to have both mass and surface fractal structure.

  20. Fractal analysis of bone structure with applications to osteoporosis and microgravity effects

    NASA Astrophysics Data System (ADS)

    Acharya, Raj S.; LeBlanc, Adrian; Shackelford, Linda; Swarnakar, Vivek; Krishnamurthy, Ram; Hausman, E.; Lin, Chin-Shoou

    1995-05-01

    We characterize the trabecular structure with the aid of fractal dimension. We use alternating sequential filters (ASF) to generate a nonlinear pyramid for fractal dimension computations. We do not make any assumptions of the statistical distributions of the underlying fractal bone structure. The only assumption of our scheme is the rudimentary definition of self-similarity. This allows us the freedom of not being constrained by statistical estimation schemes. With mathematical simulations, we have shown that the ASF methods outperform other existing methods for fractal dimension estimation. We have shown that the fractal dimension remains the same when computed with both the x-ray images and the MRI images of the patella. We have shown that the fractal dimension of osteoporotic subjects is lower than that of the normal subjects. In animal models, we have shown that the fractal dimension of osteoporotic rats was lower than that of the normal rats. In a 17 week bedrest study, we have shown that the subject's prebedrest fractal dimension is higher than that of the postbedrest fractal dimension.

  1. Fractals and the irreducibility of consciousness in plants and animals.

    PubMed

    Gardiner, John

    2013-08-01

    In both plants and animals consciousness is fractal. Since fractals can only pass information in one direction it is impossible to extrapolate backward to find the rule that governs the fractal. Thus, similarly, it will be impossible to completely determine the rule or rules that govern consciousness.

  2. Crowd-Sourced Amputee Gait Data: A Feasibility Study Using YouTube Videos of Unilateral Trans-Femoral Gait.

    PubMed

    Gardiner, James; Gunarathne, Nuwan; Howard, David; Kenney, Laurence

    2016-01-01

    Collecting large datasets of amputee gait data is notoriously difficult. Additionally, collecting data on less prevalent amputations or on gait activities other than level walking and running on hard surfaces is rarely attempted. However, with the wealth of user-generated content on the Internet, the scope for collecting amputee gait data from alternative sources other than traditional gait labs is intriguing. Here we investigate the potential of YouTube videos to provide gait data on amputee walking. We use an example dataset of trans-femoral amputees level walking at self-selected speeds to collect temporal gait parameters and calculate gait asymmetry. We compare our YouTube data with typical literature values, and show that our methodology produces results that are highly comparable to data collected in a traditional manner. The similarity between the results of our novel methodology and literature values lends confidence to our technique. Nevertheless, clear challenges with the collection and interpretation of crowd-sourced gait data remain, including long term access to datasets, and a lack of validity and reliability studies in this area.

  3. Crowd-Sourced Amputee Gait Data: A Feasibility Study Using YouTube Videos of Unilateral Trans-Femoral Gait

    PubMed Central

    Gardiner, James; Gunarathne, Nuwan; Howard, David; Kenney, Laurence

    2016-01-01

    Collecting large datasets of amputee gait data is notoriously difficult. Additionally, collecting data on less prevalent amputations or on gait activities other than level walking and running on hard surfaces is rarely attempted. However, with the wealth of user-generated content on the Internet, the scope for collecting amputee gait data from alternative sources other than traditional gait labs is intriguing. Here we investigate the potential of YouTube videos to provide gait data on amputee walking. We use an example dataset of trans-femoral amputees level walking at self-selected speeds to collect temporal gait parameters and calculate gait asymmetry. We compare our YouTube data with typical literature values, and show that our methodology produces results that are highly comparable to data collected in a traditional manner. The similarity between the results of our novel methodology and literature values lends confidence to our technique. Nevertheless, clear challenges with the collection and interpretation of crowd-sourced gait data remain, including long term access to datasets, and a lack of validity and reliability studies in this area. PMID:27764226

  4. Estimating the Mechanical Behavior of the Knee Joint during Crouch Gait: Implications for Real-Time Motor Control of Robotic Knee Orthoses

    PubMed Central

    Damiano, Diane L.; Bulea, Thomas C.

    2016-01-01

    Individuals with cerebral palsy frequently exhibit crouch gait, a pathological walking pattern characterized by excessive knee flexion. Knowledge of the knee joint moment during crouch gait is necessary for the design and control of assistive devices used for treatment. Our goal was to 1) develop statistical models to estimate knee joint moment extrema and dynamic stiffness during crouch gait, and 2) use the models to estimate the instantaneous joint moment during weight-acceptance. We retrospectively computed knee moments from 10 children with crouch gait and used stepwise linear regression to develop statistical models describing the knee moment features. The models explained at least 90% of the response value variability: peak moment in early (99%) and late (90%) stance, and dynamic stiffness of weight-acceptance flexion (94%) and extension (98%). We estimated knee extensor moment profiles from the predicted dynamic stiffness and instantaneous knee angle. This approach captured the timing and shape of the computed moment (root-mean-squared error: 2.64 Nm); including the predicted early-stance peak moment as a correction factor improved model performance (root-mean-squared error: 1.37 Nm). Our strategy provides a practical, accurate method to estimate the knee moment during crouch gait, and could be used for real-time, adaptive control of robotic orthoses. PMID:27101612

  5. Underwater gait analysis in Parkinson's disease.

    PubMed

    Volpe, Daniele; Pavan, Davide; Morris, Meg; Guiotto, Annamaria; Iansek, Robert; Fortuna, Sofia; Frazzitta, Giuseppe; Sawacha, Zimi

    2017-02-01

    Although hydrotherapy is one of the physical therapies adopted to optimize gait rehabilitation in people with Parkinson disease, the quantitative measurement of gait-related outcomes has not been provided yet. This work aims to document the gait improvements in a group of parkinsonians after a hydrotherapy program through 2D and 3D underwater and on land gait analysis. Thirty-four parkinsonians and twenty-two controls were enrolled, divided into two different cohorts. In the first one, 2 groups of patients underwent underwater or land based walking training; controls underwent underwater walking training. Hence pre-treatment 2D underwater and on land gait analysis were performed, together with post-treatment on land gait analysis. Considering that current literature documented a reduced movement amplitude in parkinsonians across all lower limb joints in all movement planes, 3D underwater and on land gait analysis were performed on a second cohort of subjects (10 parkinsonians and 10 controls) who underwent underwater gait training. Baseline land 2D and 3D gait analysis in parkinsonians showed shorter stride length and slower speed than controls, in agreement with previous findings. Comparison between underwater and on land gait analysis showed reduction in stride length, cadence and speed on both parkinsonians and controls. Although patients who underwent underwater treatment exhibited significant changes on spatiotemporal parameters and sagittal plane lower limb kinematics, 3D gait analysis documented a significant (p<0.05) improvement in all movement planes. These data deserve attention for research directions promoting the optimal recovery and maintenance of walking ability. Crown Copyright © 2016. Published by Elsevier B.V. All rights reserved.

  6. A new numerical approximation of the fractal ordinary differential equation

    NASA Astrophysics Data System (ADS)

    Atangana, Abdon; Jain, Sonal

    2018-02-01

    The concept of fractal medium is present in several real-world problems, for instance, in the geological formation that constitutes the well-known subsurface water called aquifers. However, attention has not been quite devoted to modeling for instance, the flow of a fluid within these media. We deem it important to remind the reader that the concept of fractal derivative is not to represent the fractal sharps but to describe the movement of the fluid within these media. Since this class of ordinary differential equations is highly complex to solve analytically, we present a novel numerical scheme that allows to solve fractal ordinary differential equations. Error analysis of the method is also presented. Application of the method and numerical approximation are presented for fractal order differential equation. The stability and the convergence of the numerical schemes are investigated in detail. Also some exact solutions of fractal order differential equations are presented and finally some numerical simulations are presented.

  7. From local uncertainty to global predictions: Making predictions on fractal basins

    PubMed Central

    2018-01-01

    In nonlinear systems long term dynamics is governed by the attractors present in phase space. The presence of a chaotic saddle gives rise to basins of attraction with fractal boundaries and sometimes even to Wada boundaries. These two phenomena involve extreme difficulties in the prediction of the future state of the system. However, we show here that it is possible to make statistical predictions even if we do not have any previous knowledge of the initial conditions or the time series of the system until it reaches its final state. In this work, we develop a general method to make statistical predictions in systems with fractal basins. In particular, we have applied this new method to the Duffing oscillator for a choice of parameters where the system possesses the Wada property. We have computed the statistical properties of the Duffing oscillator for different phase space resolutions, to obtain information about the global dynamics of the system. The key idea is that the fraction of initial conditions that evolve towards each attractor is scale free—which we illustrate numerically. We have also shown numerically how having partial information about the initial conditions of the system does not improve in general the predictions in the Wada regions. PMID:29668687

  8. The contributions of balance to gait capacity and motor function in chronic stroke.

    PubMed

    Lee, Kyoung Bo; Lim, Seong Hoon; Kim, Young Dong; Yang, Byung Il; Kim, Kyung Hoon; Lee, Kang Sung; Kim, Eun Ja; Hwang, Byong Yong

    2016-06-01

    [Purpose] The aim of this study was to identify the contributions of balance to gait and motor function in chronic stroke. [Subjects and Methods] Twenty-three outpatients participated in a cross-sectional assessment. Gait ability was assessed using the functional ambulation category, self-paced 10-m walking speed, and fastest 10-m walking speed. Standing balance and trunk control measures included the Berg Balance Scale and the Trunk Impairment Scale. Univariate and multivariate regression analyses were performed. [Results] Balance was the best predictor of the FAC, self-paced walking speed, and fastest walking speed, accounting for 57% to 61% of the variances. Additionally, the total score of TIS was the only predictor of the motor function of the lower limbs and the dynamic balance of TIS was a predictor of the motor function of the upper limbs, accounting for 41% and 29% of the variance, respectively. [Conclusion] This study demonstrated the relative contribution of standing balance and trunk balance to gait ability and motor function. They show that balance has a high power of explanation of gait ability and that trunk balance is a determinant of motor function rather than gait ability.

  9. The contributions of balance to gait capacity and motor function in chronic stroke

    PubMed Central

    Lee, Kyoung Bo; Lim, Seong Hoon; Kim, Young Dong; Yang, Byung Il; Kim, Kyung Hoon; Lee, Kang Sung; Kim, Eun Ja; Hwang, Byong Yong

    2016-01-01

    [Purpose] The aim of this study was to identify the contributions of balance to gait and motor function in chronic stroke. [Subjects and Methods] Twenty-three outpatients participated in a cross-sectional assessment. Gait ability was assessed using the functional ambulation category, self-paced 10-m walking speed, and fastest 10-m walking speed. Standing balance and trunk control measures included the Berg Balance Scale and the Trunk Impairment Scale. Univariate and multivariate regression analyses were performed. [Results] Balance was the best predictor of the FAC, self-paced walking speed, and fastest walking speed, accounting for 57% to 61% of the variances. Additionally, the total score of TIS was the only predictor of the motor function of the lower limbs and the dynamic balance of TIS was a predictor of the motor function of the upper limbs, accounting for 41% and 29% of the variance, respectively. [Conclusion] This study demonstrated the relative contribution of standing balance and trunk balance to gait ability and motor function. They show that balance has a high power of explanation of gait ability and that trunk balance is a determinant of motor function rather than gait ability. PMID:27390395

  10. Terminology and forensic gait analysis.

    PubMed

    Birch, Ivan; Vernon, Wesley; Walker, Jeremy; Young, Maria

    2015-07-01

    The use of appropriate terminology is a fundamental aspect of forensic gait analysis. The language used in forensic gait analysis is an amalgam of that used in clinical practice, podiatric biomechanics and the wider field of biomechanics. The result can often be a lack of consistency in the language used, the definitions used and the clarity of the message given. Examples include the use of 'gait' and 'walking' as synonymous terms, confusion between 'step' and 'stride', the mixing of anatomical, positional and pathological descriptors, and inability to describe appropriately movements of major body segments such as the torso. The purpose of this paper is to share the well-established definitions of the fundamental parameters of gait, common to all professions, and advocate their use in forensic gait analysis to establish commonality. The paper provides guidance on the selection and use of appropriate terminology in the description of gait in the forensic context. This paper considers the established definitions of the terms commonly used, identifies those terms which have the potential to confuse readers, and suggests a framework of terminology which should be utilised in forensic gait analysis. Copyright © 2015 Forensic Science Society. Published by Elsevier Ireland Ltd. All rights reserved.

  11. Gait disorders in the elderly and dual task gait analysis: a new approach for identifying motor phenotypes.

    PubMed

    Auvinet, Bernard; Touzard, Claude; Montestruc, François; Delafond, Arnaud; Goeb, Vincent

    2017-01-31

    Gait disorders and gait analysis under single and dual-task conditions are topics of great interest, but very few studies have looked for the relevance of gait analysis under dual-task conditions in elderly people on the basis of a clinical approach. An observational study including 103 patients (mean age 76.3 ± 7.2, women 56%) suffering from gait disorders or memory impairment was conducted. Gait analysis under dual-task conditions was carried out for all patients. Brain MRI was performed in the absence of contra-indications. Three main gait variables were measured: walking speed, stride frequency, and stride regularity. For each gait variable, the dual task cost was computed and a quartile analysis was obtained. Nonparametric tests were used for all the comparisons (Wilcoxon, Kruskal-Wallis, Fisher or Chi 2 tests). Four clinical subgroups were identified: gait instability (45%), recurrent falls (29%), memory impairment (18%), and cautious gait (8%). The biomechanical severity of these subgroups was ordered according to walking speed and stride regularity under both conditions, from least to most serious as follows: memory impairment, gait instability, recurrent falls, cautious gait (p < 0.01 for walking speed, p = 0.05 for stride regularity). According to the established diagnoses of gait disorders, 5 main pathological subgroups were identified (musculoskeletal diseases (n = 11), vestibular diseases (n = 6), mild cognitive impairment (n = 24), central nervous system pathologies, (n = 51), and without diagnosis (n = 8)). The dual task cost for walking speed, stride frequency and stride regularity were different among these subgroups (p < 0.01). The subgroups mild cognitive impairment and central nervous system pathologies both showed together a higher dual task cost for each variable compared to the other subgroups combined (p = 0.01). The quartile analysis of dual task cost for stride frequency and stride regularity

  12. Fractality of eroded coastlines of correlated landscapes.

    PubMed

    Morais, P A; Oliveira, E A; Araújo, N A M; Herrmann, H J; Andrade, J S

    2011-07-01

    Using numerical simulations of a simple sea-coast mechanical erosion model, we investigate the effect of spatial long-range correlations in the lithology of coastal landscapes on the fractal behavior of the corresponding coastlines. In the model, the resistance of a coast section to erosion depends on the local lithology configuration as well as on the number of neighboring sea sides. For weak sea forces, the sea is trapped by the coastline and the eroding process stops after some time. For strong sea forces erosion is perpetual. The transition between these two regimes takes place at a critical sea force, characterized by a fractal coastline front. For uncorrelated landscapes, we obtain, at the critical value, a fractal dimension D=1.33, which is consistent with the dimension of the accessible external perimeter of the spanning cluster in two-dimensional percolation. For sea forces above the critical value, our results indicate that the coastline is self-affine and belongs to the Kardar-Parisi-Zhang universality class. In the case of landscapes generated with power-law spatial long-range correlations, the coastline fractal dimension changes continuously with the Hurst exponent H, decreasing from D=1.34 to 1.04, for H=0 and 1, respectively. This nonuniversal behavior is compatible with the multitude of fractal dimensions found for real coastlines.

  13. Fractals and the irreducibility of consciousness in plants and animals

    PubMed Central

    Gardiner, John

    2013-01-01

    In both plants and animals consciousness is fractal. Since fractals can only pass information in one direction it is impossible to extrapolate backward to find the rule that governs the fractal. Thus, similarly, it will be impossible to completely determine the rule or rules that govern consciousness. PMID:23759545

  14. Gait variability and basal ganglia disorders: stride-to-stride variations of gait cycle timing in Parkinson's disease and Huntington's disease

    NASA Technical Reports Server (NTRS)

    Hausdorff, J. M.; Cudkowicz, M. E.; Firtion, R.; Wei, J. Y.; Goldberger, A. L.

    1998-01-01

    The basal ganglia are thought to play an important role in regulating motor programs involved in gait and in the fluidity and sequencing of movement. We postulated that the ability to maintain a steady gait, with low stride-to-stride variability of gait cycle timing and its subphases, would be diminished with both Parkinson's disease (PD) and Huntington's disease (HD). To test this hypothesis, we obtained quantitative measures of stride-to-stride variability of gait cycle timing in subjects with PD (n = 15), HD (n = 20), and disease-free controls (n = 16). All measures of gait variability were significantly increased in PD and HD. In subjects with PD and HD, gait variability measures were two and three times that observed in control subjects, respectively. The degree of gait variability correlated with disease severity. In contrast, gait speed was significantly lower in PD, but not in HD, and average gait cycle duration and the time spent in many subphases of the gait cycle were similar in control subjects, HD subjects, and PD subjects. These findings are consistent with a differential control of gait variability, speed, and average gait cycle timing that may have implications for understanding the role of the basal ganglia in locomotor control and for quantitatively assessing gait in clinical settings.

  15. Association of Baseline Knee Sagittal Dynamic Joint Stiffness during Gait and 2-year Patellofemoral Cartilage Damage Worsening in Knee Osteoarthritis

    PubMed Central

    Chang, Alison H.; Chmiel, Joan S.; Almagor, Orit; Guermazi, Ali; Prasad, Pottumarthi V.; Moisio, Kirsten C.; Belisle, Laura; Zhang, Yunhui; Hayes, Karen; Sharma, Leena

    2016-01-01

    Objective Knee sagittal dynamic joint stiffness (DJS) describes the biomechanical interaction between change in external knee flexion moment and flexion angular excursion during gait. In theory, greater DJS may particularly stress the patellofemoral (PF) compartment and thereby contribute to PF osteoarthritis (OA) worsening. We hypothesized that greater baseline knee sagittal DJS is associated with PF cartilage damage worsening 2 years later. Methods Participants all had OA in at least one knee. Knee kinematics and kinetics during gait were recorded using motion capture systems and force plates. Knee sagittal DJS was computed as the slope of the linear regression line for knee flexion moments vs. angles during the loading response phase. Knee MRI scans were obtained at baseline and 2 years later. We assessed the association between baseline DJS and baseline-to-2-year PF cartilage damage worsening using logistic regression with generalized estimating equations. Results Our sample had 391 knees (204 persons): mean age 64.2 years (SD 10.0); BMI 28.4 kg/m2 (5.7); 76.5% women. Baseline knee sagittal DJS was associated with baseline-to-2-year cartilage damage worsening in the lateral (OR=5.35, 95% CI: 2.37–12.05) and any PF (OR=2.99, 95% CI: 1.27–7.04) compartment. Individual components of baseline DJS (i.e., change in knee moment or angle) were not associated with subsequent PF disease worsening. Conclusion Capturing the concomitant effect of knee kinetics and kinematics during gait, knee sagittal DJS is a potentially modifiable risk factor for PF disease worsening. PMID:27729289

  16. Methods of nanoassembly of a fractal polymer and materials formed thereby

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Newkome, George R; Moorefield, Charles N

    2012-07-24

    The invention relates to the formation of synthesized fractal constructs and the methods of chemical self-assembly for the preparation of a non-dendritic, nano-scale, fractal constructs or molecules. More particularly, the invention relates to fractal constructs formed by molecular self-assembly, to create synthetic, nanometer-scale fractal shapes. In an embodiment, a nanoscale Sierpinski hexagonal gasket is formed. This non-dendritic, perfectly self-similar fractal macromolecule is comprised of bisterpyridine building blocks that are bound together by coordination to 36 Ru and 6 Fe ions to form a nearly planar array of increasingly larger hexagons around a hollow center.

  17. Methods of nanoassembly of a fractal polymer and materials formed thereby

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Newkome, George R; Moorefield, Charles N

    2014-09-23

    The invention relates to the formation of synthesized fractal constructs and the methods of chemical self-assembly for the preparation of a non-dendritic, nano-scale, fractal constructs or molecules. More particularly, the invention relates to fractal constructs formed by molecular self-assembly, to create synthetic, nanometer-scale fractal shapes. In an embodiment, a nanoscale Sierpinski hexagonal gasket is formed. This non-dendritic, perfectly self-similar fractal macromolecule is comprised of bisterpyridine building blocks that are bound together by coordination to (36) Ru and (6) Fe ions to form a nearly planar array of increasingly larger hexagons around a hollow center.

  18. Simple analytical model reveals the functional role of embodied sensorimotor interaction in hexapod gaits

    PubMed Central

    Aoi, Shinya; Nachstedt, Timo; Manoonpong, Poramate; Wörgötter, Florentin; Matsuno, Fumitoshi

    2018-01-01

    Insects have various gaits with specific characteristics and can change their gaits smoothly in accordance with their speed. These gaits emerge from the embodied sensorimotor interactions that occur between the insect’s neural control and body dynamic systems through sensory feedback. Sensory feedback plays a critical role in coordinated movements such as locomotion, particularly in stick insects. While many previously developed insect models can generate different insect gaits, the functional role of embodied sensorimotor interactions in the interlimb coordination of insects remains unclear because of their complexity. In this study, we propose a simple physical model that is amenable to mathematical analysis to explain the functional role of these interactions clearly. We focus on a foot contact sensory feedback called phase resetting, which regulates leg retraction timing based on touchdown information. First, we used a hexapod robot to determine whether the distributed decoupled oscillators used for legs with the sensory feedback generate insect-like gaits through embodied sensorimotor interactions. The robot generated two different gaits and one had similar characteristics to insect gaits. Next, we proposed the simple model as a minimal model that allowed us to analyze and explain the gait mechanism through the embodied sensorimotor interactions. The simple model consists of a rigid body with massless springs acting as legs, where the legs are controlled using oscillator phases with phase resetting, and the governed equations are reduced such that they can be explained using only the oscillator phases with some approximations. This simplicity leads to analytical solutions for the hexapod gaits via perturbation analysis, despite the complexity of the embodied sensorimotor interactions. This is the first study to provide an analytical model for insect gaits under these interaction conditions. Our results clarified how this specific foot contact sensory

  19. [Subjective Gait Stability in the Elderly].

    PubMed

    Hirsch, Theresa; Lampe, Jasmin; Michalk, Katrin; Röder, Lotte; Munsch, Karoline; Marquardt, Jonas

    2017-07-10

    It can be assumed that the feeling of gait stability or gait instability in the elderly may be independent of a possible fear of falling or a history of falling when walking. Up to now, there has been a lack of spatiotemporal gait parameters for older people who subjectively feel secure when walking. The aim of the study is to analyse the distribution of various gait parameters for older people who subjectively feel secure when walking. In a cross-sectional study, the gait parameters stride time, step time, stride length, step length, double support, single support, and walking speed were measured using a Vicon three-dimensional motion capture system (Plug-In Gait Lower-Body Marker Set) in 31 healthy people aged 65 years and older (mean age 72 ± 3.54 years) who subjectively feel secure when walking. There was a homogeneous distribution in the gait parameters examined, with no abnormalities. The mean values have a low variance with narrow confidence intervals. This study provides evidence that people who subjectively feel secure when walking demonstrate similarly objective gait parameters..

  20. Foot placement control and gait instability among people with stroke

    PubMed Central

    Dean, Jesse C.; Kautz, Steven A.

    2016-01-01

    Gait instability is a common problem following stroke, as evidenced by increases in fall risk and fear of falling. However, the mechanism underlying gait instability is currently unclear. We recently found that young, healthy humans use a consistent gait stabilization strategy of actively controlling their mediolateral foot placement based on the concurrent mechanical state of the stance limb. In the present work, we tested whether people with stroke (n = 16) and age-matched controls (n = 19) used this neuromechanical strategy. Specifically, we used multiple linear regressions to test whether (1) swing phase gluteus medius (GM) activity was influenced by the simultaneous state of the stance limb and (2) mediolateral foot placement location was influenced by swing phase GM activity and the mechanical state of the swing limb at the start of the step. We found that both age-matched controls and people with stroke classified as having a low fall risk (Dynamic Gait Index [DGI] score >19) essentially used the stabilization strategy previously described in young controls. In contrast, this strategy was disrupted for people with stroke classified as higher fall risk (DGI

  1. Applications of fractals in ecology.

    PubMed

    Sugihara, G; M May, R

    1990-03-01

    Fractal models describe the geometry of a wide variety of natural objects such as coastlines, island chains, coral reefs, satellite ocean-color images and patches of vegetation. Cast in the form of modified diffusion models, they can mimic natural and artificial landscapes having different types of complexity of shape. This article provides a brief introduction to fractals and reports on how they can be used by ecologists to answer a variety of basic questions, about scale, measurement and hierarchy in, ecological systems. Copyright © 1990. Published by Elsevier Ltd.

  2. Automated Gait Analysis Through Hues and Areas (AGATHA): a method to characterize the spatiotemporal pattern of rat gait

    PubMed Central

    Kloefkorn, Heidi E.; Pettengill, Travis R.; Turner, Sara M. F.; Streeter, Kristi A.; Gonzalez-Rothi, Elisa J.; Fuller, David D.; Allen, Kyle D.

    2016-01-01

    While rodent gait analysis can quantify the behavioral consequences of disease, significant methodological differences exist between analysis platforms and little validation has been performed to understand or mitigate these sources of variance. By providing the algorithms used to quantify gait, open-source gait analysis software can be validated and used to explore methodological differences. Our group is introducing, for the first time, a fully-automated, open-source method for the characterization of rodent spatiotemporal gait patterns, termed Automated Gait Analysis Through Hues and Areas (AGATHA). This study describes how AGATHA identifies gait events, validates AGATHA relative to manual digitization methods, and utilizes AGATHA to detect gait compensations in orthopaedic and spinal cord injury models. To validate AGATHA against manual digitization, results from videos of rodent gait, recorded at 1000 frames per second (fps), were compared. To assess one common source of variance (the effects of video frame rate), these 1000 fps videos were re-sampled to mimic several lower fps and compared again. While spatial variables were indistinguishable between AGATHA and manual digitization, low video frame rates resulted in temporal errors for both methods. At frame rates over 125 fps, AGATHA achieved a comparable accuracy and precision to manual digitization for all gait variables. Moreover, AGATHA detected unique gait changes in each injury model. These data demonstrate AGATHA is an accurate and precise platform for the analysis of rodent spatiotemporal gait patterns. PMID:27554674

  3. Automated Gait Analysis Through Hues and Areas (AGATHA): A Method to Characterize the Spatiotemporal Pattern of Rat Gait.

    PubMed

    Kloefkorn, Heidi E; Pettengill, Travis R; Turner, Sara M F; Streeter, Kristi A; Gonzalez-Rothi, Elisa J; Fuller, David D; Allen, Kyle D

    2017-03-01

    While rodent gait analysis can quantify the behavioral consequences of disease, significant methodological differences exist between analysis platforms and little validation has been performed to understand or mitigate these sources of variance. By providing the algorithms used to quantify gait, open-source gait analysis software can be validated and used to explore methodological differences. Our group is introducing, for the first time, a fully-automated, open-source method for the characterization of rodent spatiotemporal gait patterns, termed Automated Gait Analysis Through Hues and Areas (AGATHA). This study describes how AGATHA identifies gait events, validates AGATHA relative to manual digitization methods, and utilizes AGATHA to detect gait compensations in orthopaedic and spinal cord injury models. To validate AGATHA against manual digitization, results from videos of rodent gait, recorded at 1000 frames per second (fps), were compared. To assess one common source of variance (the effects of video frame rate), these 1000 fps videos were re-sampled to mimic several lower fps and compared again. While spatial variables were indistinguishable between AGATHA and manual digitization, low video frame rates resulted in temporal errors for both methods. At frame rates over 125 fps, AGATHA achieved a comparable accuracy and precision to manual digitization for all gait variables. Moreover, AGATHA detected unique gait changes in each injury model. These data demonstrate AGATHA is an accurate and precise platform for the analysis of rodent spatiotemporal gait patterns.

  4. A mechanical energy analysis of gait initiation

    NASA Technical Reports Server (NTRS)

    Miller, C. A.; Verstraete, M. C.

    1999-01-01

    The analysis of gait initiation (the transient state between standing and walking) is an important diagnostic tool to study pathologic gait and to evaluate prosthetic devices. While past studies have quantified mechanical energy of the body during steady-state gait, to date no one has computed the mechanical energy of the body during gait initiation. In this study, gait initiation in seven normal male subjects was studied using a mechanical energy analysis to compute total body energy. The data showed three separate states: quiet standing, gait initiation, and steady-state gait. During gait initiation, the trends in the energy data for the individual segments were similar to those seen during steady-state gait (and in Winter DA, Quanbury AO, Reimer GD. Analysis of instantaneous energy of normal gait. J Biochem 1976;9:253-257), but diminished in amplitude. However, these amplitudes increased to those seen in steady-state during the gait initiation event (GIE), with the greatest increase occurring in the second step due to the push-off of the foundation leg. The baseline level of mechanical energy was due to the potential energy of the individual segments, while the cyclic nature of the data was indicative of the kinetic energy of the particular leg in swing phase during that step. The data presented showed differences in energy trends during gait initiation from those of steady state, thereby demonstrating the importance of this event in the study of locomotion.

  5. Multi-Scale Fractal Analysis of Image Texture and Pattern

    NASA Technical Reports Server (NTRS)

    Emerson, Charles W.; Lam, Nina Siu-Ngan; Quattrochi, Dale A.

    1999-01-01

    Analyses of the fractal dimension of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed (10 to 80 meters). A similar analysis of Landsat Thematic Mapper images of the East Humboldt Range in Nevada taken four months apart show a more complex relation between pixel size and fractal dimension. The major visible difference between the spring and late summer NDVI images is the absence of high elevation snow cover in the summer image. This change significantly alters the relation between fractal dimension and pixel size. The slope of the fractal dimension-resolution relation provides indications of how image classification or feature identification will be affected by changes in sensor spatial resolution.

  6. Multi-Scale Fractal Analysis of Image Texture and Pattern

    NASA Technical Reports Server (NTRS)

    Emerson, Charles W.; Lam, Nina Siu-Ngan; Quattrochi, Dale A.

    1999-01-01

    Analyses of the fractal dimension of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed (10 to 80 meters). A similar analysis of Landsat Thematic Mapper images of the East Humboldt Range in Nevada taken four months apart show a more complex relation between pixel size and fractal dimension. The major visible difference between the spring and late summer NDVI images of the absence of high elevation snow cover in the summer image. This change significantly alters the relation between fractal dimension and pixel size. The slope of the fractal dimensional-resolution relation provides indications of how image classification or feature identification will be affected by changes in sensor spatial resolution.

  7. A New Classification of Diabetic Gait Pattern Based on Cluster Analysis of Biomechanical Data

    PubMed Central

    Sawacha, Zimi; Guarneri, Gabriella; Avogaro, Angelo; Cobelli, Claudio

    2010-01-01

    Background The diabetic foot, one of the most serious complications of diabetes mellitus and a major risk factor for plantar ulceration, is determined mainly by peripheral neuropathy. Neuropathic patients exhibit decreased stability while standing as well as during dynamic conditions. A new methodology for diabetic gait pattern classification based on cluster analysis has been proposed that aims to identify groups of subjects with similar patterns of gait and verify if three-dimensional gait data are able to distinguish diabetic gait patterns from one of the control subjects. Method The gait of 20 nondiabetic individuals and 46 diabetes patients with and without peripheral neuropathy was analyzed [mean age 59.0 (2.9) and 61.1(4.4) years, mean body mass index (BMI) 24.0 (2.8), and 26.3 (2.0)]. K-means cluster analysis was applied to classify the subjects' gait patterns through the analysis of their ground reaction forces, joints and segments (trunk, hip, knee, ankle) angles, and moments. Results Cluster analysis classification led to definition of four well-separated clusters: one aggregating just neuropathic subjects, one aggregating both neuropathics and non-neuropathics, one including only diabetes patients, and one including either controls or diabetic and neuropathic subjects. Conclusions Cluster analysis was useful in grouping subjects with similar gait patterns and provided evidence that there were subgroups that might otherwise not be observed if a group ensemble was presented for any specific variable. In particular, we observed the presence of neuropathic subjects with a gait similar to the controls and diabetes patients with a long disease duration with a gait as altered as the neuropathic one. PMID:20920432

  8. Lateral trunk lean and medializing the knee as gait strategies for knee osteoarthritis.

    PubMed

    Gerbrands, T A; Pisters, M F; Theeven, P J R; Verschueren, S; Vanwanseele, B

    2017-01-01

    To determine (1) if Medial Thrust or Trunk Lean reduces the knee adduction moment (EKAM) the most during gait in patients with medial knee osteoarthritis, (2) if the best overall strategy is the most effective for each patient and (3) if these strategies affect ankle and hip kinetics. Thirty patients with symptomatic medial knee osteoarthritis underwent 3-dimensional gait analysis. Participants received verbal instructions on two gait strategies (Trunk Lean and Medial Thrust) in randomized order after comfortable walking was recorded. The peaks and impulse of the EKAM and strategy-specific kinematic and kinetic variables were calculated for all conditions. Early stance EKAM peak was significantly reduced during Medial Thrust (-29%). During Trunk Lean, early and late stance EKAM peak and EKAM impulse reduced significantly (38%, 21% and -25%, respectively). In 79% of the subjects, the Trunk Lean condition was significantly more effective in reducing EKAM peak than Medial Thrust. Peak ankle dorsi and plantar flexion, knee flexion and hip extension and adduction moments were not significantly increased. Medial Thrust and Trunk Lean reduced the EKAM during gait in patients with knee osteoarthritis. Individual selection of the most effective gait modification strategy seems vital to optimally reduce dynamic knee loading during gait. No detrimental effects on external ankle and hip moments or knee flexion moments were found for these conditions. Copyright © 2016 Elsevier B.V. All rights reserved.

  9. Fractal analysis of bone structure with applications to osteoporosis and microgravity effects

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Acharya, R.S.; Swarnarkar, V.; Krishnamurthy, R.

    1995-12-31

    The authors characterize the trabecular structure with the aid of fractal dimension. The authors use Alternating Sequential filters to generate a nonlinear pyramid for fractal dimension computations. The authors do not make any assumptions of the statistical distributions of the underlying fractal bone structure. The only assumption of the scheme is the rudimentary definition of self similarity. This allows them the freedom of not being constrained by statistical estimation schemes. With mathematical simulations, the authors have shown that the ASF methods outperform other existing methods for fractal dimension estimation. They have shown that the fractal dimension remains the same whenmore » computed with both the X-Ray images and the MRI images of the patella. They have shown that the fractal dimension of osteoporotic subjects is lower than that of the normal subjects. In animal models, the authors have shown that the fractal dimension of osteoporotic rats was lower than that of the normal rats. In a 17 week bedrest study, they have shown that the subject`s prebedrest fractal dimension is higher than that of the postbedrest fractal dimension.« less

  10. Is volcanic phenomena of fractal nature?

    NASA Astrophysics Data System (ADS)

    Quevedo, R.; Lopez, D. A. L.; Alparone, S.; Hernandez Perez, P. A.; Sagiya, T.; Barrancos, J.; Rodriguez-Santana, A. A.; Ramos, A.; Calvari, S.; Perez, N. M.

    2016-12-01

    A particular resonance waveform pattern has been detected beneath different physical volcano manifestations from recent 2011-2012 period of volcanic unrest at El Hierro Island, Canary Islands, and also from other worldwide volcanoes with different volcanic typology. This mentioned pattern appears to be a fractal time dependent waveform repeated in different time scales (periods of time). This time dependent feature suggests this resonance as a new approach to volcano phenomena for predicting such interesting matters as earthquakes, gas emission, deformation etc. as this fractal signal has been discovered hidden in a wide typical volcanic parameters measurements. It is known that the resonance phenomenon occurring in nature usually denote a structure, symmetry or a subjacent law (Fermi et al., 1952; and later -about enhanced cross-sections symmetry in protons collisions), which, in this particular case, may be indicative of some physical interactions showing a sequence not completely chaotic but cyclic provided with symmetries. The resonance and fractal model mentioned allowed the authors to make predictions in cycles from a few weeks to months. In this work an equation for this waveform has been described and also correlations with volcanic parameters and fractal behavior demonstration have been performed, including also some suggestive possible explanations of this signal origin.

  11. Fractal Music: The Mathematics Behind "Techno" Music

    ERIC Educational Resources Information Center

    Padula, Janice

    2005-01-01

    This article describes sound waves, their basis in the sine curve, Fourier's theorem of infinite series, the fractal equation and its application to the composition of music, together with algorithms (such as those employed by meteorologist Edward Lorenz in his discovery of chaos theory) that are now being used to compose fractal music on…

  12. DMRT3 is associated with gait type in Mangalarga Marchador horses, but does not control gait ability.

    PubMed

    Patterson, L; Staiger, E A; Brooks, S A

    2015-04-01

    The Mangalarga Marchador (MM) is a Brazilian horse breed known for a uniquely smooth gait. A recent publication described a mutation in the DMRT3 gene that the authors claim controls the ability to perform lateral patterned gaits (Andersson et al. 2012). We tested 81 MM samples for the DMRT3 mutation using extracted DNA from hair bulbs using a novel RFLP. Horses were phenotypically categorized by their gait type (batida or picada), as recorded by the Brazilian Mangalarga Marchador Breeders Association (ABCCMM). Statistical analysis using the plink toolset (Purcell, 2007) revealed significant association between gait type and the DMRT3 mutation (P = 2.3e-22). Deviation from Hardy-Weinberg equilibrium suggests that selective pressure for gait type is altering allele frequencies in this breed (P = 1.00e-5). These results indicate that this polymorphism may be useful for genotype-assisted selection for gait type within this breed. As both batida and picada MM horses can perform lateral gaits, the DMRT3 mutation is not the only locus responsible for the lateral gait pattern. © 2015 Stichting International Foundation for Animal Genetics.

  13. Ultrasound monitoring of inter-knee distances during gait.

    PubMed

    Lai, Daniel T H; Wrigley, Tim V; Palaniswami, M

    2009-01-01

    Knee osteoarthritis is an extremely common, debilitating disease associated with pain and loss of function. There is considerable interest in monitoring lower limb alignment due to its close association with joint overload leading to disease progression. The effects of gait modifications that can lower joint loading are of particular interest. Here we describe an ultrasound-based system for monitoring an important aspect of dynamic lower limb alignment, the inter-knee distance during walking. Monitoring this gait parameter should facilitate studies in reducing knee loading, a primary risk factor of knee osteoarthritis progression. The portable device is composed of an ultrasound sensor connected to an Intel iMote2 equipped with Bluetooth wireless capability. Static tests and calibration results show that the sensor possesses an effective beam envelope of 120 degrees, with maximum distance errors of 10% at the envelope edges. Dynamic walking trials reveal close correlation of inter-knee distance trends between that measured by an optical system (Optotrak Certus NDI) and the sensor device. The maximum average root mean square error was found to be 1.46 cm. Future work will focus on improving the accuracy of the device.

  14. Association of Dual-Task Gait With Incident Dementia in Mild Cognitive Impairment: Results From the Gait and Brain Study.

    PubMed

    Montero-Odasso, Manuel M; Sarquis-Adamson, Yanina; Speechley, Mark; Borrie, Michael J; Hachinski, Vladimir C; Wells, Jennie; Riccio, Patricia M; Schapira, Marcelo; Sejdic, Ervin; Camicioli, Richard M; Bartha, Robert; McIlroy, William E; Muir-Hunter, Susan

    2017-07-01

    Gait performance is affected by neurodegeneration in aging and has the potential to be used as a clinical marker for progression from mild cognitive impairment (MCI) to dementia. A dual-task gait test evaluating the cognitive-motor interface may predict dementia progression in older adults with MCI. To determine whether a dual-task gait test is associated with incident dementia in MCI. The Gait and Brain Study is an ongoing prospective cohort study of community-dwelling older adults that enrolled 112 older adults with MCI. Participants were followed up for 6 years, with biannual visits including neurologic, cognitive, and gait assessments. Data were collected from July 2007 to March 2016. Incident all-cause dementia was the main outcome measure, and single- and dual-task gait velocity and dual-task gait costs were the independent variables. A neuropsychological test battery was used to assess cognition. Gait velocity was recorded under single-task and 3 separate dual-task conditions using an electronic walkway. Dual-task gait cost was defined as the percentage change between single- and dual-task gait velocities: ([single-task gait velocity - dual-task gait velocity]/ single-task gait velocity) × 100. Cox proportional hazard models were used to estimate the association between risk of progression to dementia and the independent variables, adjusted for age, sex, education, comorbidities, and cognition. Among 112 study participants with MCI, mean (SD) age was 76.6 (6.9) years, 55 were women (49.1%), and 27 progressed to dementia (24.1%), with an incidence rate of 121 per 1000 person-years. Slow single-task gait velocity (<0.8 m/second) was not associated with progression to dementia (hazard ratio [HR], 3.41; 95% CI, 0.99-11.71; P = .05)while high dual-task gait cost while counting backward (HR, 3.79; 95% CI, 1.57-9.15; P = .003) and naming animals (HR, 2.41; 95% CI, 1.04-5.59; P = .04) were associated with dementia progression (incidence rate, 155 per

  15. The effect of gait velocity on calcaneal balance at heel strike; Implications for orthotic prescription in injury prevention.

    PubMed

    Shanthikumar, Shivanthan; Low, Zi; Falvey, Eanna; McCrory, Paul; Franklyn-Miller, Andy

    2010-01-01

    Exercise related lower limb injuries (ERLLI), are common in the recreational and competitive sporting population. Although ERLLI are thought to be multi-factorial in aetiology, one of the critical predisposing factors is known to gait abnormality. There is little published evidence comparing walking and running gait in the same subjects, and no evidence on the effect of gait velocity on calcaneal pronation, even though this may have implications for orthotic prescription and injury prevention. In this study, the walking and running gait of 50 physically active subjects was assessed using pressure plate analysis. The results show that rearfoot pronation occurs on foot contact in both running and walking gait, and that there is significantly more rearfoot pronation in walking gait (p<0.01). The difference in the magnitude of rearfoot pronation affected foot orthoses prescription. A 63% fall in computerized correction suggested by RSscan D3D software prescription was seen, based on running vs. walking gait. The findings of this study suggest that in the athletic population orthoses prescription should be based on dynamic assessment of running gait. Crown Copyright 2009. Published by Elsevier B.V. All rights reserved.

  16. Gait analysis in a mouse model resembling Leigh disease.

    PubMed

    de Haas, Ria; Russel, Frans G; Smeitink, Jan A

    2016-01-01

    Leigh disease (LD) is one of the clinical phenotypes of mitochondrial OXPHOS disorders and also known as sub-acute necrotizing encephalomyelopathy. The disease has an incidence of 1 in 77,000 live births. Symptoms typically begin early in life and prognosis for LD patients is poor. Currently, no clinically effective treatments are available. Suitable animal and cellular models are necessary for the understanding of the neuropathology and the development of successful new therapeutic strategies. In this study we used the Ndufs4 knockout (Ndufs4(-/-)) mouse, a model of mitochondrial complex I deficiency. Ndusf4(-/-) mice exhibit progressive neurodegeneration, which closely resemble the human LD phenotype. When dissecting behavioral abnormalities in animal models it is of great importance to apply translational tools that are clinically relevant. To distinguish gait abnormalities in patients, simple walking tests can be assessed, but in animals this is not easy. This study is the first to demonstrate automated CatWalk gait analysis in the Ndufs4(-/-) mouse model. Marked differences were noted between Ndufs4(-/-) and control mice in dynamic, static, coordination and support parameters. Variation of walking speed was significantly increased in Ndufs4(-/-) mice, suggesting hampered and uncoordinated gait. Furthermore, decreased regularity index, increased base of support and changes in support were noted in the Ndufs4(-/-) mice. Here, we report the ability of the CatWalk system to sensitively assess gait abnormalities in Ndufs4(-/-) mice. This objective gait analysis can be of great value for intervention and drug efficacy studies in animal models for mitochondrial disease. Copyright © 2015 Elsevier B.V. All rights reserved.

  17. A Fractal Permeability Model for Shale Oil Reservoir

    NASA Astrophysics Data System (ADS)

    Zhang, Tao; Dong, Mingzhe; Li, Yajun

    2018-01-01

    In this work, a fractal analytical model is proposed to predict the permeability of shale reservoir. The proposed model explicitly relates the permeability to the micro-structural parameters (tortuosity, pore area fractal dimensions, porosity and slip velocity coefficient) of shale.

  18. Fractional and fractal dynamics approach to anomalous diffusion in porous media: application to landslide behavior

    NASA Astrophysics Data System (ADS)

    Martelloni, Gianluca; Bagnoli, Franco

    2016-04-01

    Richardson's treatise on turbulent diffusion in 1926 [24] and today, the list of system displaying anomalous dynamical behavior is quite extensive. We only report some examples: charge carrier transport in amorphous semiconductors [25], porous systems [26], reptation dynamics in polymeric systems [27, 28], transport on fractal geometries [29], the long-time dynamics of DNA sequences [30]. In this scenario, the fractional calculus is used to generalized the Fokker-Planck linear equation -∂P (x,t)=D ∇2P (x,t), ∂t (3) where P (x,t) is the density of probability in the space x=[x1, x2, x3] and time t, while D >0 is the diffusion coefficient. Such processes are characterized by Eq. (1). An example of Eq. (3) generalization is ∂∂tP (x,t)=D∇ αP β(x,t) - ∞ < α ≤ 2 β > - 1 , (4) where the fractional based-derivatives Laplacian Σ(∂α/∂xα)i, (i = 1, 2, 3), of non-linear term Pβ(x,t) is taken into account [31]. Another generalized form is represented by equation ∂∂tδδP(x,t)=D ∇ αP(x,t) δ > 0 α ≤ 2 , (5) that considers also the fractional time-derivative [32]. These fractional-described processes exhibit a power law patters as expressed by Eq. (2). This general introduction introduces the presented work, whose aim is to develop a theoretical model in order to forecast the triggering and propagation of landslides, using the techniques of fractional calculus. The latter is suitable for modeling the water infiltration (i.e., the pore water pressure diffusion in the soil) and the dynamical processes in the fractal media [33]. Alternatively the fractal representation of temporal and spatial derivative (the fractal order only appears in the denominator of the derivative) is considered and the results are compared to the fractional one. The prediction of landslides and the discovering of the triggering mechanism, is one of the challenging problems in earth science. Landslides can be triggered by different factors but in most cases the trigger is an

  19. Effects of progressive backward body weight suppoted treadmill training on gait ability in chronic stroke patients: A randomized controlled trial.

    PubMed

    Kim, Kyung Hun; Lee, Kyoung Bo; Bae, Young-Hyeon; Fong, Shirley S M; Lee, Suk Min

    2017-10-23

    A stroke patient with hemiplegic gait is generally described as being slow and asymmetric. Body weight-supported treadmill training and backward gait training are recent additions to therapeutic gait trainings that may help improve gait in stroke patient with hemiplegic gait. Therefore, we examined the effect of progressive backward body weight-supported treadmill training on gait in chronic stroke patients with hemiplegic gait. Thirty subjects were divided to the experimental and control groups. The experimental group consisted of 15 patients and underwent progressive backward body weight-supported treadmill training. The control group consisted of 15 patients and underwent general treadmill gait training five times per week, for a total of four weeks. The OptoGait was used to analyze gait kinematics, and the dynamic gait index (DGI) and results of the 6-minute walk test were used as the clinical evaluation indicators. A follow-up test was carried out four weeks later to examine persistence of exercise effects. The experimental group showed statistically significant results in all dependent variables week four compared to the control group. However, until the eighth week, only the dependent variables, of affected step length (ASL), stride length (SL), and DGI differed significantly between the two groups. This study verified that progressive bodyweight-supported treadmill training had a positive influence on the temporospatial characteristics of gait and clinical gait evaluation index in chronic stroke patients.

  20. Does robot-assisted gait training ameliorate gait abnormalities in multiple sclerosis? A pilot randomized-control trial.

    PubMed

    Straudi, S; Benedetti, M G; Venturini, E; Manca, M; Foti, C; Basaglia, N

    2013-01-01

    Gait disorders are common in multiple sclerosis (MS) and lead to a progressive reduction of function and quality of life. Test the effects of robot-assisted gait rehabilitation in MS subjects through a pilot randomized-controlled study. We enrolled MS subjects with Expanded Disability Status Scale scores within 4.5-6.5. The experimental group received 12 robot-assisted gait training sessions over 6 weeks. The control group received the same amount of conventional physiotherapy. Outcomes measures were both biomechanical assessment of gait, including kinematics and spatio-temporal parameters, and clinical test of walking endurance (six-minute walk test) and mobility (Up and Go Test). 16 subjects (n = 8 experimental group, n = 8 control group) were included in the final analysis. At baseline the two groups were similar in all variables, except for step length. Data showed walking endurance, as well as spatio-temporal gait parameters improvements after robot-assisted gait training. Pelvic antiversion and reduced hip extension during terminal stance ameliorated after aforementioned intervention. Robot-assisted gait training seems to be effective in increasing walking competency in MS subjects. Moreover, it could be helpful in restoring the kinematic of the hip and pelvis.

  1. Fractal continuum model for tracer transport in a porous medium.

    PubMed

    Herrera-Hernández, E C; Coronado, M; Hernández-Coronado, H

    2013-12-01

    A model based on the fractal continuum approach is proposed to describe tracer transport in fractal porous media. The original approach has been extended to treat tracer transport and to include systems with radial and uniform flow, which are cases of interest in geoscience. The models involve advection due to the fluid motion in the fractal continuum and dispersion whose mathematical expression is taken from percolation theory. The resulting advective-dispersive equations are numerically solved for continuous and for pulse tracer injection. The tracer profile and the tracer breakthrough curve are evaluated and analyzed in terms of the fractal parameters. It has been found in this work that anomalous transport frequently appears, and a condition on the fractal parameter values to predict when sub- or superdiffusion might be expected has been obtained. The fingerprints of fractality on the tracer breakthrough curve in the explored parameter window consist of an early tracer breakthrough and long tail curves for the spherical and uniform flow cases, and symmetric short tailed curves for the radial flow case.

  2. Advanced Prosthetic Gait Training Tool

    DTIC Science & Technology

    2014-10-01

    AWARD NUMBER: W81XWH-10-1-0870 TITLE: Advanced Prosthetic Gait Training Tool...October 2014 2. REPORT TYPE Annual Report 3. DATES COVERED 20 Sep 2013 to 19 Sep 2014 4. TITLE AND SUBTITLE Advanced Prosthetic Gait Training...produce a computer-based Advanced Prosthetic Gait Training Tool to aid in the training of clinicians at military treatment facilities providing care

  3. Evaluation and management of crouch gait.

    PubMed

    Kedem, Paz; Scher, David M

    2016-02-01

    Crouch gait is defined as excessive ankle dorsiflexion, knee and hip flexion during the stance phase. This gait disorder is common among patients with cerebral palsy. The present article brings an up-to-date literature review on the pathoanatomy, natural history, and treatment of this frequent gait abnormality. Hamstrings are often not shortened in patients with crouch. Patella alta must be addressed if surgery is performed. Surgical correction of joint contractures and lever arm dysfunction can be effectively achieved through a single-event multilevel surgery. Crouch gait is a common gait deviation, often seen among ambulatory diplegic and quadriplegic patients, once they reach the pubertal spurt, when weak muscles can no longer support a toe walking pattern because of rapidly increased weight. This form of gait is highly ineffective and might compromise walking ability over time. The anterior knee is overloaded; pain, extensor mechanism failure, and arthritis might develop. Its progressive nature often requires surgical intervention. The cause of crouch gait is multifactorial, and surgery should be tailored to meet the individual's specific anatomic and physiologic abnormalities.

  4. Multispectral image fusion based on fractal features

    NASA Astrophysics Data System (ADS)

    Tian, Jie; Chen, Jie; Zhang, Chunhua

    2004-01-01

    Imagery sensors have been one indispensable part of the detection and recognition systems. They are widely used to the field of surveillance, navigation, control and guide, et. However, different imagery sensors depend on diverse imaging mechanisms, and work within diverse range of spectrum. They also perform diverse functions and have diverse circumstance requires. So it is unpractical to accomplish the task of detection or recognition with a single imagery sensor under the conditions of different circumstances, different backgrounds and different targets. Fortunately, the multi-sensor image fusion technique emerged as important route to solve this problem. So image fusion has been one of the main technical routines used to detect and recognize objects from images. While, loss of information is unavoidable during fusion process, so it is always a very important content of image fusion how to preserve the useful information to the utmost. That is to say, it should be taken into account before designing the fusion schemes how to avoid the loss of useful information or how to preserve the features helpful to the detection. In consideration of these issues and the fact that most detection problems are actually to distinguish man-made objects from natural background, a fractal-based multi-spectral fusion algorithm has been proposed in this paper aiming at the recognition of battlefield targets in the complicated backgrounds. According to this algorithm, source images are firstly orthogonally decomposed according to wavelet transform theories, and then fractal-based detection is held to each decomposed image. At this step, natural background and man-made targets are distinguished by use of fractal models that can well imitate natural objects. Special fusion operators are employed during the fusion of area that contains man-made targets so that useful information could be preserved and features of targets could be extruded. The final fused image is reconstructed from the

  5. Self-perceived gait stability modulates the effect of daily life gait quality on prospective falls in older adults.

    PubMed

    Weijer, R H A; Hoozemans, M J M; van Dieën, J H; Pijnappels, M

    2018-05-01

    Quality of gait during daily life activities and perceived gait stability are both independent risk factors for future falls in older adults. We investigated whether perceived gait stability modulates the association between gait quality and falling in older adults. In this prospective cohort study, we used one-week daily-life trunk acceleration data of 272 adults over 65 years of age. Sample entropy (SE) of the 3D acceleration signals was calculated to quantify daily life gait quality. To quantify perceived gait stability, the level of concern about falling was assessed using the Falls Efficacy Scale international (FES-I) questionnaire and step length, estimated from the accelerometer data. A fall calendar was used to record fall incidence during a six-month follow up period. Logistic regression analyses were performed to study the association between falling and SE, step length or FES-I score, and their interactions. High (i.e., poor) SE in vertical direction was significantly associated with falling. FES-I scores significantly modulated this association, whereas step length did not. Subgroup analyses based on FES-I scores showed that high SE in the vertical direction was a risk factor for falls only in older adults who had a high (i.e. poor) FES-I score. In conclusion, perceived gait stability modulates the association between gait quality and falls in older adults such that an association between gait quality and falling is only present when perceived gait stability is poor. The results of the present study indicate that the effectiveness of interventions for fall prevention, aimed at improving gait quality, may be affected by a modulating effect of perceived gait stability. Results indicate that interventions to reduce falls in older adults might sort most effectiveness in populations with both a poor physiological and psychological status. Copyright © 2018 Elsevier B.V. All rights reserved.

  6. Fractal characterization of a fractured chalk reservoir - The Laegerdorf case

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Stoelum, H.H.; Koestler, A.G.; Feder, J.

    1991-03-01

    What is the matrix block size distribution of a fractured reservoir In order to answer this question and assess the potential of fractal geometry as a method of characterization of fracture networks, a pilot study has been done of the fractured chalk quarry in Laegerdorf. The fractures seen on the quarry walls were traced in the field for a total area of {approximately}200 {times} 45 m. The digitized pictures have been analyzed by a standard box-counting method. This analysis gave a fractal dimension of similarity varying from 1.33 for fractured areas between faults, to 1.43 for the fault zone, andmore » 1.53 for the highly deformed fault gouge. The amplitude showed a similar trend. The fractal dimension for the whole system of fractures is {approximately}1.55. In other words, fracture networks in chalk have a nonlinear, fractal geometry, and so matrix block size is a scaling property of chalk reservoirs. In terms of rock mechanics, the authors interpret the variation of the fractal dimension as follows: A small fractal dimension and amplitude are associated with brittle deformation in the elastic regime, while a large fractal dimension and amplitude are associated with predominantly ductile, strain softening deformation in the plastic regime. The interaction between the two regimes of deformation in the rock body is a key element of successful characterization and may be approached by seeing the rock as a non-Newtonian viscoelastic medium. The fractal dimension for the whole is close to a material independent limit that constrains the development of fractures.« less

  7. Fractal and multifractal analyses of bipartite networks

    NASA Astrophysics Data System (ADS)

    Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua

    2017-03-01

    Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.

  8. Fractal and multifractal analyses of bipartite networks.

    PubMed

    Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua

    2017-03-31

    Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.

  9. Fractal and multifractal analyses of bipartite networks

    PubMed Central

    Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua

    2017-01-01

    Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions. PMID:28361962

  10. Modeling liver physiology: combining fractals, imaging and animation.

    PubMed

    Lin, Debbie W; Johnson, Scott; Hunt, C Anthony

    2004-01-01

    Physiological modeling of vascular and microvascular networks in several key human organ systems is critical for a deeper understanding of pharmacology and the effect of pharmacotherapies on disease. Like the lung and the kidney, the morphology of its vascular and microvascular system plays a major role in its functional capability. To understand liver function in absorption and metabolism of food and drugs, one must examine the morphology and physiology at both higher and lower level liver function. We have developed validated virtualized dynamic three dimensional (3D) models of liver secondary units and primary units by combining a number of different methods: three-dimensional rendering, fractals, and animation. We have simulated particle dynamics in the liver secondary unit. The resulting models are suitable for use in helping researchers easily visualize and gain intuition on results of in silico liver experiments.

  11. Hyper-Fractal Analysis: A visual tool for estimating the fractal dimension of 4D objects

    NASA Astrophysics Data System (ADS)

    Grossu, I. V.; Grossu, I.; Felea, D.; Besliu, C.; Jipa, Al.; Esanu, T.; Bordeianu, C. C.; Stan, E.

    2013-04-01

    This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images and 3D objects (Grossu et al. (2010) [1]). The program was extended for working with four-dimensional objects stored in comma separated values files. This might be of interest in biomedicine, for analyzing the evolution in time of three-dimensional images. New version program summaryProgram title: Hyper-Fractal Analysis (Fractal Analysis v03) Catalogue identifier: AEEG_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 745761 No. of bytes in distributed program, including test data, etc.: 12544491 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 100M Classification: 14 Catalogue identifier of previous version: AEEG_v2_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 831-832 Does the new version supersede the previous version? Yes Nature of problem: Estimating the fractal dimension of 4D images. Solution method: Optimized implementation of the 4D box-counting algorithm. Reasons for new version: Inspired by existing applications of 3D fractals in biomedicine [3], we extended the optimized version of the box-counting algorithm [1, 2] to the four-dimensional case. This might be of interest in analyzing the evolution in time of 3D images. The box-counting algorithm was extended in order to support 4D objects, stored in comma separated values files. A new form was added for generating 2D, 3D, and 4D test data. The application was tested on 4D objects with known dimension, e.g. the Sierpinski hypertetrahedron gasket, Df=ln(5)/ln(2) (Fig. 1). The algorithm could be extended, with minimum effort, to

  12. Passenger flow analysis of Beijing urban rail transit network using fractal approach

    NASA Astrophysics Data System (ADS)

    Li, Xiaohong; Chen, Peiwen; Chen, Feng; Wang, Zijia

    2018-04-01

    To quantify the spatiotemporal distribution of passenger flow and the characteristics of an urban rail transit network, we introduce four radius fractal dimensions and two branch fractal dimensions by combining a fractal approach with passenger flow assignment model. These fractal dimensions can numerically describe the complexity of passenger flow in the urban rail transit network and its change characteristics. Based on it, we establish a fractal quantification method to measure the fractal characteristics of passenger follow in the rail transit network. Finally, we validate the reasonability of our proposed method by using the actual data of Beijing subway network. It has been shown that our proposed method can effectively measure the scale-free range of the urban rail transit network, network development and the fractal characteristics of time-varying passenger flow, which further provides a reference for network planning and analysis of passenger flow.

  13. Resource Letter FR-1: Fractals

    NASA Astrophysics Data System (ADS)

    Hurd, Alan J.

    1988-11-01

    This Resource Letter provides a guide to the literature on fractals. Although ``fractal'' is a relatively new term in science, unifying many new ideas with established ones, its wide application and general popularity have made it one of the fastest growing fields in statistical physics. The letter E after an item indicates elementary level or material of general interest to persons becoming informed in the field; the letter I, for intermediate level, indicates material of somewhat more specialized nature; and the letter A indicates rather specialized or advanced material. An asterisk (*) indicates those articles to be included in an accompanying Reprint Book.

  14. Effects of autonomic ganglion blockade on fractal and spectral components of blood pressure and heart rate variability in free-moving rats.

    PubMed

    Castiglioni, Paolo; Di Rienzo, Marco; Radaelli, Alberto

    2013-11-01

    Fractal analysis is a promising tool for assessing autonomic influences on heart rate (HR) and blood pressure (BP) variability. The temporal spectrum of scale coefficients, α(t), was recently proposed to describe the cardiovascular fractal dynamics. Aim of our work is to evaluate sympathetic influences on cardiovascular variability analyzing α(t) and spectral powers of HR and BP after ganglionic blockade. BP was recorded in 11 rats before and after autonomic blockade by hexamethonium infusion (HEX). Systolic and diastolic BP, pulse pressure and pulse interval were derived beat-by-beat. Segments longer than 5 min were selected at baseline and HEX to estimate power spectra and α(t). Comparisons were made by paired t-test. HEX reduced all spectral components of systolic and diastolic BP, the reduction being particularly significant around the frequency of Mayer waves; it induced a reduction on α(t) coefficients at t<2s and an increase on coefficients at t>8s. HEX reduced only slower components of pulse interval power spectrum, but decreased significantly faster scale coefficients (t<8s). HEX only marginally affected pulse pressure variability. Results indicate that the sympathetic outflow contributes to BP fractal dynamics with fractional Gaussian noise (α<1) at longer scales and fractional Brownian motion (α>1) at shorter scales. Ganglionic blockade also removes a fractional Brownian motion component at shorter scales from HR dynamics. Results may be explained by the characteristic time constants between sympathetic efferent activity and cardiovascular effectors. Therefore fractal analysis may complete spectral analysis with information on the correlation structure of the data. Copyright © 2013 Elsevier B.V. All rights reserved.

  15. Surface areas of fractally rough particles studied by scattering

    NASA Astrophysics Data System (ADS)

    Hurd, Alan J.; Schaefer, Dale W.; Smith, Douglas M.; Ross, Steven B.; Le Méhauté, Alain; Spooner, Steven

    1989-05-01

    The small-angle scattering from fractally rough surfaces has the potential to give information on the surface area at a given resolution. By use of quantitative neutron and x-ray scattering, a direct comparison of surface areas of fractally rough powders was made between scattering and adsorption techniques. This study supports a recently proposed correction to the theory for scattering from fractal surfaces. In addition, the scattering data provide an independent calibration of molecular adsorbate areas.

  16. a New Method for Calculating Fractal Dimensions of Porous Media Based on Pore Size Distribution

    NASA Astrophysics Data System (ADS)

    Xia, Yuxuan; Cai, Jianchao; Wei, Wei; Hu, Xiangyun; Wang, Xin; Ge, Xinmin

    Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.

  17. Process for applying control variables having fractal structures

    DOEpatents

    Bullock, IV, Jonathan S.; Lawson, Roger L.

    1996-01-01

    A process and apparatus for the application of a control variable having a fractal structure to a body or process. The process of the present invention comprises the steps of generating a control variable having a fractal structure and applying the control variable to a body or process reacting in accordance with the control variable. The process is applicable to electroforming where first, second and successive pulsed-currents are applied to cause the deposition of material onto a substrate, such that the first pulsed-current, the second pulsed-current, and successive pulsed currents form a fractal pulsed-current waveform.

  18. Process for applying control variables having fractal structures

    DOEpatents

    Bullock, J.S. IV; Lawson, R.L.

    1996-01-23

    A process and apparatus are disclosed for the application of a control variable having a fractal structure to a body or process. The process of the present invention comprises the steps of generating a control variable having a fractal structure and applying the control variable to a body or process reacting in accordance with the control variable. The process is applicable to electroforming where first, second and successive pulsed-currents are applied to cause the deposition of material onto a substrate, such that the first pulsed-current, the second pulsed-current, and successive pulsed currents form a fractal pulsed-current waveform. 3 figs.

  19. Comprehensive Fractal Description of Porosity of Coal of Different Ranks

    PubMed Central

    Ren, Jiangang; Zhang, Guocheng; Song, Zhimin; Liu, Gaofeng; Li, Bing

    2014-01-01

    We selected, as the objects of our research, lignite from the Beizao Mine, gas coal from the Caiyuan Mine, coking coal from the Xiqu Mine, and anthracite from the Guhanshan Mine. We used the mercury intrusion method and the low-temperature liquid nitrogen adsorption method to analyze the structure and shape of the coal pores and calculated the fractal dimensions of different aperture segments in the coal. The experimental results show that the fractal dimension of the aperture segment of lignite, gas coal, and coking coal with an aperture of greater than or equal to 10 nm, as well as the fractal dimension of the aperture segment of anthracite with an aperture of greater than or equal to 100 nm, can be calculated using the mercury intrusion method; the fractal dimension of the coal pore, with an aperture range between 2.03 nm and 361.14 nm, can be calculated using the liquid nitrogen adsorption method, of which the fractal dimensions bounded by apertures of 10 nm and 100 nm are different. Based on these findings, we defined and calculated the comprehensive fractal dimensions of the coal pores and achieved the unity of fractal dimensions for full apertures of coal pores, thereby facilitating, overall characterization for the heterogeneity of the coal pore structure. PMID:24955407

  20. Spatio-temporal gait disorder and gait fatigue index in a six-minute walk test in women with fibromyalgia.

    PubMed

    Heredia-Jimenez, Jose; Latorre-Roman, Pedro; Santos-Campos, Maria; Orantes-Gonzalez, Eva; Soto-Hermoso, Victor M

    2016-03-01

    Gait disorders in fibromyalgia patients affect several gait parameters and different muscle recruitment patterns. The aim of this study was to assess the gait differences observed during a six-minute walk test between fibromyalgia patients and healthy controls. Forty-eight women with fibromyalgia and 15 healthy women were evaluated. Fibromyalgia patients met the American College of Rheumatology criteria for fibromyalgia selected of an ambulatory care. Both patients and controls had a negative history of musculoskeletal disease, neurological disorders, and gait abnormalities. The 15 controls were healthy women matched to the patients in age, height and body weight. Spatio-temporal gait variables and the rate of perceived exertion during the six-minute walk test (all subjects) and Fibromyalgia Impact Questionnaire (fibromyalgia subjects) were evaluated. All walking sets on the GaitRITE were collected and the gait variables were selected at three stages during the six-minute walk test: two sets at the beginning, two sets at 3 min and two sets at the end of the test. In addition, the Fibromyalgia Impact Questionnaire was used for the fibromyalgia patients. Fibromyalgia patients showed a significant decrease in all spatio-temporal gait variables at each of the three stages and had a lower walk distance covered in the six-minute walk test and higher rate of perceived exertion. No correlations were found between the Fibromyalgia Impact Questionnaire and gait variables. The fibromyalgia and control subjects showed lower gait fatigue indices between the middle and last stages. Gait analysis during a six-minute walk test is a good tool to assess the fatigue and physical symptoms of patients with fibromyalgia. Copyright © 2016 Elsevier Ltd. All rights reserved.

  1. Fractal density modeling of crustal heterogeneity from the KTB deep hole

    NASA Astrophysics Data System (ADS)

    Chen, Guoxiong; Cheng, Qiuming

    2017-03-01

    Fractal or multifractal concepts have significantly enlightened our understanding of crustal heterogeneity. Much attention has focused on 1/f scaling natures of physicochemical heterogeneity of Earth crust from fractal increment perspective. In this study, fractal density model from fractal clustering point of view is used to characterize the scaling behaviors of heterogeneous sources recorded at German Continental Deep Drilling Program (KTB) main hole, and of special contribution is the local and global multifractal analysis revisited by using Haar wavelet transform (HWT). Fractal density modeling of mass accumulation generalizes the unit of rock density from integer (e.g., g/cm3) to real numbers (e.g., g/cmα), so that crustal heterogeneities with respect to source accumulation are quantified by singularity strength of fractal density in α-dimensional space. From that perspective, we found that the bulk densities of metamorphic rocks exhibit fractal properties but have a weak multifractality, decreasing with the depth. The multiscaling natures of chemical logs also have been evidenced, and the observed distinct fractal laws for mineral contents are related to their different geochemical behaviors within complex lithological context. Accordingly, scaling distributions of mineral contents have been recognized as a main contributor to the multifractal natures of heterogeneous density for low-porosity crystalline rocks. This finally allows us to use de Wijs cascade process to explain the mechanism of fractal density. In practice, the proposed local singularity analysis based on HWT is suggested as an attractive high-pass filtering to amplify weak signatures of well logs as well as to delineate microlithological changes.

  2. Relative fascicle excursion effects on dynamic strength generation during gait in children with cerebral palsy.

    PubMed

    Martín Lorenzo, T; Lerma Lara, S; Martínez-Caballero, I; Rocon, E

    2015-10-01

    Evaluation of muscle structure gives us a better understanding of how muscles contribute to force generation which is significantly altered in children with cerebral palsy (CP). While most muscle structure parameters have shown to be significantly correlated to different expressions of strength development in children with CP and typically developing (TD) children, conflicting results are found for muscle fascicle length. Muscle fascicle length determines muscle excursion and velocity, and contrary to what might be expected, correlations of fascicle length to rate of force development have not been found for children with CP. The lack of correlation between muscle fascicle length and rate of force development in children with CP could be due, on the one hand, to the non-optimal joint position adopted for force generation on the isometric strength tests as compared to the position of TD children. On the other hand, the lack of correlation could be due to the erroneous assumption that muscle fascicle length is representative of sarcomere length. Thus, the relationship between muscle architecture parameters reflecting sarcomere length, such as relative fascicle excursions and dynamic power generation, should be assessed. Understanding of the underlying mechanisms of weakness in children with CP is key for individualized prescription and assessment of muscle-targeted interventions. Findings could imply the detection of children operating on the descending limb of the sarcomere length-tension curve, which in turn might be at greater risk of developing crouch gait. Furthermore, relative muscle fascicle excursions could be used as a predictive variable of outcomes related to crouch gait prevention treatments such as strength training. Copyright © 2015 Elsevier Ltd. All rights reserved.

  3. H-fractal seismic metamaterial with broadband low-frequency bandgaps

    NASA Astrophysics Data System (ADS)

    Du, Qiujiao; Zeng, Yi; Xu, Yang; Yang, Hongwu; Zeng, Zuoxun

    2018-03-01

    The application of metamaterial in civil engineering to achieve isolation of a building by controlling the propagation of seismic waves is a substantial challenge because seismic waves, a superposition of longitudinal and shear waves, are more complex than electromagnetic and acoustic waves. In this paper, we design a broadband seismic metamaterial based on H-shaped fractal pillars and report numerical simulation of band structures for seismic surface waves propagating. Comparative study on the band structures of H-fractal seismic metamaterials with different levels shows that a new level of fractal structure creates new band gap, widens the total band gaps and shifts the same band gap towards lower frequencies. Moreover, the vibration modes for H-fractal seismic metamaterials are computed and analyzed to clarify the mechanism of widening band gaps. A numerical investigation of seismic surface waves propagation on a 2D array of fractal unit cells on the surface of semi-infinite substrate is proposed to show the efficiency of earthquake shielding in multiple complete band gaps.

  4. Fractal Dimensions of Umbral and Penumbral Regions of Sunspots

    NASA Astrophysics Data System (ADS)

    Rajkumar, B.; Haque, S.; Hrudey, W.

    2017-11-01

    The images of sunspots in 16 active regions taken at the University College of the Cayman Islands (UCCI) Observatory on Grand Cayman during June-November 2015 were used to determine their fractal dimensions using the perimeter-area method for the umbral and the penumbral region. Scale-free fractal dimensions of 2.09 ±0.42 and 1.72 ±0.4 were found, respectively. This value was higher than the value determined by Chumak and Chumak ( Astron. Astrophys. Trans. 10, 329, 1996), who used a similar method, but only for the penumbral region of their sample set. The umbral and penumbral fractal dimensions for the specific sunspots are positively correlated with r = 0.58. Furthermore, a similar time-series analysis was performed on eight images of AR 12403, from 21 August 2015 to 28 August 2015 taken from the Debrecen Photoheliographic Data (DPD). The correlation is r = 0.623 between the umbral and penumbral fractal dimensions in the time series, indicating that the complexity in morphology indicated by the fractal dimension between the umbra and penumbra followed each other in time as well.

  5. Human physiological benefits of viewing nature: EEG responses to exact and statistical fractal patterns.

    PubMed

    Hagerhall, C M; Laike, T; Küller, M; Marcheschi, E; Boydston, C; Taylor, R P

    2015-01-01

    Psychological and physiological benefits of viewing nature have been extensively studied for some time. More recently it has been suggested that some of these positive effects can be explained by nature's fractal properties. Virtually all studies on human responses to fractals have used stimuli that represent the specific form of fractal geometry found in nature, i.e. statistical fractals, as opposed to fractal patterns which repeat exactly at different scales. This raises the question of whether human responses like preference and relaxation are being driven by fractal geometry in general or by the specific form of fractal geometry found in nature. In this study we consider both types of fractals (statistical and exact) and morph one type into the other. Based on the Koch curve, nine visual stimuli were produced in which curves of three different fractal dimensions evolve gradually from an exact to a statistical fractal. The patterns were shown for one minute each to thirty-five subjects while qEEG was continuously recorded. The results showed that the responses to statistical and exact fractals differ, and that the natural form of the fractal is important for inducing alpha responses, an indicator of a wakefully relaxed state and internalized attention.

  6. Research on gait-based human identification

    NASA Astrophysics Data System (ADS)

    Li, Youguo

    Gait recognition refers to automatic identification of individual based on his/her style of walking. This paper proposes a gait recognition method based on Continuous Hidden Markov Model with Mixture of Gaussians(G-CHMM). First, we initialize a Gaussian mix model for training image sequence with K-means algorithm, then train the HMM parameters using a Baum-Welch algorithm. These gait feature sequences can be trained and obtain a Continuous HMM for every person, therefore, the 7 key frames and the obtained HMM can represent each person's gait sequence. Finally, the recognition is achieved by Front algorithm. The experiments made on CASIA gait databases obtain comparatively high correction identification ratio and comparatively strong robustness for variety of bodily angle.

  7. Anisotropic fractal media by vector calculus in non-integer dimensional space

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

    2014-08-15

    A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensionalmore » space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.« less

  8. Anisotropic fractal media by vector calculus in non-integer dimensional space

    NASA Astrophysics Data System (ADS)

    Tarasov, Vasily E.

    2014-08-01

    A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

  9. Compressive tibiofemoral force during crouch gait.

    PubMed

    Steele, Katherine M; Demers, Matthew S; Schwartz, Michael H; Delp, Scott L

    2012-04-01

    Crouch gait, a common walking pattern in individuals with cerebral palsy, is characterized by excessive flexion of the hip and knee. Many subjects with crouch gait experience knee pain, perhaps because of elevated muscle forces and joint loading. The goal of this study was to examine how muscle forces and compressive tibiofemoral force change with the increasing knee flexion associated with crouch gait. Muscle forces and tibiofemoral force were estimated for three unimpaired children and nine children with cerebral palsy who walked with varying degrees of knee flexion. We scaled a generic musculoskeletal model to each subject and used the model to estimate muscle forces and compressive tibiofemoral forces during walking. Mild crouch gait (minimum knee flexion 20-35°) produced a peak compressive tibiofemoral force similar to unimpaired walking; however, severe crouch gait (minimum knee flexion>50°) increased the peak force to greater than 6 times body-weight, more than double the load experienced during unimpaired gait. This increase in compressive tibiofemoral force was primarily due to increases in quadriceps force during crouch gait, which increased quadratically with average stance phase knee flexion (i.e., crouch severity). Increased quadriceps force contributes to larger tibiofemoral and patellofemoral loading which may contribute to knee pain in individuals with crouch gait. Copyright © 2011 Elsevier B.V. All rights reserved.

  10. How innate is locomotion in precocial animals? A study on the early development of spatio-temporal gait variables and gait symmetry in piglets.

    PubMed

    Vanden Hole, Charlotte; Goyens, Jana; Prims, Sara; Fransen, Erik; Ayuso Hernando, Miriam; Van Cruchten, Steven; Aerts, Peter; Van Ginneken, Chris

    2017-08-01

    Locomotion is one of the most important ecological functions in animals. Precocial animals, such as pigs, are capable of independent locomotion shortly after birth. This raises the question whether coordinated movement patterns and the underlying muscular control in these animals is fully innate or whether there still exists a rapid maturation. We addressed this question by studying gait development in neonatal pigs through the analysis of spatio-temporal gait characteristics during locomotion at self-selected speed. To this end, we made video recordings of piglets walking along a corridor at several time points (from 0 h to 96 h). After digitization of the footfalls, we analysed self-selected speed and spatio-temporal characteristics (e.g. stride and step lengths, stride frequency and duty factor) to study dynamic similarity, intralimb coordination and interlimb coordination. To assess the variability of the gait pattern, left-right asymmetry was studied. To distinguish neuromotor maturation from effects caused by growth, both absolute and normalized data (according to the dynamic similarity concept) were included in the analysis. All normalized spatio-temporal variables reached stable values within 4 h of birth, with most of them showing little change after the age of 2 h. Most asymmetry indices showed stable values, hovering around 10%, within 8 h of birth. These results indicate that coordinated movement patterns are not entirely innate, but that a rapid neuromotor maturation, potentially also the result of the rearrangement or recombination of existing motor modules, takes place in these precocial animals. © 2017. Published by The Company of Biologists Ltd.

  11. Development of a novel virtual reality gait intervention.

    PubMed

    Boone, Anna E; Foreman, Matthew H; Engsberg, Jack R

    2017-02-01

    Improving gait speed and kinematics can be a time consuming and tiresome process. We hypothesize that incorporating virtual reality videogame play into variable improvement goals will improve levels of enjoyment and motivation and lead to improved gait performance. To develop a feasible, engaging, VR gait intervention for improving gait variables. Completing this investigation involved four steps: 1) identify gait variables that could be manipulated to improve gait speed and kinematics using the Microsoft Kinect and free software, 2) identify free internet videogames that could successfully manipulate the chosen gait variables, 3) experimentally evaluate the ability of the videogames and software to manipulate the gait variables, and 4) evaluate the enjoyment and motivation from a small sample of persons without disability. The Kinect sensor was able to detect stride length, cadence, and joint angles. FAAST software was able to identify predetermined gait variable thresholds and use the thresholds to play free online videogames. Videogames that involved continuous pressing of a keyboard key were found to be most appropriate for manipulating the gait variables. Five participants without disability evaluated the effectiveness for modifying the gait variables and enjoyment and motivation during play. Participants were able to modify gait variables to permit successful videogame play. Motivation and enjoyment were high. A clinically feasible and engaging virtual intervention for improving gait speed and kinematics has been developed and initially tested. It may provide an engaging avenue for achieving thousands of repetitions necessary for neural plastic changes and improved gait. Copyright © 2016 Elsevier B.V. All rights reserved.

  12. Turbulent premixed flames on fractal-grid-generated turbulence

    NASA Astrophysics Data System (ADS)

    Soulopoulos, N.; Kerl, J.; Sponfeldner, T.; Beyrau, F.; Hardalupas, Y.; Taylor, A. M. K. P.; Vassilicos, J. C.

    2013-12-01

    A space-filling, low blockage fractal grid is used as a novel turbulence generator in a premixed turbulent flame stabilized by a rod. The study compares the flame behaviour with a fractal grid to the behaviour when a standard square mesh grid with the same effective mesh size and solidity as the fractal grid is used. The isothermal gas flow turbulence characteristics, including mean flow velocity and rms of velocity fluctuations and Taylor length, were evaluated from hot-wire measurements. The behaviour of the flames was assessed with direct chemiluminescence emission from the flame and high-speed OH-laser-induced fluorescence. The characteristics of the two flames are considered in terms of turbulent flame thickness, local flame curvature and turbulent flame speed. It is found that, for the same flow rate and stoichiometry and at the same distance downstream of the location of the grid, fractal-grid-generated turbulence leads to a more turbulent flame with enhanced burning rate and increased flame surface area.

  13. The gait disorder in downbeat nystagmus syndrome.

    PubMed

    Schniepp, Roman; Wuehr, Max; Huth, Sabrina; Pradhan, Cauchy; Schlick, Cornelia; Brandt, Thomas; Jahn, Klaus

    2014-01-01

    Downbeat nystagmus (DBN) is a common form of acquired fixation nystagmus with key symptoms of oscillopsia and gait disturbance. Gait disturbance could be a result of impaired visual feedback due to the involuntary ocular oscillations. Alternatively, a malfunction of cerebellar locomotor control might be involved, since DBN is considered a vestibulocerebellar disorder. Investigation of walking in 50 DBN patients (age 72 ± 11 years, 23 females) and 50 healthy controls (HS) (age 70 ± 11 years, 23 females) using a pressure sensitive carpet (GAITRite). The patient cohort comprised subjects with only ocular motor signs (DBN) and subjects with an additional limb ataxia (DBNCA). Gait investigation comprised different walking speeds and walking with eyes closed. In DBN, gait velocity was reduced (p<0.001) with a reduced stride length (p<0.001), increased base of support (p<0.050), and increased double support (p<0.001). Walking with eyes closed led to significant gait changes in both HS and DBN. These changes were more pronounced in DBN patients (p<0.001). Speed-dependency of gait variability revealed significant differences between the subgroups of DBN and DBNCA (p<0.050). (I) Impaired visual control caused by involuntary ocular oscillations cannot sufficiently explain the gait disorder. (II) The gait of patients with DBN is impaired in a speed dependent manner. (III) Analysis of gait variability allows distinguishing DBN from DBNCA: Patients with pure DBN show a speed dependency of gait variability similar to that of patients with afferent vestibular deficits. In DBNCA, gait variability resembles the pattern found in cerebellar ataxia.

  14. Wavelet-based characterization of gait signal for neurological abnormalities.

    PubMed

    Baratin, E; Sugavaneswaran, L; Umapathy, K; Ioana, C; Krishnan, S

    2015-02-01

    Studies conducted by the World Health Organization (WHO) indicate that over one billion suffer from neurological disorders worldwide, and lack of efficient diagnosis procedures affects their therapeutic interventions. Characterizing certain pathologies of motor control for facilitating their diagnosis can be useful in quantitatively monitoring disease progression and efficient treatment planning. As a suitable directive, we introduce a wavelet-based scheme for effective characterization of gait associated with certain neurological disorders. In addition, since the data were recorded from a dynamic process, this work also investigates the need for gait signal re-sampling prior to identification of signal markers in the presence of pathologies. To benefit automated discrimination of gait data, certain characteristic features are extracted from the wavelet-transformed signals. The performance of the proposed approach was evaluated using a database consisting of 15 Parkinson's disease (PD), 20 Huntington's disease (HD), 13 Amyotrophic lateral sclerosis (ALS) and 16 healthy control subjects, and an average classification accuracy of 85% is achieved using an unbiased cross-validation strategy. The obtained results demonstrate the potential of the proposed methodology for computer-aided diagnosis and automatic characterization of certain neurological disorders. Copyright © 2015 Elsevier B.V. All rights reserved.

  15. Fractal cometary dust - a window into the early Solar system

    NASA Astrophysics Data System (ADS)

    Mannel, T.; Bentley, M. S.; Schmied, R.; Jeszenszky, H.; Levasseur-Regourd, A. C.; Romstedt, J.; Torkar, K.

    2016-11-01

    The properties of dust in the protoplanetary disc are key to understanding the formation of planets in our Solar system. Many models of dust growth predict the development of fractal structures which evolve into non-fractal, porous dust pebbles representing the main component for planetesimal accretion. In order to understand comets and their origins, the Rosetta orbiter followed comet 67P/Churyumov-Gerasimenko for over two years and carried a dedicated instrument suite for dust analysis. One of these instruments, the MIDAS (Micro-Imaging Dust Analysis System) atomic force microscope, recorded the 3D topography of micro- to nanometre-sized dust. All particles analysed to date have been found to be hierarchical agglomerates. Most show compact packing; however, one is extremely porous. This paper contains a structural description of a compact aggregate and the outstanding porous one. Both particles are tens of micrometres in size and show rather narrow subunit size distributions with noticeably similar mean values of 1.48^{+0.13}_{-0.59} μm for the porous particle and 1.36^{+0.15}_{-0.59} μm for the compact. The porous particle allows a fractal analysis, where a density-density correlation function yields a fractal dimension of Df = 1.70 ± 0.1. GIADA, another dust analysis instrument on board Rosetta, confirms the existence of a dust population with a similar fractal dimension. The fractal particles are interpreted as pristine agglomerates built in the protoplanetary disc and preserved in the comet. The similar subunits of both fractal and compact dust indicate a common origin which is, given the properties of the fractal, dominated by slow agglomeration of equally sized aggregates known as cluster-cluster agglomeration.

  16. Fractal Geometry in the Arts: AN Overview across the Different Cultures

    NASA Astrophysics Data System (ADS)

    Sala, Nicoletta

    Fractal, in mathematics, is a geometric shape that is complex and detailed in structure at any level of magnification. The word "fractal" was coined less than thirty years ago by one of history's most creative and mathematicians, Benoit Mandelbrot, whose work, The Fractal Geometry of Nature, first introduced and explained concepts underlying this new vision of the geometry. Although other mathematical thinkers like Georg Cantor (1845-1918), Felix Hausdorff (1868-1942), Gaston Julia (1893-1978), Helge von Koch (1870-1924), Giuseppe Peano (1858-1932), Lewis Richardson (1891-1953), Waclaw Sierpinski (1882-1969) and others had attained isolated insights of fractal understanding, such ideas were largely ignored until Mandelbrot's genius forged them at a single blow into a gorgeously coherent and fascinating discipline. Fractal geometry is applied in different field now: engineering, physics, chemistry, biology, and architecture. The aim of this paper is to introduce an approach where the arts are analysed using a fractal point of view.

  17. Brain Activity during Mental Imagery of Gait Versus Gait-Like Plantar Stimulation: A Novel Combined Functional MRI Paradigm to Better Understand Cerebral Gait Control.

    PubMed

    Labriffe, Matthieu; Annweiler, Cédric; Amirova, Liubov E; Gauquelin-Koch, Guillemette; Ter Minassian, Aram; Leiber, Louis-Marie; Beauchet, Olivier; Custaud, Marc-Antoine; Dinomais, Mickaël

    2017-01-01

    Human locomotion is a complex sensorimotor behavior whose central control remains difficult to explore using neuroimaging method due to technical constraints, notably the impossibility to walk with a scanner on the head and/or to walk for real inside current scanners. The aim of this functional Magnetic Resonance Imaging (fMRI) study was to analyze interactions between two paradigms to investigate the brain gait control network: (1) mental imagery of gait, and (2) passive mechanical stimulation of the plantar surface of the foot with the Korvit boots. The Korvit stimulator was used through two different modes, namely an organized ("gait like") sequence and a destructured (chaotic) pattern. Eighteen right-handed young healthy volunteers were recruited (mean age, 27 ± 4.7 years). Mental imagery activated a broad neuronal network including the supplementary motor area-proper (SMA-proper), pre-SMA, the dorsal premotor cortex, ventrolateral prefrontal cortex, anterior insula, and precuneus/superior parietal areas. The mechanical plantar stimulation activated the primary sensorimotor cortex and secondary somatosensory cortex bilaterally. The paradigms generated statistically common areas of activity, notably bilateral SMA-proper and right pre-SMA, highlighting the potential key role of SMA in gait control. There was no difference between the organized and chaotic Korvit sequences, highlighting the difficulty of developing a walking-specific plantar stimulation paradigm. In conclusion, this combined-fMRI paradigm combining mental imagery and gait-like plantar stimulation provides complementary information regarding gait-related brain activity and appears useful for the assessment of high-level gait control.

  18. Association of baseline knee sagittal dynamic joint stiffness during gait and 2-year patellofemoral cartilage damage worsening in knee osteoarthritis.

    PubMed

    Chang, A H; Chmiel, J S; Almagor, O; Guermazi, A; Prasad, P V; Moisio, K C; Belisle, L; Zhang, Y; Hayes, K; Sharma, L

    2017-02-01

    Knee sagittal dynamic joint stiffness (DJS) describes the biomechanical interaction between change in external knee flexion moment and flexion angular excursion during gait. In theory, greater DJS may particularly stress the patellofemoral (PF) compartment and thereby contribute to PF osteoarthritis (OA) worsening. We hypothesized that greater baseline knee sagittal DJS is associated with PF cartilage damage worsening 2 years later. Participants all had OA in at least one knee. Knee kinematics and kinetics during gait were recorded using motion capture systems and force plates. Knee sagittal DJS was computed as the slope of the linear regression line for knee flexion moments vs angles during the loading response phase. Knee magnetic resonance imaging (MRI) scans were obtained at baseline and 2 years later. We assessed the association between baseline DJS and baseline-to-2-year PF cartilage damage worsening using logistic regression with generalized estimating equations (GEE). Our sample had 391 knees (204 persons): mean age 64.2 years (SD 10.0); body mass index (BMI) 28.4 kg/m 2 (5.7); 76.5% women. Baseline knee sagittal DJS was associated with baseline-to-2-year cartilage damage worsening in the lateral (OR = 5.35, 95% CI: 2.37-12.05) and any PF (OR = 2.99, 95% CI: 1.27-7.04) compartment. Individual components of baseline DJS (i.e., change in knee moment or angle) were not associated with subsequent PF disease worsening. Capturing the concomitant effect of knee kinetics and kinematics during gait, knee sagittal DJS is a potentially modifiable risk factor for PF disease worsening. Copyright © 2016 Osteoarthritis Research Society International. Published by Elsevier Ltd. All rights reserved.

  19. Fractal analysis as a potential tool for surface morphology of thin films

    NASA Astrophysics Data System (ADS)

    Soumya, S.; Swapna, M. S.; Raj, Vimal; Mahadevan Pillai, V. P.; Sankararaman, S.

    2017-12-01

    Fractal geometry developed by Mandelbrot has emerged as a potential tool for analyzing complex systems in the diversified fields of science, social science, and technology. Self-similar objects having the same details in different scales are referred to as fractals and are analyzed using the mathematics of non-Euclidean geometry. The present work is an attempt to correlate fractal dimension for surface characterization by Atomic Force Microscopy (AFM). Taking the AFM images of zinc sulphide (ZnS) thin films prepared by pulsed laser deposition (PLD) technique, under different annealing temperatures, the effect of annealing temperature and surface roughness on fractal dimension is studied. The annealing temperature and surface roughness show a strong correlation with fractal dimension. From the regression equation set, the surface roughness at a given annealing temperature can be calculated from the fractal dimension. The AFM images are processed using Photoshop and fractal dimension is calculated by box-counting method. The fractal dimension decreases from 1.986 to 1.633 while the surface roughness increases from 1.110 to 3.427, for a change of annealing temperature 30 ° C to 600 ° C. The images are also analyzed by power spectrum method to find the fractal dimension. The study reveals that the box-counting method gives better results compared to the power spectrum method.

  20. Influence of Turbulent Flow and Fractal Scaling on Effective Permeability of Fracture Network

    NASA Astrophysics Data System (ADS)

    Zhu, J.

    2017-12-01

    A new approach is developed to calculate hydraulic gradient dependent effective permeability of a fractal fracture network where both laminar and turbulent flows may occur in individual fractures. A critical fracture length is used to distinguish flow characteristics in individual fractures. The developed new solutions can be used for the case of a general scaling relationship, an extension to the linear scaling. We examine the impact on the effective permeability of the network of fractal fracture network characteristics, which include the fractal scaling coefficient and exponent, fractal dimension, ratio of minimum over maximum fracture lengths. Results demonstrate that the developed solution can explain more variations of the effective permeability in relation to the fractal dimensions estimated from the field observations. At high hydraulic gradient the effective permeability decreases with the fractal scaling exponent, but increases with the fractal scaling exponent at low gradient. The effective permeability increases with the scaling coefficient, fractal dimension, fracture length ratio and maximum fracture length.

  1. Gait Partitioning Methods: A Systematic Review

    PubMed Central

    Taborri, Juri; Palermo, Eduardo; Rossi, Stefano; Cappa, Paolo

    2016-01-01

    In the last years, gait phase partitioning has come to be a challenging research topic due to its impact on several applications related to gait technologies. A variety of sensors can be used to feed algorithms for gait phase partitioning, mainly classifiable as wearable or non-wearable. Among wearable sensors, footswitches or foot pressure insoles are generally considered as the gold standard; however, to overcome some inherent limitations of the former, inertial measurement units have become popular in recent decades. Valuable results have been achieved also though electromyography, electroneurography, and ultrasonic sensors. Non-wearable sensors, such as opto-electronic systems along with force platforms, remain the most accurate system to perform gait analysis in an indoor environment. In the present paper we identify, select, and categorize the available methodologies for gait phase detection, analyzing advantages and disadvantages of each solution. Finally, we comparatively examine the obtainable gait phase granularities, the usable computational methodologies and the optimal sensor placements on the targeted body segments. PMID:26751449

  2. Gait Partitioning Methods: A Systematic Review.

    PubMed

    Taborri, Juri; Palermo, Eduardo; Rossi, Stefano; Cappa, Paolo

    2016-01-06

    In the last years, gait phase partitioning has come to be a challenging research topic due to its impact on several applications related to gait technologies. A variety of sensors can be used to feed algorithms for gait phase partitioning, mainly classifiable as wearable or non-wearable. Among wearable sensors, footswitches or foot pressure insoles are generally considered as the gold standard; however, to overcome some inherent limitations of the former, inertial measurement units have become popular in recent decades. Valuable results have been achieved also though electromyography, electroneurography, and ultrasonic sensors. Non-wearable sensors, such as opto-electronic systems along with force platforms, remain the most accurate system to perform gait analysis in an indoor environment. In the present paper we identify, select, and categorize the available methodologies for gait phase detection, analyzing advantages and disadvantages of each solution. Finally, we comparatively examine the obtainable gait phase granularities, the usable computational methodologies and the optimal sensor placements on the targeted body segments.

  3. Fractal based curves in musical creativity: A critical annotation

    NASA Astrophysics Data System (ADS)

    Georgaki, Anastasia; Tsolakis, Christos

    In this article we examine fractal curves and synthesis algorithms in musical composition and research. First we trace the evolution of different approaches for the use of fractals in music since the 80's by a literature review. Furthermore, we review representative fractal algorithms and platforms that implement them. Properties such as self-similarity (pink noise), correlation, memory (related to the notion of Brownian motion) or non correlation at multiple levels (white noise), can be used to develop hierarchy of criteria for analyzing different layers of musical structure. L-systems can be applied in the modelling of melody in different musical cultures as well as in the investigation of musical perception principles. Finally, we propose a critical investigation approach for the use of artificial or natural fractal curves in systematic musicology.

  4. Study on Conversion Between Momentum and Contrarian Based on Fractal Game

    NASA Astrophysics Data System (ADS)

    Wu, Xu; Song, Guanghui; Deng, Yan; Xu, Lin

    2015-06-01

    Based on the fractal game which is performed by the majority and the minority, the fractal market theory (FMT) is employed to describe the features of investors' decision-making. Accordingly, the process of fractal games is formed in order to analyze the statistical features of conversion between momentum and contrarian. The result shows that among three fractal game mechanisms, the statistical feature of simulated return rate series is much more similar to log returns on actual series. In addition, the conversion between momentum and contrarian is also extremely similar to real situation, which can reflect the effectiveness of using fractal game in analyzing the conversion between momentum and contrarian. Moreover, it also provides decision-making reference which helps investors develop effective investment strategy.

  5. Fractal design concepts for stretchable electronics.

    PubMed

    Fan, Jonathan A; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J; Huang, Yonggang; Rogers, John A

    2014-01-01

    Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.

  6. Fractal design concepts for stretchable electronics

    NASA Astrophysics Data System (ADS)

    Fan, Jonathan A.; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J.; Huang, Yonggang; Rogers, John A.

    2014-02-01

    Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.

  7. Optics in gait analysis and anthropometry

    NASA Astrophysics Data System (ADS)

    Silva Moreno, Alejandra Alicia

    2013-11-01

    Since antiquity, human gait has been studied to understand human movement, the kind of gait, in some cases, can cause musculoskeletal disorders or other health problems; in addition, also from antiquity, anthropometry has been important for the design of human items such as workspaces, tools, garments, among others. Nowadays, thanks to the development of optics and electronics, more accurate studies of gait and anthropometry can be developed. This work will describe the most important parameters for gait analysis, anthropometry and the optical systems used.

  8. Gait and balance disorders in older adults.

    PubMed

    Salzman, Brooke

    2010-07-01

    Gait and balance disorders are common in older adults and are a major cause of falls in this population. They are associated with increased morbidity and mortality, as well as reduced level of function. Common causes include arthritis and orthostatic hypotension; however, most gait and balance disorders involve multiple contributing factors. Most changes in gait are related to underlying medical conditions and should not be considered an inevitable consequence of aging. Physicians caring for older patients should ask at least annually about falls, and should ask about or examine for difficulties with gait and balance at least once. For older adults who report a fall, physicians should ask about difficulties with gait and balance, and should observe for any gait or balance dysfunctions. The Timed Up and Go test is a fast and reliable diagnostic tool. Persons who have difficulty or demonstrate unsteadiness performing the Timed Up and Go test require further assessment, usually with a physical therapist, to help elucidate gait impairments and related functional limitations. The most effective strategy for falls prevention involves a multifactorial evaluation followed by targeted interventions for identified contributing factors. Evidence on the effectiveness of interventions for gait and balance disorders is limited because of the lack of standardized outcome measures determining gait and balance abilities. However, effective options for patients with gait and balance disorders include exercise and physical therapy. (c) 2010 American Academy of Family Physicians.

  9. The Gait Disorder in Downbeat Nystagmus Syndrome

    PubMed Central

    Schniepp, Roman; Wuehr, Max; Huth, Sabrina; Pradhan, Cauchy; Schlick, Cornelia; Brandt, Thomas; Jahn, Klaus

    2014-01-01

    Background Downbeat nystagmus (DBN) is a common form of acquired fixation nystagmus with key symptoms of oscillopsia and gait disturbance. Gait disturbance could be a result of impaired visual feedback due to the involuntary ocular oscillations. Alternatively, a malfunction of cerebellar locomotor control might be involved, since DBN is considered a vestibulocerebellar disorder. Methods Investigation of walking in 50 DBN patients (age 72±11 years, 23 females) and 50 healthy controls (HS) (age 70±11 years, 23 females) using a pressure sensitive carpet (GAITRite). The patient cohort comprised subjects with only ocular motor signs (DBN) and subjects with an additional limb ataxia (DBNCA). Gait investigation comprised different walking speeds and walking with eyes closed. Results In DBN, gait velocity was reduced (p<0.001) with a reduced stride length (p<0.001), increased base of support (p<0.050), and increased double support (p<0.001). Walking with eyes closed led to significant gait changes in both HS and DBN. These changes were more pronounced in DBN patients (p<0.001). Speed-dependency of gait variability revealed significant differences between the subgroups of DBN and DBNCA (p<0.050). Conclusions (I) Impaired visual control caused by involuntary ocular oscillations cannot sufficiently explain the gait disorder. (II) The gait of patients with DBN is impaired in a speed dependent manner. (III) Analysis of gait variability allows distinguishing DBN from DBNCA: Patients with pure DBN show a speed dependency of gait variability similar to that of patients with afferent vestibular deficits. In DBNCA, gait variability resembles the pattern found in cerebellar ataxia. PMID:25140517

  10. Fractal Analyses of High-Resolution Cloud Droplet Measurements.

    NASA Astrophysics Data System (ADS)

    Malinowski, Szymon P.; Leclerc, Monique Y.; Baumgardner, Darrel G.

    1994-02-01

    Fractal analyses of individual cloud droplet distributions using aircraft measurements along one-dimensional horizontal cross sections through clouds are performed. Box counting and cluster analyses are used to determine spatial scales of inhomogeneity of cloud droplet spacing. These analyses reveal that droplet spatial distributions do not exhibit a fractal behavior. A high variability in local droplet concentration in cloud volumes undergoing mixing was found. In these regions, thin filaments of cloudy air with droplet concentration close to those observed in cloud cores were found. Results suggest that these filaments may be anisotropic. Additional box counting analyses performed for various classes of cloud droplet diameters indicate that large and small droplets are similarly distributed, except for the larger characteristic spacing of large droplets.A cloud-clear air interface defined by a certain threshold of total droplet count (TDC) was investigated. There are indications that this interface is a convoluted surface of a fractal nature, at least in actively developing cumuliform clouds. In contrast, TDC in the cloud interior does not have fractal or multifractal properties. Finally a random Cantor set (RCS) was introduced as a model of a fractal process with an ill-defined internal scale. A uniform measure associated with the RCS after several generations was introduced to simulate the TDC records. Comparison of the model with real TDC records indicates similar properties of both types of data series.

  11. Gait recognition based on integral outline

    NASA Astrophysics Data System (ADS)

    Ming, Guan; Fang, Lv

    2017-02-01

    Biometric identification technology replaces traditional security technology, which has become a trend, and gait recognition also has become a hot spot of research because its feature is difficult to imitate and theft. This paper presents a gait recognition system based on integral outline of human body. The system has three important aspects: the preprocessing of gait image, feature extraction and classification. Finally, using a method of polling to evaluate the performance of the system, and summarizing the problems existing in the gait recognition and the direction of development in the future.

  12. On the fractal morphology of combustion-generated soot aggregates

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Koylu, U.O.

    1995-12-31

    The fractal properties of soot aggregates were investigated using ex-situ and in-situ experimental methods as well as computer simulations. Ex-situ experiments involved thermophoretic sampling and analysis by transmission electron microscopy (TEM), while in-situ measurements employed angular static light scattering and data inversion based on Rayleigh-Debye-Gans (RDG) approximation. Computer simulations used a sequential algorithm which mimics mass fractal-like structures. So from a variety of hydrocarbon-fueled laminar and turbulent nonpremixed flame environments were considered in the present study. The TEM analysis of projected soot images sampled from fuel-rich conditions of buoyant and weakly-buoyant laminar flames indicated that the fractal dimension of sootmore » was relatively independent of position in flames, fuel type and flame condition. These measurements yielded an average fractal dimension of 1.8, although other structure parameters such as the primary particle diameters and number of primary particles in aggregates had wide range of values. Fractal prefactor (lacunarity) was also measured for soot sampled from the fuel-lean conditions of turbulent flames, considering the actual morphology by tilting the samples during TEM analysis. These measurements yielded a fractal dimension of 1.65 and a lacunarity of 8.5, with experimental uncertainties (95% confidence) of 0.08 and 0.5, respectively. Relationships between the actual and projected structure properties of soot were also developed by combining TEM observations with numerical simulations. Practical approximate formulae were suggested to find radius of gyration of an aggregate from its maximum dimension, and number of primary particles in an aggregate from projected area. Finally, the fractal dimension and lacunarity of soot were obtained using light scattering for the same conditions of the above TEM measurements.« less

  13. [Recent progress of research and applications of fractal and its theories in medicine].

    PubMed

    Cai, Congbo; Wang, Ping

    2014-10-01

    Fractal, a mathematics concept, is used to describe an image of self-similarity and scale invariance. Some organisms have been discovered with the fractal characteristics, such as cerebral cortex surface, retinal vessel structure, cardiovascular network, and trabecular bone, etc. It has been preliminarily confirmed that the three-dimensional structure of cells cultured in vitro could be significantly enhanced by bionic fractal surface. Moreover, fractal theory in clinical research will help early diagnosis and treatment of diseases, reducing the patient's pain and suffering. The development process of diseases in the human body can be expressed by the fractal theories parameter. It is of considerable significance to retrospectively review the preparation and application of fractal surface and its diagnostic value in medicine. This paper gives an application of fractal and its theories in the medical science, based on the research achievements in our laboratory.

  14. Fractal markets: Liquidity and investors on different time horizons

    NASA Astrophysics Data System (ADS)

    Li, Da-Ye; Nishimura, Yusaku; Men, Ming

    2014-08-01

    In this paper, we propose a new agent-based model to study the source of liquidity and the “emergent” phenomenon in financial market with fractal structure. The model rests on fractal market hypothesis and agents with different time horizons of investments. What is interesting is that though the agent-based model reveals that the interaction between these heterogeneous agents affects the stability and liquidity of the financial market the real world market lacks detailed data to bring it to light since it is difficult to identify and distinguish the investors with different time horizons in the empirical approach. results show that in a relatively short period of time fractal market provides liquidity from investors with different horizons and the market gains stability when the market structure changes from uniformity to diversification. In the real world the fractal structure with the finite of horizons can only stabilize the market within limits. With the finite maximum horizons, the greater diversity of the investors and the fractal structure will not necessarily bring more stability to the market which might come with greater fluctuation in large time scale.

  15. Thin film growth by 3D multi-particle diffusion limited aggregation model: Anomalous roughening and fractal analysis

    NASA Astrophysics Data System (ADS)

    Nasehnejad, Maryam; Nabiyouni, G.; Gholipour Shahraki, Mehran

    2018-03-01

    In this study a 3D multi-particle diffusion limited aggregation method is employed to simulate growth of rough surfaces with fractal behavior in electrodeposition process. A deposition model is used in which the radial motion of the particles with probability P, competes with random motions with probability 1 - P. Thin films growth is simulated for different values of probability P (related to the electric field) and thickness of the layer(related to the number of deposited particles). The influence of these parameters on morphology, kinetic of roughening and the fractal dimension of the simulated surfaces has been investigated. The results show that the surface roughness increases with increasing the deposition time and scaling exponents exhibit a complex behavior which is called as anomalous scaling. It seems that in electrodeposition process, radial motion of the particles toward the growing seeds may be an important mechanism leading to anomalous scaling. The results also indicate that the larger values of probability P, results in smoother topography with more densely packed structure. We have suggested a dynamic scaling ansatz for interface width has a function of deposition time, scan length and probability. Two different methods are employed to evaluate the fractal dimension of the simulated surfaces which are "cube counting" and "roughness" methods. The results of both methods show that by increasing the probability P or decreasing the deposition time, the fractal dimension of the simulated surfaces is increased. All gained values for fractal dimensions are close to 2.5 in the diffusion limited aggregation model.

  16. Correlation between static radiographic measurements and intersegmental angular measurements during gait using a multisegment foot model.

    PubMed

    Lee, Dong Yeon; Seo, Sang Gyo; Kim, Eo Jin; Kim, Sung Ju; Lee, Kyoung Min; Farber, Daniel C; Chung, Chin Youb; Choi, In Ho

    2015-01-01

    Radiographic examination is a widely used evaluation method in the orthopedic clinic. However, conventional radiography alone does not reflect the dynamic changes between foot and ankle segments during gait. Multiple 3-dimensional multisegment foot models (3D MFMs) have been introduced to evaluate intersegmental motion of the foot. In this study, we evaluated the correlation between static radiographic indices and intersegmental foot motion indices. One hundred twenty-five females were tested. Static radiographs of full-leg and anteroposterior (AP) and lateral foot views were performed. For hindfoot evaluation, we measured the AP tibiotalar angle (TiTA), talar tilt (TT), calcaneal pitch, lateral tibiocalcaneal angle, and lateral talcocalcaneal angle. For the midfoot segment, naviculocuboid overlap and talonavicular coverage angle were calculated. AP and lateral talo-first metatarsal angles and metatarsal stacking angle (MSA) were measured to assess the forefoot. Hallux valgus angle (HVA) and hallux interphalangeal angle were measured. In gait analysis by 3D MFM, intersegmental angle (ISA) measurements of each segment (hallux, forefoot, hindfoot, arch) were recorded. ISAs at midstance phase were most highly correlated with radiography. Significant correlations were observed between ISA measurements using MFM and static radiographic measurements in the same segment. In the hindfoot, coronal plane ISA was correlated with AP TiTA (P < .001) and TT (P = .018). In the hallux, HVA was strongly correlated with transverse ISA of the hallux (P < .001). The segmental foot motion indices at midstance phase during gait measured by 3D MFM gait analysis were correlated with the conventional radiographic indices. The observed correlation between MFM measurements at midstance phase during gait and static radiographic measurements supports the fundamental basis for the use of MFM in analysis of dynamic motion of foot segment during gait. © The Author(s) 2014.

  17. A comparison of the fractal and JPEG algorithms

    NASA Technical Reports Server (NTRS)

    Cheung, K.-M.; Shahshahani, M.

    1991-01-01

    A proprietary fractal image compression algorithm and the Joint Photographic Experts Group (JPEG) industry standard algorithm for image compression are compared. In every case, the JPEG algorithm was superior to the fractal method at a given compression ratio according to a root mean square criterion and a peak signal to noise criterion.

  18. a Fractal Permeability Model Coupling Boundary-Layer Effect for Tight Oil Reservoirs

    NASA Astrophysics Data System (ADS)

    Wang, Fuyong; Liu, Zhichao; Jiao, Liang; Wang, Congle; Guo, Hu

    A fractal permeability model coupling non-flowing boundary-layer effect for tight oil reservoirs was proposed. Firstly, pore structures of tight formations were characterized with fractal theory. Then, with the empirical equation of boundary-layer thickness, Hagen-Poiseuille equation and fractal theory, a fractal torturous capillary tube model coupled with boundary-layer effect was developed, and verified with experimental data. Finally, the parameters influencing effective liquid permeability were quantitatively investigated. The research results show that effective liquid permeability of tight formations is not only decided by pore structures, but also affected by boundary-layer distributions, and effective liquid permeability is the function of fluid type, fluid viscosity, pressure gradient, fractal dimension, tortuosity fractal dimension, minimum pore radius and maximum pore radius. For the tight formations dominated with nanoscale pores, boundary-layer effect can significantly reduce effective liquid permeability, especially under low pressure gradient.

  19. Exhaled Aerosol Pattern Discloses Lung Structural Abnormality: A Sensitivity Study Using Computational Modeling and Fractal Analysis

    PubMed Central

    Xi, Jinxiang; Si, Xiuhua A.; Kim, JongWon; Mckee, Edward; Lin, En-Bing

    2014-01-01

    Background Exhaled aerosol patterns, also called aerosol fingerprints, provide clues to the health of the lung and can be used to detect disease-modified airway structures. The key is how to decode the exhaled aerosol fingerprints and retrieve the lung structural information for a non-invasive identification of respiratory diseases. Objective and Methods In this study, a CFD-fractal analysis method was developed to quantify exhaled aerosol fingerprints and applied it to one benign and three malign conditions: a tracheal carina tumor, a bronchial tumor, and asthma. Respirations of tracer aerosols of 1 µm at a flow rate of 30 L/min were simulated, with exhaled distributions recorded at the mouth. Large eddy simulations and a Lagrangian tracking approach were used to simulate respiratory airflows and aerosol dynamics. Aerosol morphometric measures such as concentration disparity, spatial distributions, and fractal analysis were applied to distinguish various exhaled aerosol patterns. Findings Utilizing physiology-based modeling, we demonstrated substantial differences in exhaled aerosol distributions among normal and pathological airways, which were suggestive of the disease location and extent. With fractal analysis, we also demonstrated that exhaled aerosol patterns exhibited fractal behavior in both the entire image and selected regions of interest. Each exhaled aerosol fingerprint exhibited distinct pattern parameters such as spatial probability, fractal dimension, lacunarity, and multifractal spectrum. Furthermore, a correlation of the diseased location and exhaled aerosol spatial distribution was established for asthma. Conclusion Aerosol-fingerprint-based breath tests disclose clues about the site and severity of lung diseases and appear to be sensitive enough to be a practical tool for diagnosis and prognosis of respiratory diseases with structural abnormalities. PMID:25105680

  20. A Fractal Excursion.

    ERIC Educational Resources Information Center

    Camp, Dane R.

    1991-01-01

    After introducing the two-dimensional Koch curve, which is generated by simple recursions on an equilateral triangle, the process is extended to three dimensions with simple recursions on a regular tetrahedron. Included, for both fractal sequences, are iterative formulae, illustrations of the first several iterations, and a sample PASCAL program.…