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Sample records for gompertz growth model

  1. Probabilistic Gompertz model of irreversible growth.

    PubMed

    Bardos, D C

    2005-05-01

    Characterizing organism growth within populations requires the application of well-studied individual size-at-age models, such as the deterministic Gompertz model, to populations of individuals whose characteristics, corresponding to model parameters, may be highly variable. A natural approach is to assign probability distributions to one or more model parameters. In some contexts, size-at-age data may be absent due to difficulties in ageing individuals, but size-increment data may instead be available (e.g., from tag-recapture experiments). A preliminary transformation to a size-increment model is then required. Gompertz models developed along the above lines have recently been applied to strongly heterogeneous abalone tag-recapture data. Although useful in modelling the early growth stages, these models yield size-increment distributions that allow negative growth, which is inappropriate in the case of mollusc shells and other accumulated biological structures (e.g., vertebrae) where growth is irreversible. Here we develop probabilistic Gompertz models where this difficulty is resolved by conditioning parameter distributions on size, allowing application to irreversible growth data. In the case of abalone growth, introduction of a growth-limiting biological length scale is then shown to yield realistic length-increment distributions.

  2. Stochastic Gompertz model of tumour cell growth.

    PubMed

    Lo, C F

    2007-09-21

    In this communication, based upon the deterministic Gompertz law of cell growth, a stochastic model in tumour growth is proposed. This model takes account of both cell fission and mortality too. The corresponding density function of the size of the tumour cells obeys a functional Fokker--Planck equation which can be solved analytically. It is found that the density function exhibits an interesting "multi-peak" structure generated by cell fission as time evolves. Within this framework the action of therapy is also examined by simply incorporating a therapy term into the deterministic cell growth term.

  3. Comparison of Gompertz and neural network models of broiler growth.

    PubMed

    Roush, W B; Dozier, W A; Branton, S L

    2006-04-01

    Neural networks offer an alternative to regression analysis for biological growth modeling. Very little research has been conducted to model animal growth using artificial neural networks. Twenty-five male chicks (Ross x Ross 308) were raised in an environmental chamber. Body weights were determined daily and feed and water were provided ad libitum. The birds were fed a starter diet (23% CP and 3,200 kcal of ME/kg) from 0 to 21 d, and a grower diet (20% CP and 3,200 kcal of ME/ kg) from 22 to 70 d. Dead and female birds were not included in the study. Average BW of 18 birds were used as the data points for the growth curve to be modeled. Training data consisted of alternate-day weights starting with the first day. Validation data consisted of BW at all other age periods. Comparison was made between the modeling by the Gompertz nonlinear regression equation and neural network modeling. Neural network models were developed with the Neuroshell Predictor. Accuracy of the models was determined by mean square error (MSE), mean absolute deviation (MAD), mean absolute percentage error (MAPE), and bias. The Gompertz equation was fit for the data. Forecasting error measurements were based on the difference between the model and the observed values. For the training data, the lowest MSE, MAD, MAPE, and bias were noted for the neural-developed neural network. For the validation data, the lowest MSE and MAD were noted with the genetic algorithm-developed neural network. Lowest bias was for the neural-developed network. As measured by bias, the Gompertz equation underestimated the values whereas the neural- and genetic-developed neural networks produced little or no overestimation of the observed BW responses. Past studies have attempted to interpret the biological significance of the estimates of the parameters of an equation. However, it may be more practical to ignore the relevance of parameter estimates and focus on the ability to predict responses.

  4. Estimation of growth parameters using a nonlinear mixed Gompertz model.

    PubMed

    Wang, Z; Zuidhof, M J

    2004-06-01

    In order to maximize the utility of simulation models for decision making, accurate estimation of growth parameters and associated variances is crucial. A mixed Gompertz growth model was used to account for between-bird variation and heterogeneous variance. The mixed model had several advantages over the fixed effects model. The mixed model partitioned BW variation into between- and within-bird variation, and the covariance structure assumed with the random effect accounted for part of the BW correlation across ages in the same individual. The amount of residual variance decreased by over 55% with the mixed model. The mixed model reduced estimation biases that resulted from selective sampling. For analysis of longitudinal growth data, the mixed effects growth model is recommended.

  5. A proposed fractional-order Gompertz model and its application to tumour growth data.

    PubMed

    Bolton, Larisse; Cloot, Alain H J J; Schoombie, Schalk W; Slabbert, Jacobus P

    2015-06-01

    A fractional-order Gompertz model of orders between 0 and 2 is proposed. The main purpose of this investigation is to determine whether the ordinary or proposed fractional Gompertz model would best fit our experimental dataset. The solutions for the proposed model are obtained using fundamental concepts from fractional calculus. The closed-form equations of both the proposed model and the ordinary Gompertz model are calibrated using an experimental dataset containing tumour growth volumes of a Rhabdomyosarcoma tumour in a mouse. With regard to the proposed model, the order, within the interval mentioned, that resulted in the best fit to the data was used in a further investigation into the prediction capability of the model. This was compared to the prediction capability of the ordinary Gompertz model. The result of the investigation was that a fractional-order Gompertz model of order 0.68 produced a better fit to our experimental dataset than the well-known ordinary Gompertz model.

  6. The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the Unified-Richards family

    PubMed Central

    Tjørve, Even

    2017-01-01

    The Gompertz model is well known and widely used in many aspects of biology. It has been frequently used to describe the growth of animals and plants, as well as the number or volume of bacteria and cancer cells. Numerous parametrisations and re-parametrisations of varying usefulness are found in the literature, whereof the Gompertz-Laird is one of the more commonly used. Here, we review, present, and discuss the many re-parametrisations and some parameterisations of the Gompertz model, which we divide into Ti (type I)- and W0 (type II)-forms. In the W0-form a starting-point parameter, meaning birth or hatching value (W0), replaces the inflection-time parameter (Ti). We also propose new “unified” versions (U-versions) of both the traditional Ti -form and a simplified W0-form. In these, the growth-rate constant represents the relative growth rate instead of merely an unspecified growth coefficient. We also present U-versions where the growth-rate parameters return absolute growth rate (instead of relative). The new U-Gompertz models are special cases of the Unified-Richards (U-Richards) model and thus belong to the Richards family of U-models. As U-models, they have a set of parameters, which are comparable across models in the family, without conversion equations. The improvements are simple, and may seem trivial, but are of great importance to those who study organismal growth, as the two new U-Gompertz forms give easy and fast access to all shape parameters needed for describing most types of growth following the shape of the Gompertz model. PMID:28582419

  7. Growth characteristics of pearl gray guinea fowl as predicted by the Richards, Gompertz, and logistic models.

    PubMed

    Nahashon, S N; Aggrey, S E; Adefope, N A; Amenyenu, A; Wright, D

    2006-02-01

    This study was undertaken to describe the growth pattern of the pearl gray Guinea fowl. Using BW data from hatch to 22 wk, 3 nonlinear mathematical functions (Richards, Gompertz, and logistic) were used to estimate growth patterns of the pearl gray guinea fowl. The logistic and Gompertz models are a special case of the Richards model, which has a variable point of inflection defined by the shape or growth trajectory parameter, m. The shape parameter m was 1.08 and 0.98 in males and females, respectively, suggesting that the growth pattern of the pearl gray female guinea fowl is Gompertz. The pearl gray guinea fowl exhibited sexual dimorphism for their growth characteristics. From the Gompertz model, the asymptotic BW, growth rate, and age at maximum growth were 1.62 kg, 0.22 kg/wk, and 6.65 wk in males, respectively, and 1.70 kg, 0.19 kg/wk, and 6.70 wk in females, respectively. The ages at maximum growth were 6.65, 6.47, and 8.12 wk for the Richards, Gompertz, and logistic models, respectively. The pearl gray guinea fowl females have a higher asymptotic BW compared with the males. The average asymptotic BW of about 1.57 kg for both sexes predicted by the logistic model was below the average predicted BW from the Richards (1.66 kg) and Gompertz (1.67 kg) models, respectively, at 22 wk of age. The inverse relationship between the asymptotic weight and both relative growth and age at maximum growth of the pearl gray guinea fowl is similar to that of chickens, quail, and ducks. Success in studying the growth characteristics of guinea fowl will contribute to the efforts of genetically improving this least-studied avian species.

  8. On the therapy effect for a stochastic growth Gompertz-type model.

    PubMed

    Albano, Giuseppina; Giorno, Virginia; Román-Román, Patricia; Torres-Ruiz, Francisco

    2012-02-01

    We consider a diffusion model based on a generalized Gompertz deterministic growth in which carrying capacity depends on the initial size of the population. The drift of the resulting process is then modified by introducing a time-dependent function, called "therapy", in order to model the effect of an exogenous factor. The transition probability density function and the related moments for the proposed process are obtained. A study of the influence of the therapy on several characteristics of the model is performed. The first-passage-time problem through time-dependent boundaries is also analyzed. Finally, an application to real data concerning a rabbit population subject to particular therapies is presented.

  9. Parameterization of European perch Perca fluviatilis length-at-age data using stochastic Gompertz growth models.

    PubMed

    Troynikov, V S; Gorfine, H K; Ložys, L; Pūtys, Z; Jakubavičiūtė, E; Day, R W

    2011-12-01

    Three stochastic versions of the Gompertz growth model were used to parameterize total length (L(T) )-at-age data for perch Perca fluviatilis, an important target species for commercial and recreational fishers and a food species for predatory fishes and aquatic birds. Each model addresses growth heterogeneity by incorporating random parameters from a specific positive distribution: Weibull, gamma or log-normal. The modelling outputs for each version of the model provide L(T) distributions for selected ages and percentiles of L(T) at age for both males and females. The results highlight the importance of using a stochastic approach and the logistic-like growth pattern for analysing growth data for P. fluviatilis in Curonian Lagoon (Lithuania). Outputs from this modelling can be extended to a stochastic analysis of fish cohort dynamics, incorporating all length-based biological relationships, and the selectivity-related interactions between fish cohorts and fishing gear.

  10. Optimization of the cell seeding density and modeling of cell growth and metabolism using the modified Gompertz model for microencapsulated animal cell culture.

    PubMed

    Wen-tao, Qi; Ying, Zhang; Juan, Ma; Xin, Guo; Yu-bing, Xie; Wei, Wang; Xiaojun, Ma

    2006-04-05

    Cell microencapsulation is one of the promising strategies for the in vitro production of proteins or in vivo delivery of therapeutic products. In order to design and fabricate the optimized microencapsulated cell system, the Gompertz model was applied and modified to describe the growth and metabolism of microencapsulated cell, including substrate consumption and product formation. The Gompertz model successfully described the cell growth kinetics and the modified Gompertz models fitted the substrate consumption and product formation well. It was demonstrated that the optimal initial cell seeding density was about 4-5 x 10(6) cells/mL of microcapsule, in terms of the maximum specific growth rate, the glucose consumption potential and the product formation potential calculated by the Gompertz and modified Gompertz models. Modeling of cell growth and metabolism in microcapsules provides a guideline for optimizing the culture of microencapsulated cells.

  11. Estimation of non-linear growth models by linearization: a simulation study using a Gompertz function.

    PubMed

    Vuori, Kaarina; Strandén, Ismo; Sevón-Aimonen, Marja-Liisa; Mäntysaari, Esa A

    2006-01-01

    A method based on Taylor series expansion for estimation of location parameters and variance components of non-linear mixed effects models was considered. An attractive property of the method is the opportunity for an easily implemented algorithm. Estimation of non-linear mixed effects models can be done by common methods for linear mixed effects models, and thus existing programs can be used after small modifications. The applicability of this algorithm in animal breeding was studied with simulation using a Gompertz function growth model in pigs. Two growth data sets were analyzed: a full set containing observations from the entire growing period, and a truncated time trajectory set containing animals slaughtered prematurely, which is common in pig breeding. The results from the 50 simulation replicates with full data set indicate that the linearization approach was capable of estimating the original parameters satisfactorily. However, estimation of the parameters related to adult weight becomes unstable in the case of a truncated data set.

  12. Estimation of vaginal probiotic lactobacilli growth parameters with the application of the Gompertz model.

    PubMed

    Juárez, TomásMaríaSilvina; de, LabandaElenaBru; de, RuizHolgadoAidaPesce; Nader-Macías, María Elena

    2002-01-01

    Lactobacilli are widely described as probiotic microorganisms used to restore the ecological balance of different animal or human tracts. For their use as probiotics, bacteria must show certain characteristics or properties related to the ability of adherence to mucosae or epithelia or show inhibition against pathogenic microorganisms. It is of primary interest to obtain the highest biomass and viability of the selected microorganisms. In this report, the growth of seven vaginal lactobacilli strains in four different growth media and at several inoculum percentages was compared, and the values of growth parameters (lag phase time, maximum growth rate, maximum optical density) were obtained by applying the Gompertz model to the experimental data. The application and estimation of this model is discussed, and the evaluation of the growth parameters is analyzed to compare the growth conditions of lactobacilli. Thus, these results in lab experiments provide a basis for testing different culture conditions to determine the best conditions in which to grow the probiotic lactobacilli for technological applications.

  13. Growth curve by Gompertz nonlinear regression model in female and males in tambaqui (Colossoma macropomum).

    PubMed

    De Mello, Fernanda; Oliveira, Carlos A L; Ribeiro, Ricardo P; Resende, Emiko K; Povh, Jayme A; Fornari, Darci C; Barreto, Rogério V; McManus, Concepta; Streit, Danilo

    2015-01-01

    Was evaluated the pattern of growth among females and males of tambaqui by Gompertz nonlinear regression model. Five traits of economic importance were measured on 145 animals during the three years, totaling 981 morphometric data analyzed. Different curves were adjusted between males and females for body weight, height and head length and only one curve was adjusted to the width and body length. The asymptotic weight (a) and relative growth rate to maturity (k) were different between sexes in animals with ± 5 kg; slaughter weight practiced by a specific niche market, very profitable. However, there was no difference between males and females up to ± 2 kg; slaughter weight established to supply the bigger consumer market. Females showed weight greater than males (± 280 g), which are more suitable for fish farming purposes defined for the niche market to larger animals. In general, males had lower maximum growth rate (8.66 g / day) than females (9.34 g / day), however, reached faster than females, 476 and 486 days growth rate, respectively. The height and length body are the traits that contributed most to the weight at 516 days (P <0.001).

  14. Evaluation of nitrogenous substrates such as peptones from fish:a new method based on Gompertz modeling of microbial growth.

    PubMed

    Dufossé, L; De La Broise, D; Guerard, F

    2001-01-01

    Fish peptones from tuna, cod, salmon, and unspecified fish were compared with a casein one by using a new method based on Gompertz modeling of microbial growth. Cumulative results obtained from six species of bacteria, yeasts, and fungi showed that, in most cases, these fish peptones are very effective. Nevertheless, this study raised some questions about the standardization of fish raw material, the enzymatic hydrolysis of fish proteins, and the composition of the culture medium used for testing the peptones.

  15. Global stability of Gompertz model of three competing populations

    NASA Astrophysics Data System (ADS)

    Yu, Yumei; Wang, Wendi; Lu, Zhengyi

    2007-10-01

    The model of three competitive populations with Gompertz growth is studied. The periodic solutions are ruled out by generalized Dulac criteria. On the basis of the analysis, we obtain conditions that ensure the asymptotic behavior of the model is simple.

  16. Analysis of a growth model inspired by Gompertz and Korf laws, and an analogous birth-death process.

    PubMed

    Di Crescenzo, Antonio; Spina, Serena

    2016-12-01

    We propose a new deterministic growth model which captures certain features of both the Gompertz and Korf laws. We investigate its main properties, with special attention to the correction factor, the relative growth rate, the inflection point, the maximum specific growth rate, the lag time and the threshold crossing problem. Some data analytic examples and their performance are also considered. Furthermore, we study a stochastic counterpart of the proposed model, that is a linear time-inhomogeneous birth-death process whose mean behaves as the deterministic one. We obtain the transition probabilities, the moments and the population ultimate extinction probability for this process. We finally treat the special case of a simple birth process, which better mimics the proposed growth model.

  17. Impact of electro-stimulation on denitrifying bacterial growth and analysis of bacterial growth kinetics using a modified Gompertz model in a bio-electrochemical denitrification reactor.

    PubMed

    Liu, Hengyuan; Chen, Nan; Feng, Chuanping; Tong, Shuang; Li, Rui

    2017-05-01

    This study aimed to investigate the effect of electro-stimulation on denitrifying bacterial growth in a bio-electrochemical reactor, and the growth were modeled using modified Gompertz model under different current densities at three C/Ns. It was found that the similar optimum current density of 250mA/m(2) was obtained at C/N=0.75, 1.00 and 1.25, correspondingly the maximum nitrate removal efficiencies were 98.0%, 99.2% and 99.9%. Moreover, ATP content and cell membrane permeability of denitrifying bacteria were significantly increased at optimum current density. Furthermore, modified Gompertz model fitted well with the microbial growth curves, and the highest maximum growth rates (µmax) and shorter lag time were obtained at the optimum current density for all C/Ns. This study demonstrated that the modified Gompertz model could be used for describing microbial growth under different current densities and C/Ns in a bio-electrochemical denitrification reactor, and it provided an alternative for improving the performance of denitrification process.

  18. Probabilistic neural networks using Bayesian decision strategies and a modified Gompertz model for growth phase classification in the batch culture of Bacillus subtilis.

    PubMed

    Simon; Nazmul Karim M

    2001-01-01

    Probabilistic neural networks (PNNs) were used in conjunction with the Gompertz model for bacterial growth to classify the lag, logarithmic, and stationary phases in a batch process. Using the fermentation time and the optical density of diluted cell suspensions, sampled from a culture of Bacillus subtilis, PNNs enabled a reliable determination of the growth phases. Based on a Bayesian decision strategy, the Gompertz based PNN used newly proposed definition of the lag and logarithmic phases to estimate the latent, logarithmic and stationary phases. This network topology has the potential for use with on-line turbidimeter for the automation and control of cultivation processes.

  19. On the effect of a therapy able to modify both the growth rates in a Gompertz stochastic model.

    PubMed

    Albano, Giuseppina; Giorno, Virginia; Román-Román, Patricia; Torres-Ruiz, Francisco

    2013-09-01

    A Gompertz-type diffusion process characterized by the presence of exogenous factors in the drift term is considered. Such a process is able to describe the dynamics of populations in which both the intrinsic rates are modified by means of time-dependent terms. In order to quantify the effect of such terms the evaluation of the relative entropy is made. The first passage time problem through suitable boundaries is studied. Moreover, some simulation results are shown in order to capture the dependence of the involved functions on the parameters. Finally, an application to tumor growth is presented and simulation results are shown.

  20. A generalization of Gompertz law compatible with the Gyllenberg-Webb theory for tumour growth.

    PubMed

    d'Onofrio, Alberto; Fasano, Antonio; Monechi, Bernardo

    2011-03-01

    We present a new extension of Gompertz law for tumour growth and anti-tumour therapy. After discussing its qualitative and analytical properties, we show, in the spirit of [16], that, like the standard Gompertz model, it is fully compatible with the two-population model of Gyllenberg and Webb, formulated in [14] in order to provide a theoretical basis to Gompertz law. Compatibility with the model proposed in [17] is also investigated. Comparisons with some experimental data confirm the practical applicability of the model. Numerical simulations about the method performance are presented.

  1. Modeling tumor growth in the presence of a therapy with an effect on rate growth and variability by means of a modified Gompertz diffusion process.

    PubMed

    Román-Román, Patricia; Román-Román, Sergio; Serrano-Pérez, Juan José; Torres-Ruiz, Francisco

    2016-10-21

    In experimental studies on tumor growth, whenever the time evolution of the relative volume of a tumor in an untreated (control) group can be fitted by a Gompertz diffusion process there is a possibility that an antiproliferative therapy, which modifies the growth rate of the process that fits the treated group, may also affect its variability. The present paper proposes several procedures for the estimation of the time function included in the infinitesimal variance of the new process, as well as the time function affecting the growth rate (which is included in the infinitesimal mean). Also, a hypothesis testing is designed to confirm or refute the need for including such a time-dependent function in the infinitesimal variance. In order to validate and compare the proposed procedures a simulation study has been carried out. In addition, a proposal is made for a strategy aimed at finding the optimal combination of procedures for each case. A real data application concerning the effects of cisplatin on a patient-derived xenograft (PDX) tumor model showcases the advantages of this model over others that have been used in the past.

  2. Gompertz kinetics model of fast chemical neurotransmission currents.

    PubMed

    Easton, Dexter M

    2005-10-01

    At a chemical synapse, transmitter molecules ejected from presynaptic terminal(s) bind reversibly with postsynaptic receptors and trigger an increase in channel conductance to specific ions. This paper describes a simple but accurate predictive model for the time course of the synaptic conductance transient, based on Gompertz kinetics. In the model, two simple exponential decay terms set the rates of development and decline of transmitter action. The first, r, triggering conductance activation, is surrogate for the decelerated rate of growth of conductance, G. The second, r', responsible for Y, deactivation of the conductance, is surrogate for the decelerated rate of decline of transmitter action. Therefore, the differential equation for the net conductance change, g, triggered by the transmitter is dg/dt=g(r-r'). The solution of that equation yields the product of G(t), representing activation, and Y(t), which defines the proportional decline (deactivation) of the current. The model fits, over their full-time course, published records of macroscopic ionic current associated with fast chemical transmission. The Gompertz model is a convenient and accurate method for routine analysis and comparison of records of synaptic current and putative transmitter time course. A Gompertz fit requiring only three independent rate constants plus initial current appears indistinguishable from a Markov fit using seven rate constants.

  3. For prediction of elder survival by a Gompertz model, number dead is preferable to number alive.

    PubMed

    Easton, Dexter M; Hirsch, Henry R

    2008-12-01

    The standard Gompertz equation for human survival fits very poorly the survival data of the very old (age 85 and above), who appear to survive better than predicted. An alternative Gompertz model based on the number of individuals who have died, rather than the number that are alive, at each age, tracks the data more accurately. The alternative model is based on the same differential equation as in the usual Gompertz model. The standard model describes the accelerated exponential decay of the number alive, whereas the alternative, heretofore unutilized model describes the decelerated exponential growth of the number dead. The alternative model is complementary to the standard and, together, the two Gompertz formulations allow accurate prediction of survival of the older as well as the younger mature members of the population.

  4. Nonselective Harvesting of a Prey-Predator Fishery with Gompertz Law of Growth

    ERIC Educational Resources Information Center

    Purohit, D.; Chaudhuri, K. S.

    2002-01-01

    This paper develops a mathematical model for the nonselective harvesting of a prey-predator system in which both the prey and the predator obey the Gompertz law of growth and some prey avoid predation by hiding. The steady states of the system are determined, and the dynamical behaviour of both species is examined. The possibility of existence of…

  5. Nonselective Harvesting of a Prey-Predator Fishery with Gompertz Law of Growth

    ERIC Educational Resources Information Center

    Purohit, D.; Chaudhuri, K. S.

    2002-01-01

    This paper develops a mathematical model for the nonselective harvesting of a prey-predator system in which both the prey and the predator obey the Gompertz law of growth and some prey avoid predation by hiding. The steady states of the system are determined, and the dynamical behaviour of both species is examined. The possibility of existence of…

  6. Gompertz model with delays and treatment: mathematical analysis.

    PubMed

    Bodnar, Marek; Piotrowska, Monika Joanna; Foryś, Urszula

    2013-06-01

    In this paper we study the delayed Gompertz model, as a typical model of tumor growth, with a term describing external interference that can reflect a treatment, e.g. chemotherapy. We mainly consider two types of delayed models, the one with the delay introduced in the per capita growth rate (we call it the single delayed model) and the other with the delay introduced in the net growth rate (the double delayed model). We focus on stability and possible stability switches with increasing delay for the positive steady state. Moreover, we study a Hopf bifurcation, including stability of arising periodic solutions for a constant treatment. The analytical results are extended by numerical simulations for a pharmacokinetic treatment function.

  7. Biological implications of the Weibull and Gompertz models of aging.

    PubMed

    Ricklefs, Robert E; Scheuerlein, Alex

    2002-02-01

    Gompertz and Weibull functions imply contrasting biological causes of demographic aging. The terms describing increasing mortality with age are multiplicative and additive, respectively, which could result from an increase in the vulnerability of individuals to extrinsic causes in the Gompertz model and the predominance of intrinsic causes at older ages in the Weibull model. Experiments that manipulate extrinsic mortality can distinguish these biological models. To facilitate analyses of experimental data, we defined a single index for the rate of aging (omega) for the Weibull and Gompertz functions. Each function described the increase in aging-related mortality in simulated ages at death reasonably well. However, in contrast to the Weibull omega(W), the Gompertz omega(G) was sensitive to variation in the initial mortality rate independently of aging-related mortality. Comparisons between wild and captive populations appear to support the intrinsic-causes model for birds, but give mixed support for both models in mammals.

  8. Estimation of genetic (co)variances of Gompertz growth function parameters in pigs.

    PubMed

    Coyne, J M; Matilainen, K; Berry, D P; Sevon-Aimonen, M-L; Mäntysaari, E A; Juga, J; Serenius, T; McHugh, N

    2017-04-01

    The objective of this study was to estimate genetic (co)variances for the Gompertz growth function parameters, asymptotic mature weight (A), the ratio of mature weight to birthweight (B) and rate of maturation (k), using alternative modelling approaches. The data set consisted of 51 893 live weight records from 10 201 growing pigs. The growth of each pig was modelled using the Gompertz model employing either a two-step fixed effect or mixed model approach or a one-step mixed model approach using restricted maximum likelihood for the estimation of genetic (co)variance. Heritability estimates for the Gompertz growth function parameters, A (0.40), B (0.69) and k (0.45), were greatest for the one-step approach, compared with the two-step fixed effects approach, A (0.10), B (0.33) and k (0.13), and the two-step mixed model approach, A (0.17), B (0.32) and k (0.18). Inferred genetic correlations (i.e. correlations of estimated breeding values) between growth function parameters within models ranged from -0.78 to 0.76, and across models ranged from 0.28 to 0.73 for parameter A, 0.75 to 0.88 for parameter B and 0.09 to 0.37 for parameter k. Correlations between predicted daily sire live weights based on the Gompertz growth curve parameters' estimated breeding values from 60 to 200 days of age between all three modelled approaches were moderately to strongly correlated (0.75 to 0.95). Results from this study provide heritability estimates for biologically interpretable parameters of pig growth through the quantification of genetic (co)variances, thereby facilitating the estimation of breeding values for inclusion in breeding objectives to aid in breeding and selection decisions.

  9. The Trans-Gompertz Function: An Alternative to the Logistic Growth Function with Faster Growth.

    PubMed

    Kozusko, F; Bourdeau, M

    2015-12-01

    The growth characteristics of the recently derived Trans-Gompertz function are compared to those of the Generalized Logistic function. Both functions are defined by one shaping parameter and one rate parameter. The functions are matched at a specified point on the growth curve by equating both the first and second derivatives. Analysis shows that the matched Trans-Gompertz function will have grown at a faster rate with a larger inflection point ratio.

  10. FBST for covariance structures of generalized Gompertz models

    NASA Astrophysics Data System (ADS)

    Maranhão, Viviane Teles de Lucca; Lauretto, Marcelo De Souza; Stern, Julio Michael

    2012-10-01

    The Gompertz distribution is commonly used in biology for modeling fatigue and mortality. This paper studies a class of models proposed by Adham and Walker, featuring a Gompertz type distribution where the dependence structure is modeled by a lognormal distribution, and develops a new multivariate formulation that facilitates several numerical and computational aspects. This paper also implements the FBST, the Full Bayesian Significance Test for pertinent sharp (precise) hypotheses on the lognormal covariance structure. The FBST's e-value, ev(H), gives the epistemic value of hypothesis, H, or the value of evidence in the observed in support of H.

  11. Dynamical Analysis and Big Bang Bifurcations of 1D and 2D Gompertz's Growth Functions

    NASA Astrophysics Data System (ADS)

    Rocha, J. Leonel; Taha, Abdel-Kaddous; Fournier-Prunaret, D.

    In this paper, we study the dynamics and bifurcation properties of a three-parameter family of 1D Gompertz's growth functions, which are defined by the population size functions of the Gompertz logistic growth equation. The dynamical behavior is complex leading to a diversified bifurcation structure, leading to the big bang bifurcations of the so-called “box-within-a-box” fractal type. We provide and discuss sufficient conditions for the existence of these bifurcation cascades for 1D Gompertz's growth functions. Moreover, this work concerns the description of some bifurcation properties of a Hénon's map type embedding: a “continuous” embedding of 1D Gompertz's growth functions into a 2D diffeomorphism. More particularly, properties that characterize the big bang bifurcations are considered in relation with this coupling of two population size functions, varying the embedding parameter. The existence of communication areas of crossroad area type or swallowtails are identified for this 2D diffeomorphism.

  12. Modified Gompertz equation for electrotherapy murine tumor growth kinetics: predictions and new hypotheses.

    PubMed

    Cabrales, Luis E Bergues; Nava, Juan J Godina; Aguilera, Andrés Ramírez; Joa, Javier A González; Ciria, Héctor M Camué; González, Maraelys Morales; Salas, Miriam Fariñas; Jarque, Manuel Verdecia; González, Tamara Rubio; Mateus, Miguel A O'Farril; Brooks, Soraida C Acosta; Palencia, Fabiola Suárez; Zamora, Lisset Ortiz; Quevedo, María C Céspedes; Seringe, Sarah Edward; Cuitié, Vladimir Crombet; Cabrales, Idelisa Bergues; González, Gustavo Sierra

    2010-10-28

    Electrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; however, several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed. Mathematical modeling is a useful instrument that can reveal some of these aspects. The aim of this paper is to describe the complete growth kinetics of unperturbed and perturbed tumors through use of the modified Gompertz equation in order to generate useful insight into the mechanisms that underpin this devastating disease. The complete tumor growth kinetics for control and treated groups are obtained by interpolation and extrapolation methods with different time steps, using experimental data of fibrosarcoma Sa-37. In the modified Gompertz equation, a delay time is introduced to describe the tumor's natural history before treatment. Different graphical strategies are used in order to reveal new information in the complete kinetics of this tumor type. The first stage of complete tumor growth kinetics is highly non linear. The model, at this stage, shows different aspects that agree with those reported theoretically and experimentally. Tumor reversibility and the proportionality between regions before and after electrotherapy are demonstrated. In tumors that reach partial remission, two antagonistic post-treatment processes are induced, whereas in complete remission, two unknown antitumor mechanisms are induced. The modified Gompertz equation is likely to lead to insights within cancer research. Such insights hold promise for increasing our understanding of tumors as self-organizing systems and, the possible existence of phase transitions in tumor growth kinetics, which, in turn, may have significant impacts both on cancer research and on clinical practice.

  13. Modified Gompertz equation for electrotherapy murine tumor growth kinetics: predictions and new hypotheses

    PubMed Central

    2010-01-01

    Background Electrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; however, several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed. Mathematical modeling is a useful instrument that can reveal some of these aspects. The aim of this paper is to describe the complete growth kinetics of unperturbed and perturbed tumors through use of the modified Gompertz equation in order to generate useful insight into the mechanisms that underpin this devastating disease. Methods The complete tumor growth kinetics for control and treated groups are obtained by interpolation and extrapolation methods with different time steps, using experimental data of fibrosarcoma Sa-37. In the modified Gompertz equation, a delay time is introduced to describe the tumor's natural history before treatment. Different graphical strategies are used in order to reveal new information in the complete kinetics of this tumor type. Results The first stage of complete tumor growth kinetics is highly non linear. The model, at this stage, shows different aspects that agree with those reported theoretically and experimentally. Tumor reversibility and the proportionality between regions before and after electrotherapy are demonstrated. In tumors that reach partial remission, two antagonistic post-treatment processes are induced, whereas in complete remission, two unknown antitumor mechanisms are induced. Conclusion The modified Gompertz equation is likely to lead to insights within cancer research. Such insights hold promise for increasing our understanding of tumors as self-organizing systems and, the possible existence of phase transitions in tumor growth kinetics, which, in turn, may have significant impacts both on cancer research and on clinical practice. PMID:21029411

  14. An Evaluation of Growth Models as Predictive Tools for Estimates at Completion (EAC)

    DTIC Science & Technology

    2009-03-01

    Composite Index methods. Our study uses the Gompertz growth curve to produce three EAC Models based on contract phase: A Production Model, a...31 9. Regression Error Results ...............................................................................................33 10. Gompertz ...36 12. Gompertz Parameter Estimates, Development

  15. Complementary Gompertz survival models: decreasing alive versus increasing dead.

    PubMed

    Easton, Dexter M

    2009-05-01

    The survival patterns of many animals can be classified into one of two asymmetric sigmoid forms: One group can be predicted from the standard, classical Gompertz assumption that, with age, the number of individuals alive in the population decreases exponentially at an exponentially increasing rate. The other can be predicted from the alternative Gompertz assumption that, with age, the number of individuals that have died increases exponentially at an exponentially decreasing rate. The two models have similar mathematical forms, but the curves are not the same. In contrast to the standard, the alternative form has an early rapid fall and terminates in a gradual decay of the number of live individuals. It fits "non-Gompertzian" survival plots that are not predicted by the number-alive assumption. Analyses of published data show one or the other survival mode in various animal populations, depending on sex, genetic strain, nutrition, or activity.

  16. Application of the Gompertz function in studies of growth in dusky salamanders (Plethodontidae: Desmognathus )

    Treesearch

    Richard C. Bruce

    2016-01-01

    Gompertz growth functions were fitted to skeletochronological data sets of three species of desmognathine salamanders from an assemblage (Wolf Creek) in the Cowee Mountains of southwestern North Carolina. The results were compared to earlier evaluations of growth in desmognathines from a nearby assemblage (Coweeta) in the Nantahala Mountains. In two of the species,...

  17. Gompertz mortality law and scaling behavior of the Penna model.

    PubMed

    Coe, J B; Mao, Y

    2005-11-01

    The Penna model is a model of evolutionary ageing through mutation accumulation where traditionally time and the age of an organism are treated as discrete variables and an organism's genome is represented by a binary bit string. We reformulate the asexual Penna model and show that a universal scale invariance emerges as we increase the number of discrete genome bits to the limit of a continuum. The continuum model, introduced by Almeida and Thomas [Int. J. Mod. Phys. C 11, 1209 (2000)] can be recovered from the discrete model in the limit of infinite bits coupled with a vanishing mutation rate per bit. Finally, we show that scale invariant properties may lead to the ubiquitous Gompertz law for mortality rates for early ages, which is generally regarded as being empirical.

  18. Gompertz mortality law and scaling behavior of the Penna model

    NASA Astrophysics Data System (ADS)

    Coe, J. B.; Mao, Y.

    2005-11-01

    The Penna model is a model of evolutionary ageing through mutation accumulation where traditionally time and the age of an organism are treated as discrete variables and an organism’s genome is represented by a binary bit string. We reformulate the asexual Penna model and show that a universal scale invariance emerges as we increase the number of discrete genome bits to the limit of a continuum. The continuum model, introduced by Almeida and Thomas [Int. J. Mod. Phys. C 11, 1209 (2000)] can be recovered from the discrete model in the limit of infinite bits coupled with a vanishing mutation rate per bit. Finally, we show that scale invariant properties may lead to the ubiquitous Gompertz law for mortality rates for early ages, which is generally regarded as being empirical.

  19. Multivariate Markov processes for stochastic systems with delays: application to the stochastic Gompertz model with delay.

    PubMed

    Frank, T D

    2002-07-01

    Using the method of steps, we describe stochastic processes with delays in terms of Markov diffusion processes. Thus, multivariate Langevin equations and Fokker-Planck equations are derived for stochastic delay differential equations. Natural, periodic, and reflective boundary conditions are discussed. Both Ito and Stratonovich calculus are used. In particular, our Fokker-Planck approach recovers the generalized delay Fokker-Planck equation proposed by Guillouzic et al. The results obtained are applied to a model for population growth: the Gompertz model with delay and multiplicative white noise.

  20. A Markovian Growth Dynamics on Rooted Binary Trees Evolving According to the Gompertz Curve

    NASA Astrophysics Data System (ADS)

    Landim, C.; Portugal, R. D.; Svaiter, B. F.

    2012-08-01

    Inspired by biological dynamics, we consider a growth Markov process taking values on the space of rooted binary trees, similar to the Aldous-Shields (Probab. Theory Relat. Fields 79(4):509-542, 1988) model. Fix n≥1 and β>0. We start at time 0 with the tree composed of a root only. At any time, each node with no descendants, independently from the other nodes, produces two successors at rate β( n- k)/ n, where k is the distance from the node to the root. Denote by Z n ( t) the number of nodes with no descendants at time t and let T n = β -1 nln( n/ln4)+(ln2)/(2 β). We prove that 2- n Z n ( T n + nτ), τ∈ℝ, converges to the Gompertz curve exp(-(ln2) e - βτ ). We also prove a central limit theorem for the martingale associated to Z n ( t).

  1. Soft bounds on diffusion produce skewed distributions and Gompertz growth

    NASA Astrophysics Data System (ADS)

    Mandrà, Salvatore; Lagomarsino, Marco Cosentino; Gherardi, Marco

    2014-09-01

    Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the increments of the diffusing variable are subject to configuration-dependent bounds. This work explores theoretically some of the revealing landmarks of such phenomenology, termed "soft bound." At long times, the system reaches a steady state irreversibly (i.e., violating detailed balance), characterized by a skewed "shoulder" in the density distribution, and by a net local probability flux, which has entropic origin. The largest point in the support of the distribution follows a saturating dynamics, expressed by the Gompertz law, in line with empirical observations. Finally, we propose a generic allometric scaling for the origin of soft bounds. These findings shed light on the impact on a system of such "scaling" constraint and on its possible generating mechanisms.

  2. Soft bounds on diffusion produce skewed distributions and Gompertz growth.

    PubMed

    Mandrà, Salvatore; Lagomarsino, Marco Cosentino; Gherardi, Marco

    2014-09-01

    Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the increments of the diffusing variable are subject to configuration-dependent bounds. This work explores theoretically some of the revealing landmarks of such phenomenology, termed "soft bound." At long times, the system reaches a steady state irreversibly (i.e., violating detailed balance), characterized by a skewed "shoulder" in the density distribution, and by a net local probability flux, which has entropic origin. The largest point in the support of the distribution follows a saturating dynamics, expressed by the Gompertz law, in line with empirical observations. Finally, we propose a generic allometric scaling for the origin of soft bounds. These findings shed light on the impact on a system of such "scaling" constraint and on its possible generating mechanisms.

  3. Flexible alternatives to the Gompertz equation for describing growth with age in turkey hens.

    PubMed

    Porter, T; Kebreab, E; Darmani Kuhi, H; Lopez, S; Strathe, A B; France, J

    2010-02-01

    A total of 49 profiles of growing turkey hens from commercial flocks were used in this study. Three flexible growth functions (von Bertalanffy, Richards, and Morgan) were evaluated with regard to their ability to describe the relationship between BW and age and were compared with the Gompertz equation with its fixed point of inflection, which might result in its overestimation. For each function, 4 ways of analysis were implemented. A basic model was fitted first, followed by implementation of a first-order autoregressive correlation structure. A model that considered only mature BW varied with year and another that considered only the rate coefficient varied with different years were applied. The results showed that the fixed point of inflection of the Gompertz equation can be a limitation and that the relationship between BW and age in turkeys was best described using flexible growth functions. However, the Richards equation failed to converge when fitted to the turkey growth data; therefore, it was not considered further. Inclusion of an autoregressive process of the first order rendered a substantially improved fit to data for the 3 growth functions. The Morgan equation provided the best fit to the data set and was used for characterizing mean growth curves for the 7 yr of production. It was estimated that the maximum growth rate occurred at 3.74, 3.65, 3.99, 4.18, 4.05, 4.01, and 3.77 kg BW for production years from 1997 to 2003, respectively. It is recommended that flexible growth functions should be considered as an alternative to the simpler functions (with a fixed point of inflection) for describing the relationship between BW and age in turkeys because they were easier to fit and very often gave a closer fit to data points because of their flexibility, and therefore a smaller residual MS value, than simpler models. It can also be recommended that studies should consider adding a first-order autoregressive process when analyzing repeated measures data with

  4. A new Gompertz-type diffusion process with application to random growth.

    PubMed

    Gutiérrez-Jáimez, Ramón; Román, Patricia; Romero, Desirée; Serrano, Juan J; Torres, Francisco

    2007-07-01

    Stochastic models describing growth kinetics are very important for predicting many biological phenomena. In this paper, a new Gompertz-type diffusion process is introduced, by means of which bounded sigmoidal growth patterns can be modeled by time-continuous variables. The main innovation of the process is that the bound can depend on the initial value, a situation that is not provided by the models considered to date. After building the model, a comprehensive study is presented, including its main characteristics and a simulation of sample paths. With the aim of applying this model to real-life situations, and given its possibilities in forecasting via the mean function, discrete sampling based inference is developed. The likelihood equations are not directly solvable, and because of difficulties that arise with the usual numerical methods employed to solve them, an iterative procedure is proposed. The possibilities of the new process are illustrated by means of an application to real data, concretely, to growth in rabbits.

  5. The gompertz function can coherently describe microbial mineralization of growth-sustaining pesticides.

    PubMed

    Johnsen, Anders R; Binning, Philip J; Aamand, Jens; Badawi, Nora; Rosenbom, Annette E

    2013-08-06

    Mineralization of (14)C-labeled tracers is a common way of studying the environmental fate of xenobiotics, but it can be difficult to extract relevant kinetic parameters from such experiments since complex kinetic functions or several kinetic functions may be needed to adequately describe large data sets. In this study, we suggest using a two-parameter, sigmoid Gompertz function for parametrizing mineralization curves. The function was applied to a data set of 252 normalized mineralization curves that represented the potential for degradation of the herbicide MCPA in three horizons of an agricultural soil. The Gompertz function fitted most of the normalized curves, and trends in the data set could be visualized by a scatter plot of the two Gompertz parameters (rate constant and time delay). For agricultural topsoil, we also tested the effect of the MCPA concentration on the mineralization kinetics. Reduced initial concentrations lead to shortened lag-phases, probably due to reduced need for bacterial growth. The effect of substrate concentration could be predicted by simply changing the time delay of the Gompertz curves. This delay could to some extent also simulate concentration effects for 2,4-D mineralization in agricultural soil and aquifer sediment and 2,6-dichlorobenzamide mineralization in single-species, mineral medium.

  6. Genetic (co)variances and breeding value estimation of Gompertz growth curve parameters in Finnish Yorkshire boars, gilts and barrows.

    PubMed

    Koivula, M; Sevón-Aimonen, M-L; Strandén, I; Matilainen, K; Serenius, T; Stalder, K J; Mäntysaari, E A

    2008-06-01

    This paper's objectives were to estimate the genetic (co)variance components of the Gompertz growth curve parameters and to evaluate the relationship of estimated breeding values (EBV) based on average daily gain (ADG) and Gompertz growth curves. Finnish Yorkshire central test station performance data was obtained from the Faba Breeding (Vantaa, Finland). The final data set included 121,488 weight records from 10,111 pigs. Heritability estimates for the Gompertz growth parameters mature weight (alpha), logarithm of mature weight to birth weight ratio (beta) and maturation rate (kappa) were 0.44, 0.55 and 0.31, respectively. Genotypic and phenotypic correlations between the growth curve parameters were high and mainly negative. The only positive relationship was found between alpha and beta. Pearson and Spearman rank correlation coefficients between EBV for ADG and daily gain calculated from Gompertz growth curves were 0.79. The Spearman rank correlation between the sire EBV for ADG and Gompertz growth curve parameter-based ADG for all sires with at least 15 progeny was 0.86. Growth curves differ significantly between individuals and this information could be utilized for selection purposes when improving growth rate in pigs.

  7. Modelling of Scenedesmus obliquus; function of nutrients with modified Gompertz model.

    PubMed

    Celekli, Abuzer; Balci, Muharrem; Bozkurt, Hüseyin

    2008-12-01

    This study attempted to investigate variation in biovolume of Scenedesmus obliquus, in the modified Johnson medium at 20+/-2 degrees C, under 16kergcm(-2)s(-1) continuous illumination. The experiments were carried out at four nitrate (8, 12, 16, and 20mM) and four phosphate (0.1, 0.3, 0.5 and 0.7mM) concentrations at pH 7 and 8. The best response for algal growth was found at 0.3mM phosphate and 12mM nitrate at pH 7, as it was obtained from weight averaging method. Besides, optimum phosphate and nitrate concentrations significantly distinguished (p<0.01) from other concentrations according to Turkey's HSD test. Key features of the growth of S. obliquus under phosphate and nitrate influenced batch culture was successfully predicted by modified Gompertz model. Through the cultivations, specific growth rate (mu) ranged from 0.30 to 1.02 day(-1), while biovolume doubling time (td) varied from 0.68 to 2.30 days. There were important differences (p<0.05) for both mu and td among response variables. Both nutrients displayed noteworthy effect (p<0.01) on the algal biovolume.

  8. Estimating Gompertz Growth Curves from Marine Mammal Strandings in the Presence of Missing Data.

    PubMed

    Shotwell, Mary; McFee, Wayne; Slate, Elizabeth H

    2010-01-01

    Stranded bottlenose dolphins (Tursiops truncatus) off the coast of South Carolina (SC) provide data essential for population health assessment. Of the 598 bottlenose dolphin strandings in SC from 1993 to 2007, 91 were of sufficient body condition to obtain organ weights. Of these 91 animals, only 52 were brought back to the laboratory for total body weight measurements. Because it is more feasible to transport smaller animals to the laboratory setting for necropsy procedures, a selection bias is present in that data for larger animals are often missing. Regression and propensity score multiple imputation methods are utilized to account for missing data needed to compute growth. Fitted Gompertz growth curves for SC animals with and without adjustment for missing data are compared to those found from the northwestern Gulf of Mexico. South Carolina animals display a trend in lower asymptotic mean total body weights and faster growth rates compared to the Gulf of Mexico population. The differences generally increased in magnitude after imputation methods. South Carolina females were originally estimated to reach larger maximum sizes than Gulf of Mexico females, but after imputation this relationship reversed. The findings suggest selection bias should be accounted for in sampling stranded dolphins.

  9. Statistical analysis of dependent competing risks model from Gompertz distribution under progressively hybrid censoring.

    PubMed

    Shi, Yimin; Wu, Min

    2016-01-01

    Previous studies have mostly considered the competing risks to be independent even when the interpretation of the failure modes implies dependency. This paper studies the dependent competing risks model from Gompertz distribution under Type-I progressively hybrid censoring scheme. We derive the maximum likelihood estimations of the model parameters, and then the asymptotic likelihood theory and Bootstrap method are used to obtain the confidence intervals. The simulation results are provided to investigate the effects of different dependence structures on the estimations of parameters. Finally, one data set was used for illustrative purpose.

  10. Comparison of yellow poplar growth models on the basis of derived growth analysis variables

    Treesearch

    Keith F. Jensen; Daniel A. Yaussy

    1986-01-01

    Quadratic and cubic polynomials, and Gompertz and Richards asymptotic models were fitted to yellow poplar growth data. These data included height, leaf area, leaf weight and new shoot height for 23 weeks. Seven growth analysis variables were estimated from each function. The Gompertz and Richards models fitted the data best and provided the most accurate derived...

  11. Kinetic models for batch ethanol production from sweet sorghum juice under normal and high gravity fermentations: Logistic and modified Gompertz models.

    PubMed

    Phukoetphim, Niphaphat; Salakkam, Apilak; Laopaiboon, Pattana; Laopaiboon, Lakkana

    2017-02-10

    The aim of this study was to model batch ethanol production from sweet sorghum juice (SSJ), under normal gravity (NG, 160g/L of total sugar) and high gravity (HG, 240g/L of total sugar) conditions with and without nutrient supplementation (9g/L of yeast extract), by Saccharomyces cerevisiae NP 01. Growth and ethanol production increased with increasing initial sugar concentration, and the addition of yeast extract enhanced both cell growth and ethanol production. From the results, either logistic or a modified Gompertz equation could be used to describe yeast growth, depending on information required. Furthermore, the modified Gompertz model was suitable for modeling ethanol production. Both the models fitted the data very well with coefficients of determination exceeding 0.98. The results clearly showed that these models can be employed in the development of ethanol production processes using SSJ under both NG and HG conditions. The models were also shown to be applicable to other ethanol fermentation systems employing pure and mixed sugars as carbon sources.

  12. Gompertz-Laird model prediction of optimum utilization of crude protein and metabolizable energy by French guinea fowl broilers.

    PubMed

    Nahashon, S N; Aggrey, S E; Adefope, N A; Amenyenu, A; Wright, D

    2010-01-01

    This study was conducted to assess the influence of dietary CP and ME on growth parameters of the French guinea fowl, a meat-type variety. In a 2 x 3 x 3 factorial arrangement, 297 one-day-old French guinea keets (162 females and 135 males) were randomly assigned to experimental diets comprising 3,050, 3,100, and 3,150 kcal of ME/kg, each containing 21, 23, and 25% CP from hatch to 4 wk of age (WOA), and 3,100, 3150, and 3,200 kcal of ME/kg, each containing 19, 21, and 23% CP at 5 to 8 WOA. Using BW and G:F data from hatch to 8 WOA, the Gompertz-Laird growth model was employed to estimate growth patterns of the French guinea fowl. Mean differences in exponential growth rate, age of maximum growth, and asymptotic BW among dietary CP and ME levels were not significant. However, instantaneous growth rate and weight at inflection point were significantly higher (P < 0.05) in birds on the 25% CP diet than those on the 21% CP diet at hatch to 4 WOA (1.12 kg/wk and 0.79 kg vs. 1.04 kg/wk and 0.74 kg, respectively). The exponential growth rate was also higher (P < 0.05) in birds fed the 3,050 kcal of ME/kg diet with either 23 or 25% CP than those fed diets containing 3,050 kcal of ME/kg and 21% CP. Mean G:F was higher (P < 0.05) in birds fed diets containing 3,050 kcal of ME/kg and either 21 or 23% CP than those in other dietary treatments. Therefore, based on the Gompertz-Laird growth model estimates, feeding 21 and 23% CP and 3,100 kcal of ME/kg at hatch to 4 WOA and 19 and 21% CP with 3,150 kcal of ME/kg at 5 to 8 WOA can be recommended as adequate for growth for the French guinea fowl broilers.

  13. Senescence rates in patients with end-stage renal disease: a critical appraisal of the Gompertz model.

    PubMed

    Koopman, J J E; Rozing, M P; Kramer, A; de Jager, D J; Ansell, D; De Meester, J M J; Prütz, K G; Finne, P; Heaf, J G; Palsson, R; Kramar, R; Jager, K J; Dekker, F W; Westendorp, R G J

    2011-04-01

    The most frequently used model to describe the exponential increase in mortality rate over age is the Gompertz equation. Logarithmically transformed, the equation conforms to a straight line, of which the slope has been interpreted as the rate of senescence. Earlier, we proposed the derivative function of the Gompertz equation as a superior descriptor of senescence rate. Here, we tested both measures of the rate of senescence in a population of patients with end-stage renal disease. It is clinical dogma that patients on dialysis experience accelerated senescence, whereas those with a functional kidney transplant have mortality rates comparable to the general population. Therefore, we calculated the age-specific mortality rates for European patients on dialysis (n=274 221; follow-up=594 767 person-years), for European patients with a functioning kidney transplant (n=61 286; follow-up=345 024 person-years), and for the general European population. We found higher mortality rates, but a smaller slope of logarithmic mortality curve for patients on dialysis compared with both patients with a functioning kidney transplant and the general population (P<0.001). A classical interpretation of the Gompertz model would imply that the rate of senescence in patients on dialysis is lower than in patients with a functioning transplant and lower than in the general population. In contrast, the derivative function of the Gompertz equation yielded the highest senescence rates for patients on dialysis, whereas the rate was similar in patients with a functioning transplant and the general population. We conclude that the rate of senescence is better described by the derivative function of the Gompertz equation. © 2010 The Authors. Aging Cell © 2010 Blackwell Publishing Ltd/Anatomical Society of Great Britain and Ireland.

  14. Exponentiated exponential model (Gompertz kinetics) of Na+ and K+ conductance changes in squid giant axon.

    PubMed Central

    Easton, D M

    1978-01-01

    The conductance changes, gK(t) and gNa(t), of squid giant axon under voltage clamp (Hodgkin and Huxley, 1952) may be modeled by exponentiated exponential functions (Gompertz kinetics) from any holding potential VO to any membrane clamp potential V. The equation constants are set by the membrane potential V, and include, for any voltage step in the case of gK, the initial conductance, gO, the asymptote conductance g, and rate constant k: gK = g exp(-be-kt) where b = 1n g/gO. Equations of similar form relate g and k to the voltage V, and govern the corresponding parameters of the gNa system. For the gNa, the fast phase y = y exp (-be-kt) is cut down in proportion to a slow process p = (1 - p)e-k't + p, and thus gNa = py. The expo-exponential functions involve fewer constants than the Hodgkin-Huxley model. In particular, the role of the n, m, h parameters appears to be filled largely by 1n (g/gO) in the case of gK and by 1n (y/yO) in the case of gNa. Membrane action potentials during current clamp may be computed from the conductances generated by use of the appropriate differential forms of the equations; diverse other membrane behaviors may be predicted. PMID:638223

  15. Voltage-clamp predictions by gompertz kinetics model relating squid-axon Na+-gating and ionic currents.

    PubMed

    Easton, Dexter M

    2005-10-01

    Gompertz kinetics is a simple, realistic, accurate, and computationally parsimonious alternative for prediction of macroscopic changes in Na+ conductance during voltage clamp. Conductance delay and time course depend on initial amplitudes and decay rates of surrogates for the macroscopic gating currents. The model is tested by the fit to published data of other authors. The proposed physical basis for the model is that membrane potential perturbation triggers motion of charged "gating" components of the axon membrane at rapid (activating) and at slow (inactivating) rates. The resulting distortion increases and more slowly diminishes the probability that conduction channels will be open.

  16. Experimental epizootiology of Zoophthora anhuiensis (Entomophthorales) against Myzus persicae (Homoptera: Aphididae) with a description of a modified Gompertz model for aphid epizootics.

    PubMed

    Feng, Ming-Guang; Li, Hui-Ping

    2003-11-01

    Epizootiological features of Zoophthora anhuiensis, a fungal pathogen specific to aphids in southern China, were studied in six aptera colonies of Myzus persicae at 16 regimes of temperature (T = 10, 15, 20 and 25 degrees C) and relative humidity (H = 90%, 95%, 98% and 100% RH) with initially infected proportion (Ip) of 0.5 in experiment (Expt) 1 or at a fixed regime of 15 degrees C and 100% RH with a variable Ip of 0.17-1.00 in Expt 2. Mycosis-caused mortalities (Mp) varied with aphid densities (D) over time after colony initiation (t) were well fitted to a Gompertz growth model modified to include the variables T, H, Ip and D in the form of Mp = 91.72exp[-5.282exp[-(0.0095T + 0.0128H/T-0.5407D2/H)t

  17. [Approximation of Time Series of Paramecia caudatum Dynamics by Verhulst and Gompertz Models: Non-traditional Approach].

    PubMed

    Nedorezov, L V

    2015-01-01

    For approximation of some well-known time series of Paramecia caudatun population dynamics (G. F. Gause, The Struggle for Existence, 1934) Verhulst and Gompertz models were used. The parameters were estimated for each of the models in two different ways: with the least squares method (global fitting) and non-traditional approach (a method of extreme points). The results obtained were compared and also with those represented by G. F. Gause. Deviations of theoretical (model) trajectories from experimental time series were tested using various non-parametric statistical tests. It was shown that the least square method-estimations lead to the results which not always meet the requirements imposed for a "fine" model. But in some cases a small modification of the least square method-estimations is possible allowing for satisfactory representations of experimental data set for approximation.

  18. A Gompertz Model Approach to Microbial Inactivation Kinetics by High-Pressure Processing (HPP): Model Selection and Experimental Validation.

    PubMed

    Serment-Moreno, Vinicio; Fuentes, Claudio; Torres, José Antonio; Welti-Chanes, Jorge

    2017-08-01

    A recently proposed Gompertz model (GMPZ) approach describing microbial inactivation kinetics by high-pressure processing (HPP) incorporated the initial microbial load (N0 ) and lower microbial quantification limit (Nlim ), and simplified the dynamic effects of come-up time (CUT). The inactivation of Listeria innocua in milk by HPP treatments at 300, 400, 500, and 600 MPa and pressure holding times (thold ) ≤10 min was determined experimentally to validate this model approach. Models based on exponential, logistic-exponential, and inverse functions were evaluated to describe the effect of pressure on the lag time (λ) and maximum inactivation rate (μmax ), whereas the asymptote difference (A) was fixed as A = log10 (N0 /Nlim ). Model performance was statistically evaluated and further validated with additional data obtained at 450 and 550 MPa. All GMPZ models adequately fitted L. innocua data according to the coefficient of determination (R(2 ) ≥ 0.95) but those including a logistic-exponential function for μmax (P) were superior (R(2 ) ≥ 0.97). These GMPZ versions predicted that approximately 597 MPa is the theoretical pressure level (Pλ ) at which microbial inactivation begins during CUT, mathematically defined as λ (P = Pλ ) = tCUT , and matching the value observed on the microbial survival curve at 600 MPa. As pressure increased, predictions tended to slightly underestimate the HPP lethality in the tail section of the survival curve. This may be overseen in practice since the observed microbial counts were below the predicted log10 N values. Overall, the modeling approach is promising, justifying further validation work for other microorganisms and food systems. © 2017 Institute of Food Technologists®.

  19. Predictive implications of Gompertz's law

    NASA Astrophysics Data System (ADS)

    Richmond, Peter; Roehner, Bertrand M.

    2016-04-01

    Gompertz's law tells us that for humans above the age of 35 the death rate increases exponentially with a doubling time of about 10 years. Here, we show that the same law continues to hold up to age 106. At that age the death rate is about 50%. Beyond 106 there is so far no convincing statistical evidence available because the number of survivors are too small even in large nations. However, assuming that Gompertz's law continues to hold beyond 106, we conclude that the mortality rate becomes equal to 1 at age 120 (meaning that there are 1000 deaths in a population of one thousand). In other words, the upper bound of human life is near 120. The existence of this fixed-point has interesting implications. It allows us to predict the form of the relationship between death rates at age 35 and the doubling time of Gompertz's law. In order to test this prediction, we first carry out a transversal analysis for a sample of countries comprising both industrialized and developing nations. As further confirmation, we also develop a longitudinal analysis using historical data over a time period of almost two centuries. Another prediction arising from this fixed-point model, is that, above a given population threshold, the lifespan of the oldest persons is independent of the size of their national community. This prediction is also supported by empirical evidence.

  20. Ever since Gompertz.

    PubMed

    Olshansky, S J; Carnes, B A

    1997-02-01

    In 1825 British actuary Benjamin Gompertz made a simple but important observation that a law of geometrical progression pervades large portions of different tables of mortality for humans. The simple formula he derived describing the exponential rise in death rates between sexual maturity and old age is commonly, referred to as the Gompertz equation-a formula that remains a valuable tool in demography and in other scientific disciplines. Gompertz's observation of a mathematical regularity in the life table led him to believe in the presence of a low of mortality that explained why common age patterns of death exist. This law of mortality has captured the attention of scientists for the past 170 years because it was the first among what are now several reliable empirical tools for describing the dying-out process of many living organisms during a significant portion of their life spans. In this paper we review the literature on Gompertz's law of mortality and discuss the importance of his observations and insights in light of research on aging that has taken place since then.

  1. An Embryonic Growth Pathway is Reactivated in Human Prostate Cancer

    DTIC Science & Technology

    2005-06-01

    assess growth of the four cell lines, a Gompertz prostatectomy (n = 2), and six prostate cancer (PC) speci- growth model was fitted to each line. Day... Gompertz model with men (N), in hyperplastic (benign) tissue from men without line-specific asymptote and growth rate was estimated via Gauss-New...histologically confirmed tumor with histologically con- The plots and Gompertz fits were generated in R version 1.6.25.1 (36). firmed benign tissue obtained from

  2. [Numerical modeling of ideal cohorts of aging organisms obeying the Gompertz-Makeham law in association with the Strehler-Mildwan correlation].

    PubMed

    Golubev, A G

    2004-01-01

    The Gompertz-Makeham law (-dn/dt x l/n(t)=C+lambdae(gammat)) so as other genuine laws of Nature is strictly applicable only to ideal objects (populations and cohorts) analogously to laws of mechanics or thermodynamics, which are exactly true only for such physical abstractions as mass points or ideal gases. Therefore, a biologically meaningful interpretation of the parameters of this law is likely to be more important for understanding the aging process than devising of alternative analytical descriptions of biodemographic processes for the sake of a better fit only. Numerical modeling of ideal cohorts of aging organisms obeying the Gompertz-Makeha law makes it possible to differentiate possible real and apparent changes in mortality patterns that occur in human history and in evolution and are observed in gerontological experiments and to demonstratively show such effects as the dependency of longevity upon population size, the evolutionarily important possibility of reciprocal changes in the mean and maximal longevity, or detection of apparent changes in negatively correlated aging rate and vitality when the Makeham term is ignored, which is usual in demography. The basic difference between the Makeham term Cand Gompertz term lambdae(gammat) is suggested to be not that the former is constant, whereas the latter is age-dependent, but that the former comprises the contributions of inherently irresistible stresses to mortality, whereas the latter comprises the contributions of resistible stresses to mortality and shows how changes in the ability to resist them is translated into changes in mortality.

  3. Use of the recursion formula of the Gompertz survival function to evaluate life-table data.

    PubMed

    Bassukas, I D

    1996-08-29

    The recursion formula of the Gompertz function is an established method for the analysis of growth processes. In the present study the recursion formula of the Gompertz survival function 1n S(t + s) = a + b x ln S(t) is introduced for the analysis of survival data, where S(t) is the survival fraction at age 1, s is the constant age increment between two consecutive measurements of the survival fraction and a and b are parameters. With the help of this method--and provided stroboscopial measurements of rates of survival are available--the Gompertz survival function, instead of the corresponding mortality function, can be determined directly using linear regression analysis. The application of the present algorithm is demonstrated by analysing two sets of data taken from the literature (survival of Drosophila imagoes and of female centenarians) using linear regression analysis to fit survival or mortality rates to the corresponding models. In both cases the quality of fit was superior by using the algorithm presently introduced. Moreover, survival functions calculated from the fits to the mortality law only poorly predict the survival data. On the contrary, the results of the present method not only fit to the measurements, but, for both sets of data the mortality parameters calculated by the present method are essentially identical to those obtained by a corresponding application of a non-linear Marquardt-Levenberg algorithm to fit the same sets of data to the explicit form of the Gompertz survival function. Taking into consideration the advantages of using a linear fit (goodness-of-fit test and efficient statistical comparison of survival patterns) the method of the recursion formula of the Gompertz survival function is the most preferable method to fit survival data to the Gompertz function.

  4. Nonlinear Gompertz Curve Models of Achievement Gaps in Mathematics and Reading

    ERIC Educational Resources Information Center

    Cameron, Claire E.; Grimm, Kevin J.; Steele, Joel S.; Castro-Schilo, Laura; Grissmer, David W.

    2015-01-01

    This study examined achievement trajectories in mathematics and reading from school entry through the end of middle school with linear and nonlinear growth curves in 2 large longitudinal data sets (National Longitudinal Study of Youth--Children and Young Adults and Early Childhood Longitudinal Study--Kindergarten Cohort [ECLS-K]). The S-shaped…

  5. Nonlinear Gompertz Curve Models of Achievement Gaps in Mathematics and Reading

    ERIC Educational Resources Information Center

    Cameron, Claire E.; Grimm, Kevin J.; Steele, Joel S.; Castro-Schilo, Laura; Grissmer, David W.

    2015-01-01

    This study examined achievement trajectories in mathematics and reading from school entry through the end of middle school with linear and nonlinear growth curves in 2 large longitudinal data sets (National Longitudinal Study of Youth--Children and Young Adults and Early Childhood Longitudinal Study--Kindergarten Cohort [ECLS-K]). The S-shaped…

  6. Modeling the Growth of Archaeon Halobacterium halobium Affected by Temperature and Light.

    PubMed

    Lu, Hao; Yuan, Wenqiao; Cheng, Jay; Rose, Robert B; Classen, John J; Simmons, Otto D

    2017-03-01

    The objective of this study was to develop sigmoidal models, including three-parameter (Quadratic, Logistic, and Gompertz) and four-parameter models (Schnute and Richards) to simulate the growth of archaeon Halobacterium halobium affected by temperature and light. The models were statistically compared by using t test and F test. In the t test, confidence bounds for parameters were used to distinguish among models. For the F test, the lack of fit of the models was compared with the prediction error. The Gompertz model was 100 % accepted by the t test and 97 % accepted by the F test when the temperature effects were considered. Results also indicated that the Gompertz model was 94 % accepted by the F test when the growth of H. halobium was studied under varying light intensities. Thus, the Gompertz model was considered the best among the models studied to describe the growth of H. halobium affected by temperature or light. In addition, the biological growth parameters, including specific growth rate, lag time, and asymptote changes under Gompertz modeling, were evaluated.

  7. Gompertz law and aging as exclusion effects.

    PubMed

    Hallén, Anund

    2007-10-01

    The exponential increase with age in mortality rate, the Gompertz law, indicates that the decrease in vitality and viability linked to aging depends on phenomena with exponential or logarithmic dynamics. Gompertz slope (alpha) is assumed to be a measure of aging rate, provided the studied cohort is homogeneous and in a supporting environment. The law provides no clue about the cause of aging, but may be formally correlated with various physical or mathematical functions. A possible correlation between the Ogston-Laurent exclusion equation and human aging is examined. An increase with age of an inert cross-linked insoluble protein network is assumed to result in a logarithmic decrease in water volume available to colloidal macromolecules. In this model, alpha is assumed to be a measure of the rate of accumulation of the polypeptide network.

  8. A genetic investigation of various growth models to describe growth of lambs of two contrasting breeds.

    PubMed

    Lambe, N R; Navajas, E A; Simm, G; Bünger, L

    2006-10-01

    This study compared the use of various models to describe growth in lambs of 2 contrasting breeds from birth to slaughter. Live BW records (n = 7559) from 240 Texel and 231 Scottish Blackface (SBF) lambs weighed at 2-wk intervals were modeled. Biologically relevant variables were estimated for each lamb from modified versions of the logistic, Gompertz, Richards, and exponential models, and from linear regression. In both breeds, all nonlinear models fitted the data well, with an average coefficient of determination (R2) of > 0.98. The linear model had a lower average R2 than any of the nonlinear models (< 0.94). The variables used to describe the best 3 models (logistic, Gompertz, and Richards) included estimated final BW (A); maximum ADG (B); age at maximum ADG (C); position of point of inflection in relation to A (D, for Richards only). The Richards and Gompertz models provided the best fit (average R2 = 0.986 to 0.989) in both breeds. Richards estimated an extra variable, allowing increased flexibility in describing individual growth patterns, but the Akaike's information criteria value (which weighs log-likelihood by number of parameters estimated) was similar to that of the Gompertz model. Variables A, B, C, and D were moderately to highly heritable in Texel lambs (h2 = 0.33 to 0.87), and genetic correlations between variables within-model ranged from -0.80 to 0.89, suggesting some flexibility to change the shape of the growth curve when selecting for different variables. In SBF lambs, only variables from the logistic and Gompertz models had moderate heritabilities (0.17 to 0.56), but with high genetic correlations between variables within each model (< -0.88 or > 0.92). Selection on growth variables seems promising (in Texel more than SBF), but high genetic correlations between variables may restrict the possibilities to change the growth curve shape. A random regression model was also fitted to the data to allow predictions of growth rates at relevant time

  9. Stochastic Modelling of Gompertzian Tumor Growth

    NASA Astrophysics Data System (ADS)

    O'Rourke, S. F. C.; Behera, A.

    2009-08-01

    We study the effect of correlated noise in the Gompertzian tumor growth model for non-zero correlation time. The steady state probability distributions and average population of tumor cells are analyzed within the Fokker-Planck formalism to investigate the importance of additive and multiplicative noise. We find that the correlation strength and correlation time have opposite effects on the steady state probability distributions. It is observed that the non-bistable Gompertzian model, driven by correlated noise exhibits a stochastic resonance and phase transition. This behaviour of the Gompertz model is unaffected with the change of correlation time and occurs as a result of multiplicative noise.

  10. Forecasting Marine Corps Enlisted Attrition Through Parametric Modeling

    DTIC Science & Technology

    2009-03-01

    OF PAGES 85 14. SUBJECT TERMS Forecasting, Attrition, Marine Corps NEAS losses, Gompertz Model, Survival Analysis 16. PRICE CODE 17. SECURITY...18 1. Parametric Proportional Hazards Models ......................................18 2. Gompertz Models...19 a. Gompertz Hazard Function....................................................19 b. Gompertz Cumulative

  11. Gompertz' survivorship law as an intrinsic principle of aging.

    PubMed

    Sas, Arthur A; Snieder, Harold; Korf, Jakob

    2012-05-01

    We defend the hypothesis that life-spanning population survivorship curves, as described by Gompertz' law and composed from cross-sectional data (here mortality), reflect an intrinsic aging principle active in each subject of that population. In other words Gompertz' law reflects aging of a prototypical subject, provided minimal (or no) external causes of death (i.e. fatal infections, starvation, accidents). Our approach deviates from the traditional (exponential) Gompertz' hazard function. For instance, the here formulated Gompertz' law accurately describes old-age deceleration of both all-cause mortality and the incidence of some ageing-associated cancers, as illustrated for the Dutch population. We consider the possibility that the old-age expression and progression of cancer and other pathologies becomes suppressed, because of random (and exponential) accumulation of damage during life. Gompertz' law may trigger new concepts and models describing life-spanning physiological and pathological processes of aging. We discuss (and reject) various aging models (e.g. a predominant role of individual variations at birth; reliability theory) and point to the explanatory potential of network models and systemic regulatory models.

  12. Gompertz-Makeham life expectancies: expressions and applications.

    PubMed

    Missov, Trifon I; Lenart, Adam

    2013-12-01

    In a population of individuals, whose mortality is governed by a Gompertz-Makeham hazard, we derive closed-form solutions to the life-expectancy integral, corresponding to the cases of homogeneous and gamma-heterogeneous populations, as well as in the presence/absence of the Makeham term. Derived expressions contain special functions that aid constructing high-accuracy approximations, which can be used to study the elasticity of life expectancy with respect to model parameters. Knowledge of Gompertz-Makeham life expectancies aids constructing life-table exposures.

  13. Applying Statistical Models to Mammographic Screening Data to Understand Growth and Progression of Ductal Carcinoma in Situ

    DTIC Science & Technology

    2005-09-01

    size with time); 2. Constant rate of doubling (exponential dependence of size on time); 3. Decreasing rate of growth with size ( Gompertz model). These...Exponential 720.4 -xoeta .0 .0rpet 0.3 203- Gompertz ോ -Gompez 0.2 0.2 0.1 0.1 0 , 0 0.1 1 10 0.1 1 10 Lesion Size Lesion Size Progressive Weakening...Models 0.8 0.7 0.6- Z,0.5 5Linear . 0.4 - -Exponential 72.4 0. •0.3 - Gompertz 0.2 0.1 0 0.1 1 10 Lesion Size Task 4: Manuscript preparation We have

  14. Modelling the growth of Japanese eel Anguilla japonica in the lower reach of the Kao-Ping River, southern Taiwan: an information theory approach.

    PubMed

    Lin, Y J; Tzeng, W N

    2009-07-01

    Information theory was applied to select the best model fitting total length (L(T))-at-age data and calculate the averaged model for Japanese eel Anguilla japonica compiled from published literature and the differences in growth between sexes were examined. Five candidate growth models were the von Bertalanffy, generalized von Bertalanffy, Gompertz, logistic and power models. The von Bertalanffy growth model with sex-specific coefficients was best supported by the data and nearly overlapped the averaged growth model based on Akaike weights, indicating a similar fit to the data. The Gompertz, generalized von Bertalanffy and power growth models were also substantially supported by the data. The L(T) at age of A. japonica were larger in females than in males according to the averaged growth mode, suggesting a sexual dimorphism in growth. Model inferences based on information theory, which deal with uncertainty in model selection and robust parameter estimates, are recommended for modelling the growth of A. japonica.

  15. Lifetime growth in wild meerkats: incorporating life history and environmental factors into a standard growth model.

    PubMed

    English, Sinéad; Bateman, Andrew W; Clutton-Brock, Tim H

    2012-05-01

    Lifetime records of changes in individual size or mass in wild animals are scarce and, as such, few studies have attempted to model variation in these traits across the lifespan or to assess the factors that affect them. However, quantifying lifetime growth is essential for understanding trade-offs between growth and other life history parameters, such as reproductive performance or survival. Here, we used model selection based on information theory to measure changes in body mass over the lifespan of wild meerkats, and compared the relative fits of several standard growth models (monomolecular, von Bertalanffy, Gompertz, logistic and Richards). We found that meerkats exhibit monomolecular growth, with the best model incorporating separate growth rates before and after nutritional independence, as well as effects of season and total rainfall in the previous nine months. Our study demonstrates how simple growth curves may be improved by considering life history and environmental factors, which may be particularly relevant when quantifying growth patterns in wild populations.

  16. Effects on generalized growth models driven by a non-Poissonian dichotomic noise

    NASA Astrophysics Data System (ADS)

    Bologna, M.; Calisto, H.

    2011-10-01

    In this paper we consider a general growth model with stochastic growth rate modelled via a symmetric non-poissonian dichotomic noise. We find an exact analytical solution for its probability distribution. We consider the, as yet, unexplored case where the deterministic growth rate is perturbed by a dichotomic noise characterized by a waiting time distribution in the two state that is a power law with power 1 < μ < 2. We apply the results to two well-known growth models; Malthus-Verhulst and Gompertz.

  17. Modeling surface growth of Escherichia coli on agar plates.

    PubMed

    Fujikawa, Hiroshi; Morozumi, Satoshi

    2005-12-01

    Surface growth of Escherichia coli cells on a membrane filter placed on a nutrient agar plate under various conditions was studied with a mathematical model. The surface growth of bacterial cells showed a sigmoidal curve with time on a semilogarithmic plot. To describe it, a new logistic model that we presented earlier (H. Fujikawa et al., Food Microbiol. 21:501-509, 2004) was modified. Growth curves at various constant temperatures (10 to 34 degrees C) were successfully described with the modified model (model III). Model III gave better predictions of the rate constant of growth and the lag period than a modified Gompertz model and the Baranyi model. Using the parameter values of model III at the constant temperatures, surface growth at various temperatures was successfully predicted. Surface growth curves at various initial cell numbers were also sigmoidal and converged to the same maximum cell numbers at the stationary phase. Surface growth curves at various nutrient levels were also sigmoidal. The maximum cell number and the rate of growth were lower as the nutrient level decreased. The surface growth curve was the same as that in a liquid, except for the large curvature at the deceleration period. These curves were also well described with model III. The pattern of increase in the ATP content of cells grown on a surface was sigmoidal, similar to that for cell growth. We discovered several characteristics of the surface growth of bacterial cells under various growth conditions and examined the applicability of our model to describe these growth curves.

  18. Evidence for the Gompertz curve in the income distribution of Brazil 1978-2005

    NASA Astrophysics Data System (ADS)

    Moura, N. J., Jr.; Ribeiro, M. B.

    2009-01-01

    This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented by a Gompertz curve of the form G(x) = exp [exp (A-Bx)], where x is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution P(x) = βx-α. This result means that similarly to other countries, Brazil’s income distribution is characterized by a well defined two class system. The parameters A, B, α, β were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazil’s economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle.

  19. Growth modeling to control (in vitro) Fusarium verticillioides and Rhizopus stolonifer with thymol and carvacrol.

    PubMed

    Ochoa-Velasco, Carlos E; Navarro-Cruz, Addí R; Vera-López, Obdulia; Palou, Enrique; Avila-Sosa, Raul

    2017-09-22

    The aim of this study was to evaluate the antifungal activity (in vitro) of thymol and carvacrol alone or in mixtures against Fusarium verticillioides and Rhizopus stolonifer, and to obtain primary growth models. Minimal inhibitory concentration (MIC) was evaluated with fungal radial growth with thymol or carvacrol concentrations (0-1600mg/l). Mixtures were evaluated using concentrations below MIC values. Radial growth curves were described by the modified Gompertz equation. MIC values of carvacrol were 200mg/l for both fungi. Meanwhile, MIC values of thymol were between 500 and 400mg/l for F. verticillioides and R. stolonifer, respectively. A synergistic effect below MIC concentrations for carvacrol (100mg/l) and thymol (100-375mg/l) was observed. Significant differences (p<0.05) between the Gompertz parameters for the antimicrobial concentrations and their tested mixtures established an inverse relationship between antimicrobial concentration and mycelial development of both fungi. Modified Gompertz parameters can be useful to determine fungistatic concentrations. Copyright © 2017 Asociación Argentina de Microbiología. Publicado por Elsevier España, S.L.U. All rights reserved.

  20. Analysis of mathematical models of Pseudomonas spp. growth in pallet-package pork stored at different temperatures.

    PubMed

    Li, Miaoyun; Niu, Huimin; Zhao, Gaiming; Tian, Lu; Huang, Xianqing; Zhang, Jianwei; Tian, Wei; Zhang, Qiuhui

    2013-04-01

    Pseudomonas of pallet-packaged raw pork grown at 0, 5, 10, 15, 20 and 25°C has been studied in this paper. The modified Gompertz, Baranyi and Huang models were used for data fitting. Statistical criteria such as residual sum of squares, mean square error, Akaike's information criterion, and pseudo-R(2) were used to evaluate model performance. Results showed that there was an apparent decline in Pseudomonas growth at initial-storage phase at low temperatures. The modified Gompertz model outperformed the others at 5, 15, and 20°C, while Baranyi model was appropriate for 0 and 25°C. The Huang model was optimal at 10°C. No single model can give a consistently preferable goodness-of-fit for all growth data. The Gompertz model, with the smallest average values of RSS, AIC, MSE and the biggest pseudo-R(2) at all temperatures, is the most appropriate model to describe the growth of Pseudomonas of raw pork under pallet packaging. Copyright © 2012 Elsevier Ltd. All rights reserved.

  1. Nonlinear Stochastic Markov Processes and Modeling Uncertainty in Populations

    DTIC Science & Technology

    2011-07-06

    growth rate g(x) = rx ( 1− x κ ) and the general tran- sition rates g(x, t) = (a0(t) − a1(t) ln x)x of which the standard Gompertz growth rates g(x) = r...probabilistic formulation (5.4) and the stochastic formulation (5.5), which nicely illustrates our earlier theoretical results. Example 5.3 ( Gompertz ...stochastic version of the generalized Gompertz model ẋ = (a0(t)− a1(t) lnx)x, which has been extensively used in biological and medical research to describe

  2. Least-squares fitting Gompertz curve

    NASA Astrophysics Data System (ADS)

    Jukic, Dragan; Kralik, Gordana; Scitovski, Rudolf

    2004-08-01

    In this paper we consider the least-squares (LS) fitting of the Gompertz curve to the given nonconstant data (pi,ti,yi), i=1,...,m, m≥3. We give necessary and sufficient conditions which guarantee the existence of the LS estimate, suggest a choice of a good initial approximation and give some numerical examples.

  3. A model for predicting Xanthomonas arboricola pv. pruni growth as a function of temperature

    PubMed Central

    Llorente, Isidre; Montesinos, Emilio; Moragrega, Concepció

    2017-01-01

    A two-step modeling approach was used for predicting the effect of temperature on the growth of Xanthomonas arboricola pv. pruni, causal agent of bacterial spot disease of stone fruit. The in vitro growth of seven strains was monitored at temperatures from 5 to 35°C with a Bioscreen C system, and a calibrating equation was generated for converting optical densities to viable counts. In primary modeling, Baranyi, Buchanan, and modified Gompertz equations were fitted to viable count growth curves over the entire temperature range. The modified Gompertz model showed the best fit to the data, and it was selected to estimate the bacterial growth parameters at each temperature. Secondary modeling of maximum specific growth rate as a function of temperature was performed by using the Ratkowsky model and its variations. The modified Ratkowsky model showed the best goodness of fit to maximum specific growth rate estimates, and it was validated successfully for the seven strains at four additional temperatures. The model generated in this work will be used for predicting temperature-based Xanthomonas arboricola pv. pruni growth rate and derived potential daily doublings, and included as the inoculum potential component of a bacterial spot of stone fruit disease forecaster. PMID:28493954

  4. Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth

    PubMed Central

    Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M. L.; Hlatky, Lynn; Hahnfeldt, Philip

    2014-01-01

    Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic. PMID:25167199

  5. Compound equation developed for postnatal growth of birds and mammals

    NASA Technical Reports Server (NTRS)

    Laird, A. K.

    1968-01-01

    Compound growth equation was developed in which the rate of this linear growth process is regarded as proportional to the mass already attained at any instant by an underlying Gompertz process. This compound growth model was fitted to the growth data of a variety of birds and mammals of both sexes.

  6. A new growth curve model for biological growth: some inferential studies on the growth of Cirrhinus mrigala.

    PubMed

    Bhowmick, Amiya Ranjan; Bhattacharya, Sabyasachi

    2014-08-01

    Growth of living organisms is a fundamental biological process. It depicts the physiological development of the species related to the environment. Mathematical development of growth curve models has a long history since its birth. We propose a mathematical model to describe the evolution of relative growth rate as a function of time based on a real life experiment on a major Indian Carp Cirrhinus mrigala. We establish that the proposed model is able to describe the fish growth dynamics more accurately for our experimental data than some existing models e.g. logistic, Gompertz, exponential. Approximate expressions of the points of inflection and the time of achieving the maximum relative growth rate are derived. We study, in detail, the existence of a nonlinear least squares estimator of the model parameters and their consistency properties. Test-statistics is developed to study the equality of points of inflection and equality of the amount of time necessary to achieve the maximum relative growth rate for a species at two different locations. Using the theory of variance stabilizing transformations, we propose a new test statistic to test the effect of the decay parameter for the proposed growth law. The testing procedure is found to be more sensitive in comparison with the test based on nonlinear least squares estimates. Our proposed model provides a general framework to model growth in other disciplines as well.

  7. An informative prior probability distribution of the gompertz parameters for bayesian approaches in paleodemography.

    PubMed

    Sasaki, Tomohiko; Kondo, Osamu

    2016-03-01

    In paleodemography, the Bayesian approach has been suggested to provide an effective means by which mortality profiles of past populations can be adequately estimated, and thus avoid problems of "age-mimicry" inherent in conventional approaches. In this study, we propose an application of the Gompertz model using an "informative" prior probability distribution by revising a recent example of the Bayesian approach based on an "uninformative" distribution. Life-table data of 134 human populations including those of contemporary hunter-gatherers were used to determine the Gompertz parameters of each population. In each population, we used both raw life-table data and the Gompertz parameters to calculate some demographic values such as the mean life-span, to confirm representativeness of the model. Then, the correlation between the two Gompertz parameters (the Strehler-Mildvan correlation) was re-established. We incorporated the correlation into the Bayesian approach as an "informative" prior probability distribution, and tested its effectiveness using simulated data. Our analyses showed that the mean life-span (≥ age 15) and the proportion of living persons aging over 45 were well-reproduced by the Gompertz model. The simulation showed that using the correlation as an informative prior provides a narrower estimation range in the Bayesian approach than does the uninformative prior. The Gompertz model can be assumed to accurately estimate the mean life-span and/or the proportion of old people in a population. We suggest that the Strehler-Mildvan correlation can be used as a useful constraint in demographic reconstructions of past human populations. © 2015 Wiley Periodicals, Inc.

  8. Reaction-diffusion model for the growth of avascular tumor

    NASA Astrophysics Data System (ADS)

    Ferreira, S. C.; Martins, M. L.; Vilela, M. J.

    2002-02-01

    A nutrient-limited model for avascular cancer growth including cell proliferation, motility, and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are characterized by its gyration radius, total number of cancer cells, and number of cells on tumor periphery. These very distinct morphological patterns follow Gompertz growth curves, but exhibit different scaling laws for their surfaces. Also, the simulated tumors incorporate a spatial structure composed of a central necrotic core, an inner rim of quiescent cells and a narrow outer shell of proliferating cells in agreement with biological data. Finally, our results indicate that the competition for nutrients among normal and cancer cells may be a determining factor in generating papillary tumor morphology.

  9. The Gompertz-Pareto income distribution

    NASA Astrophysics Data System (ADS)

    Chami Figueira, F.; Moura, N. J.; Ribeiro, M. B.

    2011-02-01

    This work analyzes the Gompertz-Pareto distribution (GPD) of personal income, formed by the combination of the Gompertz curve, representing the overwhelming majority of the economically less favorable part of the population of a country, and the Pareto power law, which describes its tiny richest part. Equations for the Lorenz curve, Gini coefficient and the percentage share of the Gompertzian part relative to the total income are all written in this distribution. We show that only three parameters, determined by linear data fitting, are required for its complete characterization. Consistency checks are carried out using income data of Brazil from 1981 to 2007 and they lead to the conclusion that the GPD is consistent and provides a coherent and simple analytical tool to describe personal income distribution data.

  10. Strehler-Mildvan correlation is a degenerate manifold of Gompertz fit.

    PubMed

    Tarkhov, Andrei E; Menshikov, Leonid I; Fedichev, Peter O

    2017-03-07

    correlation may show up as a consequence of the fitting degeneracy, its appearance is not limited to homogeneous cohorts. In fact, the problem persists even beyond the simple Gompertz mortality law. We show that the same degeneracy occurs exactly in the same way, if a more advanced Gompertz-Makeham aging model is employed to improve the modeling. We explain how SM type of relation between the demographic parameters may still be observed even in extremely large cohorts with immense statistical power, such as in human census datasets, provided that systematic historical changes are weak in nature and lead to a gradual change in the mean lifespan.

  11. A new approach to the study of Romanization in Britain: a regional perspective of cultural change in late Iron Age and Roman Dorset using the Siler and Gompertz-Makeham models of mortality

    PubMed Central

    Redfern, Rebecca C.; DeWitte, Sharon N.

    2011-01-01

    This is the first study of Romanization to use the Siler and Gompertz-Makeham models of mortality in order to investigate the health consequences of the 43 AD conquest of Britain. The study examined late Iron Age and Romano-British populations (N=518) from Dorset, England, which is the only region of Britain to display continuity in inhumation burial practice and cemetery use throughout the two periods. Skeletal evidence for frailty was assessed using cribra orbitalia, porotic hyperostosis, periosteal lesions, enamel hypoplasia, dental caries, tuberculosis, and rickets. These health variables were chosen for analysis because they are reliable indicators of general health for diachronic comparison (Steckel and Rose 2002) and are associated with the introduction of urbanism in Britain during the Roman period (Redfern 2007; Redfern 2008b; Roberts and Cox 2003). The results show that levels of frailty and mortality were lower in the late Iron Age period, and no sex differences in mortality were present. However, post-conquest, mortality risk increased for children and the elderly, and particularly for males. The latter finding challenges received wisdom concerning the benefits of Romanization and the higher status of the male body in the Roman world. Therefore, we conclude that the consequences of urbanism, changes in diet and increased population heterogeneity negatively impacted health, to the extent that the enhanced cultural buffering of males did not out-weigh underlying sex differences in biology that advantage females. PMID:20925081

  12. Predictive model for the growth kinetics of Staphylococcus aureus in raw pork developed using Integrated Pathogen Modeling Program (IPMP) 2013.

    PubMed

    Lee, Yong Ju; Jung, Byeong Su; Kim, Kee-Tae; Paik, Hyun-Dong

    2015-09-01

    A predictive model was performed to describe the growth of Staphylococcus aureus in raw pork by using Integrated Pathogen Modeling Program 2013 and a polynomial model as a secondary predictive model. S. aureus requires approximately 180 h to reach 5-6 log CFU/g at 10 °C. At 15 °C and 25 °C, approximately 48 and 20 h, respectively, are required to cause food poisoning. Predicted data using the Gompertz model was the most accurate in this study. For lag time (LT) model, bias factor (Bf) and accuracy factor (Af) values were both 1.014, showing that the predictions were within a reliable range. For specific growth rate (SGR) model, Bf and Af were 1.188 and 1.190, respectively. Additionally, both Bf and Af values of the LT and SGR models were close to 1, indicating that IPMP Gompertz model is more adequate for predicting the growth of S. aureus on raw pork than other models. Copyright © 2015 Elsevier Ltd. All rights reserved.

  13. Modeling Surface Growth of Escherichia coli on Agar Plates

    PubMed Central

    Fujikawa, Hiroshi; Morozumi, Satoshi

    2005-01-01

    Surface growth of Escherichia coli cells on a membrane filter placed on a nutrient agar plate under various conditions was studied with a mathematical model. The surface growth of bacterial cells showed a sigmoidal curve with time on a semilogarithmic plot. To describe it, a new logistic model that we presented earlier (H. Fujikawa et al., Food Microbiol. 21:501-509, 2004) was modified. Growth curves at various constant temperatures (10 to 34°C) were successfully described with the modified model (model III). Model III gave better predictions of the rate constant of growth and the lag period than a modified Gompertz model and the Baranyi model. Using the parameter values of model III at the constant temperatures, surface growth at various temperatures was successfully predicted. Surface growth curves at various initial cell numbers were also sigmoidal and converged to the same maximum cell numbers at the stationary phase. Surface growth curves at various nutrient levels were also sigmoidal. The maximum cell number and the rate of growth were lower as the nutrient level decreased. The surface growth curve was the same as that in a liquid, except for the large curvature at the deceleration period. These curves were also well described with model III. The pattern of increase in the ATP content of cells grown on a surface was sigmoidal, similar to that for cell growth. We discovered several characteristics of the surface growth of bacterial cells under various growth conditions and examined the applicability of our model to describe these growth curves. PMID:16332768

  14. Evaluation of growth models for follicle development and ovulation in Lusitano mares.

    PubMed

    Mata, F

    2012-12-01

    Several growth models are commonly used in the biological sciences, to model the follicle growth occurring in the estrous cycle. The aim of this project was to find the model that best fit the follicular size growth data for Lusitano mares. Retrospective data collected from reproduction book records of n=84 mares and n=124 cycles was used to find the series to be fitted to the models. The exponential, Gompertz, logistic, von Bertalanffy, Richards and Weibull models were used, and the most parsimonious and best fit was achieved with the logistic model (r(2)=0.999). The logistic model fits the Lusitano mare's follicle size growth data very well and its parameters were also shown to have a credible biological interpretation.

  15. Investigation of various growth mechanisms of solid tumour growth within the linear-quadratic model for radiotherapy

    NASA Astrophysics Data System (ADS)

    McAneney, H.; O'Rourke, S. F. C.

    2007-02-01

    The standard linear-quadratic survival model for radiotherapy is used to investigate different schedules of radiation treatment planning to study how these may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al (1977 Br. J. Radiol. 50 681), which was concerned with the case of exponential re-growth between treatments. Here we also consider the restricted exponential model. This has been successfully used by Panetta and Adam (1995 Math. Comput. Modelling 22 67) in the case of chemotherapy treatment planning.Treatment schedules investigated include standard fractionation of daily treatments, weekday treatments, accelerated fractionation, optimized uniform schedules and variation of the dosage and α/β ratio, where α and β are radiobiological parameters for the tumour tissue concerned. Parameters for these treatment strategies are extracted from the literature on advanced head and neck cancer, prostate cancer, as well as radiosensitive parameters. Standardized treatment protocols are also considered. Calculations based on the present analysis indicate that even with growth laws scaled to mimic initial growth, such that growth mechanisms are comparable, variation in survival fraction to orders of magnitude emerged. Calculations show that the logistic and exponential models yield similar results in tumour eradication. By comparison the Gompertz model calculations indicate that tumours described by this law result in a significantly poorer prognosis for tumour eradication than either the exponential or logistic models. The present study also shows that the faster the tumour growth rate and the higher the repair capacity of the cell line, the greater the variation in outcome of the survival fraction. Gaps in treatment, planned or unplanned, also accentuate the differences of the survival fraction given alternative growth

  16. A comparison of fitting growth models with a genetic algorithm and nonlinear regression.

    PubMed

    Roush, W B; Branton, S L

    2005-03-01

    A genetic algorithm (GA), an optimization procedure based on the theory of evolution, was compared with nonlinear regression for the ability of the 2 algorithms to fit the coefficients of poultry growth models. It was hypothesized that the nonlinear approach of using GA to define the parameters of growth equations would better fit the growth equations than the use of nonlinear regression. Two sets of growth data from the literature, consisting of male broiler BW grown for 168 and 170 d, were used in the study. The growth data were fit to 2 forms of the logistic model, the Gompertz, the Gompertz-Laird, and the saturated kinetic models using the SAS nonlinear algorithm (NLIN) procedure and a GA. There were no statistical differences for the comparison of the residuals (the difference between observed and predicted BWs) of growth models fit by a GA or nonlinear regression. The plotted residuals for the nonlinear regression and GA-determined growth values confirmed observations of others that the residuals have oscillations resembling sine waves that are not represented by the growth models. It was found that GA could successfully determine the coefficients of growth equations. A disadvantage of slowness in converging to the solution was found for the GA. The advantage of GA over traditional nonlinear regression is that only ranges need be specified for the parameters of the growth equations, whereas estimates of the coefficients need to be determined, and in some programs the derivatives of the growth equations need to be identified. Depending on the goal of the research, solving multivariable complex functions with an algorithm that considers several solutions at the same time in an evolutionary mode can be considered an advantage especially where there is a chance for the solution to converge on a local optimum when a global optimum is desired. It was concluded that the fitting of the growth equations was not so much a problem with the fitting methodology as it is

  17. A new approach to the study of Romanization in Britain: a regional perspective of cultural change in late iron age and roman dorset using the siler and gompertz-makeham models of mortality.

    PubMed

    Redfern, Rebecca C; Dewitte, Sharon N

    2011-02-01

    This is the first study of health in the Roman Empire to use the Siler and Gompertz-Makeham models of mortality to investigate the health consequences of the 43 AD conquest of Britain. The study examined late Iron Age and Romano-British populations (N = 518) from Dorset, England, which is the only region of Britain to display continuity in inhumation burial practice and cemetery use throughout the two periods. Skeletal evidence for frailty was assessed using cribra orbitalia, porotic hyperostosis, periosteal lesions, enamel hypoplasia, dental caries, tuberculosis, and rickets. These health variables were chosen for analysis because they are reliable indicators of general health for diachronic comparison (Steckel and Rose: The backbone of history: health and nutrition in the western hemisphere (2002)) and are associated with the introduction of urbanism in Britain during the Roman period (Redfern: J Rom Archaeol Supp Series 64 (2007) 171-194; Redfern: Britannia 39 (2008a) 161-191; Roberts and Cox: Health and disease in Britain: from prehistory to the present day (2003)). The results show that levels of frailty and mortality were lower in the late Iron Age period, and no sex differences in mortality was present. However, post-conquest, mortality risk increased for children and the elderly, and particularly for men. The latter finding challenges received wisdom concerning the benefits of incorporation into the Empire and the higher status of the male body in the Roman world. Therefore, we conclude that the consequences of urbanism, changes in diet, and increased population heterogeneity negatively impacted health, to the extent that the enhanced cultural buffering of men did not outweigh underlying sex differences in biology that advantage women. 2010 Wiley-Liss, Inc.

  18. Consistency Properties for Growth Model Parameters Under an Infill Asymptotics Domain

    DTIC Science & Technology

    2010-09-01

    Data. CRC Press, 2004. [4] Bertalanffy , Ludwig von. “A Quantitative Theory of Organic Growth,” Human Biology , 10 :181–213 (1938). [5] Birch, Colin P...often used for biological models, is the Bertalanffy function of [4], given by f(t;L, lo, k) = L− (L− l0) exp(−kt) (7) where L > 0 is the asymptotic...Unlike the Logistic and Gompertz curves, the Bertalanffy curve has no inflection point, and does explicitly allow for an initial length. An

  19. Use of the modified Gompertz equation to assess the Stevia rebaudiana Bertoni antilisterial kinetics.

    PubMed

    Belda-Galbis, Clara Miracle; Pina-Pérez, María Consuelo; Espinosa, Josepa; Marco-Celdrán, Aurora; Martínez, Antonio; Rodrigo, Dolores

    2014-04-01

    In order to assess the antibacterial activity of Stevia rebaudiana Bertoni (Stevia), Listeria innocua growth was characterized at 37 °C, in reference medium supplemented with a leaf infusion, a crude extract, and a steviol glycosides purified extract. Experimental data were fitted to the modified Gompertz model and the antibacterial activity of Stevia was determined based on the lag time (λ) and the maximum growth rate (μmax) reached, depending on the incubation conditions. As the leaf infusion showed the most marked elongation of λ and the most marked μmax reduction, its antimicrobial effect was evaluated at different concentrations, at 37, 22 and 10 °C. According to the results obtained, in general, the lower the temperature or the higher the Stevia concentration, the longer the λ and the lower the μmax, statistically significant being the effect of reducing temperature from 37 or 22 to 10 °C, the effect of increasing Stevia concentration from 0 or 0.5 to 1.5 or 2.5% (w/v), at 37 °C, and the elongation of λ observed in presence of 1.5 and 2.5% (w/v) of Stevia, at 22 °C. These results show that Stevia could be a bacterial growth control measure if a cold chain failure occurs. Copyright © 2013 Elsevier Ltd. All rights reserved.

  20. Mathematical modelling of the growth of human fetus anatomical structures.

    PubMed

    Dudek, Krzysztof; Kędzia, Wojciech; Kędzia, Emilia; Kędzia, Alicja; Derkowski, Wojciech

    2016-07-08

    The goal of this study was to present a procedure that would enable mathematical analysis of the increase of linear sizes of human anatomical structures, estimate mathematical model parameters and evaluate their adequacy. Section material consisted of 67 foetuses-rectus abdominis muscle and 75 foetuses- biceps femoris muscle. The following methods were incorporated to the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length-CRL (V-TUB) by Scammon and Calkins. The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size-age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz's I and II and von Bertalanffy's function. With the use of the procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body length increases, rectus abdominis total length h, its segments hI, hII, hIII, hIV, as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW). The best adjustments to measurement results were observed in the exponential and Gompertz's models.

  1. Urban tree growth modeling

    Treesearch

    E. Gregory McPherson; Paula J. Peper

    2012-01-01

    This paper describes three long-term tree growth studies conducted to evaluate tree performance because repeated measurements of the same trees produce critical data for growth model calibration and validation. Several empirical and process-based approaches to modeling tree growth are reviewed. Modeling is more advanced in the fields of forestry and...

  2. Makeham's addition to the Gompertz law re-evaluated.

    PubMed

    Hallén, Anund

    2009-08-01

    The Makeham parameter, a constant mortality rate independent of aging added to the Gompertz law of human mortality, is proposed to be a measure of the impact on mortality rate by extrinsic causes of mortality, with the effect of aging removed. A small intrinsic contribution to mortality, assumed to depend on the components involved in cellular function, is linked to the initial mortality rate of the Gompertz law. To avoid biased results and conclusions, the impact of extrinsic mortality should be eliminated from the Gompertz parameters.

  3. Use of the recursion formula of the Gompertz function for the quantitation of PCR-amplified templates.

    PubMed

    Schlereth, W; Bassukas, I D; Deubel, W; Lorenz, R; Hempel, K

    1998-02-01

    One common drawback of the currently used procedures to quantitate the polymerase chain reaction (PCR) is that the statistical evaluation of the experimental data depends on many, not just trivial, model assumptions. In the present study we report on an improvement in this crucial step of the quantitative PCR. The experimental design underlying the introduced method is exactly the same as in the case of the so-called PCR. However, by applying growth curve analysis based on the recursion formula of the Gompertz function the kinetics of the accumulation of the amplicon are estimated conjointly from data spanning both the and phases of the reaction. We demonstrate the method by determining the relative number of templates (a 206 bp segment spanning the exon 3 of the X-chromosomal murine Hprt-gene) contained in known orders of dilutions of DNA isolated from the spleen of the C57BL/6J-mouse. [32P]-dATP incorporation was used in duplicate experiments to quantify the amplicons as a function of amplification cycles. Our results: i) indicate that the accumulation of the PCR product as a function of PCR cycles follows a sigmoidal pattern compatible with the Gompertz growth model (P<0.0000001); ii) directly support the thesis that the kinetical pattern of accumulation of amplicons of a given DNA fragment does not depend on the number of corresponding DNA templates provided to the reaction; iii) permit a simple direct evaluation of the parallelity in the course of the accumulation of amplicons from different template numbers as a function of amplification cycles, which is a silent preposition in the evaluation of the so-called PCR; iv) allow an easy quantitation of the relative number of provided templates.

  4. Growth Kinetics of Listeria monocytogenes in Broth and Beef Frankfurters– Determination of Lag Phase Duration and Exponential Growth Rate under Isothermal Conditions

    USDA-ARS?s Scientific Manuscript database

    The objective of this research was to develop a new kinetic model to describe the isothermal growth of microorganisms. The new model was tested with Listeria monocytogenes in broth and frankfurters, and compared with two commonly used models - Baranyi and modified Gompertz models. Bias factor (BF)...

  5. Effects of Temperature, Water Activity, and Syrup Film Composition on the Growth of Wallemia sebi: Development and Assessment of a Model Predicting Growth Lags in Syrup Agar and Crystalline Sugar

    PubMed Central

    Vindeløv, Jannik; Arneborg, Nils

    2002-01-01

    We investigated the effects of temperature, water activity (aw), and syrup film composition on the CFU growth of Wallemia sebi in crystalline sugar. At a high aw (0.82) at both high (20°C) and low (10°C) temperatures, the CFU growth of W. sebi in both white and extrawhite sugar could be described using a modified Gompertz model. At a low aw (0.76), however, the modified Gompertz model could not be fitted to the CFU data obtained with the two sugars due to long CFU growth lags and low maximum specific CFU growth rates of W. sebi at 20°C and due to the fact that growth did not occur at 10°C. At an aw of 0.82, regardless of the temperature, the carrying capacity (i.e., the cell concentration at t = ∞) of extrawhite sugar was lower than that of white sugar. Together with the fact that the syrup film of extrawhite sugar contained less amino-nitrogen relative to other macronutrients than the syrup film of white sugar, these results suggest that CFU growth of W. sebi in extrawhite sugar may be nitrogen limited. We developed a secondary growth model which is able to predict colony growth lags of W. sebi on syrup agar as a function of temperature and aw. The ability of this model to predict CFU growth lags of W. sebi in crystalline sugar was assessed. PMID:11916681

  6. Modeling the growth of Listeria monocytogenes in mold-ripened cheeses.

    PubMed

    Lobacz, Adriana; Kowalik, Jaroslaw; Tarczynska, Anna

    2013-06-01

    This study presents possible applications of predictive microbiology to model the safety of mold-ripened cheeses with respect to bacteria of the species Listeria monocytogenes during (1) the ripening of Camembert cheese, (2) cold storage of Camembert cheese at temperatures ranging from 3 to 15°C, and (3) cold storage of blue cheese at temperatures ranging from 3 to 15°C. The primary models used in this study, such as the Baranyi model and modified Gompertz function, were fitted to growth curves. The Baranyi model yielded the most accurate goodness of fit and the growth rates generated by this model were used for secondary modeling (Ratkowsky simple square root and polynomial models). The polynomial model more accurately predicted the influence of temperature on the growth rate, reaching the adjusted coefficients of multiple determination 0.97 and 0.92 for Camembert and blue cheese, respectively. The observed growth rates of L. monocytogenes in mold-ripened cheeses were compared with simulations run with the Pathogen Modeling Program (PMP 7.0, USDA, Wyndmoor, PA) and ComBase Predictor (Institute of Food Research, Norwich, UK). However, the latter predictions proved to be consistently overestimated and contained a significant error level. In addition, a validation process using independent data generated in dairy products from the ComBase database (www.combase.cc) was performed. In conclusion, it was found that L. monocytogenes grows much faster in Camembert than in blue cheese. Both the Baranyi and Gompertz models described this phenomenon accurately, although the Baranyi model contained a smaller error. Secondary modeling and further validation of the generated models highlighted the issue of usability and applicability of predictive models in the food processing industry by elaborating models targeted at a specific product or a group of similar products.

  7. Evaluation of primary models to describe the growth of Pichia anomala and study of temperature, NaCl, and pH effects on its biological parameters by response surface methodology.

    PubMed

    Arroyo, F N; Durán Quintana, M C; Garrido Fernández, A

    2005-03-01

    Tolerance of Pichia anomala, a strain of yeast associated with olive fermentation, to salt, temperature, and pH was studied in yeast-malt-peptone-glucose medium using a nonfactorial central composite experimental design with three repetitions in the center to account for pure error. Modified Gompertz, logistic, Richards-Stannard, and Baranyi-Roberts models were used to determine maximum specific growth rate (micro(max)) and lag phase period (lambda) from the growth curves (primary models). All models produced a good fit (significant at P < 0.05), but the graphical and statistical analyses of the data indicated that the modified Gompertz and Richards-Stannard models were the most appropriate. The biological parameters obtained with the diverse models were fitted to a response surface secondary model. A significant decrease in micro(max) was observed as temperature decreased and salt increased. A significant increase in lambda was observed as temperature (linear and quadratic effects) and pH decreased and as salt content increased. Effects of interactions were complex and depended on models. Validation revealed acceptable errors and bias in micro(max) and lambda values obtained in independent experiments. Validation growth curves were best reproduced by using the values of micro(max) and lambda predicted by the response surface from the modified Gompertz and Richards-Stannard models. Results from this study can be applied to table olive fermentation or storage and for production of table olives as refrigerated commercial products without the use of preservatives or pasteurization.

  8. Evolutionary theory of ageing and the problem of correlated Gompertz parameters.

    PubMed

    Burger, Oskar; Missov, Trifon I

    2016-11-07

    The Gompertz mortality model is often used to evaluate evolutionary theories of ageing, such as the Medawar-Williams' hypothesis that high extrinsic mortality leads to faster ageing. However, fits of the Gompertz mortality model to data often find the opposite result that mortality is negatively correlated with the rate of ageing. This negative correlation has been independently discovered in several taxa and is known in actuarial studies of ageing as the Strehler-Mildvan correlation. We examine the role of mortality selection in determining late-life variation in susceptibility to death, which has been suggested to be the cause of this negative correlation. We demonstrate that fixed-frailty models that account for heterogeneity in frailty do not remove the correlation and that the correlation is an inherent statistical property of the Gompertz distribution. Linking actuarial and biological rates of ageing will continue to be a pressing challenge, but the Strehler-Mildvan correlation itself should not be used to diagnose any biological, physiological, or evolutionary process. These findings resolve some key tensions between theory and data that affect evolutionary and biological studies of ageing and mortality. Tests of evolutionary theories of ageing should include direct measures of physiological performance or condition.

  9. A robust estimation of the exponent function in the Gompertz law

    NASA Astrophysics Data System (ADS)

    Ibarra-Junquera, V.; Monsivais, M. P.; Rosu, H. C.; López-Sandoval, R.

    2006-08-01

    The estimation of the solution of a system of two differential equations introduced by Norton et al. [Predicting the course of Gompertzian growth, Nature 264 (1976) 542-544] that is equivalent to the famous Gompertz growth law is performed by means of the recent adaptive scheme of Besançon and collaborators [High gain observer based state and parameter estimation in nonlinear systems, paper 204, the sixth IFAC Symposium, Stuttgart Symposium on Nonlinear Control Systems (NOLCOS), 2004, available at ]. Results of computer simulations illustrate the robustness of the approach.

  10. Accuracy of growth model parameters: effects of frequency and duration of data collection, and missing information.

    PubMed

    Aggrey, Samuel E

    2008-01-01

    This study was done to compare the accuracy of prediction of growth parameters using the Gompertz model when (1) data was collected infrequently, (2) data collection was truncated, and (3) data was missing. Initial growth rate and rate of decay were reduced by half when the model was fitted to data collected biweekly compared to data collected weekly. This reduction led to an increase in age of maximum growth and subsequently over-predicted the asymptotic body weight. When only part of the growth duration was used for prediction, both the initial growth rate and rate of decay were reduced. The degree of data truncation also affected sexual dimorphism of the parameters estimated. Using pre-asymptotic data for growth parameter prediction does not allow the intrinsic efficiency of growth to be determined accurately. However, using growth data with body weights missing at different phases of the growth curve does not seem to significantly affect the predicted growth parameters. Speculative or diagnostic conclusions on intrinsic growth should be done with data collected at short intervals to avoid potential inaccuracies in the prediction of initial growth rate, exponential decay rate, age of maximum growth and asymptotic weight.

  11. Rethinking cell growth models.

    PubMed

    Kafri, Moshe; Metzl-Raz, Eyal; Jonas, Felix; Barkai, Naama

    2016-11-01

    The minimal description of a growing cell consists of self-replicating ribosomes translating the cellular proteome. While neglecting all other cellular components, this model provides key insights into the control and limitations of growth rate. It shows, for example, that growth rate is maximized when ribosomes work at full capacity, explains the linear relation between growth rate and the ribosome fraction of the proteome and defines the maximal possible growth rate. This ribosome-centered model also highlights the challenge of coordinating cell growth with related processes such as cell division or nutrient production. Coordination is promoted when ribosomes don't translate at maximal capacity, as it allows escaping strict exponential growth. Recent data support the notion that multiple cellular processes limit growth. In particular, increasing transcriptional demand may be as deleterious as increasing translational demand, depending on growth conditions. Consistent with the idea of trade-off, cells may forgo maximal growth to enable more efficient interprocess coordination and faster adaptation to changing conditions. © FEMS 2016. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

  12. Generalized exponential function and discrete growth models

    NASA Astrophysics Data System (ADS)

    Souto Martinez, Alexandre; Silva González, Rodrigo; Lauri Espíndola, Aquino

    2009-07-01

    Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamic models into a simple formula. A physical interpretation is given to this new introduced parameter in the context of the continuous Richards model, which remains valid for the discrete case. From the discretization of the continuous Richards’ model (generalization of the Gompertz and Verhulst models), one obtains a generalized logistic map and we briefly study its properties. Notice, however that the physical interpretation for the introduced parameter persists valid for the discrete case. Next, we generalize the (scramble competition) θ-Ricker discrete model and analytically calculate the fixed points as well as their stabilities. In contrast to previous generalizations, from the generalized θ-Ricker model one is able to retrieve either scramble or contest models.

  13. Stochastic ontogenetic growth model

    NASA Astrophysics Data System (ADS)

    West, B. J.; West, D.

    2012-02-01

    An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.

  14. Modelling urban growth patterns

    NASA Astrophysics Data System (ADS)

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

    1995-10-01

    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 attempts1á¤-3 to model urban growth using ideas from the statistical physics of clusters. In particular, the model of diffusion-limited aggregation4,5 (DLA) has been invoked to rationalize the apparently fractal nature of urban morphologies1. The DLA model predicts that there should exist only one large fractal cluster, which is almost perfectly screened from incoming á¤~development unitsᤙ (representing, for example, people, capital or resources), so that almost all of the cluster growth takes place at the tips of the clusterᤙs branches. Here we show that an alternative model, 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 (á¤~towns') in an urban system, and can also describe urban growth dynamics. Our physical model, which corresponds to the correlated percolation model6á¤-8 in the presence of a density gradient9, 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 behaviour) of urban morphologies.

  15. Flexible and fixed mathematical models describing growth patterns of chukar partridges

    NASA Astrophysics Data System (ADS)

    Aygün, Ali; Narinç, Doǧan

    2016-04-01

    In animal science, the nonlinear regression models for growth curve analysis ofgrowth patterns are separated into two groups called fixed and flexible according to their point of inflection. The aims of this study were to compare fixed and flexible growth functions and to determine the best fit model for the growth data of chukar partridges. With this aim, the growth data of partridges were modeled with widely used models, such as Gompertz, Logistic, Von Bertalanffy as well as the flexible functions, such as, Richards, Janoschek, Levakovich. So as to evaluate growth functions, the R2 (coefficient of determination), adjusted R2 (adjusted coefficient of determination), MSE (mean square error), AIC (Akaike's information criterion) and BIC (Bayesian information criterion) goodness of fit criteria were used. It has been determined that the best fit model from the point of chukar partridge growth data according to mentioned goodness of fit criteria is Janoschek function which has a flexible structure. The Janoschek model is not only important because it has a higher number of parameters with biological meaning than the other functions (the mature weight and initial weight parameters), but also because it was not previously used in the modeling of the chukar partridge growth.

  16. Growth and annual survival estimates to examine the ecology of larval lamprey and the implications of ageing error in fitting models.

    PubMed

    Schultz, L D; Chasco, B E; Whitlock, S L; Meeuwig, M H; Schreck, C B

    2017-04-01

    This study used existing western brook lamprey Lampetra richardsoni age information to fit three different growth models (i.e. von Bertalanffy, Gompertz and logistic) with and without error in age estimates. Among these growth models, there was greater support for the logistic and Gompertz models than the von Bertalanffy model, regardless of ageing error assumptions. The von Bertalanffy model, however, appeared to fit the data well enough to permit survival estimates; using length-based estimators, annual survival varied between 0·64 (95% credibility interval: 0·44-0·79) and 0·81 (0·79-0·83) depending on ageing and growth process error structure. These estimates are applicable to conservation and management of L. richardsoni and other western lampreys (e.g. Pacific lamprey Entosphenus tridentatus) and can potentially be used in the development of life-cycle models for these species. These results also suggest that estimators derived from von Bertalanffy growth models should be interpreted with caution if there is high uncertainty in age estimates. © 2016 The Fisheries Society of the British Isles.

  17. Description of Aspergillus flavus growth under the influence of different factors (water activity, incubation temperature, protein and fat concentration, pH, and cinnamon essential oil concentration) by kinetic, probability of growth, and time-to-detection models.

    PubMed

    Kosegarten, Carlos E; Ramírez-Corona, Nelly; Mani-López, Emma; Palou, Enrique; López-Malo, Aurelio

    2017-01-02

    A Box-Behnken design was used to determine the effect of protein concentration (0, 5, or 10g of casein/100g), fat (0, 3, or 6g of corn oil/100g), aw (0.900, 0.945, or 0.990), pH (3.5, 5.0, or 6.5), concentration of cinnamon essential oil (CEO, 0, 200, or 400μL/kg) and incubation temperature (15, 25, or 35°C) on the growth of Aspergillus flavus during 50days of incubation. Mold response under the evaluated conditions was modeled by the modified Gompertz equation, logistic regression, and time-to-detection model. The obtained polynomial regression models allow the significant coefficients (p<0.05) for linear, quadratic and interaction effects for the Gompertz equation's parameters to be identified, which adequately described (R(2)>0.967) the studied mold responses. After 50days of incubation, every tested model system was classified according to the observed response as 1 (growth) or 0 (no growth), then a binary logistic regression was utilized to model A. flavus growth interface, allowing to predict the probability of mold growth under selected combinations of tested factors. The time-to-detection model was utilized to estimate the time at which A. flavus visible growth begins. Water activity, temperature, and CEO concentration were the most important factors affecting fungal growth. It was observed that there is a range of possible combinations that may induce growth, such that incubation conditions and the amount of essential oil necessary for fungal growth inhibition strongly depend on protein and fat concentrations as well as on the pH of studied model systems. The probabilistic model and the time-to-detection models constitute another option to determine appropriate storage/processing conditions and accurately predict the probability and/or the time at which A. flavus growth occurs. Copyright © 2016 Elsevier B.V. All rights reserved.

  18. Mathematical models for growth in alligator (Alligator mississippiensis) embryos developing at different incubation temperatures.

    PubMed

    Bardsley, W G; Ackerman, R A; Bukhari, N A; Deeming, D C; Ferguson, M W

    1995-08-01

    A variety of model-based (growth models) and model-free (cubic splines, exponentials) equations were fitted using weighted-nonlinear least squares regression to embryonic growth data from Alligator mississippiensis eggs incubated at 30 and 33 degrees C. Goodness of fit was estimated using a chi 2 on the sum of squared, weighted residuals, and run and sign tests on the residuals. One of the growth models used (Preece & Baines, 1978) was found to be superior to the classical growth models (exponential, monomolecular, logistic, Gompertz, von Bertalanffy) and gave an adequate fit to all longitudinal measures taken from the embryonic body and embryonic mass. However, measurements taken from the head could not be fitted by growth models but were adequately fitted by weighted least squares cubic splines. Data for the stage of development were best fitted by a sum of 2 exponentials with a transition point. Comparison of the maximum growth rates and parameter values, indicated that the growth data at 30 degrees C could be scaled to 33 degrees C to multiplying the time by a scaling factor of 1.2. This is equivalent to a Q10 of about 1.86 or, after solving the Arrhenius equation, an E++ of 46.9 kJmol-1. This may be interpreted as indicating a common rate-limiting step in development at the 2 temperatures.

  19. Comparison of nonlinear and spline regression models for describing mule duck growth curves.

    PubMed

    Vitezica, Z G; Marie-Etancelin, C; Bernadet, M D; Fernandez, X; Robert-Granie, C

    2010-08-01

    This study compared models for growth (BW) before overfeeding period for male mule duck data from 7 families of a QTL experimental design. Four nonlinear models (Gompertz, logistic, Richards, and Weibull) and a spline linear regression model were used. This study compared fixed and mixed effects models to analyze growth. The Akaike information criterion was used to evaluate these alternative models. Among the nonlinear models, the mixed effects Weibull model had the best overall fit. Two parameters, the asymptotic weight and the inflexion point age, were considered random variables associated with individuals in the mixed models. In our study, asymptotic weight had a greater effect in Akaike's information criterion reduction than inflexion point age. In this data set, the between-ducks variability was mostly explained by asymptotic BW. Comparing fixed with mixed effects models, the residual SD was reduced in about 55% in the latter, pointing out the improvement in the accuracy of estimated parameters. The mixed effects spline regression model was the second best model. Given the piecewise nature of growth, this model is able to capture different growth patterns, even with data collected beyond the asymptotic BW.

  20. How could the Gompertz-Makeham law evolve.

    PubMed

    Golubev, A

    2009-05-07

    In line with the origin of life from the chemical world, biological mortality kinetics is suggested to originate from chemical decomposition kinetics described by the Arrhenius equation k = A*exp(-E/RT). Another chemical legacy of living bodies is that, by using the appropriate properties of their constituent molecules, they incorporate all their potencies, including adverse ones. In early evolution, acquiring an ability to use new molecules to increase disintegration barrier E might be associated with new adverse interactions, yielding products that might accumulate in organisms and compromise their viability. Thus, the main variable of the Arrhenius equation changed from T in chemistry to E in biology; mortality turned to rise exponentially as E declined with increasing age; and survivorship patterns turned to feature slow initial and fast late descent making the bulk of each finite cohort to expire within a short final period of its lifespan. Numerical modelling shows that such acquisition of new functions associated with faster functional decline may increase the efficiency of investing resources into progeny, in line with the antagonistic pleiotropy theory of ageing. Any evolved time trajectories of functional changes were translated into changes in mortality through exponent according to the generalised Gompertz-Makeham law mu = C(t)+Lambda*exp[-E(t)], which is reduced to the conventional form when E(t) = E0-gammat and C is constant. The proposed model explains the origin of the linear mid-age functional decline followed by its deceleration at later ages and the positive correlation between the initial vitality and the rate of ageing.

  1. Estimating and determining the effect of a therapy on tumor dynamics by means of a modified Gompertz diffusion process.

    PubMed

    Albano, Giuseppina; Giorno, Virginia; Román-Román, Patricia; Román-Román, Sergio; Torres-Ruiz, Francisco

    2015-01-07

    A modified Gompertz diffusion process is considered to model tumor dynamics. The infinitesimal mean of this process includes non-homogeneous terms describing the effect of therapy treatments able to modify the natural growth rate of the process. Specifically, therapies with an effect on cell growth and/or cell death are assumed to modify the birth and death parameters of the process. This paper proposes a methodology to estimate the time-dependent functions representing the effect of a therapy when one of the functions is known or can be previously estimated. This is the case of therapies that are jointly applied, when experimental data are available from either an untreated control group or from groups treated with single and combined therapies. Moreover, this procedure allows us to establish the nature (or, at least, the prevalent effect) of a single therapy in vivo. To accomplish this, we suggest a criterion based on the Kullback-Leibler divergence (or relative entropy). Some simulation studies are performed and an application to real data is presented.

  2. Predictive modeling of Pseudomonas fluorescens growth under different temperature and pH values.

    PubMed

    Gonçalves, Letícia Dias Dos Anjos; Piccoli, Roberta Hilsdorf; Peres, Alexandre de Paula; Saúde, André Vital

    Meat is one of the most perishable foods owing to its nutrient availability, high water activity, and pH around 5.6. These properties are highly conducive for microbial growth. Fresh meat, when exposed to oxygen, is subjected to the action of aerobic psychrotrophic, proteolytic, and lipolytic spoilage microorganisms, such as Pseudomonas spp. The spoilage results in the appearance of slime and off-flavor in food. In order to predict the growth of Pseudomonas fluorescens in fresh meat at different pH values, stored under refrigeration, and temperature abuse, microbial mathematical modeling was applied. The primary Baranyi and Roberts and the modified Gompertz models were fitted to the experimental data to obtain the growth parameters. The Ratkowsky extended model was used to determine the effect of pH and temperature on the growth parameter μmax. The program DMFit 3.0 was used for model adjustment and fitting. The experimental data showed good fit for both the models tested, and the primary and secondary models based on the Baranyi and Roberts models showed better validation. Thus, these models can be applied to predict the growth of P. fluorescens under the conditions tested.

  3. Justifying the Gompertz curve of mortality via the generalized Polya process of shocks.

    PubMed

    Cha, Ji Hwan; Finkelstein, Maxim

    2016-06-01

    A new probabilistic model of aging that can be applied to organisms is suggested and analyzed. Organisms are subject to shocks that follow the generalized Polya process (GPP), which has been recently introduced and characterized in the literature. Distinct from the nonhomogeneous Poisson process that has been widely used in applications, the important feature of this process is the dependence of its future behavior on the number of previous events (shocks). The corresponding survival and the mortality rate functions are derived and analyzed. The general approach is used for justification of the Gompertz law of human mortality.

  4. Dynamic mathematical model to predict microbial growth and inactivation during food processing.

    PubMed Central

    Van Impe, J F; Nicolaï, B M; Martens, T; De Baerdemaeker, J; Vandewalle, J

    1992-01-01

    Many sigmoidal functions to describe a bacterial growth curve as an explicit function of time have been reported in the literature. Furthermore, several expressions have been proposed to model the influence of temperature on the main characteristics of this growth curve: maximum specific growth rate, lag time, and asymptotic level. However, as the predictive value of such explicit models is most often guaranteed only at a constant temperature within the temperature range of microbial growth, they are less appropriate in optimization studies of a whole production and distribution chain. In this paper a dynamic mathematical model--a first-order differential equation--has been derived, describing the bacterial population as a function of both time and temperature. Furthermore, the inactivation of the population at temperatures above the maximum temperature for growth has been incorporated. In the special case of a constant temperature, the solution coincides exactly with the corresponding Gompertz model, which has been validated in several recent reports. However, the main advantage of this dynamic model is its ability to deal with time-varying temperatures, over the whole temperature range of growth and inactivation. As such, it is an essential building block in (time-saving) simulation studies to design, e.g., optimal temperature-time profiles with respect to microbial safety of a production and distribution chain of chilled foods. PMID:1444404

  5. Mathematical modeling of tumor growth and metastatic spreading: validation in tumor-bearing mice.

    PubMed

    Hartung, Niklas; Mollard, Séverine; Barbolosi, Dominique; Benabdallah, Assia; Chapuisat, Guillemette; Henry, Gerard; Giacometti, Sarah; Iliadis, Athanassios; Ciccolini, Joseph; Faivre, Christian; Hubert, Florence

    2014-11-15

    Defining tumor stage at diagnosis is a pivotal point for clinical decisions about patient treatment strategies. In this respect, early detection of occult metastasis invisible to current imaging methods would have a major impact on best care and long-term survival. Mathematical models that describe metastatic spreading might estimate the risk of metastasis when no clinical evidence is available. In this study, we adapted a top-down model to make such estimates. The model was constituted by a transport equation describing metastatic growth and endowed with a boundary condition for metastatic emission. Model predictions were compared with experimental results from orthotopic breast tumor xenograft experiments conducted in Nod/Scidγ mice. Primary tumor growth, metastatic spread and growth were monitored by 3D bioluminescence tomography. A tailored computational approach allowed the use of Monolix software for mixed-effects modeling with a partial differential equation model. Primary tumor growth was described best by Bertalanffy, West, and Gompertz models, which involve an initial exponential growth phase. All other tested models were rejected. The best metastatic model involved two parameters describing metastatic spreading and growth, respectively. Visual predictive check, analysis of residuals, and a bootstrap study validated the model. Coefficients of determination were [Formula: see text] for primary tumor growth and [Formula: see text] for metastatic growth. The data-based model development revealed several biologically significant findings. First, information on both growth and spreading can be obtained from measures of total metastatic burden. Second, the postulated link between primary tumor size and emission rate is validated. Finally, fast growing peritoneal metastases can only be described by such a complex partial differential equation model and not by ordinary differential equation models. This work advances efforts to predict metastatic spreading

  6. Modeling the growth of Listeria monocytogenes on the surface of smear- or mold-ripened cheese.

    PubMed

    Schvartzman, M Sol; Gonzalez-Barron, Ursula; Butler, Francis; Jordan, Kieran

    2014-01-01

    Surface-ripened cheeses are matured by means of manual or mechanical technologies posing a risk of cross-contamination, if any cheeses are contaminated with Listeria monocytogenes. In predictive microbiology, primary models are used to describe microbial responses, such as growth rate over time and secondary models explain how those responses change with environmental factors. In this way, primary models were used to assess the growth rate of L. monocytogenes during ripening of the cheeses and the secondary models to test how much the growth rate was affected by either the pH and/or the water activity (aw) of the cheeses. The two models combined can be used to predict outcomes. The purpose of these experiments was to test three primary (the modified Gompertz equation, the Baranyi and Roberts model, and the Logistic model) and three secondary (the Cardinal model, the Ratowski model, and the Presser model) mathematical models in order to define which combination of models would best predict the growth of L. monocytogenes on the surface of artificially contaminated surface-ripened cheeses. Growth on the surface of the cheese was assessed and modeled. The primary models were firstly fitted to the data and the effects of pH and aw on the growth rate (μmax) were incorporated and assessed one by one with the secondary models. The Logistic primary model by itself did not show a better fit of the data among the other primary models tested, but the inclusion of the Cardinal secondary model improved the final fit. The aw was not related to the growth of Listeria. This study suggests that surface-ripened cheese should be separately regulated within EU microbiological food legislation and results expressed as counts per surface area rather than per gram.

  7. A heterogeneous population model for the analysis of bacterial growth kinetics.

    PubMed

    McKellar, R C

    1997-05-20

    A two-compartment, heterogeneous population model (HPM) was derived using the simulation software SB ModelMaker to describe the growth of Listeria monocytogenes in bacteriological media at 5-35 degrees C. The model assumed that, at time t = 0, the inoculum was distributed between two distinct compartments, Non-Growing and Growing, and that growth could be described by four parameters: initial total cell population (N0), final maximum cell population (Nmax), maximum specific growth rate (mu(max)), and initial cell population in the Growing compartment (G0). The model was fitted to the data by optimizing the four parameters, and lag phase duration (lambda) was calculated. The resulting values of mu(max) and lambda were similar to those determined using the modified Gompertz equation. A new parameter, w0, was defined which relates to the proportion of the initial cell population capable of growth, and is a measure of the initial physiological state of the cells. A modified model in which mu(max) was replaced with a temperature function, and w0 replaced G0, was used to predict the effect of temperature on the growth of L. monocytogenes. The results of this study raise questions concerning the current definition of the lag phase.

  8. Phase transition in tumor growth: I avascular development

    NASA Astrophysics Data System (ADS)

    Izquierdo-Kulich, E.; Rebelo, I.; Tejera, E.; Nieto-Villar, J. M.

    2013-12-01

    We propose a mechanism for avascular tumor growth based on a simple chemical network. This model presents a logistic behavior and shows a “second order” phase transition. We prove the fractal origin of the empirical logistics and Gompertz constant and its relation to mitosis and apoptosis rate. Finally, the thermodynamics framework developed demonstrates the entropy production rate as a Lyapunov function during avascular tumor growth.

  9. Model-Based Tumor Growth Dynamics and Therapy Response in a Mouse Model of De Novo Carcinogenesis

    PubMed Central

    Hadjiandreou, Marios M.; Rizki, Gizem; Achilleos, Achilleas; Strati, Katerina; Mitsis, Georgios D.

    2015-01-01

    Tumorigenesis is a complex, multistep process that depends on numerous alterations within the cell and contribution from the surrounding stroma. The ability to model macroscopic tumor evolution with high fidelity may contribute to better predictive tools for designing tumor therapy in the clinic. However, attempts to model tumor growth have mainly been developed and validated using data from xenograft mouse models, which fail to capture important aspects of tumorigenesis including tumor-initiating events and interactions with the immune system. In the present study, we investigate tumor growth and therapy dynamics in a mouse model of de novo carcinogenesis that closely recapitulates tumor initiation, progression and maintenance in vivo. We show that the rate of tumor growth and the effects of therapy are highly variable and mouse specific using a Gompertz model to describe tumor growth and a two-compartment pharmacokinetic/ pharmacodynamic model to describe the effects of therapy in mice treated with 5-FU. We show that inter-mouse growth variability is considerably larger than intra-mouse variability and that there is a correlation between tumor growth and drug kill rates. Our results show that in vivo tumor growth and regression in a double transgenic mouse model are highly variable both within and between subjects and that mathematical models can be used to capture the overall characteristics of this variability. In order for these models to become useful tools in the design of optimal therapy strategies and ultimately in clinical practice, a subject-specific modelling strategy is necessary, rather than approaches that are based on the average behavior of a given subject population which could provide erroneous results. PMID:26649886

  10. Microbial growth curves: what the models tell us and what they cannot.

    PubMed

    Peleg, Micha; Corradini, Maria G

    2011-12-01

    Most of the models of microbial growth in food are Empirical algebraic, of which the Gompertz model is the most notable, Rate equations, mostly variants of the Verhulst's logistic model, or Population Dynamics models, which can be deterministic and continuous or stochastic and discrete. The models of the first two kinds only address net growth and hence cannot account for cell mortality that can occur at any phase of the growth. Almost invariably, several alternative models of all three types can describe the same set of experimental growth data. This lack of uniqueness is by itself a reason to question any mechanistic interpretation of growth parameters obtained by curve fitting alone. As argued, all the variants of the Verhulst's model, including the Baranyi-Roberts model, are empirical phenomenological models in a rate equation form. None provides any mechanistic insight or has inherent advantage over the others. In principle, models of all three kinds can predict non-isothermal growth patterns from isothermal data. Thus a modeler should choose the simplest and most convenient model for this purpose. There is no reason to assume that the dependence of the "maximum specific growth rate" on temperature, pH, water activity, or other factors follows the original or modified versions of the Arrhenius model, as the success of Ratkowsky's square root model testifies. Most sigmoid isothermal growth curves require three adjustable parameters for their mathematical description and growth curves showing a peak at least four. Although frequently observed, there is no theoretical reason that these growth parameters should always rise and fall in unison in response to changes in external conditions. Thus quantifying the effect of an environmental factor on microbial growth require that all the growth parameters are addressed, not just the "maximum specific growth rate." Different methods to determine the "lag time" often yield different values, demonstrating that it is a

  11. Lattice models of biological growth

    SciTech Connect

    Young, D.A.; Corey, E.M. )

    1990-06-15

    We show that very simple iterative rules for the growth of cells on a two-dimensional lattice can simulate biological-growth phenomena realistically. We discuss random cellular automata models for the growth of fern gametophytes, branching fungi, and leaves, and for shape transformations useful in the study of biological variation and evolution. Although there are interesting analogies between biological and physical growth processes, we stress the uniqueness of biological automata behavior. The computer growth algorithms that successfully mimic observed growth behavior may be helpful in determining the underlying biochemical mechanisms of growth regulation.

  12. A non-phenomenological model of competition and cooperation to explain population growth behaviors.

    PubMed

    Ribeiro, Fabiano L

    2015-03-01

    This paper is an extension of a previous work which proposes a non-phenomenological model of population growth that is based on the interactions among the individuals of a population. In addition to what had already been studied—that the individuals interact competitively—in the present work it is also considered that the individuals interact cooperatively. As a consequence of this new consideration, a richer dynamics is observed. For instance, besides getting the population models already reached from the original version of the model (as the Malthus, Verhulst, Gompertz, Richards, Bertalanffy and power-law growth models), the new formulation also reaches the von Foerster growth model and also a regime of divergence of the population at a finite time. An agent-based model is also presented in order to give support to the analytical results. Moreover, this new approach of the model explains the Allee effect as an emergent behavior of the cooperative and competitive interactions among the individuals. The Allee effect is the characteristic of some populations of increasing the population growth rate in a small-sized population. Whereas the models presented in the literature explain the Allee effect with phenomenological ideas, the model presented here explains this effect by the interactions between the individuals. The model is tested with empirical data to justify its formulation. Another interesting macroscopic emergent behavior from the model proposed is the observation of a regime of population divergence at a finite time. It is interesting that this characteristic is observed in humanity's global population growth. It is shown that in a regime of cooperation, the model fits very well to the human population growth data from 1000 AD to nowadays.

  13. Growth process and model simulation of three different classes of Schima superba in a natural subtropical forest in China

    NASA Astrophysics Data System (ADS)

    Wei, Hui; Deng, Xiangwen; Ouyang, Shuai; Chen, Lijun; Chu, Yonghe

    2017-01-01

    Schima superba is an important fire-resistant, high-quality timber species in southern China. Growth in height, diameter at breast height (DBH), and volume of the three different classes (overtopped, average and dominant) of S. superba were examined in a natural subtropical forest. Four growth models (Richards, edited Weibull, Logistic and Gompertz) were selected to fit the growth of the three different classes of trees. The results showed that there was a fluctuation phenomenon in height and DBH current annual growth process of all three classes. Multiple intersections were found between current annual increment (CAI) and mean annual increment (MAI) curves of both height and DBH, but there was no intersection between volume CAI and MAI curves. All selected models could be used to fit the growth of the three classes of S. superba, with determinant coefficients above 0.9637. However, the edited Weibull model performed best with the highest R2 and the lowest root of mean square error (RMSE). S. superba is a fast-growing tree with a higher growth rate during youth. The height and DBH CAIs of overtopped, average and dominant trees reached growth peaks at ages 5–10, 10–15 and 15–20 years, respectively. According to model simulation, the volume CAIs of overtopped, average and dominant trees reached growth peaks at ages 17, 55 and 76 years, respectively. The biological rotation ages of the overtopped, average and dominant trees of S. superba were 29, 85 and 128 years, respectively.

  14. Modeling Exponential Population Growth

    ERIC Educational Resources Information Center

    McCormick, Bonnie

    2009-01-01

    The concept of population growth patterns is a key component of understanding evolution by natural selection and population dynamics in ecosystems. The National Science Education Standards (NSES) include standards related to population growth in sections on biological evolution, interdependence of organisms, and science in personal and social…

  15. Modeling Exponential Population Growth

    ERIC Educational Resources Information Center

    McCormick, Bonnie

    2009-01-01

    The concept of population growth patterns is a key component of understanding evolution by natural selection and population dynamics in ecosystems. The National Science Education Standards (NSES) include standards related to population growth in sections on biological evolution, interdependence of organisms, and science in personal and social…

  16. On Selective Harvesting of an Inshore-Offshore Fishery: A Bioeconomic Model

    ERIC Educational Resources Information Center

    Purohit, D.; Chaudhuri, K. S.

    2004-01-01

    A bioeconomic model is developed for the selective harvesting of a single species, inshore-offshore fishery, assuming that the growth of the species is governed by the Gompertz law. The dynamical system governing the fishery is studied in depth; the local and global stability of its non-trivial steady state are examined. Existence of a bionomic…

  17. On Selective Harvesting of an Inshore-Offshore Fishery: A Bioeconomic Model

    ERIC Educational Resources Information Center

    Purohit, D.; Chaudhuri, K. S.

    2004-01-01

    A bioeconomic model is developed for the selective harvesting of a single species, inshore-offshore fishery, assuming that the growth of the species is governed by the Gompertz law. The dynamical system governing the fishery is studied in depth; the local and global stability of its non-trivial steady state are examined. Existence of a bionomic…

  18. Modeling microbial growth and dynamics.

    PubMed

    Esser, Daniel S; Leveau, Johan H J; Meyer, Katrin M

    2015-11-01

    Modeling has become an important tool for widening our understanding of microbial growth in the context of applied microbiology and related to such processes as safe food production, wastewater treatment, bioremediation, or microbe-mediated mining. Various modeling techniques, such as primary, secondary and tertiary mathematical models, phenomenological models, mechanistic or kinetic models, reactive transport models, Bayesian network models, artificial neural networks, as well as agent-, individual-, and particle-based models have been applied to model microbial growth and activity in many applied fields. In this mini-review, we summarize the basic concepts of these models using examples and applications from food safety and wastewater treatment systems. We further review recent developments in other applied fields focusing on models that explicitly include spatial relationships. Using these examples, we point out the conceptual similarities across fields of application and encourage the combined use of different modeling techniques in hybrid models as well as their cross-disciplinary exchange. For instance, pattern-oriented modeling has its origin in ecology but may be employed to parameterize microbial growth models when experimental data are scarce. Models could also be used as virtual laboratories to optimize experimental design analogous to the virtual ecologist approach. Future microbial growth models will likely become more complex to benefit from the rich toolbox that is now available to microbial growth modelers.

  19. Modeling tin whisker growth.

    SciTech Connect

    Weinberger, Christopher Robert

    2013-08-01

    Tin, lead, and lead-tin solders are the most commonly used solders due to their low melting temperatures. However, due to the toxicity problems, lead must now be removed from solder materials. This has lead to the re-emergence of the issue of tin whisker growth. Tin whiskers are a microelectronic packaging issue because they can lead to shorts if they grow to sufficient length. However, the cause of tin whisker growth is still not well understood and there is lack of robust methods to determine when and if whiskering will be a problem. This report summarizes some of the leading theories on whisker growth and attempts to provide some ideas towards establishing the role microstructure plays in whisker growth.

  20. Classification Scheme for Phenomenological Universalities in Growth Problems in Physics and Other Sciences

    NASA Astrophysics Data System (ADS)

    Castorina, P.; Delsanto, P. P.; Guiot, C.

    2006-05-01

    A classification in universality classes of broad categories of phenomenologies, belonging to physics and other disciplines, may be very useful for a cross fertilization among them and for the purpose of pattern recognition and interpretation of experimental data. We present here a simple scheme for the classification of nonlinear growth problems. The success of the scheme in predicting and characterizing the well known Gompertz, West, and logistic models, suggests to us the study of a hitherto unexplored class of nonlinear growth problems.

  1. Growth and Modeling of Staphylococcus aureus in Flour Products under Isothermal and Nonisothermal Conditions.

    PubMed

    Cao, Hui; Wang, Tingting; Yuan, Min; Yu, Jingsong; Xu, Fei

    2017-03-01

    This study was conducted to investigate the growth of Staphylococcus aureus in traditional Chinese flour products under isothermal (10, 15, 20, 25, 30, and 37°C) and nonisothermal (10 to 20, 20 to 30, and 25 to 37°C) conditions. Then, models for the growth of S. aureus in flour products as a function of storage temperature, pH, and water activity (aw) were developed, and the goodness of fit of models was evaluated using the determination coefficient (R(2)), root mean square error (RMSE), bias factor (Bf), and accuracy factor (Af). Based on the above information, S. aureus growth in steamed bread under nonisothermal conditions was predicted from experiments performed under isothermal conditions. It was shown that different combinations of temperature and aw in flour products have a strong influence on the growth of S. aureus . The modified Gompertz model was found to be more suitable for describing the growth data of S. aureus in flour products, with an R(2) of >0.99 and an RMSE of <0.37. The newly developed secondary models were validated, and for the specific growth rate and the lag time, the R(2) values were 0.96 and 0.97, Af was 1.12 and 1.06, and Bf was 1.13 and 1.05, respectively. The predicted nonisothermal growth curves of S. aureus were in agreement with the reported experimental ones, with RMSE <0.29, Af value 1.02 to 1.09, and Bf value 0.92 to 0.99. These results indicated that the predictive models provided useful information for the establishment of safety standards and a risk assessment for S. aureus in flour products.

  2. Deciphering death: a commentary on Gompertz (1825) 'On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies'.

    PubMed

    Kirkwood, Thomas B L

    2015-04-19

    In 1825, the actuary Benjamin Gompertz read a paper, 'On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies', to the Royal Society in which he showed that over much of the adult human lifespan, age-specific mortality rates increased in an exponential manner. Gompertz's work played an important role in shaping the emerging statistical science that underpins the pricing of life insurance and annuities. Latterly, as the subject of ageing itself became the focus of scientific study, the Gompertz model provided a powerful stimulus to examine the patterns of death across the life course not only in humans but also in a wide range of other organisms. The idea that the Gompertz model might constitute a fundamental 'law of mortality' has given way to the recognition that other patterns exist, not only across the species range but also in advanced old age. Nevertheless, Gompertz's way of representing the function expressive of the pattern of much of adult mortality retains considerable relevance for studying the factors that influence the intrinsic biology of ageing. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

  3. Deciphering death: a commentary on Gompertz (1825) ‘On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies’

    PubMed Central

    Kirkwood, Thomas B. L.

    2015-01-01

    In 1825, the actuary Benjamin Gompertz read a paper, ‘On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies’, to the Royal Society in which he showed that over much of the adult human lifespan, age-specific mortality rates increased in an exponential manner. Gompertz's work played an important role in shaping the emerging statistical science that underpins the pricing of life insurance and annuities. Latterly, as the subject of ageing itself became the focus of scientific study, the Gompertz model provided a powerful stimulus to examine the patterns of death across the life course not only in humans but also in a wide range of other organisms. The idea that the Gompertz model might constitute a fundamental ‘law of mortality’ has given way to the recognition that other patterns exist, not only across the species range but also in advanced old age. Nevertheless, Gompertz's way of representing the function expressive of the pattern of much of adult mortality retains considerable relevance for studying the factors that influence the intrinsic biology of ageing. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society. PMID:25750242

  4. Modeling Population Growth and Extinction

    ERIC Educational Resources Information Center

    Gordon, Sheldon P.

    2009-01-01

    The exponential growth model and the logistic model typically introduced in the mathematics curriculum presume that a population grows exclusively. In reality, species can also die out and more sophisticated models that take the possibility of extinction into account are needed. In this article, two extensions of the logistic model are considered,…

  5. Modeling Population Growth and Extinction

    ERIC Educational Resources Information Center

    Gordon, Sheldon P.

    2009-01-01

    The exponential growth model and the logistic model typically introduced in the mathematics curriculum presume that a population grows exclusively. In reality, species can also die out and more sophisticated models that take the possibility of extinction into account are needed. In this article, two extensions of the logistic model are considered,…

  6. Gompertz - A program for evaluation and comparison of survival curves.

    PubMed

    Klemera, P; Doubal, S

    2000-07-01

    Principles, properties and use of a program for evaluation of survival curves are described. Parameters of Gompertzian mortality curves are computed from survival data of two populations by help of nonlinear regression. The differences in parameters of both curves are evaluated statistically. This method evaluates effectively even survival data of very small populations. The results are presented in numeric, verbal and graphic forms. Finally, reading of the results is offered to distinguish changes corresponding to altered aging rate from changes caused by influences not affecting the basic mechanism of aging. Program GOMPERTZ in the form of Microsoft Excel workbook equipped with Visual Basic procedures is offered free through e-mail (klemera@faf.cuni.cz).

  7. Psychological Models of Educational Growth.

    ERIC Educational Resources Information Center

    Nucci, Larry P.; Walberg, Herbert J.

    A discussion of models of intellectual development and their application to education identifies the two major groups of such models and examines recent attempts to combine them. The two types of theories are described as the psychometric models, which see intellectual growth as the incremental amassing and associating of discrete ideas, and the…

  8. Mesoscopic model for tumor growth.

    PubMed

    Izquierdo-Kulich, Elena; Nieto-Villar, José Manuel

    2007-10-01

    In this work, we propose a mesoscopic model for tumor growth to improve our understanding of the origin of the heterogeneity of tumor cells. In this sense, this stochastic formalism allows us to not only to reproduce but also explain the experimental results presented by Brú. A significant aspect found by the model is related to the predicted values for beta growth exponent, which capture a basic characteristic of the critical surface growth dynamics. According to the model, the value for growth exponent is between 0,25 and 0,5, which includes the value proposed by Kadar-Parisi-Zhang universality class (0,33) and the value proposed by Brú (0,375) related to the molecular beam epitaxy (MBE) universality class. This result suggests that the tumor dynamics are too complex to be associated to a particular universality class.

  9. Growth curve prediction from optical density data.

    PubMed

    Mytilinaios, I; Salih, M; Schofield, H K; Lambert, R J W

    2012-03-15

    A fundamental aspect of predictive microbiology is the shape of the microbial growth curve and many models are used to fit microbial count data, the modified Gompertz and Baranyi equation being two of the most widely used. Rapid, automated methods such as turbidimetry have been widely used to obtain growth parameters, but do not directly give the microbial growth curve. Optical density (OD) data can be used to obtain the specific growth rate and if used in conjunction with the known initial inocula, the maximum population data and knowledge of the microbial number at a predefined OD at a known time then all the information required for the reconstruction of a standard growth curve can be obtained. Using multiple initial inocula the times to detection (TTD) at a given standard OD were obtained from which the specific growth rate was calculated. The modified logistic, modified Gompertz, 3-phase linear, Baranyi and the classical logistic model (with or without lag) were fitted to the TTD data. In all cases the modified logistic and modified Gompertz failed to reproduce the observed linear plots of the log initial inocula against TTD using the known parameters (initial inoculum, MPD and growth rate). The 3 phase linear model (3PLM), Baranyi and classical logistic models fitted the observed data and were able to reproduce elements of the OD incubation-time curves. Using a calibration curve relating OD and microbial numbers, the Baranyi equation was able to reproduce OD data obtained for Listeria monocytogenes at 37 and 30°C as well as data on the effect of pH (range 7.05 to 3.46) at 30°C. The Baranyi model was found to be the most capable primary model of those examined (in the absence of lag it defaults to the classic logistic model). The results suggested that the modified logistic and the modified Gompertz models should not be used as Primary models for TTD data as they cannot reproduce the observed data.

  10. Czochralski crystal growth: Modeling study

    NASA Technical Reports Server (NTRS)

    Dudukovic, M. P.; Ramachandran, P. A.; Srivastava, R. K.; Dorsey, D.

    1986-01-01

    The modeling study of Czochralski (Cz) crystal growth is reported. The approach was to relate in a quantitative manner, using models based on first priniciples, crystal quality to operating conditions and geometric variables. The finite element method is used for all calculations.

  11. Inhibitory effect of chlorine and ultraviolet radiation on growth of Listeria monocytogenes in chicken breast and development of predictive growth models.

    PubMed

    Oh, S R; Kang, I; Oh, M H; Ha, S D

    2014-01-01

    The inhibitory effect of chlorine (50, 100, and 200 mg/kg) was investigated with and without UV radiation (300 mW·s/cm(2)) for the growth of Listeria monocytogenes in chicken breast meat. Using a polynomial model, predictive growth models were also developed as a function of chlorine concentration, UV exposure, and storage temperature (4, 10, and 15°C). A maximum L. monocytogenes reduction (0.8 log cfu, cfu/g) was obtained when combining chlorine at 200 mg/kg and UV at 300 mW·s/cm(2), and a maximum synergistic effect (0.4 log cfu/g) was observed when using chlorine at 100 mg/kg and UV at 300 mW·s/cm(2). Primary models developed for specific growth rate and lag time showed a good fitness (R(2) > 0.91), as determined by the reparameterized Gompertz equation. Secondary polynomial models were obtained using nonlinear regression analysis. The developed models were validated with mean square error, bias factor, and accuracy factor, which were 0.0003, 0.96, and 1.11, respectively, for specific growth rate and 7.69, 0.99, and 1.04, respectively, for lag time. The treatment of chlorine and UV did not change the color and texture of chicken breast after 7 d of storage at 4°C. As a result, the combination of chlorine at 100 mg/kg and UV at 300 mW·s/cm(2) appears to an effective method into inhibit L. monocytogenes growth in broiler carcasses with no negative effects on color and textural quality. Based on the validation results, the predictive models can be used to accurately predict L. monocytogenes growth in chicken breast.

  12. Growth characteristics and development of a predictive model for Bacillus cereus in fresh wet noodles with added ethanol and thiamine.

    PubMed

    Kim, Bo-Yeon; Lee, Ji-Young; Ha, Sang-Do

    2011-04-01

    Response surface methodology was used to determine growth characteristics and to develop a predictive model to describe specific growth rates of Bacillus cereus in wet noodles containing a combination of ethanol (0 to 2% [vol/wt]) and vitamin B(1) (0 to 2 g/liter). B. cereus F4810/72, which produces an emetic toxin, was used in this study. The noodles containing B. cereus were incubated at 10°C. The growth curves were fitted to the modified Gompertz equation using nonlinear regression, and the growth rate values from the curves were used to establish the predictive model using a response surface methodology quadratic polynomial equation as a function of concentrations of ethanol and vitamin B(1). The model was shown to fit the data very well (r(2) = 0.9505 to 0.9991) and could be used to accurately predict growth rates. The quadratic polynomial model was validated, and the predicted growth rate values were in good agreement with the experimental values. The polynomial model was found to be an appropriate secondary model for growth rate (GR) and lag time (LT) based on the correlation of determination (r(2) = 0.9899 for GR, 0.9782 for LT), bias factor (B(f) = 1.006 for GR, 0.992 for LT), and accuracy factor (A(f) = 1.024 for GR, 1.011 for LT). Thus, this model holds great promise for use in predicting the growth of B. cereus in fresh wet noodles using only the bacterial concentration, an important contribution to the manufacturing of safe products.

  13. A new application of Gompertz function in photohemolysis: the effect of temperature on red blood cell hemolysis photosensitized by protoporphyrin IX.

    PubMed

    Al-Akhras, M

    2006-08-01

    Photosensitization by protoporphyrin IX (PpIX) is accelerated at different irradiation temperatures, different dark incubation temperatures (Tinc) and different irradiation times. The applicability of Gompertz function to the fractional photohemolysis ratio, a and the rate of fractional photohemolysis, b is found to be the most appropriate model to fit the experimental data with minimum parameters and minimum errors. The reduction in Gompertz parameters, the fractional ratio values of a, and increase in the fractional rate values b, for 20 microM PpIX irradiated with black light at low irradiation temperature 5 degrees C and higher Tinc 37 degrees C was noticed. The parameter a has higher values at lower irradiation time and lower irradiation temperatures which indicates a longer photohemolysis process and longer t 50. Values of the parameter b were found to be strongly temperature-dependent, and always increase with increasing irradiation time and Tinc with lower values at lower irradiation time and lower Tinc. There are no significant changes in the lysis of RBCs process at irradiation temperatures equal to or higher than 35 degrees C. Similarly, no significant change on t50 at higher irradiation time at Tinc 24 and 37 degrees C. In conclusion, Gompertz analysis technique adapts to study the photohemolysis process at different conditions as a best-fit model.

  14. Fingering in Stochastic Growth Models

    PubMed Central

    Aristotelous, Andreas C.; Durrett, Richard

    2015-01-01

    Motivated by the widespread use of hybrid-discrete cellular automata in modeling cancer, two simple growth models are studied on the two dimensional lattice that incorporate a nutrient, assumed to be oxygen. In the first model the oxygen concentration u(x, t) is computed based on the geometry of the growing blob, while in the second one u(x, t) satisfies a reaction-diffusion equation. A threshold θ value exists such that cells give birth at rate β(u(x, t) − θ)+ and die at rate δ(θ − u(x, t)+. In the first model, a phase transition was found between growth as a solid blob and “fingering” at a threshold θc = 0.5, while in the second case fingering always occurs, i.e., θc = 0. PMID:26430353

  15. Development of a predictive model for growth of Listeria monocytogenes in a skim milk medium and validation studies in a range of dairy products.

    PubMed

    Murphy, P M; Rea, M C; Harrington, D

    1996-05-01

    A predictive model based on growth of Listeria monocytogenes in milk is described. The main aim of this work was to generate a predictive model in milk acidified with lactic acid to mimic conditions found in a range of dairy products. A complete factorial design was employed to determine the effects of pH (4.5-7.5), temperature (3-35 degrees C) and salt concentration (0-8%) on growth of the organism. There were 210 design points and growth curves were individually fitted for the Gompertz function using non-linear regression. Descriptors of the curves, such as lag phase duration (LPD), exponential growth rate (EGR) and generation time (GT) were calculated and polynomial models were developed relating these to pH, temperature and salt concentration. The selected cubic polynomial model gave acceptable predictive estimates of growth and was stable, i.e. predictions were repeatable over the range of environmental variables studied. The model was further tested to determine its capacity for predicting growth of listeria in a range of dairy foods and these validation studies confirm its usefulness as a rapid means of estimating growth of the organism under specified environmental conditions.

  16. Use of nonlinear models for describing scrotal circumference growth in Guzerat bulls raised under grazing conditions.

    PubMed

    Loaiza-Echeverri, A M; Bergmann, J A G; Toral, F L B; Osorio, J P; Carmo, A S; Mendonça, L F; Moustacas, V S; Henry, M

    2013-03-15

    The objective was to use various nonlinear models to describe scrotal circumference (SC) growth in Guzerat bulls on three farms in the state of Minas Gerais, Brazil. The nonlinear models were: Brody, Logistic, Gompertz, Richards, Von Bertalanffy, and Tanaka, where parameter A is the estimated testis size at maturity, B is the integration constant, k is a maturating index and, for the Richards and Tanaka models, m determines the inflection point. In Tanaka, A is an indefinite size of the testis, and B and k adjust the shape and inclination of the curve. A total of 7410 SC records were obtained every 3 months from 1034 bulls with ages varying between 2 and 69 months (<240 days of age = 159; 241-365 days = 451; 366-550 days = 1443; 551-730 days = 1705; and >731 days = 3652 SC measurements). Goodness of fit was evaluated by coefficients of determination (R(2)), error sum of squares, average prediction error (APE), and mean absolute deviation. The Richards model did not reach the convergence criterion. The R(2) were similar for all models (0.68-0.69). The error sum of squares was lowest for the Tanaka model. All models fit the SC data poorly in the early and late periods. Logistic was the model which best estimated SC in the early phase (based on APE and mean absolute deviation). The Tanaka and Logistic models had the lowest APE between 300 and 1600 days of age. The Logistic model was chosen for analysis of the environmental influence on parameters A and k. Based on absolute growth rate, SC increased from 0.019 cm/d, peaking at 0.025 cm/d between 318 and 435 days of age. Farm, year, and season of birth significantly affected size of adult SC and SC growth rate. An increase in SC adult size (parameter A) was accompanied by decreased SC growth rate (parameter k). In conclusion, SC growth in Guzerat bulls was characterized by an accelerated growth phase, followed by decreased growth; this was best represented by the Logistic model. The inflection point occurred at

  17. Growth kinetics of Listeria monocytogenes in broth and beef frankfurters--determination of lag phase duration and exponential growth rate under isothermal conditions.

    PubMed

    Huang, L

    2008-06-01

    The objective of this study was to develop a new kinetic model to describe the isothermal growth of microorganisms. The new model was tested with Listeria monocytogenes in tryptic soy broth and frankfurters, and compared with 2 commonly used models-Baranyi and modified Gompertz models. Bias factor (BF), accuracy factor (AF), and root mean square errors (RMSE) were used to evaluate the 3 models. Either in broth or in frankfurter samples, there were no significant differences in BF (approximately 1.0) and AF (1.02 to 1.04) among the 3 models. In broth, the mean RMSE of the new model was very close to that of the Baranyi model, but significantly lower than that of the modified Gompertz model. However, in frankfurters, there were no significant differences in the mean RMSE values among the 3 models. These results suggest that these models are equally capable of describing isothermal bacterial growth curves. Almost identical to the Baranyi model in the exponential and stationary phases, the new model has a more identifiable lag phase and also suggests that the bacteria population would increase exponentially until the population approaches to within 1 to 2 logs from the stationary phase. In general, there is no significant difference in the means of the lag phase duration and specific growth rate between the new and Baranyi models, but both are significantly lower than those determined from the modified Gompertz models. The model developed in this study is directly derived from the isothermal growth characteristics and is more accurate in describing the kinetics of bacterial growth in foods.

  18. Predictive modeling for growth of non- and cold-adapted Listeria monocytogenes on fresh-cut cantaloupe at different storage temperatures.

    PubMed

    Hong, Yoon-Ki; Yoon, Won Byong; Huang, Lihan; Yuk, Hyun-Gyun

    2014-06-01

    The aim of this study was to determine the growth kinetics of Listeria monocytogenes, with and without cold-adaption, on fresh-cut cantaloupe under different storage temperatures. Fresh-cut samples, spot inoculated with a 4-strain cocktail of L. monocytogenes (∼3.2 log CFU/g), were exposed to constant storage temperatures held at 10, 15, 20, 25, or 30 °C. All growth curves of L. monocytogenes were fitted to the Baranyi, modified Gompertz, and Huang models. Regardless of conditions under which cells grew, the time needed to reach 5 log CFU/g decreased with the elevated storage temperature. Experimental results showed that there were no significant differences (P > 0.05) in the maximum growth rate k (log CFU/g h(-1) ) and lag phase duration λ (h) between the cultures of L. monocytogenes with or without previous cold-adaption treatments. No distinct difference was observed in the growth pattern among 3 primary models at various storage temperatures. The growth curves of secondary modeling were fitted on an Arrhenius-type model for describing the relationship between k and temperature of the L. monocytogenes on fresh-cut cantaloupe from 10 to 30 °C. The root mean square error values of secondary models for non- and cold-adapted cells were 0.018, 0.021, and 0.024, and 0.039, 0.026, and 0.017 at the modified Gompertz, Baranyi, and Huang model, respectively, indicating that these 3 models presented the good statistical fit. This study may provide valuable information to predict the growth of L. monocytogenes on fresh-cut cantaloupes at different storage conditions. Listeriosis has occurred and increased along with the increased demand of fresh and fresh-cut fruits and vegetables. This study was conducted to predict the growth of non- and cold-adapted L. monocytogenes on fresh-cut cantaloupe at different temperature using mathematical model. These results can be helpful for risk assessments of L. monocytogenes in fresh-cut cantaloupe. This study provides valuable

  19. Modeling the Effect of Storage Temperatures on the Growth of Listeria monocytogenes on Ready-to-Eat Ham and Sausage.

    PubMed

    Luo, Ke; Hong, Sung-Sam; Oh, Deog-Hwan

    2015-09-01

    The aim of this study was to model the growth kinetics of Listeria monocytogenes on ready-to-eat ham and sausage at different temperatures (4 to 35°C). The observed data fitted well with four primary models (Baranyi, modified Gompertz, logistic, and Huang) with high coefficients of determination (R(2) > 0.98) at all measured temperatures. After the mean square error (0.009 to 0.051), bias factors (0.99 to1.06), and accuracy factors (1.01 to 1.09) were obtained in all models, the square root and the natural logarithm model were employed to describe the relation between temperature and specific growth rate (SGR) and lag time (LT) derived from the primary models. These models were validated against the independent data observed from additional experiments using the acceptable prediction zone method and the proportion of the standard error of prediction. All secondary models based on each of the four primary models were acceptable to describe the growth of the pathogen in the two samples. The validation results indicate that the optimal primary model for estimating the SGR was the Baranyi model, and the optimal primary model for estimating LT was the logistic model in ready-to-eat (RTE) ham. The Baranyi model was also the optimal model to estimate the SGR and LT in RTE sausage. These results could be used to standardize predictive models, which are commonly used to identify critical control points in hazard analysis and critical control point systems or for the quantitative microbial risk assessment to improve the food safety of RTE meat products.

  20. A unified approach to the Richards-model family for use in growth analyses: why we need only two model forms.

    PubMed

    Tjørve, Even; Tjørve, Kathleen M C

    2010-12-07

    This paper advances a unified approach to the modeling of sigmoid organismal growth. There are numerous studies on growth, and there have been several proposals and applications of candidate models. Still, a lack of interpretation of the parameter values persists and, consequently, differences in growth patterns have riddled this field. A candidate regression model as a tool should be able to assess and compare growth-curve shapes, systematically and precisely. The Richards models constitute a useful family of growth models that amongst a multitude of parameterizations, re-parameterizations and special cases, include familiar models such as the negative exponential, the logistic, the Bertalanffy and the Gompertz. We have reviewed and systemized this family of models. We demonstrate that two specific parameterizations (or re-parameterizations) of the Richards model are able to substitute, and thus to unify all other forms and models. This unified-Richards model (with its two forms) constitutes a powerful tool for an interpretation of important characteristics of observed growth patterns, namely, [I] maximum (relative) growth rate (i.e., slope at inflection), [II] age at maximum growth rate (i.e., time at inflection), [III] relative mass or length at maximum growth rate (i.e., relative value at an inflection), [IV] value at age zero (i.e., birth, hatching or germination), and [V] asymptotic value (i.e., adult weight or length). These five parameters can characterize uniquely any sigmoid-growth data. To date most studies only compare what is referred to as the "growth-rate constant" or simply "growth rate" (k). This parameter can be interpreted as neither relative nor actual growth rate, but only as a parameter that affects the slope at inflection. We fitted the unified-Richards and five other candidate models to six artificial data sets, generated from the same models, and made a comparison based on the corrected Akaike's Information Criterion (AICc). The outcome may

  1. Microbial modeling of Alicyclobacillus acidoterrestris CRA 7152 growth in orange juice with nisin added.

    PubMed

    Peña, Wilmer Edgard Luera; de Massaguer, Pilar Rodriguez

    2006-08-01

    The adaptation time of Alicyclobacillus acidoterrestris CRA 7152 in orange juice was determined as a response to pH (3 to 5.8), temperature (20 to 54 degrees C), soluble solids concentration ((o)Brix; 11 to 19 (o)Brix), and nisin concentration (0 to 70 IU/ ml) effects. A four-factor central composite rotational design was used. Viable microorganisms were enumerated by plating on K medium (pH 3.7). Two primary models were used to represent growth and adaptation time. A second-order polynomial model was applied to analyze the effects of factors. Results showed that the Baranyi and Roberts model was better than the modified Gompertz model, considering the determination coefficient (R2) for experimental data description. Inhibition of bacteria can be obtained through several studied combinations for at least 47 days of storage. The shortest period of adaptation was observed between 37 to 45 degrees C, with pHs between 4 and 5, yet the longest periods of adaptation could be obtained around 20 degrees C with pHs close to 3.0. Statistical analysis of the quadratic model showed that the adaptation time increased as temperature or pH decreased, and as nisin concentration or soluble solids increased. The model showed that adaptation time has a minimum value for juice without nisin added, with 13.5% soluble solids, pH 5.0, and incubated at 43.8 degrees C. The statistical parameters that validated this model were an R2 of 0.816, a bias factor of 0.96, and an accuracy factor of 1.14. Manipulation of more than one factor, as well as the use of an antimicrobial agent, can be an alternative to preventing the development of A. acidoterrestris in orange juice, thus contributing to increased orange juice shelf life.

  2. A Vernacular for Linear Latent Growth Models

    ERIC Educational Resources Information Center

    Hancock, Gregory R.; Choi, Jaehwa

    2006-01-01

    In its most basic form, latent growth modeling (latent curve analysis) allows an assessment of individuals' change in a measured variable X over time. For simple linear models, as with other growth models, parameter estimates associated with the a construct (amount of X at a chosen temporal reference point) and b construct (growth in X per unit…

  3. Repopulation Kinetics and the Linear-Quadratic Model

    NASA Astrophysics Data System (ADS)

    O'Rourke, S. F. C.; McAneney, H.; Starrett, C.; O'Sullivan, J. M.

    2009-08-01

    The standard Linear-Quadratic (LQ) survival model for radiotherapy is used to investigate different schedules of radiation treatment planning for advanced head and neck cancer. We explore how these treament protocols may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al. [1], which was concerned with the case of exponential repopulation between treatments. Treatment schedules investigated include standarized and accelerated fractionation. Calculations based on the present work show, that even with growth laws scaled to ensure that the repopulation kinetics for advanced head and neck cancer are comparable, considerable variation in the survival fraction to orders of magnitude emerged. Calculations show that application of the Gompertz model results in a significantly poorer prognosis for tumour eradication. Gaps in treatment also highlight the differences in the LQ model with the effect of repopulation kinetics included.

  4. Is cancer a pure growth curve or does it follow a kinetics of dynamical structural transformation?

    PubMed

    González, Maraelys Morales; Joa, Javier Antonio González; Cabrales, Luis Enrique Bergues; Pupo, Ana Elisa Bergues; Schneider, Baruch; Kondakci, Suleyman; Ciria, Héctor Manuel Camué; Reyes, Juan Bory; Jarque, Manuel Verdecia; Mateus, Miguel Angel O'Farril; González, Tamara Rubio; Brooks, Soraida Candida Acosta; Cáceres, José Luis Hernández; González, Gustavo Victoriano Sierra

    2017-03-07

    Unperturbed tumor growth kinetics is one of the more studied cancer topics; however, it is poorly understood. Mathematical modeling is a useful tool to elucidate new mechanisms involved in tumor growth kinetics, which can be relevant to understand cancer genesis and select the most suitable treatment. The classical Kolmogorov-Johnson-Mehl-Avrami as well as the modified Kolmogorov-Johnson-Mehl-Avrami models to describe unperturbed fibrosarcoma Sa-37 tumor growth are used and compared with the Gompertz modified and Logistic models. Viable tumor cells (1×10(5)) are inoculated to 28 BALB/c male mice. Modified Gompertz, Logistic, Kolmogorov-Johnson-Mehl-Avrami classical and modified Kolmogorov-Johnson-Mehl-Avrami models fit well to the experimental data and agree with one another. A jump in the time behaviors of the instantaneous slopes of classical and modified Kolmogorov-Johnson-Mehl-Avrami models and high values of these instantaneous slopes at very early stages of tumor growth kinetics are observed. The modified Kolmogorov-Johnson-Mehl-Avrami equation can be used to describe unperturbed fibrosarcoma Sa-37 tumor growth. It reveals that diffusion-controlled nucleation/growth and impingement mechanisms are involved in tumor growth kinetics. On the other hand, tumor development kinetics reveals dynamical structural transformations rather than a pure growth curve. Tumor fractal property prevails during entire TGK.

  5. Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model

    NASA Astrophysics Data System (ADS)

    Cabella, Brenno Caetano Troca; Ribeiro, Fabiano; Martinez, Alexandre Souto

    2012-02-01

    We consider a generalized two-species population dynamic model and analytically solve it for the amensalism and commensalism ecological interactions. These two-species models can be simplified to a one-species model with a time dependent extrinsic growth factor. With a one-species model with an effective carrying capacity one is able to retrieve the steady state solutions of the previous one-species model. The equivalence obtained between the effective carrying capacity and the extrinsic growth factor is complete only for a particular case, the Gompertz model. Here we unveil important aspects of sigmoid growth curves, which are relevant to growth processes and population dynamics.

  6. Mathematical modeling of Microcystis aeruginosa growth and [D-Leu(1)] microcystin-LR production in culture media at different temperatures.

    PubMed

    Melina Celeste, Crettaz Minaglia; Lorena, Rosso; Jorge Oswaldo, Aranda; Sandro, Goñi; Daniela, Sedan; Dario, Andrinolo; Leda, Giannuzzi

    2017-07-01

    The effect of temperature (26°C, 28°C, 30°C and 35°C) on the growth of native CAAT-3-2005 Microcystis aeruginosa and the production of Chlorophyll-a (Chl-a) and Microcystin-LR (MC-LR) were examined through laboratory studies. Kinetic parameters such as specific growth rate (μ), lag phase duration (LPD) and maximum population density (MPD) were determined by fitting the modified Gompertz equation to the M. aeruginosa strain cell count (cellsmL(-1)). A 4.8-fold increase in μ values and a 10.8-fold decrease in the LPD values were found for M. aeruginosa growth when the temperature changed from 15°C to 35°C. The activation energy of the specific growth rate (Eμ) and of the adaptation rate (E1/LPD) were significantly correlated (R(2)=0.86). The cardinal temperatures estimated by the modified Ratkowsky model were minimum temperature=8.58±2.34°C, maximum temperature=45.04±1.35°C and optimum temperature=33.39±0.55°C. Maximum MC-LR production decreased 9.5-fold when the temperature was increased from 26°C to 35°C. The maximum production values were obtained at 26°C and the maximum depletion rate of intracellular MC-LR was observed at 30-35°C. The MC-LR cell quota was higher at 26 and 28°C (83 and 80fgcell(-1), respectively) and the MC-LR Chl-a quota was similar at all the different temperatures (0.5-1.5fgng(-1)). The Gompertz equation and dynamic model were found to be the most appropriate approaches to calculate M. aeruginosa growth and production of MC-LR, respectively. Given that toxin production decreased with increasing temperatures but growth increased, this study demonstrates that growth and toxin production processes are uncoupled in M. aeruginosa. These data and models may be useful to predict M. aeruginosa bloom formation in the environment. Copyright © 2017 Elsevier B.V. All rights reserved.

  7. Capital Growth Paths of the Neoclassical Growth Model

    PubMed Central

    Takahashi, Taro

    2012-01-01

    This paper derives the first-order approximated paths of both types of capital in the two-capital neoclassical growth model. The derived capital growth paths reveal that the short-run growth effect of capital injection differs considerably depending on which type of capital is enhanced. This result demonstrates the importance of well-targeted capital enhancement programs such as public sector projects and foreign aid. PMID:23185344

  8. Latent Growth Modeling for Logistic Response Functions

    ERIC Educational Resources Information Center

    Choi, Jaehwa; Harring, Jeffrey R.; Hancock, Gregory R.

    2009-01-01

    Throughout much of the social and behavioral sciences, latent growth modeling (latent curve analysis) has become an important tool for understanding individuals' longitudinal change. Although nonlinear variations of latent growth models appear in the methodological and applied literature, a notable exclusion is the treatment of growth following…

  9. Latent Growth Modeling for Logistic Response Functions

    ERIC Educational Resources Information Center

    Choi, Jaehwa; Harring, Jeffrey R.; Hancock, Gregory R.

    2009-01-01

    Throughout much of the social and behavioral sciences, latent growth modeling (latent curve analysis) has become an important tool for understanding individuals' longitudinal change. Although nonlinear variations of latent growth models appear in the methodological and applied literature, a notable exclusion is the treatment of growth following…

  10. Modelling the growth of feather crystals

    SciTech Connect

    Wood, H.J.; Hunt, J.D.; Evans, P.V.

    1997-02-01

    An existing numerical model of dendritic growth has been adapted to model the growth of twinned columnar dendrites (feather crystals) in a binary aluminium alloy, Examination of the effect of dendrite tip angle on growth has led to an hypothesis regarding the stability of a pointed tip morphology in these crystals.

  11. A Growth Model for Multilevel Ordinal Data

    ERIC Educational Resources Information Center

    Segawa, Eisuke

    2005-01-01

    Multi-indicator growth models were formulated as special three-level hierarchical generalized linear models to analyze growth of a trait latent variable measured by ordinal items. Items are nested within a time-point, and time-points are nested within subject. These models are special because they include factor analytic structure. This model can…

  12. A Simulation To Model Exponential Growth.

    ERIC Educational Resources Information Center

    Appelbaum, Elizabeth Berman

    2000-01-01

    Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)

  13. A Simulation To Model Exponential Growth.

    ERIC Educational Resources Information Center

    Appelbaum, Elizabeth Berman

    2000-01-01

    Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)

  14. Assessment of models for anaerobic biodegradation of a model bioplastic: Poly(hydroxybutyrate-co-hydroxyvalerate).

    PubMed

    Ryan, Cecily A; Billington, Sarah L; Criddle, Craig S

    2017-03-01

    Kinetic models of anaerobic digestion (AD) are widely applied to soluble and particulate substrates, but have not been systematically evaluated for bioplastics. Here, five models are evaluated to determine their suitability for modeling of anaerobic biodegradation of the bioplastic poly(hydroxybutyrate-co-hydroxyvalerate) (PHBV): (1) first-order kinetics with and without a lag phase, (2) two-step first-order, (3) Monod (4) Contois, and (5) Gompertz. Three models that couple biomass growth with substrate hydrolysis (Monod, Contois, and Gompertz) gave the best overall fits for the data (R(2)>0.98), with reasonable estimates of ultimate CH4 production. The particle size limits of these models were then evaluated. Below a particle size of 0.8mm, rates of hydrolysis and acetogenesis exceeded rates of methanogenesis with accumulation of intermediates leading to a temporary inhibition of CH4 production. Based on model fit and simplicity, the Gompertz model is recommended for applications in which particle size is greater than 0.8mm. Copyright © 2016 Elsevier Ltd. All rights reserved.

  15. A novel measurement method of microorganism growth by tunable diode laser-absorption spectroscopy

    NASA Astrophysics Data System (ADS)

    Xiang, Jindong; Shao, Jie; Ying, Chaofu; Wang, Liming; Guo, Jie

    2015-05-01

    The objective of this work was to attain essential parameters by using a Gompertz model that employed a new approach of wavelength modulation spectroscopy (WMS) to describe the microorganism growth. The measurement method of WMS introduces noninvasive technique instead of complicated invasive microorganism operation analysis and quickly obtains the accurate real-time measurement results. By using the WMS measurement, the specific growth curve of microorganism growth clearly displayed every three minute, which has characteristics of high sensitivity, high spectral resolution, fast time response and overcomes the randomness and error operation of traditional analysis methods. The measurement value of BF and AF in the range of 1.008 to 1.043 and the lower MSE showed that Gompertz model can fit the data well and be capable of describing bacteria growth rate and lag time. The results of experiment data suggested that the specific growth rate of microorganism depends on the temperature. With the increase of temperature ranging from 25 °C to 42 °C , the lag time of bacteria growth has been shortened. And the suitable temperature of bacteria growth is about 37 °C . Judging from the growth rate of microorganisms, we can identify the microbial species, not only to improve the precision and efficiency, but also to provides a rapidly sensitive way for microbial detection. The lag time of microorganism growth also provides a great application prospect for shelf life of the food safety.

  16. [The issue of feasibility of a general theory of aging I. Generalized Gompertz-Makeham Law].

    PubMed

    Golubev, A G

    2009-01-01

    Aging and longevity are interrelated so intimately that they should be treated with a unified theory. The longevity of every single cohort of living beings is determined by the rate of their dying-out. In most cases, mortality rates increase in accelerated fashions to reach values making the bulk of each finite cohort completely exhausted within a relatively narrow time interval shifted to the end of its resulting lifespan. Among simple functions with biologically interpretable parameters, the best fit to this pattern is demonstrated by the Gompertz-Makeham Law (GML): mu = C + lambda x e(gamma x t). A generalized form of GML mu = C(t) + lambda x e(-E(t)) is suggested and interpreted as a law of the dependency of mortality upon vitality rather than on age. It is reduced to the conventional GML when E depends linearly on t, that the age is an observable correlate of unobservable vitality. C(t) captures the inherently irresistible causes of death. The generalized GML can accommodate any mode of age-dependent functional decline, which should be placed into the exponent index to be translated into changes in mortality rate, and is compatible with any sort of cohort heterogeneity, which may be captured by substituting of GML parameters with relevant distributions or by combining of several generalized GML models. The generalized GML is suggested to result from the origin of life from the chemical world, which was associated with the transition of the role of the main variable in the Arrhenius equation k = A x exp[-Ea/(R x T)] for the dependency of chemical disintegration on temperature from T to Ea upon the transition from molecular to multimolecular prebiotic entities. Thus, the generalized GML is not a result of biological evolution but is a sort of chemical legacy of biology, which makes an important condition for life to evolve.

  17. A MODEL OF GROWTH AND GROWTH CONTROL IN MATHEMATICAL TERMS

    PubMed Central

    Weiss, Paul; Kavanau, J. Lee

    1957-01-01

    A practicable model of the growth process, which gives better definition to the problem of growth and growth regulation and greater precision to related experimental work than do earlier models, is developed on the basis of the following assumptions: "Growth" is the net balance of mass produced and retained over mass destroyed and otherwise lost, implying continual metabolic degradation and replacement. Terminal size represents stationary equilibrium between incremental and decremental components. The mass of an organic system consists of two functionally different components,—generative and differentiated. Generative mass increases by the catalytic action of key compounds ("templates") characteristic of each cell type. Each cell also produces specific freely diffusible compounds antagonistic to these templates ("antitemplates"). Growth regulation occurs automatically by a negative "feedback" in which increasing numbers of antitemplates progressively block the corresponding templates. Differential equations expressing these interrelationships are formulated, integrated, and the solutions evaluated for the case of chick growth. These specific solutions lead to descriptions of the normal growth of a biological system which are in good agreement with known facts, and to predictions of the course of automatic growth regulations after experimental or pathological disturbances which reproduce adequately biological observations in this domain. PMID:13463267

  18. Testing mechanistic models of growth in insects.

    PubMed

    Maino, James L; Kearney, Michael R

    2015-11-22

    Insects are typified by their small size, large numbers, impressive reproductive output and rapid growth. However, insect growth is not simply rapid; rather, insects follow a qualitatively distinct trajectory to many other animals. Here we present a mechanistic growth model for insects and show that increasing specific assimilation during the growth phase can explain the near-exponential growth trajectory of insects. The presented model is tested against growth data on 50 insects, and compared against other mechanistic growth models. Unlike the other mechanistic models, our growth model predicts energy reserves per biomass to increase with age, which implies a higher production efficiency and energy density of biomass in later instars. These predictions are tested against data compiled from the literature whereby it is confirmed that insects increase their production efficiency (by 24 percentage points) and energy density (by 4 J mg(-1)) between hatching and the attainment of full size. The model suggests that insects achieve greater production efficiencies and enhanced growth rates by increasing specific assimilation and increasing energy reserves per biomass, which are less costly to maintain than structural biomass. Our findings illustrate how the explanatory and predictive power of mechanistic growth models comes from their grounding in underlying biological processes.

  19. Testing mechanistic models of growth in insects

    PubMed Central

    Maino, James L.; Kearney, Michael R.

    2015-01-01

    Insects are typified by their small size, large numbers, impressive reproductive output and rapid growth. However, insect growth is not simply rapid; rather, insects follow a qualitatively distinct trajectory to many other animals. Here we present a mechanistic growth model for insects and show that increasing specific assimilation during the growth phase can explain the near-exponential growth trajectory of insects. The presented model is tested against growth data on 50 insects, and compared against other mechanistic growth models. Unlike the other mechanistic models, our growth model predicts energy reserves per biomass to increase with age, which implies a higher production efficiency and energy density of biomass in later instars. These predictions are tested against data compiled from the literature whereby it is confirmed that insects increase their production efficiency (by 24 percentage points) and energy density (by 4 J mg−1) between hatching and the attainment of full size. The model suggests that insects achieve greater production efficiencies and enhanced growth rates by increasing specific assimilation and increasing energy reserves per biomass, which are less costly to maintain than structural biomass. Our findings illustrate how the explanatory and predictive power of mechanistic growth models comes from their grounding in underlying biological processes. PMID:26609084

  20. Comparative evaluation of mathematical functions to describe growth and efficiency of phosphorus utilization in growing pigs.

    PubMed

    Kebreab, E; Schulin-Zeuthen, M; Lopez, S; Soler, J; Dias, R S; de Lange, C F M; France, J

    2007-10-01

    Success of pig production depends on maximizing return over feed costs and addressing potential nutrient pollution to the environment. Mathematical modeling has been used to describe many important aspects of inputs and outputs of pork production. This study was undertaken to compare 4 mathematical functions for the best fit in terms of describing specific data sets on pig growth and, in a separate experiment, to compare these 4 functions for describing of P utilization for growth. Two data sets with growth data were used to conduct growth analysis and another data set was used for P efficiency analysis. All data sets were constructed from independent trials that measured BW, age, and intake. Four growth functions representing diminishing returns (monomolecular), sigmoidal with a fixed point of inflection (Gompertz), and sigmoidal with a variable point of inflection (Richards and von Bertalanffy) were used. Meta-analysis of the data was conducted to identify the most appropriate functions for growth and P utilization. Based on Bayesian information criteria, the Richards equation described the BW vs. age data best. The additional parameter of the Richards equation was necessary because the data required a lower point of inflection (138 d) than the Gompertz, with a fixed point of inflexion at 1/e times the final BW (189 d), could accommodate. Lack of flexibility in the Gompertz equation was a limitation to accurate prediction. The monomolecular equation was best at determining efficiencies of P utilization for BW gain compared with the sigmoidal functions. The parameter estimate for the rate constant in all functions decreased as available P intake increased. Average efficiencies during different stages of growth were calculated and offer insight into targeting stages where high feed (nutrient) input is required and when adjustments are needed to accommodate the loss of efficiency and the reduction of potential pollution problems. It is recommended that the Richards

  1. A continuous growth model for plant tissue

    NASA Astrophysics Data System (ADS)

    Bozorg, Behruz; Krupinski, Pawel; Jönsson, Henrik

    2016-12-01

    Morphogenesis in plants and animals involves large irreversible deformations. In plants, the response of the cell wall material to internal and external forces is determined by its mechanical properties. An appropriate model for plant tissue growth must include key features such as anisotropic and heterogeneous elasticity and cell dependent evaluation of mechanical variables such as turgor pressure, stress and strain. In addition, a growth model needs to cope with cell divisions as a necessary part of the growth process. Here we develop such a growth model, which is capable of employing not only mechanical signals but also morphogen signals for regulating growth. The model is based on a continuous equation for updating the resting configuration of the tissue. Simultaneously, material properties can be updated at a different time scale. We test the stability of our model by measuring convergence of growth results for a tissue under the same mechanical and material conditions but with different spatial discretization. The model is able to maintain a strain field in the tissue during re-meshing, which is of particular importance for modeling cell division. We confirm the accuracy of our estimations in two and three-dimensional simulations, and show that residual stresses are less prominent if strain or stress is included as input signal to growth. The approach results in a model implementation that can be used to compare different growth hypotheses, while keeping residual stresses and other mechanical variables updated and available for feeding back to the growth and material properties.

  2. Growth and mortality of larval Myctophum affine (Myctophidae, Teleostei).

    PubMed

    Namiki, C; Katsuragawa, M; Zani-Teixeira, M L

    2015-04-01

    The growth and mortality rates of Myctophum affine larvae were analysed based on samples collected during the austral summer and winter of 2002 from south-eastern Brazilian waters. The larvae ranged in size from 2·75 to 14·00 mm standard length (L(S)). Daily increment counts from 82 sagittal otoliths showed that the age of M. affine ranged from 2 to 28 days. Three models were applied to estimate the growth rate: linear regression, exponential model and Laird-Gompertz model. The exponential model best fitted the data, and L(0) values from exponential and Laird-Gompertz models were close to the smallest larva reported in the literature (c. 2·5 mm L(S)). The average growth rate (0·33 mm day(-1)) was intermediate among lanternfishes. The mortality rate (12%) during the larval period was below average compared with other marine fish species but similar to some epipelagic fishes that occur in the area.

  3. Mathematical models for Isoptera (Insecta) mound growth.

    PubMed

    Buschini, M L T; Abuabara, M A P; Petrere-Jr, Miguel

    2008-08-01

    In this research we proposed two mathematical models for Isoptera mound growth derived from the Von Bertalanffy growth curve, one appropriated for Nasutitermes coxipoensis, and a more general formulation. The mean height and the mean diameter of ten small colonies were measured each month for twelve months, from April, 1995 to April, 1996. Through these data, the monthly volumes were calculated for each of them. Then the growth in height and in volume was estimated and the models proposed.

  4. Multiple mild heat-shocks decrease the Gompertz component of mortality in Caenorhabditis elegans.

    PubMed

    Wu, Deqing; Cypser, James R; Yashin, Anatoli I; Johnson, Thomas E

    2009-09-01

    Exposure to mild heat-stress (heat-shock) can significantly increase the life expectancy of the nematode Caenorhabditis elegans. A single heat-shock early in life extends longevity by 20% or more and affects life-long mortality by decreasing initial mortality only; the rate of increase in subsequent mortality (Gompertz component) is unchanged. Repeated mild heat-shocks throughout life have a larger effect on life span than does a single heat-shock early in life. Here, we ask how multiple heat-shocks affect the mortality trajectory in nematodes and find increases of life expectancy of close to 50% and of maximum longevity as well. We examined mortality using large numbers of animals and found that multiple heat-shocks not only decrease initial mortality, but also slow the Gompertz rate of increase in mortality. Thus, multiple heat-shocks have anti-aging hormetic effects and represent an effective approach for modulating aging.

  5. Modeling tissue growth within nonwoven scaffolds pores.

    PubMed

    Edwards, Sharon L; Church, Jeffrey S; Alexander, David L J; Russell, Stephen J; Ingham, Eileen; Ramshaw, John A M; Werkmeister, Jerome A

    2011-02-01

    In this study we present a novel approach for predicting tissue growth within the pores of fibrous tissue engineering scaffolds. Thin nonwoven polyethylene terephthalate scaffolds were prepared to characterize tissue growth within scaffold pores, by mouse NR6 fibroblast cells. On the basis of measurements of tissue lengths at fiber crossovers and along fiber segments, mathematical models were determined during the proliferative phase of cell growth. Tissue growth at fiber crossovers decreased with increasing interfiber angle, with exponential relationships determined on day 6 and 10 of culture. Analysis of tissue growth along fiber segments determined two growth profiles, one with enhanced growth as a result of increased tissue lengths near the fiber crossover, achieved in the latter stage of culture. Derived mathematical models were used in the development of a software program to visualize predicted tissue growth within a pore. This study identifies key pore parameters that contribute toward tissue growth, and suggests models for predicting this growth, based on fibroblast cells. Such models may be used in aiding scaffold design, for optimum pore infiltration during the tissue engineering process.

  6. Evaluation of mathematical models to describe testicular growth in Blackbelly ram lambs.

    PubMed

    Jiménez-Severiano, H; Reynoso, M L; Román-Ponce, S I; Robledo, V M

    2010-10-15

    The primary objective was to compare various mathematical models to describe scrotal circumference (SC) and paired testis volume development in Blackbelly ram lambs. The study was conducted in the state of Querétaro, México (20° 43' N, 100° 15' W). Spring-born Blackbelly ram lambs (n = 41) were housed outdoors and fed alfalfa hay and concentrate. Body weight, SC, and testis length, diameter, and volume were recorded every 2 wk from 24 to 172 d of age (June 18 to November 3). The following mathematical functions were used to model SC-age and testis volume-age relationship: Von Bertalanffy, Brody, Gompertz, Logistic, and Richards. The suitability of the models was evaluated based on parameter values and standard errors, residual mean square, the coefficient of determination (R(2)), and the average prediction error (APE). All models, except for Brody's, had good fit to SC (R(2) > 0.98) and testis volume (R(2) > 0.95), and produced similar growth curves in the range of ages studied. The logistic model predicted SC at maturity quite well, 33.6 ± 0.6 cm as compared with 33.9 ± 0.5 cm observed in adult animals; all models had APE's smaller than ± 7% between 56 and 168 d of age. The Bertalanffy model predicted testis volume at maturity quite well, 513 ± 22 cm(3) as compared with 488 ± 20 cm(3) calculated for adult animals. The logistic model had a good fit to testis volume during the period of study, but underestimated the volume at maturity by 28%. All models, except for Brody's, had APE's smaller than ± 14% between 98 and 168 d of age. The logistic and Bertalanffy models predicted the inflection point for SC at 83 and 59 d of age, and testis volume at 116 and 109 d of age, respectively. In conclusion, all models, except for Brody's, had good fit to actual SC and testis volume data in the range of age evaluated, whereas the logistic and Bertalanffy's models made the best predictions for adult SC and testis volume, respectively.

  7. Design issues for population growth models

    PubMed Central

    López Fidalgo, J.; Ortiz Rodríguez, I.M.

    2010-01-01

    We briefly review and discuss design issues for population growth and decline models. We then use a flexible growth and decline model as an illustrative example and apply optimal design theory to find optimal sampling times for estimating model parameters, specific parameters and interesting functions of the model parameters for the model with two real applications. Robustness properties of the optimal designs are investigated when nominal values or the model is mis-specified, and also under a different optimality criterion. To facilitate use of optimal design ideas in practice, we also introduce a website for generating a variety of optimal designs for popular models from different disciplines. PMID:21647244

  8. A multivariate Bayesian model for embryonic growth.

    PubMed

    Willemsen, Sten P; Eilers, Paul H C; Steegers-Theunissen, Régine P M; Lesaffre, Emmanuel

    2015-04-15

    Most longitudinal growth curve models evaluate the evolution of each of the anthropometric measurements separately. When applied to a 'reference population', this exercise leads to univariate reference curves against which new individuals can be evaluated. However, growth should be evaluated in totality, that is, by evaluating all body characteristics jointly. Recently, Cole et al. suggested the Superimposition by Translation and Rotation (SITAR) model, which expresses individual growth curves by three subject-specific parameters indicating their deviation from a flexible overall growth curve. This model allows the characterization of normal growth in a flexible though compact manner. In this paper, we generalize the SITAR model in a Bayesian way to multiple dimensions. The multivariate SITAR model allows us to create multivariate reference regions, which is advantageous for prediction. The usefulness of the model is illustrated on longitudinal measurements of embryonic growth obtained in the first semester of pregnancy, collected in the ongoing Rotterdam Predict study. Further, we demonstrate how the model can be used to find determinants of embryonic growth.

  9. Image based modeling of tumor growth.

    PubMed

    Meghdadi, N; Soltani, M; Niroomand-Oscuii, H; Ghalichi, F

    2016-09-01

    Tumors are a main cause of morbidity and mortality worldwide. Despite the efforts of the clinical and research communities, little has been achieved in the past decades in terms of improving the treatment of aggressive tumors. Understanding the underlying mechanism of tumor growth and evaluating the effects of different therapies are valuable steps in predicting the survival time and improving the patients' quality of life. Several studies have been devoted to tumor growth modeling at different levels to improve the clinical outcome by predicting the results of specific treatments. Recent studies have proposed patient-specific models using clinical data usually obtained from clinical images and evaluating the effects of various therapies. The aim of this review is to highlight the imaging role in tumor growth modeling and provide a worthwhile reference for biomedical and mathematical researchers with respect to tumor modeling using the clinical data to develop personalized models of tumor growth and evaluating the effect of different therapies.

  10. A Practitioner's Guide to Growth Models

    ERIC Educational Resources Information Center

    Castellano, Katherine E.; Ho, Andrew D.

    2013-01-01

    This "Practitioner's Guide to Growth Models," commissioned by the Technical Issues in Large-Scale Assessment (TILSA) and Accountability Systems & Reporting (ASR), collaboratives of the "Council of Chief State School Officers," describes different ways to calculate student academic growth and to make judgments about the…

  11. A Practitioner's Guide to Growth Models

    ERIC Educational Resources Information Center

    Castellano, Katherine E.; Ho, Andrew D.

    2013-01-01

    This "Practitioner's Guide to Growth Models," commissioned by the Technical Issues in Large-Scale Assessment (TILSA) and Accountability Systems & Reporting (ASR), collaboratives of the "Council of Chief State School Officers," describes different ways to calculate student academic growth and to make judgments about the…

  12. Adjusting STEMS growth model for Wisconsin forests.

    Treesearch

    Margaret R. Holdaway

    1985-01-01

    Describes a simple procedure for adjusting growth in the STEMS regional tree growth model to compensate for subregional differences. Coefficients are reported to adjust Lake States STEMS to the forests of Northern and Central Wisconsin--an area of essentially uniform climate and similar broad physiographic features. Errors are presented for various combinations of...

  13. Growth model of Escherichia coli O157:H7 at various storage temperatures on kale treated by thermosonication combined with slightly acidic electrolyzed water.

    PubMed

    Mansur, Ahmad Rois; Wang, Jun; Park, Myeong-Su; Oh, Deog-Hwan

    2014-01-01

    This study was conducted to investigate the disinfection efficacy of hurdle treatments (thermosonication plus slightly acidic electrolyzed water [SAcEW]) and to develop a model for describing the effect of storage temperatures (4, 10, 15, 20, 25, 30, and 35°C) on the growth of Escherichia coli O157:H7 on fresh-cut kale treated with or without (control) thermosonication combined with SAcEW. The hurdle treatments of thermosonication plus SAcEW had strong bactericidal effects against E. coli O157:H7 on kale, with approximately 3.3-log reductions. A modified Gompertz model was used to describe growth parameters such as specific growth rate (SGR) and lag time (LT) as a function of storage temperature, with high coefficients of determination (R(2) > 0.98). SGR increased and LT declined with rising temperatures in all samples. A significant difference was found between the SGR values obtained from treated and untreated samples. Secondary models were established for SGR and LT to evaluate the effects of storage temperature on the growth kinetics of E. coli O157:H7 in treated and untreated kale. Statistical evaluation was carried out to validate the performance of the developed models, based on the additional experimental data not used for the model development. The validation step indicated that the overall predictions were inside the acceptable prediction zone and had lower standard errors, indicating that this new growth model can be used to assess the risk of E. coli O157:H7 contamination on kale.

  14. Model-based characterisation of growth performance and l-lactic acid production with high optical purity by thermophilic Bacillus coagulans in a lignin-supplemented mixed substrate medium.

    PubMed

    Glaser, Robert; Venus, Joachim

    2017-02-08

    Three Bacillus coagulans strains were characterised in terms of their ability to grow in lignin-containing fermentation media and to consume the lignocellulose-related sugars glucose, xylose, and arabinose. An optical-density high-throughput screening was used for precharacterisation by means of different mathematical models for comparison (Logistic, Gompertz, Baranyi, Richards & Stannard, and Schnute). The growth response was characterised by the maximum growth rate and lag time. For a comparison of the screening and fermentation results, an unstructured mathematical model was proposed to characterise the lactate production, bacterial growth and substrate consumption. The growth model was then applied to fermentation procedures using wheat straw hydrolysates. The results indicated that the unstructured growth model can be used to evaluate lactate producing fermentation. Under the experimental fermentation conditions, one strain showed the ability to tolerate a high lignin concentration (2.5g/L) but lacked the capacity for sufficient pentose uptake. The lactate yield of the strains that were able to consume all sugar fractions of glucose, xylose and arabinose was ∼83.4%. A photometric measurement at 280nm revealed a dynamic change in alkali-lignin concentrations during lactate producing fermentation. A test of decolourisation of vanillin, ferulic acid, and alkali-lignin samples also showed the decolourisation performance of the B. coagulans strains under study.

  15. Diameter Growth Models for Inventory Applications

    Treesearch

    Ronald E. McRoberts; Christopher W. Woodall; Veronica C. Lessard; Margaret R. Holdaway

    2002-01-01

    Distant-independent, individual-tree, diametar growth models were constructed to update information for forest inventory plots measured in previous years. The models are nonlinear in the parameters and were calibrated weighted nonlinear least squares techniques and forest inventory plot data. Analyses of residuals indicated that model predictions compare favorably to...

  16. Cluster growth modeling of plateau erosion

    NASA Technical Reports Server (NTRS)

    Stark, Colin P.

    1994-01-01

    The pattern of erosion of a plateau along an escarpment may be modeled usng cluster growth techniques, recently popularized in models of drainage network evolution. If erosion on the scarp takes place in discrete events at rates subject to local substrate strength, the whole range of behavior is described by a combination of three cluster growth mechanisms: invasion percolation, Eden growth and diffusion-limited aggregation (DLA). These model the relative importance of preexisting substrate strength, background weathering, and seepage weathering and erosion respectively. The rate of seepage processes is determined by the efflux of groundwater at the plateau margin, which in turn is determined by the pressure field in the plateau aquifer. If this process acted alone, it would produce erosion patterns in the form of Laplacian fractals, with groundwater recharge from a distant source, or Poissionian fractals, with groundwater recharge uniform over the plateau. DLA is used to mimic the Laplacian or Poissonian potential field and the corresponding seepage growth process. The scaling structure of clusters grown by pure DLA, invasion percolation, or Eden growth is well known; this study presents a model which combines all three growth mechanisms for the first time. Mixed growth processes create clusters with different scaling properties and morphologies over distinct length scale ranges, and this is demonstrable in natural examples of plateau erosion.

  17. Developmental Stages in Dynamic Plant Growth Models

    NASA Astrophysics Data System (ADS)

    Maclean, Heather; Dochain, Denis; Waters, Geoff; Stasiak, Michael; Dixon, Mike; Van Der Straeten, Dominique

    2011-09-01

    During the growth of red beet plants in a closed environment plant growth chamber, a change in metabolism was observed (decreasing photosynthetic quotient) which was not predicted by a previously developed simple dynamic model of photosynthesis and respiration reactions. The incorporation of developmental stages into the model allowed for the representation of this change in metabolism without adding unnecessary complexity. Developmental stages were implemented by dividing the model into two successive sub-models with independent yields. The transition between the phases was detected based on online measurements. Results showed an accurate prediction of carbon dioxide and oxygen fluxes.

  18. Challenges in modeling of bulk crystal growth

    NASA Astrophysics Data System (ADS)

    Müller, G.; Friedrich, J.

    2004-05-01

    This paper tries to analyze some of the presently existing problems and challenges in the field of modeling bulk crystal growth processes. Strategies will be discussed to meet and overcome these problems and challenges. The different topics will be illustrated by typical examples of bulk growth of semiconductor and optical crystals. Experimental results will be used for a comparison and validation of the numerical results in order to demonstrate the status and maturity of the models. The following topics are considered: modeling of transport phenomena and three-dimensional effects, process optimization by soft computing, modeling of defect formation and finally the speed-up of computations by using PC clusters and paralellization.

  19. Contour Instabilities in Early Tumor Growth Models

    NASA Astrophysics Data System (ADS)

    Ben Amar, M.; Chatelain, C.; Ciarletta, P.

    2011-04-01

    Recent tumor growth models are often based on the multiphase mixture framework. Using bifurcation theory techniques, we show that such models can give contour instabilities. Restricting to a simplified but realistic version of such models, with an elastic cell-to-cell interaction and a growth rate dependent on diffusing nutrients, we prove that the tumor cell concentration at the border acts as a control parameter inducing a bifurcation with loss of the circular symmetry. We show that the finite wavelength at threshold has the size of the proliferating peritumoral zone. We apply our predictions to melanoma growth since contour instabilities are crucial for early diagnosis. Given the generality of the equations, other relevant applications can be envisaged for solving problems of tissue growth and remodeling.

  20. Modeling Math Growth Trajectory--An Application of Conventional Growth Curve Model and Growth Mixture Model to ECLS K-5 Data

    ERIC Educational Resources Information Center

    Lu, Yi

    2016-01-01

    To model students' math growth trajectory, three conventional growth curve models and three growth mixture models are applied to the Early Childhood Longitudinal Study Kindergarten-Fifth grade (ECLS K-5) dataset in this study. The results of conventional growth curve model show gender differences on math IRT scores. When holding socio-economic…

  1. Modeling plant growth and development.

    PubMed

    Prusinkiewicz, Przemyslaw

    2004-02-01

    Computational plant models or 'virtual plants' are increasingly seen as a useful tool for comprehending complex relationships between gene function, plant physiology, plant development, and the resulting plant form. The theory of L-systems, which was introduced by Lindemayer in 1968, has led to a well-established methodology for simulating the branching architecture of plants. Many current architectural models provide insights into the mechanisms of plant development by incorporating physiological processes, such as the transport and allocation of carbon. Other models aim at elucidating the geometry of plant organs, including flower petals and apical meristems, and are beginning to address the relationship between patterns of gene expression and the resulting plant form.

  2. Modeling Error Distributions of Growth Curve Models through Bayesian Methods

    ERIC Educational Resources Information Center

    Zhang, Zhiyong

    2016-01-01

    Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is…

  3. A quasi-chemical model for the growth and death of microorganisms in foods by non-thermal and high-pressure processing.

    PubMed

    Doona, Christopher J; Feeherry, Florence E; Ross, Edward W

    2005-04-15

    Predictive microbial models generally rely on the growth of bacteria in laboratory broth to approximate the microbial growth kinetics expected to take place in actual foods under identical environmental conditions. Sigmoidal functions such as the Gompertz or logistics equation accurately model the typical microbial growth curve from the lag to the stationary phase and provide the mathematical basis for estimating parameters such as the maximum growth rate (MGR). Stationary phase data can begin to show a decline and make it difficult to discern which data to include in the analysis of the growth curve, a factor that influences the calculated values of the growth parameters. In contradistinction, the quasi-chemical kinetics model provides additional capabilities in microbial modelling and fits growth-death kinetics (all four phases of the microbial lifecycle continuously) for a general set of microorganisms in a variety of actual food substrates. The quasi-chemical model is differential equations (ODEs) that derives from a hypothetical four-step chemical mechanism involving an antagonistic metabolite (quorum sensing) and successfully fits the kinetics of pathogens (Staphylococcus aureus, Escherichia coli and Listeria monocytogenes) in various foods (bread, turkey meat, ham and cheese) as functions of different hurdles (a(w), pH, temperature and anti-microbial lactate). The calculated value of the MGR depends on whether growth-death data or only growth data are used in the fitting procedure. The quasi-chemical kinetics model is also exploited for use with the novel food processing technology of high-pressure processing. The high-pressure inactivation kinetics of E. coli are explored in a model food system over the pressure (P) range of 207-345 MPa (30,000-50,000 psi) and the temperature (T) range of 30-50 degrees C. In relatively low combinations of P and T, the inactivation curves are non-linear and exhibit a shoulder prior to a more rapid rate of microbial

  4. Residual Structures in Latent Growth Curve Modeling

    ERIC Educational Resources Information Center

    Grimm, Kevin J.; Widaman, Keith F.

    2010-01-01

    Several alternatives are available for specifying the residual structure in latent growth curve modeling. Two specifications involve uncorrelated residuals and represent the most commonly used residual structures. The first, building on repeated measures analysis of variance and common specifications in multilevel models, forces residual variances…

  5. A stochastic model of eye lens growth.

    PubMed

    Šikić, Hrvoje; Shi, Yanrong; Lubura, Snježana; Bassnett, Steven

    2015-07-07

    The size and shape of the ocular lens must be controlled with precision if light is to be focused sharply on the retina. The lifelong growth of the lens depends on the production of cells in the anterior epithelium. At the lens equator, epithelial cells differentiate into fiber cells, which are added to the surface of the existing fiber cell mass, increasing its volume and area. We developed a stochastic model relating the rates of cell proliferation and death in various regions of the lens epithelium to deposition of fiber cells and radial lens growth. Epithelial population dynamics were modeled as a branching process with emigration and immigration between proliferative zones. Numerical simulations were in agreement with empirical measurements and demonstrated that, operating within the strict confines of lens geometry, a stochastic growth engine can produce the smooth and precise growth necessary for lens function. Copyright © 2015 Elsevier Ltd. All rights reserved.

  6. A Stochastic Model of Eye Lens Growth

    PubMed Central

    Šikić, Hrvoje; Shi, Yanrong; Lubura, Snježana; Bassnett, Steven

    2015-01-01

    The size and shape of the ocular lens must be controlled with precision if light is to be focused sharply on the retina. The lifelong growth of the lens depends on the production of cells in the anterior epithelium. At the lens equator, epithelial cells differentiate into fiber cells, which are added to the surface of the existing fiber cell mass, increasing its volume and area. We developed a stochastic model relating the rates of cell proliferation and death in various regions of the lens epithelium to deposition of fiber cells and lens growth. Epithelial population dynamics were modeled as a branching process with emigration and immigration between various proliferative zones. Numerical simulations were in agreement with empirical measurements and demonstrated that, operating within the strict confines of lens geometry, a stochastic growth engine can produce the smooth and precise growth necessary for lens function. PMID:25816743

  7. Activist model of political party growth

    NASA Astrophysics Data System (ADS)

    Jeffs, Rebecca A.; Hayward, John; Roach, Paul A.; Wyburn, John

    2016-01-01

    The membership of British political parties has a direct influence on their political effectiveness. This paper applies the mathematics of epidemiology to the analysis of the growth and decline of such memberships. The party members are divided into activists and inactive members, where all activists influence the quality of party recruitment, but only a subset of activists recruit and thus govern numerical growth. The activists recruit for only a limited period, which acts as a restriction on further party growth. This Limited Activist model is applied to post-war and recent memberships of the Labour, Scottish National and Conservative parties. The model reproduces data trends, and relates realistically to historical narratives. It is concluded that the political parties analysed are not in danger of extinction but experience repeated periods of growth and decline in membership, albeit at lower numbers than in the past.

  8. Testing the Goodwin growth-cycle macroeconomic dynamics in Brazil

    NASA Astrophysics Data System (ADS)

    Moura, N. J.; Ribeiro, Marcelo B.

    2013-05-01

    This paper discusses the empirical validity of Goodwin’s (1967) macroeconomic model of growth with cycles by assuming that the individual income distribution of the Brazilian society is described by the Gompertz-Pareto distribution (GPD). This is formed by the combination of the Gompertz curve, representing the overwhelming majority of the population (˜99%), with the Pareto power law, representing the tiny richest part (˜1%). In line with Goodwin’s original model, we identify the Gompertzian part with the workers and the Paretian component with the class of capitalists. Since the GPD parameters are obtained for each year and the Goodwin macroeconomics is a time evolving model, we use previously determined, and further extended here, Brazilian GPD parameters, as well as unemployment data, to study the time evolution of these quantities in Brazil from 1981 to 2009 by means of the Goodwin dynamics. This is done in the original Goodwin model and an extension advanced by Desai et al. (2006). As far as Brazilian data is concerned, our results show partial qualitative and quantitative agreement with both models in the studied time period, although the original one provides better data fit. Nevertheless, both models fall short of a good empirical agreement as they predict single center cycles which were not found in the data. We discuss the specific points where the Goodwin dynamics must be improved in order to provide a more realistic representation of the dynamics of economic systems.

  9. Age, growth and fall diet of channel catfish in Cheat Lake, West Virginia

    USGS Publications Warehouse

    Hilling, Corbin D.; Welsh, Stuart A.; Smith, Dustin M.

    2016-01-01

    Acidification has historically impaired Cheat Lake's fish community, but recent mitigation efforts within the Cheat River watershed have improved water quality and species richness. Presently, channel catfish Ictalurus punctatus are abundant and attain desirable sizes for anglers. We evaluated the age, growth, and fall diet of the population. We collected a sample of 155 channel catfish from Cheat Lake from 5 August to 4 December 2014, a subset of which we aged (n = 148) using lapillus otoliths. We fit four growth models (von Bertalanffy, logistic, Gompertz, and power) to length-at-age data and compared models using an information theoretic approach. We collected fall diets from 55 fish sampled from 13 October to 4 December 2014. Total lengths of individuals in the sample ranged from 154 to 721 mm and ages ranged from 2 to 19 y. We AICc-selected the von Bertalanffy growth model as the best approximating model, and the power and Gompertz models also had considerable support. Diets were numerically dominated by Diptera larvae, specifically Chironomidae and Chaoboridae, while 39% of stomachs contained terrestrial food items. This study provides baseline data for management of Cheat Lake's channel catfish population. Further, this study fills a knowledge gap in the scientific literature on channel catfish, because few previously published studies have examined the population ecology of channel catfish in the Central Appalachian region.

  10. A Decentralized Wireless Solution to Monitor and Diagnose PV Solar Module Performance Based on Symmetrized-Shifted Gompertz Functions

    PubMed Central

    Molina-García, Angel; Campelo, José Carlos; Blanc, Sara; Serrano, Juan José; García-Sánchez, Tania; Bueso, María C.

    2015-01-01

    This paper proposes and assesses an integrated solution to monitor and diagnose photovoltaic (PV) solar modules based on a decentralized wireless sensor acquisition system. Both DC electrical variables and environmental data are collected at PV module level using low-cost and high-energy efficiency node sensors. Data is real-time processed locally and compared with expected PV module performances obtained by a PV module model based on symmetrized-shifted Gompertz functions (as previously developed and assessed by the authors). Sensor nodes send data to a centralized sink-computing module using a multi-hop wireless sensor network architecture. Such integration thus provides extensive analysis of PV installations, and avoids off-line tests or post-processing processes. In comparison with previous approaches, this solution is enhanced with a low-cost system and non-critical performance constraints, and it is suitable for extensive deployment in PV power plants. Moreover, it is easily implemented in existing PV installations, since no additional wiring is required. The system has been implemented and assessed in a Spanish PV power plant connected to the grid. Results and estimations of PV module performances are also included in the paper. PMID:26230694

  11. A Decentralized Wireless Solution to Monitor and Diagnose PV Solar Module Performance Based on Symmetrized-Shifted Gompertz Functions.

    PubMed

    Molina-García, Angel; Campelo, José Carlos; Blanc, Sara; Serrano, Juan José; García-Sánchez, Tania; Bueso, María C

    2015-07-29

    This paper proposes and assesses an integrated solution to monitor and diagnose photovoltaic (PV) solar modules based on a decentralized wireless sensor acquisition system. Both DC electrical variables and environmental data are collected at PV module level using low-cost and high-energy efficiency node sensors. Data is real-time processed locally and compared with expected PV module performances obtained by a PV module model based on symmetrized-shifted Gompertz functions (as previously developed and assessed by the authors). Sensor nodes send data to a centralized sink-computing module using a multi-hop wireless sensor network architecture. Such integration thus provides extensive analysis of PV installations, and avoids off-line tests or post-processing processes. In comparison with previous approaches, this solution is enhanced with a low-cost system and non-critical performance constraints, and it is suitable for extensive deployment in PV power plants. Moreover, it is easily implemented in existing PV installations, since no additional wiring is required. The system has been implemented and assessed in a Spanish PV power plant connected to the grid. Results and estimations of PV module performances are also included in the paper.

  12. Thermal models pertaining to continental growth

    NASA Technical Reports Server (NTRS)

    Morgan, Paul; Ashwal, Lew

    1988-01-01

    Thermal models are important to understanding continental growth as the genesis, stabilization, and possible recycling of continental crust are closely related to the tectonic processes of the earth which are driven primarily by heat. The thermal energy budget of the earth was slowly decreasing since core formation, and thus the energy driving the terrestrial tectonic engine was decreasing. This fundamental observation was used to develop a logic tree defining the options for continental growth throughout earth history.

  13. Modeling Stromatolite Growth Under Oscillatory Flows

    NASA Astrophysics Data System (ADS)

    Patel, H. J.; Gong, J.; Tice, M. M.

    2014-12-01

    Stromatolite growth models based on diffusion limited aggregation (DLA) has been fairly successful at producing features commonly recognized in stromatolitic structures in the rock record. These models generally require slow mixing of solutes at time scales comparable to the growth of organisms and largely ignore fluid erosions. Recent research on microbial mats suggests that fluid flow might have a dominant control on the formation, deformation and erosion of surface microbial structures, raising the possibility that different styles of fluid flow may influence the morphology of stromatolites. Many stromatolites formed in relatively high energy, shallow water environments under oscillatory currents driven by wind-induced waves. In order to investigate the potential role of oscillatory flows in shaping stromatolites, we are constructing a numerical model of stromatolite growth parameterized by flume experiments with cyanobacterial biofilms. The model explicitly incorporates reaction-diffusion processes, surface deformation and erosion, biomass growth, sedimentation and mineral precipitation. A Lattice-Boltzmann numerical scheme was applied to the reaction-diffusion equations in order to boost computational efficiency. A basic finite element method was employed to compute surface deformation and erosion. Growth of biomass, sedimentation and carbonate precipitation was based on a modified discrete cellular automata scheme. This model will be used to test an alternative hypothesis for the formation of stromatolites in higher energy, shallow and oscillatory flow environments.

  14. Plant Growth Modelling and Applications: The Increasing Importance of Plant Architecture in Growth Models

    PubMed Central

    Fourcaud, Thierry; Zhang, Xiaopeng; Stokes, Alexia; Lambers, Hans; Körner, Christian

    2008-01-01

    Background Modelling plant growth allows us to test hypotheses and carry out virtual experiments concerning plant growth processes that could otherwise take years in field conditions. The visualization of growth simulations allows us to see directly and vividly the outcome of a given model and provides us with an instructive tool useful for agronomists and foresters, as well as for teaching. Functional–structural (FS) plant growth models are nowadays particularly important for integrating biological processes with environmental conditions in 3-D virtual plants, and provide the basis for more advanced research in plant sciences. Scope In this viewpoint paper, we ask the following questions. Are we modelling the correct processes that drive plant growth, and is growth driven mostly by sink or source activity? In current models, is the importance of soil resources (nutrients, water, temperature and their interaction with meristematic activity) considered adequately? Do classic models account for architectural adjustment as well as integrating the fundamental principles of development? Whilst answering these questions with the available data in the literature, we put forward the opinion that plant architecture and sink activity must be pushed to the centre of plant growth models. In natural conditions, sinks will more often drive growth than source activity, because sink activity is often controlled by finite soil resources or developmental constraints. PMA06 This viewpoint paper also serves as an introduction to this Special Issue devoted to plant growth modelling, which includes new research covering areas stretching from cell growth to biomechanics. All papers were presented at the Second International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications (PMA06), held in Beijing, China, from 13–17 November, 2006. Although a large number of papers are devoted to FS models of agricultural and forest crop species, physiological and genetic

  15. Reliability growth models for NASA applications

    NASA Technical Reports Server (NTRS)

    Taneja, Vidya S.

    1991-01-01

    The objective of any reliability growth study is prediction of reliability at some future instant. Another objective is statistical inference, estimation of reliability for reliability demonstration. A cause of concern for the development engineer and management is that reliability demands an excessive number of tests for reliability demonstration. For example, the Space Transportation Main Engine (STME) program requirements call for .99 reliability at 90 pct. confidence for demonstration. This requires running 230 tests with zero failure if a classical binomial model is used. It is therefore also an objective to explore the reliability growth models for reliability demonstration and tracking and their applicability to NASA programs. A reliability growth model is an analytical tool used to monitor the reliability progress during the development program and to establish a test plan to demonstrate an acceptable system reliability.

  16. Assessment of MARMOT Grain Growth Model

    SciTech Connect

    Fromm, B.; Zhang, Y.; Schwen, D.; Brown, D.; Pokharel, R.

    2015-12-01

    This report assesses the MARMOT grain growth model by comparing modeling predictions with experimental results from thermal annealing. The purpose here is threefold: (1) to demonstrate the validation approach of using thermal annealing experiments with non-destructive characterization, (2) to test the reconstruction capability and computation efficiency in MOOSE, and (3) to validate the grain growth model and the associated parameters that are implemented in MARMOT for UO2. To assure a rigorous comparison, the 2D and 3D initial experimental microstructures of UO2 samples were characterized using non-destructive Synchrotron x-ray. The same samples were then annealed at 2273K for grain growth, and their initial microstructures were used as initial conditions for simulated annealing at the same temperature using MARMOT. After annealing, the final experimental microstructures were characterized again to compare with the results from simulations. So far, comparison between modeling and experiments has been done for 2D microstructures, and 3D comparison is underway. The preliminary results demonstrated the usefulness of the non-destructive characterization method for MARMOT grain growth model validation. A detailed analysis of the 3D microstructures is in progress to fully validate the current model in MARMOT.

  17. A Dynamic Systems Model of Cognitive and Language Growth.

    ERIC Educational Resources Information Center

    van Geert, Paul

    1991-01-01

    A conceptual framework of cognitive growth is sketched and a mathematical model of cognitive growth is presented with the conclusion that the most plausible model is a model of logistic growth with delayed feedback. The model is transformed into a dynamic systems model based on the logistic-growth equation. (SLD)

  18. Some novel growth functions and their application with reference to growth in ostrich.

    PubMed

    Faridi, A; López, S; Ammar, H; Salwa, K S; Golian, A; Thornley, J H M; France, J

    2015-06-01

    Four novel growth functions, namely, Pareto, extreme value distribution (EVD), Lomolino, and cumulative β-P distribution (CBP), are derived, and their ability to describe ostrich growth curves is evaluated. The functions were compared with standard growth equations, namely, the monomolecular, Michaelis-Menten (MM), Gompertz, Richards, and generalized MM (gMM). For this purpose, 2 separate comparisons were conducted. In the first, all the functions were fitted to 40 individual growth curves (5 males and 35 females) of ostriches using nonlinear regression. In the second, performance of the functions was assessed when data from 71 individuals were composited (570 data points). This comparison was undertaken using nonlinear mixed models and considering 3 approaches: 1) models with no random effect, 2) random effect incorporated as the intercept, and 3) random effect incorporated into the asymptotic weight parameter (Wf). The results from the first comparison showed that the functions generally gave acceptable values of R2 and residual variance. On the basis of the Akaike information criterion (AIC), CBP gave the best fit, whereas the Gompertz and Lomolino equations were the preferred functions on the basis of corrected AIC (AICc). Bias, accuracy factor, the Durbin-Watson statistic, and the number of runs of sign were used to analyze the residuals. CBP gave the best distribution of residuals but also produced more residual autocorrelation (significant Durbin-Watson statistic). The functions were applied to sample data for a more conventional farm species (2 breeds of cattle) to verify the results of the comparison of fit among functions and their applicability across species. In the second comparison, analysis of mixed models showed that incorporation of a random effect into Wf gave the best fit, resulting in smaller AIC and AIC values compared with those in the other 2 approaches. On the basis of AICc, best fit was achieved with CBP, followed by gMM, Lomolino, and

  19. New theories of root growth modelling

    NASA Astrophysics Data System (ADS)

    Landl, Magdalena; Schnepf, Andrea; Vanderborght, Jan; Huber, Katrin; Javaux, Mathieu; Bengough, A. Glyn; Vereecken, Harry

    2016-04-01

    In dynamic root architecture models, root growth is represented by moving root tips whose line trajectory results in the creation of new root segments. Typically, the direction of root growth is calculated as the vector sum of various direction-affecting components. However, in our simulations this did not reproduce experimental observations of root growth in structured soil. We therefore developed a new approach to predict the root growth direction. In this approach we distinguish between, firstly, driving forces for root growth, i.e. the force exerted by the root which points in the direction of the previous root segment and gravitropism, and, secondly, the soil mechanical resistance to root growth or penetration resistance. The latter can be anisotropic, i.e. depending on the direction of growth, which leads to a difference between the direction of the driving force and the direction of the root tip movement. Anisotropy of penetration resistance can be caused either by microscale differences in soil structure or by macroscale features, including macropores. Anisotropy at the microscale is neglected in our model. To allow for this, we include a normally distributed random deflection angle α to the force which points in the direction of the previous root segment with zero mean and a standard deviation σ. The standard deviation σ is scaled, so that the deflection from the original root tip location does not depend on the spatial resolution of the root system model. Similarly to the water flow equation, the direction of the root tip movement corresponds to the water flux vector while the driving forces are related to the water potential gradient. The analogue of the hydraulic conductivity tensor is the root penetrability tensor. It is determined by the inverse of soil penetration resistance and describes the ease with which a root can penetrate the soil. By adapting the three dimensional soil and root water uptake model R-SWMS (Javaux et al., 2008) in this way

  20. Combined effects of chlorine and thiamine dilauryl sulfate on reduction of Listeria monocytogenes in chicken breast and development of predictive growth models.

    PubMed

    Oh, Se-Ra; Park, Shin Young; Ha, Sang-Do

    2014-06-01

    The inhibitory effect of chlorine (50, 100, and 200 mL/kg) and thiamine dilauryl sulfate (TDS: 100, 500, and 1,000 mg/kg) on Listeria monocytogenes in chicken breast was investigated. Also, predictive growth models as a function of chlorine and TDS concentration, and storage temperature (4, 10, and 15°C) were developed using a polynomial model. Listeria monocytogenes counts were significantly (P < 0.05) different in samples treated with sterile distilled water and combinations of chlorine and TDS. The maximum reduction effect was 0.5 log cfu/g by combined treatment of 200 mL/kg chlorine and 1,000 mg/kg TDS. The largest synergistic effect was 0.38 log cfu/g by combined treatment of 100 mL/kg chlorine and 1,000 mg/kg TDS. The primary models that were developed to obtain the specific growth rates (SGR) and lag time (LT) had good fitness (R(2) > 0.91) determined by the reparameterized Gompertz equation. The secondary polynomial models were calculated by nonlinear regression analysis. In the validation of the developed models, the bias factor (Bf) and accuracy factor (Af) for SGR were 0.54 and 1.84, respectively, whereas those for LT were 0.97 and 1.04, respectively. In quality analysis, chlorine and TDS did not change the color or texture of chicken breast meat during storage at 4°C for 7 d. Thus, our findings indicate that a combined treatment of 100 mL/kg chlorine and 1,000 mg/kg TDS appears to an effective method into reduce L. monocytogenes in broiler carcasses with no negative effects on color and textural quality. The predictive models were in good agreement with the validation and may be used to predict L. monocytogenes growth in chicken breast.

  1. Modeling duckweed growth in wastewater treatment systems

    USGS Publications Warehouse

    Landesman, L.; Parker, N.C.; Fedler, C.B.; Konikoff, M.

    2005-01-01

    Species of the genera Lemnaceae, or duckweeds, are floating aquatic plants that show great promise for both wastewater treatment and livestock feed production. Research conducted in the Southern High Plains of Texas has shown that Lemna obscura grew well in cattle feedlot runoff water and produced leaf tissue with a high protein content. A model or mathematical expression derived from duckweed growth data was used to fit data from experiments conducted in a greenhouse in Lubbock, Texas. The relationship between duckweed growth and the total nitrogen concentration in the mediium follows the Mitscherlich Function and is similar to that of other plants. Empirically derived model equations have successfully predicted the growth response of Lemna obscura.

  2. A toy model of sea ice growth

    NASA Technical Reports Server (NTRS)

    Thorndike, Alan S.

    1992-01-01

    My purpose here is to present a simplified treatment of the growth of sea ice. By ignoring many details, it is possible to obtain several results that help to clarify the ways in which the sea ice cover will respond to climate change. Three models are discussed. The first deals with the growth of sea ice during the cold season. The second describes the cycle of growth and melting for perennial ice. The third model extends the second to account for the possibility that the ice melts away entirely in the summer. In each case, the objective is to understand what physical processes are most important, what ice properties determine the ice behavior, and to which climate variables the system is most sensitive.

  3. Theoretical model of crystal growth shaping process

    NASA Astrophysics Data System (ADS)

    Tatarchenko, V. A.; Uspenski, V. S.; Tatarchenko, E. V.; Nabot, J. Ph.; Duffar, T.; Roux, B.

    1997-10-01

    A theoretical investigation of the crystal growth shaping process is carried out on the basis of the dynamic stability concept. The capillary dynamic stability of shaped crystal growth processes for various forms of the liquid menisci is analyzed using the mathematical model of the phenomena in the axisymmetric case. The catching boundary condition of the capillary boundary problem is considered and the limits of its application for shaped crystal growth modeling are discussed. The static stability of a liquid free surface is taken into account by means of the Jacobi equation analysis. The result is that a large number of menisci having drop-like shapes are statically unstable. A few new non-traditional liquid meniscus shapes (e.g., bubbles and related shapes) are proposed for the case of a catching boundary condition.

  4. A tumor growth model with deformable ECM.

    PubMed

    Sciumè, G; Santagiuliana, R; Ferrari, M; Decuzzi, P; Schrefler, B A

    2014-11-26

    Existing tumor growth models based on fluid analogy for the cells do not generally include the extracellular matrix (ECM), or if present, take it as rigid. The three-fluid model originally proposed by the authors and comprising tumor cells (TC), host cells (HC), interstitial fluid (IF) and an ECM, considered up to now only a rigid ECM in the applications. This limitation is here relaxed and the deformability of the ECM is investigated in detail. The ECM is modeled as a porous solid matrix with Green-elastic and elasto-visco-plastic material behavior within a large strain approach. Jauman and Truesdell objective stress measures are adopted together with the deformation rate tensor. Numerical results are first compared with those of a reference experiment of a multicellular tumor spheroid (MTS) growing in vitro, then three different tumor cases are studied: growth of an MTS in a decellularized ECM, growth of a spheroid in the presence of host cells and growth of a melanoma. The influence of the stiffness of the ECM is evidenced and comparison with the case of a rigid ECM is made. The processes in a deformable ECM are more rapid than in a rigid ECM and the obtained growth pattern differs. The reasons for this are due to the changes in porosity induced by the tumor growth. These changes are inhibited in a rigid ECM. This enhanced computational model emphasizes the importance of properly characterizing the biomechanical behavior of the malignant mass in all its components to correctly predict its temporal and spatial pattern evolution.

  5. A tumor growth model with deformable ECM

    PubMed Central

    Sciumè, G; Santagiuliana, R; Ferrari, M; Decuzzi, P; Schrefler, B A

    2015-01-01

    Existing tumor growth models based on fluid analogy for the cells do not generally include the extracellular matrix (ECM), or if present, take it as rigid. The three-fluid model originally proposed by the authors and comprising tumor cells (TC), host cells (HC), interstitial fluid (IF) and an ECM, considered up to now only a rigid ECM in the applications. This limitation is here relaxed and the deformability of the ECM is investigated in detail. The ECM is modeled as a porous solid matrix with Green-elastic and elasto-visco-plastic material behavior within a large strain approach. Jauman and Truesdell objective stress measures are adopted together with the deformation rate tensor. Numerical results are first compared with those of a reference experiment of a multicellular tumor spheroid (MTS) growing in vitro, then three different tumor cases are studied: growth of an MTS in a decellularized ECM, growth of a spheroid in the presence of host cells and growth of a melanoma. The influence of the stiffness of the ECM is evidenced and comparison with the case of a rigid ECM is made. The processes in a deformable ECM are more rapid than in a rigid ECM and the obtained growth pattern differs. The reasons for this are due to the changes in porosity induced by the tumor growth. These changes are inhibited in a rigid ECM. This enhanced computational model emphasizes the importance of properly characterizing the biomechanical behavior of the malignant mass in all its components to correctly predict its temporal and spatial pattern evolution. PMID:25427284

  6. Modelling oxide formation and growth on platinum

    NASA Astrophysics Data System (ADS)

    Baroody, Heather A.; Jerkiewicz, Gregory; Eikerling, Michael H.

    2017-04-01

    We present a mathematical model of oxide formation and growth on platinum. The motivation stems from the necessity to understand platinum dissolution in the cathode catalyst layer of polymer electrolyte fuel cells. As is known, platinum oxide formation and reduction are strongly linked to platinum dissolution processes. However, a consistent model of the oxidation processes on platinum does not exist. Our oxide growth model links interfacial exchange processes between platinum and oxygen ions with the transport of oxygen ion vacancies via diffusion and migration. A parametric analysis is performed to rationalize vital trends in oxide growth kinetics. The rate determining step of oxide formation and growth is identified as the extraction of platinum atoms at the metal-oxide interface. A kinetic effect is observed while adjusting the potential when growing the oxide layer, and the solution indicates that a structural change occurs at high potentials, around 1.5 VRHE. The model compares well to experimental data for various materials from various sources.

  7. Modeling Fish Growth in Low Dissolved Oxygen

    ERIC Educational Resources Information Center

    Neilan, Rachael Miller

    2013-01-01

    This article describes a computational project designed for undergraduate students as an introduction to mathematical modeling. Students use an ordinary differential equation to describe fish weight and assume the instantaneous growth rate depends on the concentration of dissolved oxygen. Published laboratory experiments suggest that continuous…

  8. Modeling Fish Growth in Low Dissolved Oxygen

    ERIC Educational Resources Information Center

    Neilan, Rachael Miller

    2013-01-01

    This article describes a computational project designed for undergraduate students as an introduction to mathematical modeling. Students use an ordinary differential equation to describe fish weight and assume the instantaneous growth rate depends on the concentration of dissolved oxygen. Published laboratory experiments suggest that continuous…

  9. Ruminant models of prenatal growth restriction.

    PubMed

    Anthony, R V; Scheaffer, A N; Wright, C D; Regnault, T R H

    2003-01-01

    Intrauterine growth restriction (IUGR) is a significant health issue that not only affects infant mortality and morbidity, but may also predispose individuals to coronary heart disease, diabetes, hypertension and stroke as adults. The majority of IUGR pregnancies in humans are characterized by asymmetric fetal growth, resulting from inadequate nutrient transfer to the fetus. Furthermore, most of these pregnancies involve functional placental insufficiency, and may also show altered umbilical velocimetry. As the severity of IUGR increases, the fetus becomes increasingly hypoxic, hypoglycaemic and acidotic. In addition, placental transfer or utilization of some amino acids is known to be altered in IUGR pregnancies. Although a great deal has been learned from clinical studies of human IUGR, appropriate animal models are required to define completely the mechanisms involved in the development of IUGR. The pregnant sheep is a long-standing model for placental-fetal interactions, and fetal growth restriction can be induced in pregnant sheep by maternal nutrient restriction, maternal nutrient excess, administration of glucocorticoid, utero-placental embolization, carunclectomy and maternal hyperthermia. Although all of these sheep models are capable of inducing fetal growth restriction, the degree of restriction is variable. This review compares these sheep models of IUGR with the characteristics of human IUGR.

  10. Incorporating Student Mobility in Achievement Growth Modeling: A Cross-Classified Multiple Membership Growth Curve Model.

    PubMed

    Grady, Matthew W; Beretvas, S Natasha

    2010-05-28

    Multiple membership random effects models (MMREMs) have been developed for use in situations where individuals are members of multiple higher level organizational units. Despite their availability and the frequency with which multiple membership structures are encountered, no studies have extended the MMREM approach to hierarchical growth curve modeling (GCM). This study introduces a cross-classified multiple membership growth curve model (CCMM-GCM) for modeling, for example, academic achievement trajectories in the presence of student mobility. Real data are used to demonstrate and compare growth curve model estimates using the CCMM-GCM and a conventional GCM that ignores student mobility. Results indicate that the CCMM-GCM represents a promising option for modeling growth for multiple membership data structures.

  11. Unrestricted Mixture Models for Class Identification in Growth Mixture Modeling

    ERIC Educational Resources Information Center

    Liu, Min; Hancock, Gregory R.

    2014-01-01

    Growth mixture modeling has gained much attention in applied and methodological social science research recently, but the selection of the number of latent classes for such models remains a challenging issue, especially when the assumption of proper model specification is violated. The current simulation study compared the performance of a linear…

  12. Interaction Effects in Growth Modeling: A Full Model.

    ERIC Educational Resources Information Center

    Wen, Zhonglin; Marsh, Herbert W.; Hau, Kit-Tai

    2002-01-01

    Points out two concerns with recent research by F. Li and others (2000) and T. Duncan and others (1999) that extended the structural equation model of latent interactions developed by K. Joreskog and F. Yang (1996) to latent growth modeling. Used mathematical derivation and a comparison of alternative models fitted to simulated data to develop a…

  13. Adaptive importance sampling for network growth models

    PubMed Central

    Holmes, Susan P.

    2016-01-01

    Network Growth Models such as Preferential Attachment and Duplication/Divergence are popular generative models with which to study complex networks in biology, sociology, and computer science. However, analyzing them within the framework of model selection and statistical inference is often complicated and computationally difficult, particularly when comparing models that are not directly related or nested. In practice, ad hoc methods are often used with uncertain results. If possible, the use of standard likelihood-based statistical model selection techniques is desirable. With this in mind, we develop an Adaptive Importance Sampling algorithm for estimating likelihoods of Network Growth Models. We introduce the use of the classic Plackett-Luce model of rankings as a family of importance distributions. Updates to importance distributions are performed iteratively via the Cross-Entropy Method with an additional correction for degeneracy/over-fitting inspired by the Minimum Description Length principle. This correction can be applied to other estimation problems using the Cross-Entropy method for integration/approximate counting, and it provides an interpretation of Adaptive Importance Sampling as iterative model selection. Empirical results for the Preferential Attachment model are given, along with a comparison to an alternative established technique, Annealed Importance Sampling. PMID:27182098

  14. Mathematical foundations of the dendritic growth models.

    PubMed

    Villacorta, José A; Castro, Jorge; Negredo, Pilar; Avendaño, Carlos

    2007-11-01

    At present two growth models describe successfully the distribution of size and topological complexity in populations of dendritic trees with considerable accuracy and simplicity, the BE model (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) and the S model (Van Pelt and Verwer in Bull. Math. Biol. 48:197-211, 1986). This paper discusses the mathematical basis of these models and analyzes quantitatively the relationship between the BE model and the S model assumed in the literature by developing a new explicit equation describing the BES model (a dendritic growth model integrating the features of both preceding models; Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997). In numerous studies it is implicitly presupposed that the S model is conditionally linked to the BE model (Granato and Van Pelt in Brain Res. Dev. Brain Res. 142:223-227, 2003; Uylings and Van Pelt in Network 13:397-414, 2002; Van Pelt, Dityatev and Uylings in J. Comp. Neurol. 387:325-340, 1997; Van Pelt and Schierwagen in Math. Biosci. 188:147-155, 2004; Van Pelt and Uylings in Network. 13:261-281, 2002; Van Pelt, Van Ooyen and Uylings in Modeling Dendritic Geometry and the Development of Nerve Connections, pp 179, 2000). In this paper we prove the non-exactness of this assumption, quantify involved errors and determine the conditions under which the BE and S models can be separately used instead of the BES model, which is more exact but considerably more difficult to apply. This study leads to a novel expression describing the BE model in an analytical closed form, much more efficient than the traditional iterative equation (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) in many neuronal classes. Finally we propose a new algorithm in order to obtain the values of the parameters of the BE model when this growth model is matched to experimental data, and discuss its advantages and improvements over the more commonly used procedures.

  15. Mechanobiological model of arterial growth and remodeling.

    PubMed

    Keshavarzian, Maziyar; Meyer, Clark A; Hayenga, Heather N

    2017-08-19

    A coupled agent-based model (ABM) and finite element analysis (FEA) computational framework is developed to study the interplay of bio-chemo-mechanical factors in blood vessels and their role in maintaining homeostasis. The agent-based model implements the power of REPAST Simphony libraries and adapts its environment for biological simulations. Coupling a continuum-level model (FEA) to a cellular-level model (ABM) has enabled this computational framework to capture the response of blood vessels to increased or decreased levels of growth factors, proteases and other signaling molecules (on the micro scale) as well as altered blood pressure. Performance of the model is assessed by simulating porcine left anterior descending artery under normotensive conditions and transient increases in blood pressure and by analyzing sensitivity of the model to variations in the rule parameters of the ABM. These simulations proved that the model is stable under normotensive conditions and can recover from transient increases in blood pressure. Sensitivity studies revealed that the model is most sensitive to variations in the concentration of growth factors that affect cellular proliferation and regulate extracellular matrix composition (mainly collagen).

  16. Simultaneous identification of growth law and estimation of its rate parameter for biological growth data: a new approach.

    PubMed

    Bhowmick, Amiya Ranjan; Chattopadhyay, Gaurangadeb; Bhattacharya, Sabyasachi

    2014-01-01

    Scientific formalizations of the notion of growth and measurement of the rate of growth in living organisms are age-old problems. The most frequently used metric, "Average Relative Growth Rate" is invariant under the choice of the underlying growth model. Theoretically, the estimated rate parameter and relative growth rate remain constant for all mutually exclusive and exhaustive time intervals if the underlying law is exponential but not for other common growth laws (e.g., logistic, Gompertz, power, general logistic). We propose a new growth metric specific to a particular growth law and show that it is capable of identifying the underlying growth model. The metric remains constant over different time intervals if the underlying law is true, while the extent of its variation reflects the departure of the assumed model from the true one. We propose a new estimator of the relative growth rate, which is more sensitive to the true underlying model than the existing one. The advantage of using this is that it can detect crucial intervals where the growth process is erratic and unusual. It may help experimental scientists to study more closely the effect of the parameters responsible for the growth of the organism/population under study.

  17. A simple model for black hole growth

    NASA Astrophysics Data System (ADS)

    Schawinski, Kevin; Weigel, Anna K. K.; Caplar, Neven; Wong, Ivy

    2017-01-01

    We present a simple phenomenological model for black hole growth in the z~0 universe. We show that nuclear activity can be described by two separate, mass-independent Eddington Ratio Distribution Functions (ERDFs) operating in blue and red galaxies, respectively. Our forward-modeling approach constrains these two ERDFs by comparing to the observed X-ray and radio luminosity functions. Alternative ERDFs with mass-dependence, such as those expected from AGN-driven mass-quenching of galaxies, are ruled out. We discuss the implications of this model and outline potential applications

  18. Alternative growth functions for predicting body, carcass, and breast weight in ducks: Lomolino equation and extreme value function.

    PubMed

    Faridi, A; Murawska, D; Golian, A; Mottaghitalab, M; Gitoee, A; Lopez, S; France, J

    2014-04-01

    In this study, 2 alternative growth functions, the Lomolino and the extreme value function (EVF), are introduced and their ability to predict body, carcass, and breast weight in ducks evaluated. A comparative study was carried out of these equations with standard growth functions: Gompertz, exponential, Richards, and generalized Michaelis-Menten. Goodness of fit of the functions was evaluated using R(2), mean square error, Akaike information criterion, and Bayesian information criterion, whereas bias factor, accuracy factor, Durbin-Watson statistic, and number of runs of sign were the criteria used for analysis of residuals. Results showed that predictive performance of all functions was acceptable, though the Richards and exponential equations failed to converge in a few cases for both male and female ducks. Based on goodness-of-fit statistics, the Richards, Gompertz, and EVF were the best equations whereas the worst fits to the data were obtained with the exponential. Analysis of residuals indicated that, for the different traits investigated, the least biased and the most accurate equations were the Gompertz, EVF, Richards, and generalized Michaelis-Menten, whereas the exponential was the most biased and least accurate. Based on the Durbin-Watson statistic, all models generally behaved well and only the exponential showed evidence of autocorrelation for all 3 traits investigated. Results showed that with all functions, estimated final weights of males were higher than females for the body, carcass, and breast weight profiles. The alternative functions introduced here have desirable advantages including flexibility and a low number of parameters. However, because this is probably the first study to apply these functions to predict growth patterns in poultry or other animals, further analysis of these new models is suggested.

  19. Multiscale modeling of growth plate cartilage mechanobiology.

    PubMed

    Gao, Jie; Williams, John L; Roan, Esra

    2017-04-01

    Growth plate chondrocytes are responsible for bone growth through proliferation and differentiation. However, the way they experience physiological loads and regulate bone formation, especially during the later developmental phase in the mature growth plate, is still under active investigation. In this study, a previously developed multiscale finite element model of the growth plate is utilized to study the stress and strain distributions within the cartilage at the cellular level when rapidly compressed to 20 %. Detailed structures of the chondron are included in the model to examine the hypothesis that the same combination of mechanoregulatory signals shown to maintain cartilage or stimulate osteogenesis or fibrogenesis in the cartilage anlage or fracture callus also performs the same function at the cell level within the chondrons of growth plate cartilage. Our cell-level results are qualitatively and quantitatively in agreement with tissue-level theories when both hydrostatic cellular stress and strain are considered simultaneously in a mechanoregulatory phase diagram similar to that proposed at the tissue level by Claes and Heigele for fracture healing. Chondrocytes near the reserve/proliferative zone border are subjected to combinations of high compressive hydrostatic stresses ([Formula: see text] MPa), and cell height and width strains of [Formula: see text] to [Formula: see text] respectively, that maintain cartilage and keep chondrocytes from differentiating and provide conditions favorable for cell division, whereas chondrocytes closer to the hypertrophic/calcified zone undergo combinations of lower compressive hydrostatic stress ([Formula: see text] MPa) and cell height and width strains as low as [Formula: see text] to +4 %, respectively, that promote cell differentiation toward osteogenesis; cells near the outer periphery of the growth plate structure experience a combination of low compressive hydrostatic stress (0 to [Formula: see text] MPa) and

  20. Stochastic roots of growth phenomena

    NASA Astrophysics Data System (ADS)

    De Lauro, E.; De Martino, S.; De Siena, S.; Giorno, V.

    2014-05-01

    We show that the Gompertz equation describes the evolution in time of the median of a geometric stochastic process. Therefore, we induce that the process itself generates the growth. This result allows us further to exploit a stochastic variational principle to take account of self-regulation of growth through feedback of relative density variations. The conceptually well defined framework so introduced shows its usefulness by suggesting a form of control of growth by exploiting external actions.

  1. Modeling Growth of Nanostructures in Plasmas

    NASA Technical Reports Server (NTRS)

    Hwang, Helen H.; Bose, Deepak; Govindan, T. R.; Meyyappan, M.

    2004-01-01

    As semiconductor circuits shrink to CDs below 0.1 nm, it is becoming increasingly critical to replace and/or enhance existing technology with nanoscale structures, such as nanowires for interconnects. Nanowires grown in plasmas are strongly dependent on processing conditions, such as gas composition and substrate temperature. Growth occurs at specific sites, or step-edges, with the bulk growth rate of the nanowires determined from the equation of motion of the nucleating crystalline steps. Traditional front-tracking algorithms, such as string-based or level set methods, suffer either from numerical complications in higher spatial dimensions, or from difficulties in incorporating surface-intense physical and chemical phenomena. Phase field models have the robustness of the level set method, combined with the ability to implement surface-specific chemistry that is required to model crystal growth, although they do not necessarily directly solve for the advancing front location. We have adopted a phase field approach and will present results of the adatom density and step-growth location in time as a function of processing conditions, such as temperature and plasma gas composition.

  2. Modeling Growth of Nanostructures in Plasmas

    NASA Technical Reports Server (NTRS)

    Hwang, Helen H.; Bose, Deepak; Govindan, T. R.; Meyyappan, M.

    2004-01-01

    As semiconductor circuits shrink to CDs below 0.1 nm, it is becoming increasingly critical to replace and/or enhance existing technology with nanoscale structures, such as nanowires for interconnects. Nanowires grown in plasmas are strongly dependent on processing conditions, such as gas composition and substrate temperature. Growth occurs at specific sites, or step-edges, with the bulk growth rate of the nanowires determined from the equation of motion of the nucleating crystalline steps. Traditional front-tracking algorithms, such as string-based or level set methods, suffer either from numerical complications in higher spatial dimensions, or from difficulties in incorporating surface-intense physical and chemical phenomena. Phase field models have the robustness of the level set method, combined with the ability to implement surface-specific chemistry that is required to model crystal growth, although they do not necessarily directly solve for the advancing front location. We have adopted a phase field approach and will present results of the adatom density and step-growth location in time as a function of processing conditions, such as temperature and plasma gas composition.

  3. Calibration of the STEMS diameter growth model using FIA data

    Treesearch

    Veronica C. Lessard

    2000-01-01

    The diameter growth model used in STEMS, the Stand and Tree Evaluation and Modeling System, was originally calibrated using data from permanent growth plots in Minnesota, Wisconsin, and Michigan. Because the model has been applied in predicting growth using Forest Inventory and Analysis (FIA) data, it was appropriate to refit the model to FIA data. The model was...

  4. Growth models for tree stems and vines

    NASA Astrophysics Data System (ADS)

    Bressan, Alberto; Palladino, Michele; Shen, Wen

    2017-08-01

    The paper introduces a PDE model for the growth of a tree stem or a vine. The equations describe the elongation due to cell growth, and the response to gravity and to external obstacles. An additional term accounts for the tendency of a vine to curl around branches of other plants. When obstacles are present, the model takes the form of a differential inclusion with state constraints. At each time t, a cone of admissible reactions is determined by the minimization of an elastic deformation energy. The main theorem shows that local solutions exist and can be prolonged globally in time, except when a specific ;breakdown configuration; is reached. Approximate solutions are constructed by an operator-splitting technique. Some numerical simulations are provided at the end of the paper.

  5. Modeling Interaction Effects in Latent Growth Curve Models.

    ERIC Educational Resources Information Center

    Li, Fuzhong; Duncan, Terry E.; Acock, Alan

    2000-01-01

    Presents an extension of the method of estimating interaction effects among latent variables to latent growth curve models developed by K. Joreskog and F. Yang (1996). Illustrates the procedure and discusses results in terms of practical and statistical problems associated with interaction analyses in latent curve models and structural equation…

  6. Modeling Interaction Effects in Latent Growth Curve Models.

    ERIC Educational Resources Information Center

    Li, Fuzhong; Duncan, Terry E.; Acock, Alan

    2000-01-01

    Presents an extension of the method of estimating interaction effects among latent variables to latent growth curve models developed by K. Joreskog and F. Yang (1996). Illustrates the procedure and discusses results in terms of practical and statistical problems associated with interaction analyses in latent curve models and structural equation…

  7. Discrete growth models on deterministic fractal substrate

    NASA Astrophysics Data System (ADS)

    Tang, Gang; Xun, Zhipeng; Wen, Rongji; Han, Kui; Xia, Hui; Hao, Dapeng; Zhou, Wei; Yang, Xiquan; Chen, Yuling

    2010-11-01

    The growth of the modified Family model and the Etching model on the Sierpinski carpet is studied by means of numerical simulations. The evolving interface of the aggregates is described by the well-established Family-Vicsek dynamic scaling approach. The results of the modified Family model prove the universality of the fractional Langevin equation introduced by Lee and Kim [S.B. Lee, J.M. Kim, Phys. Rev. E 80 (2009) 021101]. The Etching model also shows good scaling behavior. We conjecture that the systematic deviations of the data found in the ballistic deposition [C.M. Horowitz, F. Romá, E.V. Albano, Phys. Rev. E 78 (2008) 061118] may be due to the finite-size effects of the Ballistic Deposition model.

  8. Polyp oriented modelling of coral growth.

    PubMed

    Merks, Roeland M H; Hoekstra, Alfons G; Kaandorp, Jaap A; Sloot, Peter M A

    2004-06-21

    The morphogenesis of colonial stony corals is the result of the collective behaviour of many coral polyps depositing coral skeleton on top of the old skeleton on which they live. Yet, models of coral growth often consider the polyps as a single continuous surface. In the present work, the polyps are modelled individually. Each polyp takes up resources, deposits skeleton, buds off new polyps and dies. In this polyp oriented model, spontaneous branching occurs. We argue that branching is caused by a so called "polyp fanning effect" by which polyps on a convex surface have a competitive advantage relative to polyps on a flat or concave surface. The fanning effect generates a more potent branching mechanism than the Laplacian growth mechanism that we have studied previously. We discuss the application of the polyp oriented model to the study of environmentally driven morphological plasticity in stony corals. In a few examples we show how the properties of the individual polyps influence the whole colony morphology. In our model, the spacing of polyps influences the thickness of coral branches and the overall compactness of the colony. Density variations in the coral skeleton may also be important for the whole colony morphology, which we address by studying two variants of the model. Finally, we discuss the importance of small scale resource translocation in the coral colony and its effects on the morphology of the colony.

  9. Bayesian MCMC inference for the Gompertz distribution based on progressive first-failure censoring data

    NASA Astrophysics Data System (ADS)

    Soliman, Ahmed A.; Al Sobhi, Mashail M.

    2015-02-01

    This article deals with the problem of estimating parameters of the Gompertz distribution (GD) based on progressive first-failure censored data using Bayesian and non-Bayesian approaches. The two-sample prediction problem is considered to derive Bayesian prediction bounds for both future order statistics and future record values based on progressive first failure censored informative samples from GD. The sampling schemes such as, first-failure censoring, progressive type II censoring, type II censoring and complete sample can be obtained as special cases of the progressive first-failure censored scheme. Markov chain Monte Carlo (MCMC) method with Gibbs sampling procedure is used to compute the Bayes estimates and also to construct the corresponding credible intervals of the parameters. A simulation study has been conducted in order to compare the proposed Bayes estimators with the maximum likelihood estimators MLE. Finally, some numerical computations with real data set are presented for illustrating all the proposed inferential procedures.

  10. A non-autonomous stochastic predator-prey model.

    PubMed

    Buonocore, Aniello; Caputo, Luigia; Pirozzi, Enrica; Nobile, Amelia G

    2014-04-01

    The aim of this paper is to consider a non-autonomous predator-prey-like system, with a Gompertz growth law for the prey. By introducing random variations in both prey birth and predator death rates, a stochastic model for the predator-prey-like system in a random environment is proposed and investigated. The corresponding Fokker-Planck equation is solved to obtain the joint probability density for the prey and predator populations and the marginal probability densities. The asymptotic behavior of the predator-prey stochastic model is also analyzed.

  11. Dendritic growth model of multilevel marketing

    NASA Astrophysics Data System (ADS)

    Pang, James Christopher S.; Monterola, Christopher P.

    2017-02-01

    Biologically inspired dendritic network growth is utilized to model the evolving connections of a multilevel marketing (MLM) enterprise. Starting from agents at random spatial locations, a network is formed by minimizing a distance cost function controlled by a parameter, termed the balancing factor bf, that weighs the wiring and the path length costs of connection. The paradigm is compared to an actual MLM membership data and is shown to be successful in statistically capturing the membership distribution, better than the previously reported agent based preferential attachment or analytic branching process models. Moreover, it recovers the known empirical statistics of previously studied MLM, specifically: (i) a membership distribution characterized by the existence of peak levels indicating limited growth, and (ii) an income distribution obeying the 80 - 20 Pareto principle. Extensive types of income distributions from uniform to Pareto to a "winner-take-all" kind are also modeled by varying bf. Finally, the robustness of our dendritic growth paradigm to random agent removals is explored and its implications to MLM income distributions are discussed.

  12. Enhancement and modeling of microparticle-added Rhizopus oryzae lactic acid production.

    PubMed

    Coban, Hasan Bugra; Demirci, Ali

    2016-02-01

    Lactic acid has a wide industrial application area and can be produced by fungal strains. However, excessive bulk growth form of fungi during the fermentations is a major problem, which limits the fermentation performance. Microparticles are excellent tools to prevent bulk fungal growth and provide homogenized fermentation broth to increase uniformity and the prediction performance of the models. Therefore, in this study, addition of aluminum oxide and talcum microparticles into fermentations was evaluated to enhance the production of lactic acid by Rhizopus oryzae. The results showed that the bulk fungal growth was prevented and the lactic acid concentration increased from 6.02 to 13.88 and 24.01 g/L, when 15 g/L of aluminum oxide or 10 g/L of talcum was used, respectively, in the shake-flask fermentations. Additionally, substrate concentration, pH, and agitation were optimized in the bioreactors using response surface methodology, and optimum values were determined as 126 g/L of glucose, 6.22 pH, and 387 rpm, respectively. Under these conditions, lactic acid production further increased to 75.1 ± 1.5 g/L with 10 g/L of talcum addition. Also, lactic acid production and glucose consumption in the batch fermentation were successfully modeled with modified Gompertz model and modified logistic model. RMSE and MAE values for lactic acid production were calculated as 2.279 and 1.498 for the modified Gompertz model; 3.6 and 4.056 for the modified logistic model. Additionally, modified logistic model predicted glucose consumption with -2.088 MAE and 2.868 RMSE, whereas these values were calculated as 2.035 and 3.946 for the modified Gompertz model.

  13. Growth/reflectance model interface for wheat and corresponding model

    NASA Technical Reports Server (NTRS)

    Suits, G. H.; Sieron, R.; Odenweller, J.

    1984-01-01

    The use of modeling to explore the possibility of discovering new and useful crop condition indicators which might be available from the Thematic Mapper and to connect these symptoms to the biological causes in the crop is discussed. A crop growth model was used to predict the day to day growth features of the crop as it responds biologically to the various environmental factors. A reflectance model was used to predict the character of the interaction of daylight with the predicted growth features. An atmospheric path radiance was added to the reflected daylight to simulate the radiance appearing at the sensor. Finally, the digitized data sent to a ground station were calculated. The crop under investigation is wheat.

  14. A physiological model of softwood cambial growth.

    PubMed

    Hölttä, Teemu; Mäkinen, Harri; Nöjd, Pekka; Mäkelä, Annikki; Nikinmaa, Eero

    2010-10-01

    Cambial growth was modelled as a function of detailed levelled physiological processes for cell enlargement and water and sugar transport to the cambium. Cambial growth was described at the cell level where local sugar concentration and turgor pressure induce irreversible cell expansion and cell wall synthesis. It was demonstrated how transpiration and photosynthesis rates, metabolic and physiological processes and structural features of a tree mediate their effects directly on the local water and sugar status and influence cambial growth. Large trees were predicted to be less sensitive to changes in the transient water and sugar status, compared with smaller ones, as they have more water and sugar storage and were, therefore, less coupled to short-term changes in the environment. Modelling the cambial dynamics at the individual cell level turned out to be a complex task as the radial short-distance transport of water and sugars and control signals determining cell division and cessation of cell enlargement and cell wall synthesis had to be described simultaneously.

  15. Network growth models and genetic regulatory networks

    NASA Astrophysics Data System (ADS)

    Foster, D. V.; Kauffman, S. A.; Socolar, J. E. S.

    2006-03-01

    We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with the innovation of new links, allowing for the possibility that input and output links from a newly created node may have different probabilities of survival. We find some counterintuitive trends as the parameters are varied, including the broadening of the in-degree distribution when the probability for retaining input links is decreased. We also find that both the scaling of transcription factors with genome size and the measured degree distributions for genes in yeast can be reproduced by the growth algorithm if and only if a special seed is used to initiate the process.

  16. Network growth models and genetic regulatory networks

    NASA Astrophysics Data System (ADS)

    Socolar, Joshua; Foster, David; Kauffman, Stuart

    2006-03-01

    We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new links, allowing for the possibility that input and output links from a newly created node may have different probabilities of survival. We find some counterintuitive trends as parameters are varied, including the broadening of indegree distribution when the probability for retaining input links is decreased. We also find that both the scaling of transcription factors with genome size and the measured degree distributions for genes in yeast can be reproduced by the growth algorithm if and only if a special seed is used to initiate the process.

  17. SOA multiday growth: Model artifact or reality?

    NASA Astrophysics Data System (ADS)

    Lee-Taylor, J. M.; Madronich, S.; Aumont, B.; Hodzic, A.; Camredon, M.; Valorso, R.

    2013-12-01

    Simulations of SOA gas-particle partitioning with the explicit gas-phase chemical mechanism generator GECKO-A show significant SOA mass growth continuing for several days, even as the initial air parcel is diluted into the regional atmosphere. This result is a robust feature of our model and occurs with both anthropogenic and biogenic precursors. The growth originates from continuing oxidation of gas-phase precursors which persist in equilibrium with the particle phase. This result implies that sources of aerosol precursors could influence the chemical and radiative characteristics of the atmosphere over a wider region than previously imagined, and that SOA measurements near precursor sources may routinely underestimate this influence. It highlights the need to better understand the sink terms in the SOA budget.

  18. Detecting Appropriate Trajectories of Growth in Latent Growth Models: The Performance of Information-Based Criteria

    ERIC Educational Resources Information Center

    Whittaker, Tiffany A.; Khojasteh, Jam

    2017-01-01

    Latent growth modeling (LGM) is a popular and flexible technique that may be used when data are collected across several different measurement occasions. Modeling the appropriate growth trajectory has important implications with respect to the accurate interpretation of parameter estimates of interest in a latent growth model that may impact…

  19. State Growth Models for School Accountability: Progress on Development and Reporting Measures of Student Growth

    ERIC Educational Resources Information Center

    Blank, Rolf K.

    2010-01-01

    The Council of Chief State School Officers (CCSSO) is working to respond to increased interest in the use of growth models for school accountability. Growth models are based on tracking change in individual student achievement scores over multiple years. While growth models have been used for decades in academic research and program evaluation, a…

  20. 2D motility tracking of Pseudomonas putida KT2440 in growth phases using video microscopy

    PubMed Central

    Davis, Michael L.; Mounteer, Leslie C.; Stevens, Lindsey K.; Miller, Charles D.; Zhou, Anhong

    2011-01-01

    Pseudomonas putida KT2440 is a gram negative motile soil bacterium important in bioremediation and biotechnology. Thus, it is important to understand its motility characteristics as individuals and in populations. Population characteristics were determined using a modified Gompertz model. Video microscopy and imaging software were utilized to analyze two dimensional (2D) bacteria movement tracks to quantify individual bacteria behavior. It was determined that inoculum density increased the lag time as seeding densities decreased, and that the maximum specific growth rate decreased as seeding densities increased. Average bacterial velocity remained relatively similar throughout exponential growth phase (~20.9 µm/sec), while maximum velocities peak early in exponential growth phase at a velocity of 51.2 µm/sec. Pseudomonas putida KT2440 also favor smaller turn angles indicating they often continue in the same direction after a change in flagella rotation throughout the exponential growth phase. PMID:21334971

  1. Quantitative Modeling of Growth and Dispersal in Population Models.

    DTIC Science & Technology

    1986-01-01

    partial differential equations. Applications to dispersal and nonlinear growth/predation models arc dnsity- depresented . Computational iresults using...depend only on size x. The ideas we present here can be readily modified to treat theoretically and computationally the more general case where g and m

  2. [Modification and its application of generalized Schumacher model].

    PubMed

    Hong, Wei; Wu, Chengzhen; Yan, Shujun

    2004-02-01

    Based on the concrete analysis on growth equations presented by others, a modified Schumacher growth equation was proposed as, which included Gompertz function, Schumacher equation and generalized Schumacher equation, and had stronger self-adaptability and practicality. The analytic character and adaptability of the modified Schumacher equation were analyzed. According to the genetic algorithms method, this model was used to fit the growth data of endangered plant of Tsuga longibracteata and Platycladus orientalis. The results showed that the modified Schumacher equation was not only better than Schumacher equation and generalized Schumacher equation significantly, but also better than classical Logistic model and Li's self-adaptive model. So it could be used to study the dynamics simulation for tree growth and dynamics law for population growth.

  3. Skew-t fits to mortality data--can a Gaussian-related distribution replace the Gompertz-Makeham as the basis for mortality studies?

    PubMed

    Clark, Jeremy S C; Kaczmarczyk, Mariusz; Mongiało, Zbigniew; Ignaczak, Paweł; Czajkowski, Andrzej A; Klęsk, Przemysław; Ciechanowicz, Andrzej

    2013-08-01

    Gompertz-related distributions have dominated mortality studies for 187 years. However, nonrelated distributions also fit well to mortality data. These compete with the Gompertz and Gompertz-Makeham data when applied to data with varying extents of truncation, with no consensus as to preference. In contrast, Gaussian-related distributions are rarely applied, despite the fact that Lexis in 1879 suggested that the normal distribution itself fits well to the right of the mode. Study aims were therefore to compare skew-t fits to Human Mortality Database data, with Gompertz-nested distributions, by implementing maximum likelihood estimation functions (mle2, R package bbmle; coding given). Results showed skew-t fits obtained lower Bayesian information criterion values than Gompertz-nested distributions, applied to low-mortality country data, including 1711 and 1810 cohorts. As Gaussian-related distributions have now been found to have almost universal application to error theory, one conclusion could be that a Gaussian-related distribution might replace Gompertz-related distributions as the basis for mortality studies.

  4. Comparison of Models for Estimating Individual Growth Curves.

    ERIC Educational Resources Information Center

    Burchinal, Margaret R.

    Growth curve models are a useful tool for developmentalists because they can estimate an attribute's developmental function by providing a mathematical description of growth on an attribute over time. However, selection of a growth curve model appropriate for estimating individual developmental functions is problematic. The ideal model is the one…

  5. Gompertz type dechanneling functions for protons in <1 0 0>, <1 1 0> and <1 1 1> Si crystal channels

    NASA Astrophysics Data System (ADS)

    Petrović, S.; Erić, M.; Kokkoris, M.; Nešković, N.

    2007-03-01

    In this work the energy dependences of the Gompertz type sigmoidal dechanneling function parameters for protons in <1 0 0>, <1 1 0> and <1 1 1> Si crystal channels is investigated theoretically. The proton energy range considered is between 1 and 10 MeV. The original dechanneling functions are generated using a realistic Monte Carlo computer simulation code. We show that the Gompertz type dechanneling function, having two parameters, lc and k, representing the dechanneling range and rate, respectively, approximate accurately the original dechanneling function. It is also shown that the energy dependences of parameters lc and k can be approximated by a linear function and a sum of two exponential functions, respectively. The results obtained can be used for accurate reproduction of experimental proton channeling spectra recorded in the backscattering geometry.

  6. A competition model for wormhole growth

    NASA Astrophysics Data System (ADS)

    Cabeza Diaz de Cerio, Yoar; Carrera, Jesus; Hidalgo, Juan J.

    2016-04-01

    Flow preferential pathways generated by dissolution are commonly known as wormholes. Wormhole generation and evolution are topics of interest not only for karst aquifer studies but also for fields as CO2 storage and oil industry among others. The objective of this work is to show that given an initial perturbation, the development of the dissolution pattern can be considered deterministic. This means that the evolution of the effective hydraulic conductivity can be predicted. To this end we use a wormhole growth model in which wormholes compete for the available water. In the competition model the wormholes grow proportionally to the flow rate through them. The wormhole flow rate is a function of the wormholes lengths and distances between them. We derive empirical expressions for the flow rates from steady state flow synthetic models with different geometries. Finally, we perform series of simulations using this competition model, applying random initial perturbations and different number of wormholes for each set of simulations and we study the evolution of the dissolution pattern. We find that the resulting wormhole patterns are in good agreement with others generated with much more complex models.

  7. Evolutionary model of an anonymous consumer durable market

    NASA Astrophysics Data System (ADS)

    Kaldasch, Joachim

    2011-07-01

    An analytic model is presented that considers the evolution of a market of durable goods. The model suggests that after introduction goods spread always according to a Bass diffusion. However, this phase will be followed by a diffusion process for durable consumer goods governed by a variation-selection-reproduction mechanism and the growth dynamics can be described by a replicator equation. The theory suggests that products play the role of species in biological evolutionary models. It implies that the evolution of man-made products can be arranged into an evolutionary tree. The model suggests that each product can be characterized by its product fitness. The fitness space contains elements of both sites of the market, supply and demand. The unit sales of products with a higher product fitness compared to the mean fitness increase. Durables with a constant fitness advantage replace other goods according to a logistic law. The model predicts in particular that the mean price exhibits an exponential decrease over a long time period for durable goods. The evolutionary diffusion process is directly related to this price decline and is governed by Gompertz equation. Therefore it is denoted as Gompertz diffusion. Describing the aggregate sales as the sum of first, multiple and replacement purchase the product life cycle can be derived. Replacement purchase causes periodic variations of the sales determined by the finite lifetime of the good (Juglar cycles). The model suggests that both, Bass- and Gompertz diffusion may contribute to the product life cycle of a consumer durable. The theory contains the standard equilibrium view of a market as a special case. It depends on the time scale, whether an equilibrium or evolutionary description is more appropriate. The evolutionary framework is used to derive also the size, growth rate and price distribution of manufacturing business units. It predicts that the size distribution of the business units (products) is lognormal

  8. Regime Switching in the Latent Growth Curve Mixture Model

    ERIC Educational Resources Information Center

    Dolan, Conor V.; Schmittmann, Verena D.; Lubke, Gitta H.; Neale, Michael C.

    2005-01-01

    A linear latent growth curve mixture model is presented which includes switching between growth curves. Switching is accommodated by means of a Markov transition model. The model is formulated with switching as a highly constrained multivariate mixture model and is fitted using the freely available Mx program. The model is illustrated by analyzing…

  9. Continuum models for epitaxial growth with elasticity

    NASA Astrophysics Data System (ADS)

    Xiang, Yang

    In heteroepitaxial growth, the mismatch between the lattice constants in the film and the substrate causes misfit strain in the film, making a flat surface unstable to small perturbations. This morphological instability is called Asaro-Tiller-Grinfeld (ATG) instability, which can drive the film to self-organize into nanostructures such as quantum wires or quantum dots. At low temperature, the surface consists of steps and facets, when the misfit strain causes step bunching, traditional continuum models for ATG instability does not apply directly. In the first part of this thesis, we derive a PDE model for step bunching by taking the continuum limit of the discrete models proposed by Tersoff et al and Duport et al. We study the linear instability of a uniform step train with small perturbations and compare our results with those of discrete models and continuum models for traditional ATG instability. We numerically study the nonlinear evolution of this instability and compare our results with those of discrete models. We also study the equilibrium shapes of step bunches and explain their coalescence. In the second part of this thesis, we derive a nonlinear approximate PDE for the ATG instability. In the ATG instability, the misfit strain is coupled with surface morphology and an elasticity problem must be solved numerically. Linear approximation is made in some cases such as when computing the equilibrium island shapes. Using the exact solution for a cycloid surface obtained by Chiu and Gao, we find that our nonlinear approximation has a wider range of applicability than linear approximation. Numerical simulation using our nonlinear PDE model predicts formation of a cusp-like surface morphology from initially small perturbations of flat surfaces, which agrees well with the result obtained by Spencer and Meiron by solving the elasticity problem numerically.

  10. Modeling Hematite Bioreduction under Growth Conditions

    NASA Astrophysics Data System (ADS)

    Yu, J.; Chen, C.; Yeh, G.; Burgos, W. D.; Mynyard, M. L.

    2004-12-01

    The focus of this work is on simulating and analyzing bioreduction kinetics of natural hematite-coated sand by dissimilatory metal-reducing bacterium (DMRB), Shewanella putrefaciens CN32, under growth conditions with lactate as the electron donor. A reaction-based biogeochemical model was used. A series of batch experiments with different initial conditions were performed to determine the rate formulations/parameters for hematite bioreduction and related reactions. Three different kinetic reaction rate formations were used to model hematite bioreduction. The consistency of mass conservation equations was assessed. Assumptions regarding equilibrium reactions were also assessed. Column experiments focused on transient reactive transport were conducted under otherwise identical conditions, except that the flow rate was systematically varied. The determined rate formulations/parameters were systematically tested with these column experiments using a reactive biogeochemical transport model that coupled hydrologic transport and reactive biogeochemistry. The model simulated the hematite bioreduction of hematite-coated sand in column experiments reasonably well using rate formulation/parameters determined from batch experiments. This study supports the hypothesis that mechanistic-based reaction rates of batch experiments can be scaled up and ported to column experiments.

  11. Flower Power: Sunflowers as a Model for Logistic Growth

    ERIC Educational Resources Information Center

    Fernandez, Eileen; Geist, Kristi A.

    2011-01-01

    Logistic growth displays an interesting pattern: It starts fast, exhibiting the rapid growth characteristic of exponential models. As time passes, it slows in response to constraints such as limited resources or reallocation of energy. The growth continues to slow until it reaches a limit, called capacity. When the growth describes a population,…

  12. Flower Power: Sunflowers as a Model for Logistic Growth

    ERIC Educational Resources Information Center

    Fernandez, Eileen; Geist, Kristi A.

    2011-01-01

    Logistic growth displays an interesting pattern: It starts fast, exhibiting the rapid growth characteristic of exponential models. As time passes, it slows in response to constraints such as limited resources or reallocation of energy. The growth continues to slow until it reaches a limit, called capacity. When the growth describes a population,…

  13. Modeling LX-17 Detonation Growth and Decay Using the Ignition and Growth Model

    NASA Astrophysics Data System (ADS)

    Tarver, Craig M.; Chidester, Steven K.

    2009-12-01

    The previously established Ignition and Growth reactive flow model for the detonating triaminotrinitrobenzene (TATB) based plastic bonded explosive LX-17 is applied to recent experimental detonation propagation/failure experiments using unconfined, Lucite confined, and copper confined cylinders. The model also simulates two corner turning experiments in which steel and Lucite act as boundary materials. Finally, the model is used to calculate a one-inch diameter "Hockey Puck" test in which the booster explosive is HMX-based rather than TATB-based. Since the LX-17 Ignition and Growth model parameters are normalized to a great deal of one-, two- and three-dimensional detonation propagation data, they accurately predict all of this new experimental detonation velocity and arrival time data.

  14. Incorporating Student Mobility in Achievement Growth Modeling: A Cross-Classified Multiple Membership Growth Curve Model

    ERIC Educational Resources Information Center

    Grady, Matthew W.; Beretvas, S. Natasha

    2010-01-01

    Multiple membership random effects models (MMREMs) have been developed for use in situations where individuals are members of multiple higher level organizational units. Despite their availability and the frequency with which multiple membership structures are encountered, no studies have extended the MMREM approach to hierarchical growth curve…

  15. Incorporating Student Mobility in Achievement Growth Modeling: A Cross-Classified Multiple Membership Growth Curve Model

    ERIC Educational Resources Information Center

    Grady, Matthew W.; Beretvas, S. Natasha

    2010-01-01

    Multiple membership random effects models (MMREMs) have been developed for use in situations where individuals are members of multiple higher level organizational units. Despite their availability and the frequency with which multiple membership structures are encountered, no studies have extended the MMREM approach to hierarchical growth curve…

  16. Comparing models for growth and management of forest tracts

    Treesearch

    J.J. Colbert; Michael Schuckers; Desta Fekedulegn

    2003-01-01

    The Stand Damage Model (SDM) is a PC-based model that is easily installed, calibrated and initialized for use in exploring the future growth and management of forest stands or small wood lots. We compare the basic individual tree growth model incorporated in this model with alternative models that predict the basal area growth of trees. The SDM is a gap-type simulator...

  17. Measuring aging rates of mice subjected to caloric restriction and genetic disruption of growth hormone signaling

    PubMed Central

    Koopman, Jacob J.E.; van Heemst, Diana; van Bodegom, David; Bonkowski, Michael S.; Sun, Liou Y.; Bartke, Andrzej

    2016-01-01

    Caloric restriction and genetic disruption of growth hormone signaling have been shown to counteract aging in mice. The effects of these interventions on aging are examined through age-dependent survival or through the increase in age-dependent mortality rates on a logarithmic scale fitted to the Gompertz model. However, these methods have limitations that impede a fully comprehensive disclosure of these effects. Here we examine the effects of these interventions on murine aging through the increase in age-dependent mortality rates on a linear scale without fitting them to a model like the Gompertz model. Whereas these interventions negligibly and non-consistently affected the aging rates when examined through the age-dependent mortality rates on a logarithmic scale, they caused the aging rates to increase at higher ages and to higher levels when examined through the age-dependent mortality rates on a linear scale. These results add to the debate whether these interventions postpone or slow aging and to the understanding of the mechanisms by which they affect aging. Since different methods yield different results, it is worthwhile to compare their results in future research to obtain further insights into the effects of dietary, genetic, and other interventions on the aging of mice and other species. PMID:26959761

  18. Measuring aging rates of mice subjected to caloric restriction and genetic disruption of growth hormone signaling.

    PubMed

    Koopman, Jacob J E; van Heemst, Diana; van Bodegom, David; Bonkowski, Michael S; Sun, Liou Y; Bartke, Andrzej

    2016-03-01

    Caloric restriction and genetic disruption of growth hormone signaling have been shown to counteract aging in mice. The effects of these interventions on aging are examined through age-dependent survival or through the increase in age-dependent mortality rates on a logarithmic scale fitted to the Gompertz model. However, these methods have limitations that impede a fully comprehensive disclosure of these effects. Here we examine the effects of these interventions on murine aging through the increase in age-dependent mortality rates on a linear scale without fitting them to a model like the Gompertz model. Whereas these interventions negligibly and non-consistently affected the aging rates when examined through the age-dependent mortality rates on a logarithmic scale, they caused the aging rates to increase at higher ages and to higher levels when examined through the age-dependent mortality rates on a linear scale. These results add to the debate whether these interventions postpone or slow aging and to the understanding of the mechanisms by which they affect aging. Since different methods yield different results, it is worthwhile to compare their results in future research to obtain further insights into the effects of dietary, genetic, and other interventions on the aging of mice and other species.

  19. Growth model for arbuscular mycorrhizal fungi.

    PubMed

    Schnepf, A; Roose, T; Schweiger, P

    2008-07-06

    In order to quantify the contribution of arbuscular mycorrhizal (AM) fungi to plant phosphorus nutrition, the development and extent of the external fungal mycelium and its nutrient uptake capacity are of particular importance. We develop and analyse a model of the growth of AM fungi associated with plant roots, suitable for describing mechanistically the effects of the fungi on solute uptake by plants. The model describes the development and distribution of the fungal mycelium in soil in terms of the creation and death of hyphae, tip-tip and tip-hypha anastomosis, and the nature of the root-fungus interface. It is calibrated and corroborated using published experimental data for hyphal length densities at different distances away from root surfaces. A good agreement between measured and simulated values was found for three fungal species with different morphologies: Scutellospora calospora (Nicol. & Gerd.) Walker & Sanders; Glomus sp.; and Acaulospora laevis Gerdemann & Trappe associated with Trifolium subterraneum L. The model and findings are expected to contribute to the quantification of the role of AM fungi in plant mineral nutrition and the interpretation of different foraging strategies among fungal species.

  20. Model of particle growth in silane discharges

    PubMed

    Gallagher

    2000-08-01

    The growth of silicon particles in the neutral plasma region of pure silane, rf capacitively coupled, steady-state discharges is calculated with a homogeneous, plasma-chemistry model. Plasma conditions are typical of those used in hydrogenated amorphous silicon (a-Si:H) device production. SiH3 and SiH-3 grow into particles by the step-by-step addition of silicon atoms, primarily due to reactions with SiH3. Attrition of growing Si(x)H(z)(m) radicals and ions with z charges, which are "particles" for large x, occurs by diffusion of neutral and positively charged radicals to the electrodes. Rate coefficients for electron, ion, radical, and silane collisions with the Si(x)H(z)(m) for x=1-10(5) are estimated from detailed considerations of the literature and relevant physics. Self-consistent anion, cation (n(+)), and electron (n(e)) densities and charge fluxes are used, and charge neutrality is maintained. Typically n(+)/n(e) congruent with100, which causes a large fraction of neutral particles and thereby a major particle flux into the growing a-Si:H film. The density of visible particles (x>10(4)) varies many orders of magnitude with relatively minor changes in discharge power, pressure, and electrode gap. This parameter dependence agrees with experiment, and by adjusting collision parameters within a reasonable range the calculated particle densities can be brought into exact agreement with experiment. An additional result of the model, which has not yet been detected, is that Si(x)H(m) clusters with 3growth.

  1. Disseminated thrombosis-induced growth plate necrosis in rat: a unique model for growth plate arrest.

    PubMed

    Nyska, Meir; Shabat, Shay; Long, Philip H; Howard, Charles; Ezov, Nathan; Levin-Harrus, Tal; Mittelman, Moshe; Redlich, Meir; Yedgar, Saul; Nyska, Abraham

    2005-01-01

    Exposure of rats to 2-butoxyethanol (BE) produces early hemolytic anemia and disseminated thrombosis. This leads to infarctions in multiple organs, including bones and cartilage. BE, administered for different durations of exposure in two separate experiments, produced metaphyseal vascular thrombosis, growth plate infarction, and partial or complete physeal growth arrest. This reproducible model may serve as a useful tool in the study of some conditions that manifest growth plate damage. The suitability of this model for investigating the pathogenesis of growth plate necrosis and as a model for potential therapy for various human growth plate disorders are discussed.

  2. [Postnatal growth patterns in eight species of herons and egrets (Ciconiiformes: Ardeidae)].

    PubMed

    Avila, Dennis Denis

    2011-06-01

    Avian postnatal growth has received considerable attention and its ecological implications have been deeply analyzed. In this current paper, I describe the patterns of culmen and tarsus growth, as well as of weight gain patterns in eight species of herons and egrets (Aves: Ardeidae) found in the Birama Swamp in Eastern Cuba. Between 1998 and 2006,714 nestlings of the following species were measured every two days: Butorides virescens, Bubulcus ibis, Egretta thula, E. tricolor, E. caerulea, E. rufescens, Ardea alba and Nycticorax nycticorax. Logistic and Gompertz equations were adjusted to data using non-lineal regression models with adult values as the asymptote. For each species, the following were determined and recorded: growth rate, age at inflexion, instantaneous growth rates at each age interval, and time taken to reach 90% of adult size. Reported hatchling sizes were similar in other localities, with a variation coefficient ranging between 10-19%. At hatch, each species exhibited differing sizes relative to adult values. In all cases, Gompertz equations were best fitted to explain more variance and lesser residuals. Rates of weight change and tarsus growth were alometrically related to the log of adult weight. Two main growth processes were identified: a physical extension in dimensions of each measurement reflecting inter-specific morphometric differences, and a lineal increase of the growth period from Green Heron to Great Egret. The Black-crowned Night Heron, Cattle Egret and Reddish Egret exhibited some unique measurement characteristics in comparison to the remaining members of the family. All results support the hypothesis that hypermorphosis, as the main evolutionary process in the microevolution of Ardeidae, is caused by a delayed final moment of growth.

  3. Uneven futures of human lifespans: reckonings from Gompertz mortality rates, climate change, and air pollution.

    PubMed

    Finch, Caleb E; Beltrán-Sánchez, Hiram; Crimmins, Eileen M

    2014-01-01

    The past 200 years have enabled remarkable increases in human lifespans through improvements in the living environment that have nearly eliminated infections as a cause of death through improved hygiene, public health, medicine, and nutrition. We argue that the limit to lifespan may be approaching. Since 1997, no one has exceeded Jeanne Calment's record of 122.5 years, despite an exponential increase of centenarians. Moreover, the background mortality may be approaching a lower limit. We calculate from Gompertz coefficients that further increases in longevity to approach a life expectancy of 100 years in 21st century cohorts would require 50% slower mortality rate accelerations, which would be a fundamental change in the rate of human aging. Looking into the 21st century, we see further challenges to health and longevity from the continued burning of fossil fuels that contribute to air pollution as well as global warming. Besides increased heat waves to which elderly are vulnerable, global warming is anticipated to increase ozone levels and facilitate the spread of pathogens. We anticipate continuing socioeconomic disparities in life expectancy.

  4. Incidence of the Bertillon and Gompertz effects on the outcome of clinical trials

    NASA Astrophysics Data System (ADS)

    Roehner, Bertrand M.

    2014-11-01

    The accounts of medical trials provide very detailed information about the patients’ health conditions. On the contrary, almost no vital data such as marital status or age distribution are usually given. Yet, some of these factors can have a notable impact on the overall death rate, thereby changing the outcome and conclusions of the trial. This paper focuses on two of these variables. The first is marital status; its effect on life expectancy (which will be referred to as the Bertillon effect) may double death rates in all age intervals. The second variable is the age distribution of the oldest patients. Because of the exponential nature of Gompertz’s law changes in the distribution of ages in the oldest age group can have dramatic consequences on the overall number of deaths. One should recall that the death rate at the age of 82 is 40 times higher than at the age of 37. It will be seen that randomization alone can hardly take care of these problems. Appropriate remedies are easy to formulate however. First, the marital status of patients as well as the age distribution of those over 65 should be documented for both study groups. Then, thanks to these data and based on the Bertillon and Gompertz laws, it will become possible to perform appropriate corrections. Such corrections will notably improve the reliability and accuracy of the conclusions, especially in trials which include a large proportion of elderly subjects.

  5. Modelling the unsteady growth state population balance for a nonlinear growth model in an MSMPR crystallizer

    SciTech Connect

    Carver, C.; Chipman, N.A.; Carleson, T.E.

    1994-03-01

    The precipitation of zirconium and other metal species as hydroxides (hydrous oxides) from simulated nuclear waste process solutions has been investigated as a potential method to reduce radioactive waste volumes. The reaction of ammonium hexaflourozirconate was used to simulate these waste streams. Studies were conducted to investigate the unsteady state response of crystallization in mixed suspension, mixed product removal (MSMPR) crystallizer. Size distributions below 40 {mu}m from laboratory batch and MSMPR data indicate size-dependent growth may be occurring because they may fit the Abegg, Stevens and Larson (ASL) model. However, these distributions also may fit a transient growth model based on the Method of Lines numerical solution to the unsteady state population balance equation. The development of the Method of Lines solution as well as experimental agreement with both models were studied.

  6. A model of urban rational growth based on grey prediction

    NASA Astrophysics Data System (ADS)

    Xiao, Wenjing

    2017-04-01

    Smart growth focuses on building sustainable cities, using compact development to prevent urban sprawl. This paper establishes a series of models to implement smart growth theories into city design. Besides two specific city design cases are shown. Firstly, We establishes Smart Growth Measure Model to measure the success of smart growth of a city. And we use Full Permutation Polygon Synthetic Indicator Method to calculate the Comprehensive Indicator (CI) which is used to measure the success of smart growth. Secondly, this paper uses the principle of smart growth to develop a new growth plan for two cities. We establish an optimization model to maximum CI value. The Particle Swarm Optimization (PSO) algorithm is used to solve the model. Combined with the calculation results and the specific circumstances of cities, we make their the smart growth plan respectively.

  7. Reactive burn models and ignition & growth concept

    SciTech Connect

    Menikoff, Ralph S; Shaw, Milton S

    2010-01-01

    Plastic-bonded explosives are heterogeneous materials. Experimentally, shock initiation is sensitive to small amounts of porosity, due to the formation of hot spots (small localized regions of high temperature). This leads to the Ignition and Growth concept, introduced by Lee and Tarver in 1980, as the basis for reactive burn models. A homogeneized burn rate needs to account for three mesoscale physical effects (i) the density of burnt hot spots, which depends on the lead shock strength; (ii) the growth of the burn fronts triggered by hot spots, which depends on the local deflagration speed; (iii) a geometric factor that accounts for the overlap of deflagration wavelets from adjacent hot spots. These effects can be combined and the burn model defined by specifying the reaction progress variable {lambda}(t) as a function of a dimensionless reaction length {tau}{sub hs}(t)/{ell}{sub hs}, rather than by xpecifying an explicit burn rate. The length scale {ell}{sub hs} is the average distance between hot spots, which is proportional to [N{sub hs}(P{sub s})]{sup -1/3}, where N{sub hs} is the number density of hot spots activated by the lead shock. The reaction length {tau}{sub hs}(t) = {line_integral}{sub 0}{sup t} D(P(t'))dt' is the distance the burn front propagates from a single hot spot, where D is the deflagration speed and t is the time since the shock arrival. A key implementation issue is how to determine the lead shock strength in conjunction with a shock capturing scheme. They have developed a robust algorithm for this purpose based on the Hugoniot jump condition for the energy. The algorithm utilizes the time dependence of density, pressure and energy within each cell. The method is independent of the numerical dissipation used for shock capturing. It is local and can be used in one or more space dimensions. The burn model has a small number of parameters which can be calibrated to fit velocity gauge data from shock initiation experiments.

  8. Numeric Modeling of Granular Asteroid Growth

    NASA Astrophysics Data System (ADS)

    Beaumont, Benjamin; Lazzati, D.

    2014-01-01

    It is believed that planetesimals and asteroids are created by the constructive collisions of smaller objects, loosely bound under the effect of self-gravity and/or contact forces. However, the internal dynamics of these collisions and whether they trigger growth or fragmentation are poorly understood. Prior research in the topic has established regimes for the results of constructive collisions of particles under contact forces, but neglects gravity, a critical component once particles are no longer touching, and force chains, an uneven distribution of force inherent to granular materials. We run simulations binary collisions of clusters of particles modeled as hard spheres. Our simulations take into account self-gravity, dissipation of energy, friction, and use a potential function for overlapping particles to study force chains. We present here the collision outcome for clusters with variable masses, particle counts, velocities, and impact parameter. We compare our results to other models and simulations, and find that the collisions remain constructive at higher energies than classically predicted.

  9. Growth rate modeling for selective tungsten LPCVD

    NASA Astrophysics Data System (ADS)

    Wolf, H.; Streiter, R.; Schulz, S. E.; Gessner, T.

    1995-10-01

    Selective chemical vapor deposition of tungsten plugs on sputtered tungsten was performed in a single-wafer cold-wall reactor using silane (SiH 4) and tungsten hexafluoride (WF 6). Extensive SEM measurements of film thickness were carried out to study the dependence of growth rates on various process conditions, wafer loading, and via dimensions. The results have been interpreted by numerical calculations based on a simulation model which is also presented. Both continuum fluid dynamics and the ballistic line-of-sight approach are used for transport modeling. The reaction rate is described by an empirical rate expression using coefficients fitted from experimental data. In the range 0.2 < p( SiH 4) /p( WF 6) < 0.75 , the reaction order was determined as 1.55 and -0.55 with respect to SiH 4 and WF 6, respectively. For higher partial pressure ratios the second-order rate dependence on p(SiH 4) and the minus first-order dependence on p(WF 6) were confirmed.

  10. Trans-theta logistics: a new family of population growth sigmoid functions.

    PubMed

    Kozusko, F; Bourdeau, M

    2011-12-01

    Sigmoid functions have been applied in many areas to model self limited population growth. The most popular functions; General Logistic (GL), General von Bertalanffy (GV), and Gompertz (G), comprise a family of functions called Theta Logistic ([Formula: see text] L). Previously, we introduced a simple model of tumor cell population dynamics which provided a unifying foundation for these functions. In the model the total population (N) is divided into reproducing (P) and non-reproducing/quiescent (Q) sub-populations. The modes of the rate of change of ratio P/N was shown to produce GL, GV or G growth. We now generalize the population dynamics model and extend the possible modes of the P/N rate of change. We produce a new family of sigmoid growth functions, Trans-General Logistic (TGL), Trans-General von Bertalanffy (TGV) and Trans-Gompertz (TG)), which as a group we have named Trans-Theta Logistic (T [Formula: see text] L) since they exist when the [Formula: see text] L are translated from a two parameter into a three parameter phase space. Additionally, the model produces a new trigonometric based sigmoid (TS). The [Formula: see text] L sigmoids have an inflection point size fixed by a single parameter and an inflection age fixed by both of the defining parameters. T [Formula: see text] L and TS sigmoids have an inflection point size defined by two parameters in bounding relationships and inflection point age defined by three parameters (two bounded). While the Theta Logistic sigmoids provided flexibility in defining the inflection point size, the Trans-Theta Logistic sigmoids provide flexibility in defining the inflection point size and age. By matching the slopes at the inflection points we compare the range of values of inflection point age for T [Formula: see text] L versus [Formula: see text] L for model growth curves.

  11. Growth and development of chicks of two species of partridge: the grey partridge (Perdix perdix) and the chukar (Alectoris chukar).

    PubMed

    Pis, Tomasz

    2012-01-01

    1. In two partridge species, the grey partridge (Perdix perdix) and chukar (Alectoris chukar), from hatching up to 120 d, the growth rate and development of body mass, wing, tarsus, and bill length were measured and fitted by Gompertz equations. 2. As a typical precocial species, partridges hatched with relatively well developed legs and bills, and wing growth followed a gradual development of thermoregulation. 3. Gompertz growth constants for body mass growth were 0·039 and 0·038 for grey partridges and chukars, respectively. 4. The allometric relationship between tarsus length and body mass followed a geometric similarity (1/3 power) in both grey partridges and chukars.

  12. Local Solutions in the Estimation of Growth Mixture Models

    ERIC Educational Resources Information Center

    Hipp, John R.; Bauer, Daniel J.

    2006-01-01

    Finite mixture models are well known to have poorly behaved likelihood functions featuring singularities and multiple optima. Growth mixture models may suffer from fewer of these problems, potentially benefiting from the structure imposed on the estimated class means and covariances by the specified growth model. As demonstrated here, however,…

  13. Forest Growth and Yield Models Viewed From a Different Perspective

    Treesearch

    Jeffery C. Goelz

    2002-01-01

    Typically, when different forms of growth and yield models are considered, they are grouped into convenient discrete classes. As a heuristic device, I chose to use a contrasting perspective, that all growth and yield models are diameter distribution models that merely differ in regard to which diameter distribution is employed and how the distribution is projected to...

  14. Parameter Estimates in Differential Equation Models for Population Growth

    ERIC Educational Resources Information Center

    Winkel, Brian J.

    2011-01-01

    We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and two-species competition models. We discuss student-evolved strategies and offer "Mathematica" code for a gradient search approach. We use historical (1930s) data from microbial studies of the Russian biologist,…

  15. Parameter Estimates in Differential Equation Models for Population Growth

    ERIC Educational Resources Information Center

    Winkel, Brian J.

    2011-01-01

    We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and two-species competition models. We discuss student-evolved strategies and offer "Mathematica" code for a gradient search approach. We use historical (1930s) data from microbial studies of the Russian biologist,…

  16. Suitability Analysis of Continuous-Use Reliability Growth Projection Models

    DTIC Science & Technology

    2015-03-26

    exists for all types, shapes, and sizes. The primary focus of this study is a comparison of reliability growth projection models designed for...requirements to use reliability growth models, recent studies have noted trends in reliability failures throughout the DoD. In [14] Dr. Michael Gilmore...so a strict exponential distribu- tion was used to stay within their assumptions. In reality, however, reliability growth models often must be used

  17. Predictive growth model of LID: light intensification model

    NASA Astrophysics Data System (ADS)

    Tan, ChingSeong; Patel, D.; Wang, X.; Schlitz, D.; Dehkordi, P. S.; Menoni, C. S.; Chong, E. K. P.

    2013-11-01

    General precursors and growth model of Laser Induced Damage (LID) have been the focus of research in fused silica material, such as polishing residues, fractures, and contaminations. Assuming the absorption due to trapped material and mechanical strength is the same across the surfaces, various studies have shown that the LID could be minimized by reducing the light field intensification of the layers upon the laser strikes. By revisiting the definition of non-ionising radiation damage, this paper presents the modelling work and simulation of light intensification of laser induced damage condition. Our contribution is to predict the LID growth that take into various factors, specifically on the light intensification problem. The light intensification problem is a function of the inter-layer or intra-layer micro-optical properties, such as transmittance and absorption coefficient of the material at micro- or sub-micro-meter range. The proposed model will first estimate the light propagation that convoluted with the multiply scattering light and subsequently the field intensification within the nodule dimension. This will allow us to evaluate the geometrical factor of the nodule effect over the intensification. The result show that the light intensification is higher whenever the backscattering and multiple scattering components are higher due to its interference with the incoming wave within its coherency.

  18. Island growth as a growth mode in atomic layer deposition: A phenomenological model

    NASA Astrophysics Data System (ADS)

    Puurunen, Riikka L.; Vandervorst, Wilfried

    2004-12-01

    Atomic layer deposition (ALD) has recently gained world-wide attention because of its suitability for the fabrication of conformal material layers with thickness in the nanometer range. Although the principles of ALD were realized about 40 years ago, the description of many physicochemical processes that occur during ALD growth is still under development. A constant amount of material deposited in an ALD reaction cycle, that is, growth-per-cycle (GPC), has been a paradigm in ALD through decades. The GPC may vary, however, especially in the beginning of the ALD growth. In this work, a division of ALD processes to four classes is proposed, on the basis of how the GPC varies with the number of ALD reaction cycles: linear growth, substrate-enhanced growth, and substrate-inhibited growth of type 1 and type 2. Island growth is identified as a likely origin for type 2 substrate-inhibited growth, where the GPC increases and goes through a maximum before it settles to a constant value characteristic of a steady growth. A simple phenomenological model is developed to describe island growth in ALD. The model assumes that the substrate is unreactive with the ALD reactants, except for reactive defects. ALD growth is assumed to proceed symmetrically from the defects, resulting islands of a conical shape. Random deposition is the growth mode on the islands. The model allows the simulation of GPC curves, surface fraction curves, and surface roughness, with physically significant parameters. When the model is applied to the zirconium tetrachloride/water and the trimethylaluminum/water ALD processes on hydrogen-terminated silicon, the calculated GPC curves and surface fractions agree with the experiments. The island growth model can be used to assess the occurrence of island growth, the size of islands formed, and point of formation of a continuous ALD-grown film. The benefits and limitations of the model and the general characteristics of type 2 substrate-inhibited ALD are

  19. An autocatalytic kinetic model for describing microbial growth during fermentation.

    PubMed

    Ibarz, Albert; Augusto, Pedro E D

    2015-01-01

    The mathematical modelling of the behaviour of microbial growth is widely desired in order to control, predict and design food and bioproduct processing, stability and safety. This work develops and proposes a new semi-empirical mathematical model, based on an autocatalytic kinetic, to describe the microbial growth through its biomass concentration. The proposed model was successfully validated using 15 microbial growth patterns, covering the three most important types of microorganisms in food and biotechnological processing (bacteria, yeasts and moulds). Its main advantages and limitations are discussed, as well as the interpretation of its parameters. It is shown that the new model can be used to describe the behaviour of microbial growth.

  20. Nanowire growth process modeling and reliability models for nanodevices

    NASA Astrophysics Data System (ADS)

    Fathi Aghdam, Faranak

    Nowadays, nanotechnology is becoming an inescapable part of everyday life. The big barrier in front of its rapid growth is our incapability of producing nanoscale materials in a reliable and cost-effective way. In fact, the current yield of nano-devices is very low (around 10 %), which makes fabrications of nano-devices very expensive and uncertain. To overcome this challenge, the first and most important step is to investigate how to control nano-structure synthesis variations. The main directions of reliability research in nanotechnology can be classified either from a material perspective or from a device perspective. The first direction focuses on restructuring materials and/or optimizing process conditions at the nano-level (nanomaterials). The other direction is linked to nano-devices and includes the creation of nano-electronic and electro-mechanical systems at nano-level architectures by taking into account the reliability of future products. In this dissertation, we have investigated two topics on both nano-materials and nano-devices. In the first research work, we have studied the optimization of one of the most important nanowire growth processes using statistical methods. Research on nanowire growth with patterned arrays of catalyst has shown that the wire-to-wire spacing is an important factor affecting the quality of resulting nanowires. To improve the process yield and the length uniformity of fabricated nanowires, it is important to reduce the resource competition between nanowires during the growth process. We have proposed a physical-statistical nanowire-interaction model considering the shadowing effect and shared substrate diffusion area to determine the optimal pitch that would ensure the minimum competition between nanowires. A sigmoid function is used in the model, and the least squares estimation method is used to estimate the model parameters. The estimated model is then used to determine the optimal spatial arrangement of catalyst arrays

  1. Growth and yield models for central hardwoods

    Treesearch

    Martin E. Dale; Donald E. Hilt

    1989-01-01

    Over the last 20 years computers have become an efficient tool to estimate growth and yield. Computerized yield estimates vary from simple approximation or interpolation of traditional normal yield tables to highly sophisticated programs that simulate the growth and yield of each individual tree.

  2. Spiral Growth in Plants: Models and Simulations

    ERIC Educational Resources Information Center

    Allen, Bradford D.

    2004-01-01

    The analysis and simulation of spiral growth in plants integrates algebra and trigonometry in a botanical setting. When the ideas presented here are used in a mathematics classroom/computer lab, students can better understand how basic assumptions about plant growth lead to the golden ratio and how the use of circular functions leads to accurate…

  3. Spiral Growth in Plants: Models and Simulations

    ERIC Educational Resources Information Center

    Allen, Bradford D.

    2004-01-01

    The analysis and simulation of spiral growth in plants integrates algebra and trigonometry in a botanical setting. When the ideas presented here are used in a mathematics classroom/computer lab, students can better understand how basic assumptions about plant growth lead to the golden ratio and how the use of circular functions leads to accurate…

  4. Brain tumor modeling: glioma growth and interaction with chemotherapy

    NASA Astrophysics Data System (ADS)

    Banaem, Hossein Y.; Ahmadian, Alireza; Saberi, Hooshangh; Daneshmehr, Alireza; Khodadad, Davood

    2011-10-01

    In last decade increasingly mathematical models of tumor growths have been studied, particularly on solid tumors which growth mainly caused by cellular proliferation. In this paper we propose a modified model to simulate the growth of gliomas in different stages. Glioma growth is modeled by a reaction-advection-diffusion. We begin with a model of untreated gliomas and continue with models of polyclonal glioma following chemotherapy. From relatively simple assumptions involving homogeneous brain tissue bounded by a few gross anatomical landmarks (ventricles and skull) the models have been expanded to include heterogeneous brain tissue with different motilities of glioma cells in grey and white matter. Tumor growth is characterized by a dangerous change in the control mechanisms, which normally maintain a balance between the rate of proliferation and the rate of apoptosis (controlled cell death). Result shows that this model closes to clinical finding and can simulate brain tumor behavior properly.

  5. Gompertzian growth and decay: a powerful descriptive tool for neuroscience.

    PubMed

    Easton, Dexter M

    2005-10-15

    First-order kinetics is based on simple exponential decay, usually expressed in base e (Naperian) notation. "Nonexponential" processes, for example, S-shaped functions, are frequently modeled as sums of that elemental construct, and the number of rate constants increases with the number of such terms. A powerful descriptive alternative to sums of simple exponentials is the Gompertz function. In Gompertz kinetics, the rate coefficient of an exponential process is assumed to change exponentially with the independent variable. Nonexponential processes are easily modeled, more efficiently and more accurately than is possible with standard kinetics. Application of Gompertz kinetics to neuroscience research topics ranging from cognitive to molecular is presented to illustrate the power of the model: distribution of nerve fiber diameters, conditioning-testing responses of excitable nerve, psychophysical estimates of taste intensity magnitude, time course of synaptic current, and behavior of membrane conductance during voltage clamp of squid axon.

  6. Detecting Growth Shape Misspecifications in Latent Growth Models: An Evaluation of Fit Indexes

    ERIC Educational Resources Information Center

    Leite, Walter L.; Stapleton, Laura M.

    2011-01-01

    In this study, the authors compared the likelihood ratio test and fit indexes for detection of misspecifications of growth shape in latent growth models through a simulation study and a graphical analysis. They found that the likelihood ratio test, MFI, and root mean square error of approximation performed best for detecting model misspecification…

  7. Detecting Growth Shape Misspecifications in Latent Growth Models: An Evaluation of Fit Indexes

    ERIC Educational Resources Information Center

    Leite, Walter L.; Stapleton, Laura M.

    2011-01-01

    In this study, the authors compared the likelihood ratio test and fit indexes for detection of misspecifications of growth shape in latent growth models through a simulation study and a graphical analysis. They found that the likelihood ratio test, MFI, and root mean square error of approximation performed best for detecting model misspecification…

  8. Extended Eden model reproduces growth of an acellular slime mold

    NASA Astrophysics Data System (ADS)

    Wagner, Geri; Halvorsrud, Ragnhild; Meakin, Paul

    1999-11-01

    A stochastic growth model was used to simulate the growth of the acellular slime mold Physarum polycephalum on substrates where the nutrients were confined in separate drops. Growth of Physarum on such substrates was previously studied experimentally and found to produce a range of different growth patterns [Phys. Rev. E 57, 941 (1998)]. The model represented the aging of cluster sites and differed from the original Eden model in that the occupation probability of perimeter sites depended on the time of occupation of adjacent cluster sites. This feature led to a bias in the selection of growth directions. A moderate degree of persistence was found to be crucial to reproduce the biological growth patterns under various conditions. Persistence in growth combined quick propagation in heterogeneous environments with a high probability of locating sources of nutrients.

  9. Extended Eden model reproduces growth of an acellular slime mold.

    PubMed

    Wagner, G; Halvorsrud, R; Meakin, P

    1999-11-01

    A stochastic growth model was used to simulate the growth of the acellular slime mold Physarum polycephalum on substrates where the nutrients were confined in separate drops. Growth of Physarum on such substrates was previously studied experimentally and found to produce a range of different growth patterns [Phys. Rev. E 57, 941 (1998)]. The model represented the aging of cluster sites and differed from the original Eden model in that the occupation probability of perimeter sites depended on the time of occupation of adjacent cluster sites. This feature led to a bias in the selection of growth directions. A moderate degree of persistence was found to be crucial to reproduce the biological growth patterns under various conditions. Persistence in growth combined quick propagation in heterogeneous environments with a high probability of locating sources of nutrients.

  10. Genetic parameter estimates of growth curve and reproduction traits in Japanese quail.

    PubMed

    Narinc, Dogan; Karaman, Emre; Aksoy, Tulin; Firat, Mehmet Ziya

    2014-01-01

    The goal of selection studies in broilers is to obtain genetically superior chicks in terms of major economic traits, which are mainly growth rate, meat yield, and feed conversion ratio. Multiple selection schedules for growth and reproduction are used in selection programs within commercial broiler dam lines. Modern genetic improvement methods have not been applied in experimental quail lines. The current research was conducted to estimate heritabilities and genetic correlations for growth and reproduction traits in a Japanese quail flock. The Gompertz equation was used to determine growth curve parameters. The Gibbs sampling under a multi-trait animal model was applied to estimate the heritabilities and genetic correlations for these traits. A total of 948 quail were used with complete pedigree information to estimate the genetic parameters. Heritability estimates of BW, absolute and relative growth rates at 5 wk of age (AGR and RGR), β0 and β2 parameters, and age at point of inflection (IPT) of Gompertz growth curve, total egg number (EN) from the day of first lay to 24 wk of age were moderate to high, with values ranging from 0.25 to 0.40. A low heritability (0.07) for fertility (FR) and a strong genetic correlation (0.83) between FR and EN were estimated in our study. Body weight exhibited negative genetic correlation with EN, FR, RGR, and IPT. This genetic antagonism among the mentioned traits may be overcome using modern poultry breeding methods such as selection using multi-trait best linear unbiased prediction and crossbreeding.

  11. Dendritic growth shapes in kinetic Monte Carlo models

    NASA Astrophysics Data System (ADS)

    Krumwiede, Tim R.; Schulze, Tim P.

    2017-02-01

    For the most part, the study of dendritic crystal growth has focused on continuum models featuring surface energies that yield six pointed dendrites. In such models, the growth shape is a function of the surface energy anisotropy, and recent work has shown that considering a broader class of anisotropies yields a correspondingly richer set of growth morphologies. Motivated by this work, we generalize nanoscale models of dendritic growth based on kinetic Monte Carlo simulation. In particular, we examine the effects of extending the truncation radius for atomic interactions in a bond-counting model. This is done by calculating the model’s corresponding surface energy and equilibrium shape, as well as by running KMC simulations to obtain nanodendritic growth shapes. Additionally, we compare the effects of extending the interaction radius in bond-counting models to that of extending the number of terms retained in the cubic harmonic expansion of surface energy anisotropy in the context of continuum models.

  12. The model muddle: in search of tumor growth laws.

    PubMed

    Gerlee, Philip

    2013-04-15

    In this article, we will trace the historical development of tumor growth laws, which in a quantitative fashion describe the increase in tumor mass/volume over time. These models are usually formulated in terms of differential equations that relate the growth rate of the tumor to its current state and range from the simple one-parameter exponential growth model to more advanced models that contain a large number of parameters. Understanding the assumptions and consequences of such models is important, as they often underpin more complex models of tumor growth. The conclusion of this brief survey is that although much improvement has occurred over the last century, more effort and new models are required if we are to understand the intricacies of tumor growth.

  13. Computational modeling of hypertensive growth in the human carotid artery

    NASA Astrophysics Data System (ADS)

    Sáez, Pablo; Peña, Estefania; Martínez, Miguel Angel; Kuhl, Ellen

    2014-06-01

    Arterial hypertension is a chronic medical condition associated with an elevated blood pressure. Chronic arterial hypertension initiates a series of events, which are known to collectively initiate arterial wall thickening. However, the correlation between macrostructural mechanical loading, microstructural cellular changes, and macrostructural adaptation remains unclear. Here, we present a microstructurally motivated computational model for chronic arterial hypertension through smooth muscle cell growth. To model growth, we adopt a classical concept based on the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. Motivated by clinical observations, we assume that the driving force for growth is the stretch sensed by the smooth muscle cells. We embed our model into a finite element framework, where growth is stored locally as an internal variable. First, to demonstrate the features of our model, we investigate the effects of hypertensive growth in a real human carotid artery. Our results agree nicely with experimental data reported in the literature both qualitatively and quantitatively.

  14. A Mathematical Model Coupling Tumor Growth and Angiogenesis

    PubMed Central

    Gomez, Hector

    2016-01-01

    We present a mathematical model for vascular tumor growth. We use phase fields to model cellular growth and reaction-diffusion equations for the dynamics of angiogenic factors and nutrients. The model naturally predicts the shift from avascular to vascular growth at realistic scales. Our computations indicate that the negative regulation of the Delta-like ligand 4 signaling pathway slows down tumor growth by producing a larger density of non-functional capillaries. Our results show good quantitative agreement with experiments. PMID:26891163

  15. Centrality Fingerprints for Power Grid Network Growth Models

    NASA Astrophysics Data System (ADS)

    Gurfinkel, Aleks Jacob; Silva, Daniel A.; Rikvold, Per Arne

    In our previous work, we have shown that many of the properties of the Florida power grid are reproduced by deterministic network growth models based on the minimization of energy dissipation Ediss. As there is no a priori best Ediss minimizing growth model, we here present a tool, called the "centrality fingerprint," for probing the behavior of different growth models. The centrality fingerprints are comparisons of the current flow into/out of the network with the values of various centrality measures calculated at every step of the growth process. Finally, we discuss applications to the Maryland power grid.

  16. Modeling the effects of ozone on soybean growth and yield.

    PubMed

    Kobayashi, K; Miller, J E; Flagler, R B; Heck, W W

    1990-01-01

    A simple mechanistic model was developed based on an existing growth model in order to address the mechanisms of the effects of ozone on growth and yield of soybean [Glycine max. (L.) Merr. 'Davis'] and interacting effects of other environmental stresses. The model simulates daily growth of soybean plants using environmental data including shortwave radiation, temperature, precipitation, irrigation and ozone concentration. Leaf growth, dry matter accumulation, water budget, nitrogen input and seed growth linked to senescence and abscission of leaves are described in the model. The effects of ozone are modeled as reduced photosynthate production and accelerated senescence. The model was applied to the open-top chamber experiments in which soybean plants were exposed to ozone under two levels of soil moisture regimes. After calibrating the model to the growth data and seed yield, goodness-of-fit of the model was tested. The model fitted well for top dry weight in the vegetative growth phase and also at maturity. The effect of ozone on seen yield was also described satisfactorily by the model. The simulation showed apparent interaction between the effect of ozone and soil moisture stress on the seed yield. The model revealed that further work is needed concerning the effect of ozone on the senescence process and the consequences of alteration of canopy microclimate by the open-top chambers.

  17. Growth dynamics of geographically different arbuscular mycorrhizal fungal isolates belonging to the 'Rhizophagus clade' under monoxenic conditions.

    PubMed

    Silvani, Vanesa Analía; Bidondo, Laura Fernández; Bompadre, María Josefina; Colombo, Roxana Paula; Pérgola, Mariana; Bompadre, Agustín; Fracchia, Sebastián; Godeas, Alicia

    2014-01-01

    The growth dynamics of extraradical mycelium and spore formation of 14 "Rhizophagus" isolates from different sites in Argentina were evaluated under monoxenic conditions. A modified Gompertz model was used to characterize the development of mycelium and spores for each isolate under the same conditions. The lag time, maximal growth rate and total quantity of both extraradical hyphae and spores were determined. Wide variability among isolates was detected, and all growth parameters were significantly altered by fungal isolate. Discriminant analysis differentiated isolates primarily based on the extent of extraradical hyphae produced, yet such differences did not conclusively correspond to phylogenetic relationships among closely related isolates based on partial SSU sequences. Given that the "Rhizophagus" isolates were grown under controlled conditions for many generations, the expression of phenotypic variability could be attributed to genetic differences that are not completely resolved by phylogenetic analysis employing the small ribosomal gene. © 2014 by The Mycological Society of America.

  18. Stochastic growth logistic model with aftereffect for batch fermentation process

    SciTech Connect

    Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

    2014-06-19

    In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

  19. Stochastic growth logistic model with aftereffect for batch fermentation process

    NASA Astrophysics Data System (ADS)

    Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

    2014-06-01

    In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

  20. Agent-Based Modeling of Growth Processes

    ERIC Educational Resources Information Center

    Abraham, Ralph

    2014-01-01

    Growth processes abound in nature, and are frequently the target of modeling exercises in the sciences. In this article we illustrate an agent-based approach to modeling, in the case of a single example from the social sciences: bullying.

  1. Agent-Based Modeling of Growth Processes

    ERIC Educational Resources Information Center

    Abraham, Ralph

    2014-01-01

    Growth processes abound in nature, and are frequently the target of modeling exercises in the sciences. In this article we illustrate an agent-based approach to modeling, in the case of a single example from the social sciences: bullying.

  2. Analyzing The Uncertainty Of Diameter Growth Model Predictions

    Treesearch

    Ronald E. McRoberts; Veronica C. Lessard; Margaret R. Holdaway

    1999-01-01

    The North Central Research Station of the USDA Forest Service is developing a new set of individual tree, diameter growth models to be used as a component of an annual forest inventory system. The criterion for selection of predictor variables for these models is the uncertainty in 5-, 10-, and 20-year diameter growth predictions estimated using Monte Carlo simulations...

  3. Nonlinear Growth Models in M"plus" and SAS

    ERIC Educational Resources Information Center

    Grimm, Kevin J.; Ram, Nilam

    2009-01-01

    Nonlinear growth curves or growth curves that follow a specified nonlinear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this article we describe how a variety of sigmoid curves can be fit using the M"plus" structural modeling program and the nonlinear…

  4. A generalized system of models forecasting Central States tree growth.

    Treesearch

    Stephen R. Shifley

    1987-01-01

    Describes the development and testing of a system of individual tree-based growth projection models applicable to species in Indiana, Missouri, and Ohio. Annual tree basal area growth is estimated as a function of tree size, crown ratio, stand density, and site index. Models are compatible with the STEMS and TWIGS Projection System.

  5. Evaluating growth models: A case study using PrognosisBC

    Treesearch

    Peter Marshall; Pablo Parysow; Shadrach Akindele

    2008-01-01

    The ability of the PrognosisBC (Version 3.0) growth model to predict tree and stand growth was assessed against a series of remeasured permanent sample plots, including some which had been precommercially thinned. In addition, the model was evaluated for logical consistency across a variety of stand structures using simulation. By the end of the...

  6. Prediction of Salmonella Enteritidis growth in pasteurized and unpasteurized liquid egg products with a growth model.

    PubMed

    Sakha, Mohammad Zaher; Fujikawa, Hiroshi

    2013-01-01

    Growth prediction of a four-strain cocktail of Salmonella Enteritidis in commercial products of pasteurized and unpasteurized liquid whole egg was studied with the new logistic model that we developed. The growth data of the pathogen in the liquid egg products at constant temperatures in our recent study (Sakha and Fujikawa, Biocont. Sci., 2012) were used for prediction. With estimated values of the parameters in the model, it successfully predicted the Salmonella growth in the liquid egg products at dynamic temperature conditions in the high and low ranges. The Baranyi model, which is well known worldwide, could predict Salmonella growth in the pasteurized product at the dynamic temperature conditions in the high range only. This study would be, in our knowledge, the first report on the prediction of Salmonella growth in both pasteurized and unpasteurized liquid egg products at dynamic temperature conditions with a mathematical model.

  7. Growth rate in the dynamical dark energy models.

    PubMed

    Avsajanishvili, Olga; Arkhipova, Natalia A; Samushia, Lado; Kahniashvili, Tina

    Dark energy models with a slowly rolling cosmological scalar field provide a popular alternative to the standard, time-independent cosmological constant model. We study the simultaneous evolution of background expansion and growth in the scalar field model with the Ratra-Peebles self-interaction potential. We use recent measurements of the linear growth rate and the baryon acoustic oscillation peak positions to constrain the model parameter [Formula: see text] that describes the steepness of the scalar field potential.

  8. A theoretical model for tissue growth in confined geometries

    NASA Astrophysics Data System (ADS)

    Dunlop, J. W. C.; Fischer, F. D.; Gamsjäger, E.; Fratzl, P.

    2010-08-01

    It is known that cells proliferate and produce extracellular matrix in response to biochemical and mechanical stimuli. Constitutive models considering these phenomena are needed to quantitatively describe the process of tissue growth in the context of tissue engineering and regenerative medicine. In this paper we re-examine the theoretical framework provided by Ambrosi and Guana (2007) and Ambrosi and Guillou (2007). We show how a volumetric growth rate term can be obtained (both in a large and small strain setting), which is consistent with the laws of thermodynamics and then apply the model to a simple geometry of tissue growth within a circular pore. The model, despite its simplicity, is comparable with experimental measurements of tissue growth and highlights the contribution of the mechanical stresses produced during tissue growth on the growth rate itself.

  9. Application of a statistical bootstrapping technique to calculate growth rate variance for modelling psychrotrophic pathogen growth.

    PubMed

    Schaffner, D W

    1994-12-01

    The inherent variability or 'variance' of growth rate measurements is critical to the development of accurate predictive models in food microbiology. A large number of measurements are typically needed to estimate variance. To make these measurements requires a significant investment of time and effort. If a single growth rate determination is based on a series of independent measurements, then a statistical bootstrapping technique can be used to simulate multiple growth rate measurements from a single set of experiments. Growth rate variances were calculated for three large datasets (Listeria monocytogenes, Listeria innocua, and Yersinia enterocolitica) from our laboratory using this technique. This analysis revealed that the population of growth rate measurements at any given condition are not normally distributed, but instead follow a distribution that is between normal and Poisson. The relationship between growth rate and temperature was modeled by response surface models using generalized linear regression. It was found that the assumed distribution (i.e. normal, Poisson, gamma or inverse normal) of the growth rates influenced the prediction of each of the models used. This research demonstrates the importance of variance and assumptions about the statistical distribution of growth rates on the results of predictive microbiological models.

  10. Graphene growth process modeling: a physical-statistical approach

    NASA Astrophysics Data System (ADS)

    Wu, Jian; Huang, Qiang

    2014-09-01

    As a zero-band semiconductor, graphene is an attractive material for a wide variety of applications such as optoelectronics. Among various techniques developed for graphene synthesis, chemical vapor deposition on copper foils shows high potential for producing few-layer and large-area graphene. Since fabrication of high-quality graphene sheets requires the understanding of growth mechanisms, and methods of characterization and control of grain size of graphene flakes, analytical modeling of graphene growth process is therefore essential for controlled fabrication. The graphene growth process starts with randomly nucleated islands that gradually develop into complex shapes, grow in size, and eventually connect together to cover the copper foil. To model this complex process, we develop a physical-statistical approach under the assumption of self-similarity during graphene growth. The growth kinetics is uncovered by separating island shapes from area growth rate. We propose to characterize the area growth velocity using a confined exponential model, which not only has clear physical explanation, but also fits the real data well. For the shape modeling, we develop a parametric shape model which can be well explained by the angular-dependent growth rate. This work can provide useful information for the control and optimization of graphene growth process on Cu foil.

  11. Insulin-like growth factor-I gene expression in three models of accelerated lung growth.

    PubMed

    Nobuhara, K K; DiFiore, J W; Ibla, J C; Siddiqui, A M; Ferretti, M L; Fauza, D O; Schnitzer, J J; Wilson, J M

    1998-07-01

    We have learned previously that in utero tracheal ligation reverses the structural and physiological effects of surgically created congenital diaphragmatic hernia. In addition, we have discovered that postnatal lung growth similarly can be accelerated using liquid-based airway distension with perfluorocarbon. Another model of accelerated lung growth is that of compensatory growth seen after neonatal pneumonectomy. In all of these models, growth has occurred because of an increase in alveolar number rather than enlargement of preexisting alveoli. However, the molecular mechanisms underlying these processes remain unknown. The purpose of this study was to determine if gene expression could be altered by changes in physical forces in the prenatal and postnatal lung. The three models of accelerated lung growth studied were the following: (1) The prenatal group, consisted of fetal lambs (n = 12) that underwent the surgical creation of a left diaphragmatic hernia at 90 days' gestation. Six of these animals also underwent simultaneous tracheal ligation. (2) The PFC group consisted of five neonatal animals that underwent isolation of the superior segment of the right upper lobe, with intrabronchial distension with perfluorocarbon to 7 to 10 mm Hg pressure for a 3-week period. (3) The postpneumonectomy group consisted of four neonatal animals that underwent left pneumonectomy. In the fetal study, lungs were retrieved at term (130 days), and in the postnatal study, lungs were retrieved 3 weeks after initial intervention. In all cases, RNA was extracted from snap-frozen lung samples and Northern blot analysis performed. Insulinlike growth factor-I, insulinlike growth factor-II, and vascular endothelial growth factor gene expression were analyzed by densitometry. Insulinlike growth factor-I gene expression was found to be decreased in association with experimental diaphragmatic hernia (P = .005), but restored to normal with tracheal ligation. Insulinlike growth factor-I gene

  12. Modelling cyanobacteria: from metabolism to integrative models of phototrophic growth.

    PubMed

    Steuer, Ralf; Knoop, Henning; Machné, Rainer

    2012-03-01

    Cyanobacteria are phototrophic microorganisms of global importance and have recently attracted increasing attention due to their capability to convert sunlight and atmospheric CO(2) directly into organic compounds, including carbon-based biofuels. The utilization of cyanobacteria as a biological chassis to generate third-generation biofuels would greatly benefit from an increased understanding of cyanobacterial metabolism and its interplay with other cellular processes. In this respect, metabolic modelling has been proposed as a way to overcome the traditional trial and error methodology that is often employed to introduce novel pathways. In particular, flux balance analysis and related methods have proved to be powerful tools to investigate the organization of large-scale metabolic networks-with the prospect of predicting modifications that are likely to increase the yield of a desired product and thereby to streamline the experimental progress and avoid futile avenues. This contribution seeks to describe the utilization of metabolic modelling as a research tool to understand the metabolism and phototrophic growth of cyanobacteria. The focus of the contribution is on a mathematical description of the metabolic network of Synechocystis sp. PCC 6803 and its analysis using constraint-based methods. A particular challenge is to integrate the description of the metabolic network with other cellular processes, such as the circadian clock, the photosynthetic light reactions, carbon concentration mechanism, and transcriptional regulation-aiming at a predictive model of a cyanobacterium in silico.

  13. A modeling study of GaN growth by MOVPE

    SciTech Connect

    Safvi, S.A.; Kuech, T.F.; Redwing, J.M.; Tischler, M.A.

    1996-11-01

    A model for the growth of gallium nitride in a vertical metalorganic vapor phase epitaxy reactor is presented. For a mixture of non-dilute gases, the flow temperature and concentration profiles are predicted. The results show that the growth of GaN epilayers is through an intermediate adduct of TMG and ammonia. Growth rates are predicted based on simple reaction mechanisms and compared with those obtained experimentally. Loss of adduct species due to polymerization leads to lowering in growth rate. An attempt to quantify loss of reacting species is made based on experimentally observed growth rates.

  14. When growth models are not universal: evidence from marine invertebrates

    PubMed Central

    Hirst, Andrew G.; Forster, Jack

    2013-01-01

    The accumulation of body mass, as growth, is fundamental to all organisms. Being able to understand which model(s) best describe this growth trajectory, both empirically and ultimately mechanistically, is an important challenge. A variety of equations have been proposed to describe growth during ontogeny. Recently, the West Brown Enquist (WBE) equation, formulated as part of the metabolic theory of ecology, has been proposed as a universal model of growth. This equation has the advantage of having a biological basis, but its ability to describe invertebrate growth patterns has not been well tested against other, more simple models. In this study, we collected data for 58 species of marine invertebrate from 15 different taxa. The data were fitted to three growth models (power, exponential and WBE), and their abilities were examined using an information theoretic approach. Using Akaike information criteria, we found changes in mass through time to fit an exponential equation form best (in approx. 73% of cases). The WBE model predominantly overestimates body size in early ontogeny and underestimates it in later ontogeny; it was the best fit in approximately 14% of cases. The exponential model described growth well in nine taxa, whereas the WBE described growth well in one of the 15 taxa, the Amphipoda. Although the WBE has the advantage of being developed with an underlying proximate mechanism, it provides a poor fit to the majority of marine invertebrates examined here, including species with determinate and indeterminate growth types. In the original formulation of the WBE model, it was tested almost exclusively against vertebrates, to which it fitted well; the model does not however appear to be universal given its poor ability to describe growth in benthic or pelagic marine invertebrates. PMID:23945691

  15. When growth models are not universal: evidence from marine invertebrates.

    PubMed

    Hirst, Andrew G; Forster, Jack

    2013-10-07

    The accumulation of body mass, as growth, is fundamental to all organisms. Being able to understand which model(s) best describe this growth trajectory, both empirically and ultimately mechanistically, is an important challenge. A variety of equations have been proposed to describe growth during ontogeny. Recently, the West Brown Enquist (WBE) equation, formulated as part of the metabolic theory of ecology, has been proposed as a universal model of growth. This equation has the advantage of having a biological basis, but its ability to describe invertebrate growth patterns has not been well tested against other, more simple models. In this study, we collected data for 58 species of marine invertebrate from 15 different taxa. The data were fitted to three growth models (power, exponential and WBE), and their abilities were examined using an information theoretic approach. Using Akaike information criteria, we found changes in mass through time to fit an exponential equation form best (in approx. 73% of cases). The WBE model predominantly overestimates body size in early ontogeny and underestimates it in later ontogeny; it was the best fit in approximately 14% of cases. The exponential model described growth well in nine taxa, whereas the WBE described growth well in one of the 15 taxa, the Amphipoda. Although the WBE has the advantage of being developed with an underlying proximate mechanism, it provides a poor fit to the majority of marine invertebrates examined here, including species with determinate and indeterminate growth types. In the original formulation of the WBE model, it was tested almost exclusively against vertebrates, to which it fitted well; the model does not however appear to be universal given its poor ability to describe growth in benthic or pelagic marine invertebrates.

  16. A von Bertalanffy growth model with a seasonally varying coefficient

    USGS Publications Warehouse

    Cloern, James E.; Nichols, Frederic H.

    1978-01-01

    The von Bertalanffy model of body growth is inappropriate for organisms whose growth is restricted to a seasonal period because it assumes that growth rate is invariant with time. Incorporation of a time-varying coefficient significantly improves the capability of the von Bertalanffy equation to describe changing body size of both the bivalve mollusc Macoma balthicain San Francisco Bay and the flathead sole, Hippoglossoides elassodon, in Washington state. This simple modification of the von Bertalanffy model should offer improved predictions of body growth for a variety of other aquatic animals.

  17. Applications of individual growth curve modeling for pediatric psychology research.

    PubMed

    DeLucia, Christian; Pitts, Steven C

    2006-01-01

    To provide a brief, nontechnical introduction to individual growth curve modeling for the analysis of longitudinal data. Several applications of individual growth curve modeling for pediatric psychology research are discussed. To illustrate these applications, we analyze data from an ongoing pediatric psychology study of the possible impact of spina bifida on child and family development (N = 135). Three repeated observations, spaced by approximately 2 years, contributed to the analyses (M age at baseline = 8.84). Results indicated that individual linear growth curves of emotional autonomy varied as a function of the youth gender by spina bifida group membership interaction. Strengths of individual growth curve modeling relative to more traditional methods of analysis are highlighted (e.g., completely flexible specification of the time variable, explicit modeling of both aggregate-level and individual-level growth curves).

  18. Modeling growth curves to track growing obesity

    USDA-ARS?s Scientific Manuscript database

    Our purpose was to examine the relationship between total physical activity (PA) and PA at various intensity levels with insulin resistance at increasing waist circumference and skinfold thickness levels. Being able to describe growth appropriately and succinctly is important in many nutrition and p...

  19. Correlated noise in a logistic growth model

    NASA Astrophysics Data System (ADS)

    Ai, Bao-Quan; Wang, Xian-Ju; Liu, Guo-Tao; Liu, Liang-Gang

    2003-02-01

    The logistic differential equation is used to analyze cancer cell population, in the presence of a correlated Gaussian white noise. We study the steady state properties of tumor cell growth and discuss the effects of the correlated noise. It is found that the degree of correlation of the noise can cause tumor cell extinction.

  20. "Growth Models" Gaining in Accountability Debate

    ERIC Educational Resources Information Center

    Hoff, David J.

    2007-01-01

    In the debate over the future of the No Child Left Behind Act, policymakers, educators, and researchers seem to agree on one thing: The federal law's accountability system should be rewritten so it rewards or sanctions schools on the basis of students' academic growth. The U.S. Department of Education recently reaffirmed the Bush administration's…

  1. Charter School Innovations: A Teacher Growth Model

    ERIC Educational Resources Information Center

    Radoslovich, Julie; Roberts, Shelley; Plaza, Andres

    2014-01-01

    Committed to being a charter school with a professional learning community that empowers teachers, New Mexico's South Valley Academy (SVA) staff transformed its state evaluation process into a practitioner action research process (Anderson, Herr, & Nihlen, 2007). While teachers self-diagnose growth needs and play active roles in improving…

  2. Variation in growth form and precocity at birth in eutherian mammals.

    PubMed Central

    Gaillard, J M; Pontier, D; Allaine, D; Loison, A; Herve, J C; Heizmann, A

    1997-01-01

    Using the flexible Chapman-Richards model for describing the growth curves from birth to adulthood of 69 species of eutherian mammals, we demonstrate that growth form differs among eutherian mammals. Thereby the commonly used Gompertz model can no longer be considered as the general model for describing mammalian growth. Precocial mammals have their peak growth rate earlier in the growth process than altricial mammals. However, the position on the altricial-precocial continuum accounts for most growth-form differences only between mammalian lineages. Within mammalian genera differences in growth form are not related to precocity at birth. This indicates that growth form may have been associated with precocity at birth early in mammalian evolution, when broad patterns of body development radiated. We discuss four non-exclusive interpretations to account for the role of precocity at birth on the observed variation in growth form among mammals. Precocial and altricial mammals could differ according to (i) the distribution of energy output by the mother, (ii) the ability of the young to assimilate the milk yield, (iii) the allocation of energy by the young between competing functions and (iv) the position of birth between conception and attainment of physical maturity. PMID:9225478

  3. Direct Observation of Aggregative Nanoparticle Growth: Kinetic Modeling of the Size Distribution and Growth Rate

    SciTech Connect

    Woehl, Taylor J.; Park, Chiwoo; Evans, James E.; Arslan, Ilke; Ristenpart, William D.; Browning, Nigel D.

    2014-01-08

    Direct observations of solution-phase nanoparticle growth using in situ liquid transmission electron microscopy (TEM) have demonstrated the importance of “non-classical” growth mechanisms, such as aggregation and coalescence, on the growth and final morphology of nanocrystals at the atomic and single nanoparticle scales. To date, groups have quantitatively interpreted the mean growth rate of nanoparticles in terms of the Lifshitz-Slyozov-Wagner (LSW) model for Ostwald ripening, but less attention has been paid to modeling the corresponding particle size distribution. Here we use in situ fluid stage scanning TEM to demonstrate that silver nanoparticles grow by a length-scale dependent mechanism, where individual nanoparticles grow by monomer attachment but ensemble-scale growth is dominated by aggregation. Although our observed mean nanoparticle growth rate is consistent with the LSW model, we show that the corresponding particle size distribution is broader and more symmetric than predicted by LSW. Following direct observations of aggregation, we interpret the ensemble-scale growth using Smoluchowski kinetics and demonstrate that the Smoluchowski model quantitatively captures the mean growth rate and particle size distribution.

  4. Application of enthalpy model for floating zone silicon crystal growth

    NASA Astrophysics Data System (ADS)

    Krauze, A.; Bergfelds, K.; Virbulis, J.

    2017-09-01

    A 2D simplified crystal growth model based on the enthalpy method and coupled with a low-frequency harmonic electromagnetic model is developed to simulate the silicon crystal growth near the external triple point (ETP) and crystal melting on the open melting front of a polycrystalline feed rod in FZ crystal growth systems. Simulations of the crystal growth near the ETP show significant influence of the inhomogeneities of the EM power distribution on the crystal growth rate for a 4 in floating zone (FZ) system. The generated growth rate fluctuations are shown to be larger in the system with higher crystal pull rate. Simulations of crystal melting on the open melting front of the polycrystalline rod show the development of melt-filled grooves at the open melting front surface. The distance between the grooves is shown to grow with the increase of the skin-layer depth in the solid material.

  5. Initial Status in Growth Curve Modeling for Randomized Trials

    PubMed Central

    Chou, Chih-Ping; Chi, Felicia; Weisner, Constance; Pentz, MaryAnn; Hser, Yih-Ing

    2010-01-01

    The growth curve modeling (GCM) technique has been widely adopted in longitudinal studies to investigate progression over time. The simplest growth profile involves two growth factors, initial status (intercept) and growth trajectory (slope). Conventionally, all repeated measures of outcome are included as components of the growth profile, and the first measure is used to reflect the initial status. Selection of the initial status, however, can greatly influence study findings, especially for randomized trials. In this article, we propose an alternative GCM approach involving only post-intervention measures in the growth profile and treating the first wave after intervention as the initial status. We discuss and empirically illustrate how choices of initial status may influence study conclusions in addressing research questions in randomized trials using two longitudinal studies. Data from two randomized trials are used to illustrate that the alternative GCM approach proposed in this article offers better model fitting and more meaningful results. PMID:21572585

  6. Stochastic Gompertzian model for breast cancer growth process

    NASA Astrophysics Data System (ADS)

    Mazlan, Mazma Syahidatul Ayuni Binti; Rosli, Norhayati

    2017-05-01

    In this paper, a stochastic Gompertzian model is developed to describe the growth process of a breast cancer by incorporating the noisy behavior into a deterministic Gompertzian model. The prediction quality of the stochastic Gompertzian model is measured by comparing the simulated result with the clinical data of breast cancer growth. The kinetic parameters of the model are estimated via maximum likelihood procedure. 4-stage stochastic Runge-Kutta (SRK4) is used to simulate the sample path of the model. Low values of mean-square error (MSE) of stochastic model indicate good fits. It is shown that the stochastic Gompertzian model is adequate in explaining the breast cancer growth process compared to the deterministic model counterpart.

  7. Modelling the Growth of Swine Flu

    ERIC Educational Resources Information Center

    Thomson, Ian

    2010-01-01

    The spread of swine flu has been a cause of great concern globally. With no vaccine developed as yet, (at time of writing in July 2009) and given the fact that modern-day humans can travel speedily across the world, there are fears that this disease may spread out of control. The worst-case scenario would be one of unfettered exponential growth.…

  8. Simulating unstressed crop development and growth using the Unified Plant Growth Model (UPGM)

    USDA-ARS?s Scientific Manuscript database

    Since development of the EPIC model in 1989, many versions of the plant growth component have been incorporated into other erosion and crop management models and subsequently modified to meet model objectives (e.g., WEPS, WEPP, SWAT, ALMANAC, GPFARM). This has resulted in different versions of the ...

  9. A Nonlinear Viscous Model for Sn-Whisker Growth

    NASA Astrophysics Data System (ADS)

    Yang, Fuqian

    2016-12-01

    Based on the mechanism of the grain boundary fluid flow, a nonlinear viscous model for the growth of Sn-whiskers is proposed. This model consists of two units, one with a stress exponent of one and one with a stress exponent of n -1. By letting one of the constants be zero in the model, the constitutive relationship reduces to a linear flow relation or a power-law relation, representing the flow behavior of various metals. Closed-form solutions for the growth behavior of a whisker are derived, which can be used to predict the whisker growth and the stress evolution.

  10. Dissipative-particle-dynamics model of biofilm growth.

    PubMed

    Xu, Zhijie; Meakin, Paul; Tartakovsky, Alexandre; Scheibe, Timothy D

    2011-06-01

    A dissipative-particle-dynamics model for the quantitative simulation of biofilm growth controlled by substrate (nutrient) consumption, advective and diffusive substrate transport, and hydrodynamic interactions with fluid flow (including fragmentation and reattachment) is described. The model was used to simulate biomass growth, decay, and spreading. It predicts how the biofilm morphology depends on flow conditions, biofilm growth kinetics, the rheomechanical properties of the biofilm, and adhesion to solid surfaces. The morphology of the model biofilm depends strongly on its rigidity and the magnitude of the body force that drives the fluid over the biofilm.

  11. Dissipative-particle-dynamics model of biofilm growth

    NASA Astrophysics Data System (ADS)

    Xu, Zhijie; Meakin, Paul; Tartakovsky, Alexandre; Scheibe, Timothy D.

    2011-06-01

    A dissipative-particle-dynamics model for the quantitative simulation of biofilm growth controlled by substrate (nutrient) consumption, advective and diffusive substrate transport, and hydrodynamic interactions with fluid flow (including fragmentation and reattachment) is described. The model was used to simulate biomass growth, decay, and spreading. It predicts how the biofilm morphology depends on flow conditions, biofilm growth kinetics, the rheomechanical properties of the biofilm, and adhesion to solid surfaces. The morphology of the model biofilm depends strongly on its rigidity and the magnitude of the body force that drives the fluid over the biofilm.

  12. Dissipative-particle-dynamics model of biofilm growth

    SciTech Connect

    Xu, Zhijie; Meakin, Paul; Tartakovsky, Alexandre M.; Scheibe, Timothy D.

    2011-06-13

    A dissipative particle dynamics (DPD) model for the quantitative simulation of biofilm growth controlled by substrate (nutrient) consumption, advective and diffusive substrate transport, and hydrodynamic interactions with fluid flow (including fragmentation and reattachment) is described. The model was used to simulate biomass growth, decay, and spreading. It predicts how the biofilm morphology depends on flow conditions, biofilm growth kinetics, the rheomechanical properties of the biofilm and adhesion to solid surfaces. The morphology of the model biofilm depends strongly on its rigidity and the magnitude of the body force that drives the fluid over the biofilm.

  13. Plant Growth Models Using Artificial Neural Networks

    NASA Technical Reports Server (NTRS)

    Bubenheim, David

    1997-01-01

    In this paper, we descrive our motivation and approach to devloping models and the neural network architecture. Initial use of the artificial neural network for modeling the single plant process of transpiration is presented.

  14. Plant Growth Models Using Artificial Neural Networks

    NASA Technical Reports Server (NTRS)

    Bubenheim, David

    1997-01-01

    In this paper, we descrive our motivation and approach to devloping models and the neural network architecture. Initial use of the artificial neural network for modeling the single plant process of transpiration is presented.

  15. MAGIC: Models of Aggregate Growth in China

    DTIC Science & Technology

    1991-01-01

    gross output, a hypothesis consistent with constant returns to scale. Previous problems remain in the trade sector. Haruki Niwa has built a Chinese model...with agricultural goods, industrial goods, and other sectors ( Haruki Niwa, 1985). This model suffers from exogenous investment, an unstable trade...D.C., July 1975. Haruki Niwa, "China Model," in Shinichi Ichimura and Mitsuo Ezaki (eds.), Econometric Models of Asian Link, Springer-Verlag, 1985

  16. Recent advances in crop growth modeling

    USDA-ARS?s Scientific Manuscript database

    Crop simulation models and model-based decision support systems are increasingly used to assist agricultural research and development. The systems approach and modelling tools have been linked down to scales of functional genomics and up to regional scales of natural resource management. Although cr...

  17. Modeling the Growth of Infrarenal Abdominal Aortic Aneurysms

    PubMed Central

    Bailey, Marc A.; Baxter, Paul D.; Jiang, Tao; Charnell, Aimee M.; Griffin, Kathryn J.; Johnson, Anne B.; Bridge, Katherine I.; Sohrabi, Soroush; Scott, D. Julian A.

    2013-01-01

    Background: Abdominal aortic aneurysm (AAA) growth is a complex process that is incompletely understood. Significant heterogeneity in growth trajectories between patients has led to difficulties in accurately modeling aneurysm growth across cohorts of patients. We set out to compare four models of aneurysm growth commonly used in the literature and confirm which best fits the patient data of our AAA cohort. Methods: Patients with AAA were included in the study if they had two or more abdominal ultrasound scans greater than 3 months apart. Patients were censored from analysis once their AAA exceeded 5.5 cm. Four models were applied using the R environment for statistical computing. Growth estimates and goodness of fit (using the Akaike Information Criterion, AIC) were compared, with p-values based on likelihood ratio testing. Results: Of 510 enrolled patients, 264 met the inclusion criteria, yielding a total of 1861 imaging studies during 932 cumulative years of surveillance. Overall, growth rates were: (1) 0.35 (0.31,0.39) cm/yr in the growth/time calculation, (2) 0.056 (0.042,0.068) cm/yr in the linear regression model, (3) 0.19 (0.17,0.21) cm/yr in the linear multilevel model, and (4) 0.21 (0.18,0.24) cm/yr in the quadratic multilevel model at time 0, slowing to 0.15 (0.12,0.17) cm/yr at 10 years. AIC was lowest in the quadratic multilevel model (1508) compared to other models (P < 0.0001). Conclusion: AAA growth was heterogeneous between patients; the nested nature of the data is most appropriately modeled by multilevel modeling techniques. PMID:26798704

  18. Modeling the Growth of Infrarenal Abdominal Aortic Aneurysms.

    PubMed

    Bailey, Marc A; Baxter, Paul D; Jiang, Tao; Charnell, Aimee M; Griffin, Kathryn J; Johnson, Anne B; Bridge, Katherine I; Sohrabi, Soroush; Scott, D Julian A

    2013-12-01

    Abdominal aortic aneurysm (AAA) growth is a complex process that is incompletely understood. Significant heterogeneity in growth trajectories between patients has led to difficulties in accurately modeling aneurysm growth across cohorts of patients. We set out to compare four models of aneurysm growth commonly used in the literature and confirm which best fits the patient data of our AAA cohort. Patients with AAA were included in the study if they had two or more abdominal ultrasound scans greater than 3 months apart. Patients were censored from analysis once their AAA exceeded 5.5 cm. Four models were applied using the R environment for statistical computing. Growth estimates and goodness of fit (using the Akaike Information Criterion, AIC) were compared, with p-values based on likelihood ratio testing. Of 510 enrolled patients, 264 met the inclusion criteria, yielding a total of 1861 imaging studies during 932 cumulative years of surveillance. Overall, growth rates were: (1) 0.35 (0.31,0.39) cm/yr in the growth/time calculation, (2) 0.056 (0.042,0.068) cm/yr in the linear regression model, (3) 0.19 (0.17,0.21) cm/yr in the linear multilevel model, and (4) 0.21 (0.18,0.24) cm/yr in the quadratic multilevel model at time 0, slowing to 0.15 (0.12,0.17) cm/yr at 10 years. AIC was lowest in the quadratic multilevel model (1508) compared to other models (P < 0.0001). AAA growth was heterogeneous between patients; the nested nature of the data is most appropriately modeled by multilevel modeling techniques.

  19. Crop growth dynamics modeling using time-series satellite imagery

    NASA Astrophysics Data System (ADS)

    Zhao, Yu

    2014-11-01

    In modern agriculture, remote sensing technology plays an essential role in monitoring crop growth and crop yield prediction. To monitor crop growth and predict crop yield, accurate and timely crop growth information is significant, in particularly for large scale farming. As the high cost and low data availability of high-resolution satellite images such as RapidEye, we focus on the time-series low resolution satellite imagery. In this research, NDVI curve, which was retrieved from satellite images of MODIS 8-days 250m surface reflectance, was applied to monitor soybean's yield. Conventional model and vegetation index for yield prediction has problems on describing the growth basic processes affecting yield component formation. In our research, a novel method is developed to well model the Crop Growth Dynamics (CGD) and generate CGD index to describe the soybean's yield component formation. We analyze the standard growth stage of soybean and to model the growth process, we have two key calculate process. The first is normalization of the NDVI-curve coordinate and division of the crop growth based on the standard development stages using EAT (Effective accumulated temperature).The second is modeling the biological growth on each development stage through analyzing the factors of yield component formation. The evaluation was performed through the soybean yield prediction using the CGD Index in the growth stage when the whole dataset for modeling is available and we got precision of 88.5% which is about 10% higher than the conventional method. The validation results showed that prediction accuracy using our CGD modeling is satisfied and can be applied in practice of large scale soybean yield monitoring.

  20. Crystal growth kinetics of the two-step model

    NASA Astrophysics Data System (ADS)

    Tai, Clifford Y.; Lin, Chiu-Hsiung

    1987-03-01

    The single crystal technique was used to measure the growth rate of the potassium alum (111) face and the magnesium sulfate (110) face. The two-step model was found appropriate to describe the growth kinetics with the surface integration order of two for potassium alum crystal and of one for magnesium sulfate crystal. The individual rate constants, Kd and Kr, were determined accordingly.

  1. Evaluating the Predictive Value of Growth Prediction Models

    ERIC Educational Resources Information Center

    Murphy, Daniel L.; Gaertner, Matthew N.

    2014-01-01

    This study evaluates four growth prediction models--projection, student growth percentile, trajectory, and transition table--commonly used to forecast (and give schools credit for) middle school students' future proficiency. Analyses focused on vertically scaled summative mathematics assessments, and two performance standards conditions (high…

  2. Knowledge Growth: Applied Models of General and Individual Knowledge Evolution

    ERIC Educational Resources Information Center

    Silkina, Galina Iu.; Bakanova, Svetlana A.

    2016-01-01

    The article considers the mathematical models of the growth and accumulation of scientific and applied knowledge since it is seen as the main potential and key competence of modern companies. The problem is examined on two levels--the growth and evolution of objective knowledge and knowledge evolution of a particular individual. Both processes are…

  3. Crop Growth Modeling in the Wind Erosion Prediction System

    USDA-ARS?s Scientific Manuscript database

    On land used for the production of food and fiber, the amount of growing crop and crop residue remaining on the field during no growth periods often determine whether the field is susceptible to the erosion of the soil by wind. The crop growth sub-model component of the Wind Erosion Prediction Syste...

  4. Evaluating the Predictive Value of Growth Prediction Models

    ERIC Educational Resources Information Center

    Murphy, Daniel L.; Gaertner, Matthew N.

    2014-01-01

    This study evaluates four growth prediction models--projection, student growth percentile, trajectory, and transition table--commonly used to forecast (and give schools credit for) middle school students' future proficiency. Analyses focused on vertically scaled summative mathematics assessments, and two performance standards conditions (high…

  5. The Aponeurotic Tension Model of Craniofacial Growth in Man

    PubMed Central

    Standerwick, Richard G; Roberts, W. Eugene

    2009-01-01

    Craniofacial growth is a scientific crossroad for the fundamental mechanisms of musculoskeletal physiology. Better understanding of growth and development will provide new insights into repair, regeneration and adaptation to applied loads. Traditional craniofacial growth concepts are insufficient to explain the dynamics of airway/vocal tract development, cranial rotation, basicranial flexion and the role of the cranial base in expression of facial proportions. A testable hypothesis is needed to explore the physiological pressure propelling midface growth and the role of neural factors in expression of musculoskeletal adaptation after the cessation of anterior cranial base growth. A novel model for craniofacial growth is proposed for: 1. brain growth and craniofacial adaptation up to the age of 20; 2. explaining growth force vectors; 3. defining the role of muscle plasticity as a conduit for craniofacial growth forces; and 4. describing the effect of cranial rotation in the expression of facial form. Growth of the viscerocranium is believed to be influenced by the superficial musculoaponeurotic systems (SMAS) of the head through residual tension in the occipitofrontalis muscle as a result of cephalad brain growth and cranial rotation. The coordinated effects of the regional SMAS develop a craniofacial musculoaponeurotic system (CFMAS), which is believed to affect maxillary and mandibular development. PMID:19572022

  6. The aponeurotic tension model of craniofacial growth in man.

    PubMed

    Standerwick, Richard G; Roberts, W Eugene

    2009-05-22

    Craniofacial growth is a scientific crossroad for the fundamental mechanisms of musculoskeletal physiology. Better understanding of growth and development will provide new insights into repair, regeneration and adaptation to applied loads. Traditional craniofacial growth concepts are insufficient to explain the dynamics of airway/vocal tract development, cranial rotation, basicranial flexion and the role of the cranial base in expression of facial proportions. A testable hypothesis is needed to explore the physiological pressure propelling midface growth and the role of neural factors in expression of musculoskeletal adaptation after the cessation of anterior cranial base growth. A novel model for craniofacial growth is proposed for: 1. brain growth and craniofacial adaptation up to the age of 20; 2. explaining growth force vectors; 3. defining the role of muscle plasticity as a conduit for craniofacial growth forces; and 4. describing the effect of cranial rotation in the expression of facial form.Growth of the viscerocranium is believed to be influenced by the superficial musculoaponeurotic systems (SMAS) of the head through residual tension in the occipitofrontalis muscle as a result of cephalad brain growth and cranial rotation. The coordinated effects of the regional SMAS develop a craniofacial musculoaponeurotic system (CFMAS), which is believed to affect maxillary and mandibular development.

  7. Actual measurement, hygrothermal response experiment and growth prediction analysis of microbial contamination of central air conditioning system in Dalian, China

    PubMed Central

    Lv, Yang; Hu, Guangyao; Wang, Chunyang; Yuan, Wenjie; Wei, Shanshan; Gao, Jiaoqi; Wang, Boyuan; Song, Fangchao

    2017-01-01

    The microbial contamination of central air conditioning system is one of the important factors that affect the indoor air quality. Actual measurement and analysis were carried out on microbial contamination in central air conditioning system at a venue in Dalian, China. Illumina miseq method was used and three fungal samples of two units were analysed by high throughput sequencing. Results showed that the predominant fungus in air conditioning unit A and B were Candida spp. and Cladosporium spp., and two fungus were further used in the hygrothermal response experiment. Based on the data of Cladosporium in hygrothermal response experiment, this paper used the logistic equation and the Gompertz equation to fit the growth predictive model of Cladosporium genera in different temperature and relative humidity conditions, and the square root model was fitted based on the two environmental factors. In addition, the models were carried on the analysis to verify the accuracy and feasibility of the established model equation. PMID:28367963

  8. Actual measurement, hygrothermal response experiment and growth prediction analysis of microbial contamination of central air conditioning system in Dalian, China.

    PubMed

    Lv, Yang; Hu, Guangyao; Wang, Chunyang; Yuan, Wenjie; Wei, Shanshan; Gao, Jiaoqi; Wang, Boyuan; Song, Fangchao

    2017-04-03

    The microbial contamination of central air conditioning system is one of the important factors that affect the indoor air quality. Actual measurement and analysis were carried out on microbial contamination in central air conditioning system at a venue in Dalian, China. Illumina miseq method was used and three fungal samples of two units were analysed by high throughput sequencing. Results showed that the predominant fungus in air conditioning unit A and B were Candida spp. and Cladosporium spp., and two fungus were further used in the hygrothermal response experiment. Based on the data of Cladosporium in hygrothermal response experiment, this paper used the logistic equation and the Gompertz equation to fit the growth predictive model of Cladosporium genera in different temperature and relative humidity conditions, and the square root model was fitted based on the two environmental factors. In addition, the models were carried on the analysis to verify the accuracy and feasibility of the established model equation.

  9. Mathematical models to characterize early epidemic growth: A review

    NASA Astrophysics Data System (ADS)

    Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

    2016-09-01

    There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.

  10. Mathematical models to characterize early epidemic growth: A Review

    PubMed Central

    Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

    2016-01-01

    There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-15 Ebola epidemic in West Africa. PMID:27451336

  11. Computational Morphodynamics: A modeling framework to understand plant growth

    PubMed Central

    Chickarmane, Vijay; Roeder, Adrienne H.K.; Tarr, Paul T.; Cunha, Alexandre; Tobin, Cory; Meyerowitz, Elliot M.

    2014-01-01

    Computational morphodynamics utilizes computer modeling to understand the development of living organisms over space and time. Results from biological experiments are used to construct accurate and predictive models of growth. These models are then used to make novel predictions providing further insight into the processes in question, which can be tested experimentally to either confirm or rule out the validity of the computational models. This review highlights two fundamental issues: (1.) models should span and integrate single cell behavior with tissue development and (2.) the necessity to understand the feedback between mechanics of growth and chemical or molecular signaling. We review different approaches to model plant growth and discuss a variety of model types that can be implemented, with the aim of demonstrating how this methodology can be used, to explore the morphodynamics of plant development. PMID:20192756

  12. A size-structured model of bacterial growth and reproduction.

    PubMed

    Ellermeyer, S F; Pilyugin, S S

    2012-01-01

    We consider a size-structured bacterial population model in which the rate of cell growth is both size- and time-dependent and the average per capita reproduction rate is specified as a model parameter. It is shown that the model admits classical solutions. The population-level and distribution-level behaviours of these solutions are then determined in terms of the model parameters. The distribution-level behaviour is found to be different from that found in similar models of bacterial population dynamics. Rather than convergence to a stable size distribution, we find that size distributions repeat in cycles. This phenomenon is observed in similar models only under special assumptions on the functional form of the size-dependent growth rate factor. Our main results are illustrated with examples, and we also provide an introductory study of the bacterial growth in a chemostat within the framework of our model.

  13. A Gompertzian model with random effects to cervical cancer growth

    SciTech Connect

    Mazlan, Mazma Syahidatul Ayuni; Rosli, Norhayati

    2015-05-15

    In this paper, a Gompertzian model with random effects is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via maximum likehood estimation. We apply 4-stage Runge-Kutta (SRK4) for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of the cervical cancer growth. Low values of root mean-square error (RMSE) of Gompertzian model with random effect indicate good fits.

  14. Gompertzian stochastic model with delay effect to cervical cancer growth

    NASA Astrophysics Data System (ADS)

    Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

    2015-02-01

    In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

  15. A Gompertzian model with random effects to cervical cancer growth

    NASA Astrophysics Data System (ADS)

    Mazlan, Mazma Syahidatul Ayuni; Rosli, Norhayati

    2015-05-01

    In this paper, a Gompertzian model with random effects is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via maximum likehood estimation. We apply 4-stage Runge-Kutta (SRK4) for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of the cervical cancer growth. Low values of root mean-square error (RMSE) of Gompertzian model with random effect indicate good fits.

  16. Gompertzian stochastic model with delay effect to cervical cancer growth

    SciTech Connect

    Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

    2015-02-03

    In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

  17. 3D modeling of metallic grain growth

    SciTech Connect

    George, D.; Carlson, N.; Gammel, J.T.; Kuprat, A.

    1999-06-01

    This paper will describe simulating metallic grain growth using the Gradient Weighted Moving Finite Elements code, GRAIN3D. The authors also describe the set of mesh topology change operations developed to respond to changes in the physical topology such as the collapse of grains and to maintain uniform calculational mesh quality. Validation of the method is demonstrated by comparison to analytic calculations. The authors present results of multigrain simulations where grain boundaries evolve by mean curvature motion and include results which incorporate grain boundary orientation dependence.

  18. Alexandrium minutum growth controlled by phosphorus . An applied model

    NASA Astrophysics Data System (ADS)

    Chapelle, A.; Labry, C.; Sourisseau, M.; Lebreton, C.; Youenou, A.; Crassous, M. P.

    2010-11-01

    Toxic algae are a worldwide problem threatening aquaculture, public health and tourism. Alexandrium, a toxic dinoflagellate proliferates in Northwest France estuaries (i.e. the Penzé estuary) causing Paralytic Shellfish Poisoning events. Vegetative growth, and in particular the role of nutrient uptake and growth rate, are crucial parameters to understand toxic blooms. With the goal of modelling in situ Alexandrium blooms related to environmental parameters, we first try to calibrate a zero-dimensional box model of Alexandrium growth. This work focuses on phosphorus nutrition. Our objective is to calibrate Alexandrium minutum as well as Heterocapsa triquetra (a non-toxic dinoflagellate) growth under different rates of phosphorus supply, other factors being optimal and constant. Laboratory experiments are used to calibrate two growth models and three uptake models for each species. Models are then used to simulate monospecific batch and semi-continuous experiments as well as competition between the two algae (mixed cultures). Results show that the Droop growth model together with linear uptake versus quota can represent most of our observations, although a power law uptake function can more accurately simulate our phosphorus uptake data. We note that such models have limitations in non steady-state situations and cell quotas can depend on a variety of factors, so care must be taken in extrapolating these results beyond the specific conditions studied.

  19. Modeling the response of peach fruit growth to water stress.

    PubMed

    Génard, M; Huguet, J G

    1996-04-01

    We applied a semi-mechanistic model of fresh matter accumulation to peach fruit during the stage of rapid mesocarp development. The model, which is based on simple hypotheses of fluid flows into and out of the fruit, assumes that solution flow into the fruit increases with fruit weight and transpiration per unit weight, and decreases with the maximum daily shrinkage of the trunk, which was used as an indicator of water stress. Fruit transpiration was assumed to increase with fruit size and with radiation. Fruit respiration was considered to be related to fruit growth and to temperature. The model simulates variability in growth among fruits according to climatic conditions, degree of water stress and weight of the fruit at the beginning of the simulation. We used data obtained from well-watered and water-stressed trees grown in containers to estimate model parameters and to test the model. There was close agreement between the simulated and measured values. A sensitivity analysis showed that initial fruit weight partly determined the variation in growth among fruits. The analysis also indicated that there was an optimal irradiance for fruit growth and that the effect of high global radiation on growth varied according to the stage of fruit development. Water stress, which was the most important factor influencing fruit growth, rapidly depressed growth, particularly when applied late in the season.

  20. Modeling the Growth Rates of Tetragonal Lysozyme Crystal Faces

    NASA Technical Reports Server (NTRS)

    Li, Meirong; Nadarajah, Arunan; Pusey, Marc L.

    1998-01-01

    with respect to its concentration at saturation in order to apply growth rate models to this process. The measured growth rates were then compared with the predicted ones from several dislocation and 2D nucleation growth models, employing tetramer and octamer growth units in polydisperse solutions and monomer units in monodisperse solutions. For the (110) face, the calculations consistently showed that the measured growth rates followed the expected model relations with octamer growth units. For the (101) face, it is not possible to obtain a clear agreement between the predicted and measured growth rates for a single growth unit as done for the (110) face. However, the calculations do indicate that the average size of the growth unit is between a tetramer and an octamer. This suggests that tetramers, octamers and other intermediate size growth units all participate in the growth process for this face. These calculations show that it is possible to model the macroscopic protein crystal growth rates if the molecular level processes can be account for, particularly protein aggregation processes in the bulk solution. Our recent investigations of tetragonal lysozyme crystals employing high resolution atomic force microscopy scans have further confirmed the growth of these crystals by aggregate growth units corresponding to 4(sub 3) helices.

  1. 2D modeling of the regeneration surface growth on crystals

    NASA Astrophysics Data System (ADS)

    Thomas, V. G.; Gavryushkin, P. N.; Fursenko, D. A.

    2012-11-01

    A physical model is proposed to describe the growth of regeneration surfaces (flat crystal surfaces that are not parallel to any possible faces). According to this model, the change in the growth rate of a regeneration surface during its evolution and the decrease in the number of subindividuals forming the growth front can be explained by the implementation of two types of geometric selection: within each subindividual (the absorption of rapidly growing faces by slowly growing ones) and between subindividuals (when subindividuals absorb each other). A numerical modeling of the growth of the regeneration surface (30.30.19) of potassium alum crystals showed quantitative agreement between the model proposed and the experimental data.

  2. A Model for the Growth of Self-Concept

    ERIC Educational Resources Information Center

    Guest, Gerald R.; Thomson, Eric W.

    1972-01-01

    Teachers must play a more consciously active role in fostering healthy self esteem in children. To make such action more likely to occur successfully, a model is presented to conceptualize the dynamics of growth in positive self concept. (Author)

  3. The phase-field model in tumor growth

    NASA Astrophysics Data System (ADS)

    Travasso, Rui D. M.; Castro, Mario; Oliveira, Joana C. R. E.

    2011-01-01

    Tumor growth is becoming a central problem in biophysics both from its social and medical interest and, more fundamentally, because it is a remarkable example of an emergent complex system. Focusing on the description of the spatial and dynamical features of tumor growth, in this paper we review recent tumor modeling approaches using a technique borrowed from materials science: the phase-field models. These models allow us, with a large degree of generality, to identify the paramount mechanisms causing the uncontrolled growth of tumor cells as well as to propose new guidelines for experimentation both in simulation and in the laboratory. We finish by discussing open directions of research in phase-field modeling of tumor growth to catalyze the interest of physicists and mathematicians in this emergent field.

  4. Forest growth modeling and prediction (Volumes 1 & 2).

    Treesearch

    Alan R. Ek; Stephen R. Shifley; Thomas E. Burk

    1988-01-01

    Proceedings of the August 23-27 IUFRO Conference, Minneapolis, Minnesota. Includes 143 manuscripts dealing with growth and yield modeling; regeneration; site characterization; effects of fertilization, genetics, and disturbance; density management; evaluation; estimation; inventory; and application.

  5. Growth/no growth models for Zygosaccharomyces rouxii associated with acidic, sweet intermediate moisture food products.

    PubMed

    Marvig, C L; Kristiansen, R M; Nielsen, D S

    2015-01-02

    The most notorious spoilage organism of sweet intermediate moisture foods (IMFs) is Zygosaccharomyces rouxii, which can grow at low water activity, low pH and in the presence of organic acids. Together with an increased consumer demand for preservative free and healthier food products with less sugar and fat and a traditionally long self-life of sweet IMFs, the presence of Z. rouxii in the raw materials for IMFs has made assessment of the microbiological stability a significant hurdle in product development. Therefore, knowledge on growth/no growth boundaries of Z. rouxii in sweet IMFs is important to ensure microbiological stability and aid product development. Several models have been developed for fat based, sweet IMFs. However, fruit/sugar based IMFs, such as fruit based chocolate fillings and jams, have lower pH and aw than what is accounted for in previously developed models. In the present study growth/no growth models for acidified sweet IMFs were developed with the variables aw (0.65-0.80), pH (2.5-4.0), ethanol (0-14.5% (w/w) in water phase) and time (0-90 days). Two different strains of Z. rouxii previously found to show pronounced resistance to the investigated variables were included in model development, to account for strain differences. For both strains data sets with and without the presence of sorbic acid (250 ppm on product basis) were built. Incorporation of time as an exploratory variable in the models gave the possibility to predict the growth/no growth boundaries at each time between 0 and 90 days without decreasing the predictive power of the models. The influence of ethanol and aw on the growth/no growth boundary of Z. rouxii was most pronounced in the first 30 days and 60 days of incubation, respectively. The effect of pH was almost negligible in the range of 2.5-4.0. The presence of low levels of sorbic acid (250 ppm) eliminated growth of both strains at all conditions tested. The two strains tested have previously been shown to have

  6. Evaluating Teachers and Schools Using Student Growth Models

    ERIC Educational Resources Information Center

    Schafer, William D.; Lissitz, Robert W.; Zhu, Xiaoshu; Zhang, Yuan; Hou, Xiaodong; Li, Ying

    2012-01-01

    Interest in Student Growth Modeling (SGM) and Value Added Modeling (VAM) arises from educators concerned with measuring the effectiveness of teaching and other school activities through changes in student performance as a companion and perhaps even an alternative to status. Several formal statistical models have been proposed for year-to-year…

  7. Latent Growth Curves within Developmental Structural Equation Models.

    ERIC Educational Resources Information Center

    McArdle, J. J.; Epstein, David

    1987-01-01

    Uses structural equation modeling to combine traditional ideas from repeated-measures ANOVA with some traditional ideas from longitudinal factor analysis. The model describes a latent growth curve model that permits the estimation of parameters representing individual and group dynamics. (Author/RH)

  8. Mediation Analysis in a Latent Growth Curve Modeling Framework

    ERIC Educational Resources Information Center

    von Soest, Tilmann; Hagtvet, Knut A.

    2011-01-01

    This article presents several longitudinal mediation models in the framework of latent growth curve modeling and provides a detailed account of how such models can be constructed. Logical and statistical challenges that might arise when such analyses are conducted are also discussed. Specifically, we discuss how the initial status (intercept) and…

  9. Mediation Analysis in a Latent Growth Curve Modeling Framework

    ERIC Educational Resources Information Center

    von Soest, Tilmann; Hagtvet, Knut A.

    2011-01-01

    This article presents several longitudinal mediation models in the framework of latent growth curve modeling and provides a detailed account of how such models can be constructed. Logical and statistical challenges that might arise when such analyses are conducted are also discussed. Specifically, we discuss how the initial status (intercept) and…

  10. Latent Growth Curves within Developmental Structural Equation Models.

    ERIC Educational Resources Information Center

    McArdle, J. J.; Epstein, David

    1987-01-01

    Uses structural equation modeling to combine traditional ideas from repeated-measures ANOVA with some traditional ideas from longitudinal factor analysis. The model describes a latent growth curve model that permits the estimation of parameters representing individual and group dynamics. (Author/RH)

  11. Evaluating Teachers and Schools Using Student Growth Models

    ERIC Educational Resources Information Center

    Schafer, William D.; Lissitz, Robert W.; Zhu, Xiaoshu; Zhang, Yuan; Hou, Xiaodong; Li, Ying

    2012-01-01

    Interest in Student Growth Modeling (SGM) and Value Added Modeling (VAM) arises from educators concerned with measuring the effectiveness of teaching and other school activities through changes in student performance as a companion and perhaps even an alternative to status. Several formal statistical models have been proposed for year-to-year…

  12. Growth of Cognitive Abilities: Dynamic Models and Scaling.

    ERIC Educational Resources Information Center

    Eckstein, Shulamith Graus

    2000-01-01

    Extends dynamic model of cognitive growth proposed by van Geert in three directions: (1) added a term to consider exposure to material to be learned; (2) developed method to apply model to cross-sectional studies; and (3) developed procedure to scale cognitive abilities tests with items of varying difficulty. Tests model with 2- to 15-year-olds'…

  13. Evaluating Latent Variable Growth Models through Ex Post Simulation.

    ERIC Educational Resources Information Center

    Kaplan, David; George, Rani

    1998-01-01

    The use of ex post (historical) simulation statistics as means of evaluating latent growth models is considered, and a variety of simulation quality statistics are applied to such models. Results illustrate the importance of using these measures as adjuncts to more traditional forms of model evaluation. (SLD)

  14. Solving Cocoa Pod Sigmoid Growth Model with Newton Raphson Method

    NASA Astrophysics Data System (ADS)

    Chang, Albert Ling Sheng; Maisin, Navies

    Cocoa pod growth modelling are useful in crop management, pest and disease management and yield forecasting. Recently, the Beta Growth Function has been used to determine the pod growth model due to its unique for the plant organ growth which is zero growth rate at both the start and end of a precisely defined growth period. Specific pod size (7cm to 10cm in length) is useful in cocoa pod borer (CPB) management for pod sleeving or pesticide spraying. The Beta Growth Function is well-fitted to the pods growth data of four different cocoa clones under non-linear function with time (t) as its independent variable which measured pod length and diameter weekly started at 8 weeks after fertilization occur until pods ripen. However, the same pod length among the clones did not indicate the same pod age since the morphological characteristics for cocoa pods vary among the clones. Depending on pod size for all the clones as guideline in CPB management did not give information on pod age, therefore it is important to study the pod age at specific pod sizes on different clones. Hence, Newton Raphson method is used to solve the non-linear equation of the Beta Growth Function of four different group of cocoa pod at specific pod size.

  15. Escherichia coli growth under modeled reduced gravity

    NASA Technical Reports Server (NTRS)

    Baker, Paul W.; Meyer, Michelle L.; Leff, Laura G.

    2004-01-01

    Bacteria exhibit varying responses to modeled reduced gravity that can be simulated by clino-rotation. When Escherichia coli was subjected to different rotation speeds during clino-rotation, significant differences between modeled reduced gravity and normal gravity controls were observed only at higher speeds (30-50 rpm). There was no apparent affect of removing samples on the results obtained. When E. coli was grown in minimal medium (at 40 rpm), cell size was not affected by modeled reduced gravity and there were few differences in cell numbers. However, in higher nutrient conditions (i.e., dilute nutrient broth), total cell numbers were higher and cells were smaller under reduced gravity compared to normal gravity controls. Overall, the responses to modeled reduced gravity varied with nutrient conditions; larger surface to volume ratios may help compensate for the zone of nutrient depletion around the cells under modeled reduced gravity.

  16. Escherichia coli growth under modeled reduced gravity

    NASA Technical Reports Server (NTRS)

    Baker, Paul W.; Meyer, Michelle L.; Leff, Laura G.

    2004-01-01

    Bacteria exhibit varying responses to modeled reduced gravity that can be simulated by clino-rotation. When Escherichia coli was subjected to different rotation speeds during clino-rotation, significant differences between modeled reduced gravity and normal gravity controls were observed only at higher speeds (30-50 rpm). There was no apparent affect of removing samples on the results obtained. When E. coli was grown in minimal medium (at 40 rpm), cell size was not affected by modeled reduced gravity and there were few differences in cell numbers. However, in higher nutrient conditions (i.e., dilute nutrient broth), total cell numbers were higher and cells were smaller under reduced gravity compared to normal gravity controls. Overall, the responses to modeled reduced gravity varied with nutrient conditions; larger surface to volume ratios may help compensate for the zone of nutrient depletion around the cells under modeled reduced gravity.

  17. Tumor Growth Model with PK Input for Neuroblastoma Drug Development

    DTIC Science & Technology

    2015-09-01

    AWARD NUMBER: W81XWH-14-1-0103 TITLE: Tumor Growth Model with PK Input for Neuroblastoma Drug Development PRINCIPAL INVESTIGATOR: Clinton...AND SUBTITLE 5a. CONTRACT NUMBER W81XWH-14-1-0103 Tumor Growth Model with PK Input for Neuroblastoma Drug Development 5b. GRANT NUMBER 5c...STATEMENT Approved for Public Release; Distribution Unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT The long-term goal for our project is to develop a

  18. The Role of Growth Hormone and Insulin-Like Growth Factor 1 in Human Breast Cancer Growth in a Mouse Xenograft Model

    DTIC Science & Technology

    1998-10-01

    The purpose of this research is to determine the role of human growth hormone (hGH) and insulin-like growth factor 1(IGF-1) in the development of an...progression of tumor growth in the animal model. In addition, growth hormone may be semi-inhibitory to growth for tumors dependent upon estrogen

  19. The Role of Growth Hormone and Insulin-Like Growth Factor-1 in Human Breast Cancer Growth in a Mouse Xenograft Model

    DTIC Science & Technology

    1999-10-01

    The purpose of this research is to determine the role of human growth hormone (hGH) and insulin-like growth factor 1 (IGF- 1) in the development of...the progression of tumor growth in the animal model. In addition growth hormone may be semi-inhibitory to growth for tumors dependent upon estrogen

  20. Growth model of binary alloy nanopowders for thermal plasma synthesis

    SciTech Connect

    Shigeta, Masaya; Watanabe, Takayuki

    2010-08-15

    A new model is developed for numerical analysis of the entire growth process of binary alloy nanopowders in thermal plasma synthesis. The model can express any nanopowder profile in the particle size-composition distribution (PSCD). Moreover, its numerical solution algorithm is arithmetic and straightforward so that the model is easy to use. By virtue of these features, the model effectively simulates the collective and simultaneous combined process of binary homogeneous nucleation, binary heterogeneous cocondensation, and coagulation among nanoparticles. The effect of the freezing point depression due to nanoscale particle diameters is also considered in the model. In this study, the metal-silicon systems are particularly chosen as representative binary systems involving cocondensation processes. In consequence, the numerical calculation with the present model reveals the growth mechanisms of the Mo-Si and Ti-Si nanopowders by exhibiting their PSCD evolutions. The difference of the materials' saturation pressures strongly affects the growth behaviors and mature states of the binary alloy nanopowder.

  1. An Integrated Model of Posttraumatic Stress and Growth.

    PubMed

    Lancaster, Steven L; Klein, Keith R; Nadia, Cyrus; Szabo, Lisa; Mogerman, Ben

    2015-01-01

    A number of recent models have examined cognitive predictors of posttraumatic stress and posttraumatic growth (S. Barton, A. Boals, & L. Knowles, 2013; J. Groleau, L. Calhoun, A. Cann, & G. Tedeschi, 2013; K. N. Triplett, R. G. Tedeschi, A. Cann, L. G. Calhoun, & C. L. Reeve, 2012). The current study examined an integrated model of predictors of distress and perceived growth in 194 college undergraduates. Domains covered included the roles of core belief challenge, event centrality, posttrauma cognitions, and event-related rumination. Negative cognitions about the self and the centrality of the event directly predicted both growth and distress, although intrusive rumination predicted only posttraumatic stress disorder symptoms, and deliberate rumination predicted only posttraumatic growth. Future research should continue to examine the shared and unique predictors of postevent growth and distress.

  2. Modelling the ontogeny of ectotherms exhibiting indeterminate growth.

    PubMed

    Dumas, André; France, James

    2008-09-07

    Numerous growth functions exist to describe the ontogeny of animals. Such functions (e.g., von Bertalanffy's equation, thermal-unit growth coefficient) are currently applied to ectotherms even though they fail to provide analytical expressions that adapt to a wide range of fluctuating temperatures. The underlying mechanisms responsible for the ontogeny of ectotherms exhibiting indeterminate growth have not yet been summarised in terms of a simple but meaningful mathematical equation. Here, a growth function is developed, with parameters having physical or biological interpretation that accommodates indeterminate growth under fluctuating temperatures assuming the latter vary seasonally. The equation is derived as a special case of von Bertalanffy's equation providing realistic growth trajectories throughout the ontogeny of several groups of ectotherms (R(2)>0.90). The results suggest that the effect of temperature on growth trajectory supersedes that of reproduction in an environment with fluctuating temperature. Furthermore, values of the allometric weight exponent (0growth function circumvents problems associated with models based on thermodynamic and chemical kinetic principles (e.g., inability to predict growth of organisms in which ontogeny exceeds 3 months) and on rule of thermal summation (e.g., reliable only in a certain range of temperature). The growth function can handle a wide range of temperature fluctuations, encompass life stages and apply to key organisms in ecology, fisheries and agriculture.

  3. The Study on Business Growth Process Management Entropy Model

    NASA Astrophysics Data System (ADS)

    Jing, Duan

    Enterprise's growth is a dynamic process. The factors of enterprise development are changing all the time. For this reason, it is difficult to study management entropy growth-oriented enterprises from static view. Its characteristic is the business enterprise growth stage, and puts forward a kind of measuring and calculating model based on enterprise management entropy for business scale, the enterprise ability and development speed. According to entropy measured by the model, enterprise can adopt revolution measure in the moment of truth. It can make the enterprise avoid crisis and take the road of sustainable development.

  4. A monomer-trimer model supports intermittent glucagon fibril growth

    PubMed Central

    Košmrlj, Andrej; Cordsen, Pia; Kyrsting, Anders; Otzen, Daniel E.; Oddershede, Lene B.; Jensen, Mogens H.

    2015-01-01

    We investigate in vitro fibrillation kinetics of the hormone peptide glucagon at various concentrations using confocal microscopy and determine the glucagon fibril persistence length 60μm. At all concentrations we observe that periods of individual fibril growth are interrupted by periods of stasis. The growth probability is large at high and low concentrations and is reduced for intermediate glucagon concentrations. To explain this behavior we propose a simple model, where fibrils come in two forms, one built entirely from glucagon monomers and one entirely from glucagon trimers. The opposite building blocks act as fibril growth blockers, and this generic model reproduces experimental behavior well. PMID:25758791

  5. Modeling of thin-film GaAs growth

    NASA Technical Reports Server (NTRS)

    Heinbockel, J. H.

    1982-01-01

    A model of crystal growth is discussed that takes into account the processes of nucleation on the growing surface and also considers the processes of surface migration and desorption of adatoms. The solid on solid (SOS) model of crystal growth is represented by a rectangular array of integers where each integer represents the number of adatoms in a column perpendicular to some reference frame. The adatoms can represent atoms or molecules that are being stacked. This SOS method is used to simulate epitaxial growth of crystals. Output of the computer program developed can be graphic or quantitative.

  6. A monomer-trimer model supports intermittent glucagon fibril growth

    NASA Astrophysics Data System (ADS)

    Košmrlj, Andrej; Cordsen, Pia; Kyrsting, Anders; Otzen, Daniel E.; Oddershede, Lene B.; Jensen, Mogens H.

    2015-03-01

    We investigate in vitro fibrillation kinetics of the hormone peptide glucagon at various concentrations using confocal microscopy and determine the glucagon fibril persistence length 60μm. At all concentrations we observe that periods of individual fibril growth are interrupted by periods of stasis. The growth probability is large at high and low concentrations and is reduced for intermediate glucagon concentrations. To explain this behavior we propose a simple model, where fibrils come in two forms, one built entirely from glucagon monomers and one entirely from glucagon trimers. The opposite building blocks act as fibril growth blockers, and this generic model reproduces experimental behavior well.

  7. Modelling Fractal Growth of Bacillus subtilis on Agar Plates

    NASA Astrophysics Data System (ADS)

    Fogedby, Hans C.

    1991-02-01

    The observed fractal growth of a bacterial colony of Bacillus subtilis on agar plates is simulated by a simple computer model in two dimensions. Growth morphologies are shown and the fractal dimension is computed. The concentration of nutrients and the time scale ratio of bacterial multiplication and nutrient diffusion are the variable parameters in the model. Fractal growth is observed in the simulations for moderate concentrations and time scale ratios. The simulated morphologies are similar to the ones grown in the biological experiment. The phenomenon is analogous to the fractal morphologies of lipid layers grown on a water surface.

  8. An introduction to latent variable mixture modeling (part 2): longitudinal latent class growth analysis and growth mixture models.

    PubMed

    Berlin, Kristoffer S; Parra, Gilbert R; Williams, Natalie A

    2014-03-01

    Pediatric psychologists are often interested in finding patterns in heterogeneous longitudinal data. Latent variable mixture modeling is an emerging statistical approach that models such heterogeneity by classifying individuals into unobserved groupings (latent classes) with similar (more homogenous) patterns. The purpose of the second of a 2-article set is to offer a nontechnical introduction to longitudinal latent variable mixture modeling. 3 latent variable approaches to modeling longitudinal data are reviewed and distinguished. Step-by-step pediatric psychology examples of latent growth curve modeling, latent class growth analysis, and growth mixture modeling are provided using the Early Childhood Longitudinal Study-Kindergarten Class of 1998-1999 data file. Latent variable mixture modeling is a technique that is useful to pediatric psychologists who wish to find groupings of individuals who share similar longitudinal data patterns to determine the extent to which these patterns may relate to variables of interest.

  9. Another brick in the cell wall: biosynthesis dependent growth model.

    PubMed

    Barbacci, Adelin; Lahaye, Marc; Magnenet, Vincent

    2013-01-01

    Expansive growth of plant cell is conditioned by the cell wall ability to extend irreversibly. This process is possible if (i) a tensile stress is developed in the cell wall due to the coupling effect between turgor pressure and the modulation of its mechanical properties through enzymatic and physicochemical reactions and if (ii) new cell wall elements can be synthesized and assembled to the existing wall. In other words, expansive growth is the result of coupling effects between mechanical, thermal and chemical energy. To have a better understanding of this process, models must describe the interplay between physical or mechanical variable with biological events. In this paper we propose a general unified and theoretical framework to model growth in function of energy forms and their coupling. This framework is based on irreversible thermodynamics. It is then applied to model growth of the internodal cell of Chara corallina modulated by changes in pressure and temperature. The results describe accurately cell growth in term of length increment but also in term of cell pectate biosynthesis and incorporation to the expanding wall. Moreover, the classical growth model based on Lockhart's equation such as the one proposed by Ortega, appears as a particular and restrictive case of the more general growth equation developed in this paper.

  10. A model for neurite growth and neuronal morphogenesis.

    PubMed

    Li, G H; Qin, C D

    1996-02-01

    A model is presented for tensile regulation of neuritic growth. It is proposed that the neurite tension can be determined by Hooke's law and determines the growth rate of neurites. The growth of a neurite is defined as the change in its unstretched length. Neuritic growth rate is assumed to increase in proportion to tension magnitude over a certain threshold [Dennerll et al., J. Cell Biol. 107: 665-674 (1988)]. The movement of branch nodes also contributes to the neuronal morphogenesis. It is supposed that the rate of a branch-node displacement is in proportion to the resultant neuritic tension exerted on this node. To deal with the growth-cone movement, it is further supposed that the environment exerts a traction force on the growth cone and the rate of growth-cone displacement is determined by the vector sum of the neuritic tension and the traction force. A group of differential equations are used to describe the model. The key point of the model is that the traction force and the neuritic tension are in opposition to generate a temporal contrast-enhancing mechanism. Results of a simulation study suggest that the model can explain some phenomena related to neuronal morphogenesis.

  11. Eye growth and myopia development: Unifying theory and Matlab model.

    PubMed

    Hung, George K; Mahadas, Kausalendra; Mohammad, Faisal

    2016-03-01

    The aim of this article is to present an updated unifying theory of the mechanisms underlying eye growth and myopia development. A series of model simulation programs were developed to illustrate the mechanism of eye growth regulation and myopia development. Two fundamental processes are presumed to govern the relationship between physiological optics and eye growth: genetically pre-programmed signaling and blur feedback. Cornea/lens is considered to have only a genetically pre-programmed component, whereas eye growth is considered to have both a genetically pre-programmed and a blur feedback component. Moreover, based on the Incremental Retinal-Defocus Theory (IRDT), the rate of change of blur size provides the direction for blur-driven regulation. The various factors affecting eye growth are shown in 5 simulations: (1 - unregulated eye growth): blur feedback is rendered ineffective, as in the case of form deprivation, so there is only genetically pre-programmed eye growth, generally resulting in myopia; (2 - regulated eye growth): blur feedback regulation demonstrates the emmetropization process, with abnormally excessive or reduced eye growth leading to myopia and hyperopia, respectively; (3 - repeated near-far viewing): simulation of large-to-small change in blur size as seen in the accommodative stimulus/response function, and via IRDT as well as nearwork-induced transient myopia (NITM), leading to the development of myopia; (4 - neurochemical bulk flow and diffusion): release of dopamine from the inner plexiform layer of the retina, and the subsequent diffusion and relay of neurochemical cascade show that a decrease in dopamine results in a reduction of proteoglycan synthesis rate, which leads to myopia; (5 - Simulink model): model of genetically pre-programmed signaling and blur feedback components that allows for different input functions to simulate experimental manipulations that result in hyperopia, emmetropia, and myopia. These model simulation programs

  12. Regular variation, Paretian distributions, and the interplay of light and heavy tails in the fractality of asymptotic models

    NASA Astrophysics Data System (ADS)

    Pestana, Dinis D.; Aleixo, Sandra M.; Rocha, J. Leonel

    Classical central limit theorems, culminating in the theory of infinite divisibility, accurately describe the behaviour of stochastic phenomena with asymptotically negligible components. The classical theory fails when a single component may assume an extreme protagonism. The early developments of the speculation theory didn't incorporate the pioneer work of Pareto on heavy tailed models, and the proper setup to conciliate regularity and abrupt changes, in a wide range of natural phenomena, is Karamata's concept of regular variation and the role it plays in the theory of domains of attraction, [8], and Resnick's tail equivalence leading to the importance of generalized Pareto distribution is the scope of extreme value theory, [13]. Waliszewski and Konarski discussed the applicability of the Gompertz curve and its fractal behaviour for instance in modeling healthy and neoplasic cells tissue growth, [15]. Gompertz function is the Gumbel extreme value model, whose broad domain of attraction contains intermediate tail weight laws with a wide range of behaviour. Aleixo et al. investigated fractality associated with Beta (p,q) models, [1], [2], [10] and [11]. In this work, we introduce a new family of probability density functions tied to the classical beta family, the Beta*(p,q) models, some of which are generalized Pareto, that span the possible regular variation of tails. We extend the investigation to other extreme stable models, namely Fréchet's and Weibull's types in the General Extreme Value (GEV) model.

  13. Development, Selection, and Validation of Tumor Growth Models

    NASA Astrophysics Data System (ADS)

    Shahmoradi, Amir; Lima, Ernesto; Oden, J. Tinsley

    In recent years, a multitude of different mathematical approaches have been taken to develop multiscale models of solid tumor growth. Prime successful examples include the lattice-based, agent-based (off-lattice), and phase-field approaches, or a hybrid of these models applied to multiple scales of tumor, from subcellular to tissue level. Of overriding importance is the predictive power of these models, particularly in the presence of uncertainties. This presentation describes our attempt at developing lattice-based, agent-based and phase-field models of tumor growth and assessing their predictive power through new adaptive algorithms for model selection and model validation embodied in the Occam Plausibility Algorithm (OPAL), that brings together model calibration, determination of sensitivities of outputs to parameter variances, and calculation of model plausibilities for model selection. Institute for Computational Engineering and Sciences.

  14. A New Model for Root Growth in Soil with Macropores

    NASA Astrophysics Data System (ADS)

    Landl, M.; Huber, K.; Schnepf, A.; Vanderborght, J.; Javaux, M.; Bengough, G.; Vereecken, H.

    2016-12-01

    In order to study soil-root interaction processes, dynamic root architecture models which are linked to models that simulate water flow and nutrient transport in the soil-root system are needed. Such models can be used to predict the impact of soil structural features, e.g. the presence of macropores in dense subsoil, on water and nutrient uptake by plants. In dynamic root architecture models, root growth is represented by moving root tips whose growth trajectory results in the creation of linear root segments. Typically, the direction of each new root segment is calculated as the vector sum of various direction-affecting components. The use of these established methods to simulate root growth in soil containing macropores, however, failed to reproduce experimentally observed root growth patterns. We therefore developed an alternative modelling approach where we distinguish between, firstly, the driving force for root growth which is determined by the orientation of the previous root segment as well as the influence of gravitropism and, secondly, soil mechanical resistance to root growth. The latter is expressed by root conductance which represents the inverse of soil penetration resistance and is treated similarly to hydraulic conductivity in Darcy's law. At the presence of macropores, root conductance is anisotropic which leads to a difference between the direction of the driving force and the direction of the root tip movement. The model was tested using data from the literature, at pot scale, at macropore scale, and in a series of simulations where sensitivity to gravity and macropore orientation was evaluated. The model simulated root growth trajectories in structured soil at both single root and whole root-system scales, generating root systems that were similar to images from experiments. Its implementation in the three dimensional soil and root water uptake model R-SWMS enables the use of the model in the future to evaluate the effect of macropores on crop

  15. Modeling microbial populations with the original and modified versions of the continuous and discrete logistic equations.

    PubMed

    Peleg, M

    1997-08-01

    The life histories of microbial populations, under favorable and adverse conditions, exhibit a variety of growth, decay, and fluctuation patterns. They have been described by numerous mathematical models that varies considerably in structure and number of constants. The continuous logistic equation alone and combined with itself or with its mirror image, the Fermi function, can produce many of the observed growth patterns. They include those that are traditionally described by the Gompertz equation and peaked curves, with the peak being symmetric or asymmetric narrow or wide. The shape of survival and dose response curves appears to be determined by the distribution of the resistance's to the lethal agent among the individual organisms. Thus, exponential decay and Fermian or Gompertz-type curves can be considered manifestations of skewed to the right, symmetric, and skewed to the left distributions, respectively. Because of the mathematical constraints and determinism, the original discrete logistic equation can rarely be an adequate model of real microbial populations. However, by making its proportionality constant a normal-random variate it can simulate realistic histories of fluctuating microbial populations, including scenarios of aperiodic population explosions of varying intensities of the kind found in food-poisoning episodes.

  16. Age and growth parameters of shark-like batoids.

    PubMed

    White, J; Simpfendorfer, C A; Tobin, A J; Heupel, M R

    2014-05-01

    Estimates of life-history parameters were made for shark-like batoids of conservation concern Rhynchobatus spp. (Rhynchobatus australiae, Rhynchobatus laevis and Rhynchobatus palpebratus) and Glaucostegus typus using vertebral ageing. The sigmoid growth functions, Gompertz and logistic, best described the growth of Rhynchobatus spp. and G. typus, providing the best statistical fit and most biologically appropriate parameters. The two-parameter logistic was the preferred model for Rhynchobatus spp. with growth parameter estimates (both sexes combined) L(∞) = 2045 mm stretch total length, LST and k = 0·41 year⁻¹. The same model was also preferred for G. typus with growth parameter estimates (both sexes combined) L∞  = 2770 mm LST and k = 0·30 year⁻¹. Annual growth-band deposition could not be excluded in Rhynchobatus spp. using mark-recaptured individuals. Although morphologically similar G. typus and Rhynchobatus spp. have differing life histories, with G. typus longer lived, slower growing and attaining a larger maximum size. © 2014 The Fisheries Society of the British Isles.

  17. The deviation of growth model for transparent conductive graphene

    PubMed Central

    2014-01-01

    An approximate growth model was employed to predict the time required to grow a graphene film by chemical vapor deposition (CVD). Monolayer graphene films were synthesized on Cu foil at various hydrogen flow rates from 10 to 50 sccm. The sheet resistance of the graphene film was 310Ω/□ and the optical transmittance was 97.7%. The Raman intensity ratio of the G-peak to the 2D peak of the graphene film was as high as ~4 when the hydrogen flow rate was 30 sccm. The fitting curve obtained by the deviation equation of growth model closely matches the data. We believe that under the same conditions and with the same setup, the presented growth model can help manufacturers and academics to predict graphene growth time more accurately. PMID:25364316

  18. A mathematical model of microalgae growth in cylindrical photobioreactor

    NASA Astrophysics Data System (ADS)

    Bakeri, Noorhadila Mohd; Jamaian, Siti Suhana

    2017-08-01

    Microalgae are unicellular organisms, which exist individually or in chains or groups but can be utilized in many applications. Researchers have done various efforts in order to increase the growth rate of microalgae. Microalgae have a potential as an effective tool for wastewater treatment, besides as a replacement for natural fuel such as coal and biodiesel. The growth of microalgae can be estimated by using Geider model, which this model is based on photosynthesis irradiance curve (PI-curve) and focused on flat panel photobioreactor. Therefore, in this study a mathematical model for microalgae growth in cylindrical photobioreactor is proposed based on the Geider model. The light irradiance is the crucial part that affects the growth rate of microalgae. The absorbed photon flux will be determined by calculating the average light irradiance in a cylindrical system illuminated by unidirectional parallel flux and considering the cylinder as a collection of differential parallelepipeds. Results from this study showed that the specific growth rate of microalgae increases until the constant level is achieved. Therefore, the proposed mathematical model can be used to estimate the rate of microalgae growth in cylindrical photobioreactor.

  19. Modelling the effect of fluctuating herbicide concentrations on algae growth.

    PubMed

    Copin, Pierre-Jean; Coutu, Sylvain; Chèvre, Nathalie

    2015-03-01

    Herbicide concentrations fluctuate widely in watercourses after crop applications and rain events. The level of concentrations in pulses can exceed the water chronic quality criteria. In the present study, we proposed modelling the effects of successive pulse exposure on algae. The deterministic model proposed is based on two parameters: (i) the typical growth rate of the algae, obtained by monitoring growth rates of several successive batch cultures in growth media, characterizing both the growth of the control and during the recovery periods; (ii) the growth rate of the algae exposed to pulses, determined from a dose-response curve obtained with a standard toxicity test. We focused on the herbicide isoproturon and on the freshwater alga Scenedesmus vacuolatus, and we validated the model prediction based on effect measured during five sequential pulse exposures in laboratory. The comparison between the laboratory and the modelled effects illustrated that the results yielded were consistent, making the model suitable for effect prediction of the herbicide photosystem II inhibitor isoproturon on the alga S. vacuolatus. More generally, modelling showed that both pulse duration and level of concentration play a crucial role. The application of the model to a real case demonstrated that both the highest peaks and the low peaks with a long duration affect principally the cell density inhibition of the alga S. vacuolatus. It is therefore essential to detect these characteristic pulses when monitoring of herbicide concentrations are conducted in rivers.

  20. Large-scale growth evolution in the Szekeres inhomogeneous cosmological models with comparison to growth data

    NASA Astrophysics Data System (ADS)

    Peel, Austin; Ishak, Mustapha; Troxel, M. A.

    2012-12-01

    We use the Szekeres inhomogeneous cosmological models to study the growth of large-scale structure in the universe including nonzero spatial curvature and a cosmological constant. In particular, we use the Goode and Wainwright formulation of the solution, as in this form the models can be considered to represent exact nonlinear perturbations of an averaged background. We identify a density contrast in both classes I and II of the models, for which we derive growth evolution equations. By including Λ, the time evolution of the density contrast as well as kinematic quantities of interest can be tracked through the matter- and Λ-dominated cosmic eras up to the present and into the future. In class I, we consider a localized cosmic structure representing an overdensity neighboring a central void, surrounded by an almost Friedmann-Lemaître-Robertson-Walker background, while for class II, the exact perturbations exist globally. In various models of class I and class II, the growth rate is found to be stronger in the matter-dominated era than that of the standard lambda-cold dark matter (ΛCDM) cosmology, and it is suppressed at later times due to the presence of the cosmological constant. We find that there are Szekeres models able to provide a growth history similar to that of ΛCDM while requiring less matter content and nonzero spatial curvature, which speaks to the importance of including the effects of large-scale inhomogeneities in analyzing the growth of large-scale structure. Using data for the growth factor f from redshift space distortions and the Lyman-α forest, we obtain best fit parameters for class II models and compare their ability to match observations with ΛCDM. We find that there is negligible difference between best fit Szekeres models with no priors and those for ΛCDM, both including and excluding Lyman-α data. We also find that the standard growth index γ parametrization cannot be applied in a simple way to the growth in Szekeres models, so

  1. Modeling Dynamic Height and Crown Growth in Trees

    NASA Astrophysics Data System (ADS)

    Franklin, O.; Fransson, P.; Brännström, Å.

    2015-12-01

    Previously we have shown how principles based on productivity maximization (e.g. maximization of net primary production, net growth maximization, or functional balance) can explain allocation responses to resources, such as nutrients and light (Franklin et al., 2012). However, the success of these approaches depend on how well they align with the ultimate driver of plant behavior, fitness, or life time reproductive success. Consequently, they may not fully explain how allocation changes during the life cycle of trees where not only growth but also survival and reproduction are important. In addition, maximizing instantaneous productivity does not account for path dependence of tree growth. For example, maximizing productivity during early growth in shade may delay emergence in the forest canopy and reduce lifetime fitness compared to a more height oriented strategy. Here we present an approach to model how growth of stem diameter and leaf area in relation to stem height dynamically responds to light conditions in a way that maximizes life-time fitness (rather than instantaneous growth). The model is able to predict growth of trees growing in different types of forests, including trees emerging under a closed canopy and seedlings planted in a clear-cut area. It can also predict the response to sudden changes in the light environment, due to disturbances or harvesting. We envisage two main applications of the model, (i) Modeling effects of forest management, including thinning and planting (ii) Elucidating height growth strategies in trees and how they can be represented in vegetation models. ReferenceFranklin O, Johansson J, Dewar RC, Dieckmann U, McMurtrie RE, Brännström Å, Dybzinski R. 2012. Modeling carbon allocation in trees: a search for principles. Tree Physiology 32(6): 648-666.

  2. A Bayesian analysis of the effect of selection for growth rate on growth curves in rabbits

    PubMed Central

    Blasco, Agustín; Piles, Miriam; Varona, Luis

    2003-01-01

    Gompertz growth curves were fitted to the data of 137 rabbits from control (C) and selected (S) lines. The animals came from a synthetic rabbit line selected for an increased growth rate. The embryos from generations 3 and 4 were frozen and thawed to be contemporary of rabbits born in generation 10. Group C was the offspring of generations 3 and 4, and group S was the contemporary offspring of generation 10. The animals were weighed individually twice a week during the first four weeks of life, and once a week thereafter, until 20 weeks of age. Subsequently, the males were weighed weekly until 40 weeks of age. The random samples of the posterior distributions of the growth curve parameters were drawn by using Markov Chain Monte Carlo (MCMC) methods. As a consequence of selection, the selected animals were heavier than the C animals throughout the entire growth curve. Adult body weight, estimated as a parameter of the Gompertz curve, was 7% higher in the selected line. The other parameters of the Gompertz curve were scarcely affected by selection. When selected and control growth curves are represented in a metabolic scale, all differences disappear. PMID:12605849

  3. Modelling mould growth under suboptimal environmental conditions and inoculum size.

    PubMed

    Garcia, Daiana; Ramos, Antonio J; Sanchis, Vicente; Marín, Sonia

    2010-10-01

    Predictive models can be a tool to develop strategies to prevent mould development and consequently mycotoxin production. The aims of this work were to assess the impact of a) high/low levels of inoculum and b) optimal/suboptimal environmental conditions on fungal responses based on both kinetic and probabilistic models. Different levels of spore suspensions of Aspergillus carbonarius and Penicillium expansum were prepared and inoculated centrally with a needlepoint load on malt extract agar (MEA) with 50 replicates. While optimum conditions led to a colony diameter increase which followed Baranyi's function, suboptimal conditions led to different grow functions. In general, growth rate (mu) and lag phase (lambda) were normally distributed. Specifically, the growth rate (mu) showed similar distributions under optimal growth conditions, regardless of the inoculum level, while suboptimal a(w) and temperature conditions led to higher kurtosis distributions, mainly when the inoculum levels were low. Regarding lambda, more skewed distributions were observed, mainly when the inoculum levels were low. Probability models were not much affected by the inoculum size. Lower probabilities of growth were in general predicted under marginal conditions at a given time for both strains. The slopes of the probability curves were smaller under suboptimal growth conditions due to wider distributions. Results showed that a low inoculum level and suboptimal conditions lead to high variability of the estimated growth parameters and growth probability.

  4. Estimating Reliability with Discrete Growth Models.

    DTIC Science & Technology

    1988-03-01

    MODELS .. 3 A . BA C KG RO UN D ........................................... ) B. FAILURE DISCOUNTING ................................... 3 1...dditionailv. systenis being produced presently are more complex and claim a much higher reliability than those produced just a few years ago...this iden- tification process is dependent upon the type of system being evaluated and the purpose of the test. If a complex system is being evaluated

  5. Small Business Training Models for Community Growth.

    ERIC Educational Resources Information Center

    Jellison, Holly M., Ed.

    Nine successful community college programs for small business management training are described in this report in terms of their college and economic context, purpose, offerings, delivery modes, operating and marketing strategies, community outreach, support services, faculty and staff, evaluation, and future directions. The model programs are…

  6. Exponential order statistic models of software reliability growth

    NASA Technical Reports Server (NTRS)

    Miller, D. R.

    1985-01-01

    Failure times of a software reliabilty growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.

  7. Exponential order statistic models of software reliability growth

    NASA Technical Reports Server (NTRS)

    Miller, D. R.

    1986-01-01

    Failure times of a software reliability growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.

  8. Modeling the effect of insulin-like growth factor-1 on human cell growth.

    PubMed

    Phillips, Gemma M A; Shorten, Paul R; Wake, Graeme C; Guan, Jian

    2015-01-01

    Insulin-like growth factor-1 (IGF-1) plays a key role in human growth and development. The interactions of IGF-1 with IGF-1 receptors and IGF-1 binding proteins (IGFBPs) regulate IGF-1 function. Recent research suggests that a metabolite of IGF-1, cyclo-glycyl-proline (cGP), has a role in regulating IGF-1 homeostasis. A component of this interaction is believed to be the competitive binding of IGF-1 and cGP to IGFBPs. In this paper we describe a mathematical model of the interaction between IGF-1 and cGP on human cell growth. The model can be used to understand the interaction between IGF-1, IGFBPs, cGP and IGF-1 receptors along with the kinetics of cell growth. An explicit model of the known interactions between IGF-1, cGP, IGFBPs, IGF-1 receptors explained a large portion of the variance in cell growth (R(2) = 0.83). An implicit model of the interactions between IGF-1, cGP, IGFBPs, IGF-1 receptors that included a hypothesized feedback of cGP on IGF-1 receptors explained nonlinear features of interaction between IGF-1 and cGP not described by the explicit model (R(2) = 0.84). The model also explained the effect of IGFBP antibody on the interaction between cGP and IGF-1 (R(2) = 0.78). This demonstrates that the competitive binding of IGF-1 and cGP to IGFBPs plays a large role in the interaction between IGF-1 and cGP, but that other factors potentially play a role in the interaction between cGP and IGF-1. These models can be used to predict the complex interaction between IGF-1 and cGP on human cell growth and form a basis for further research in this field.

  9. Monte Carlo grain growth modeling with local temperature gradients

    NASA Astrophysics Data System (ADS)

    Tan, Y.; Maniatty, A. M.; Zheng, C.; Wen, J. T.

    2017-09-01

    This work investigated the development of a Monte Carlo (MC) simulation approach to modeling grain growth in the presence of non-uniform temperature field that may vary with time. We first scale the MC model to physical growth processes by fitting experimental data. Based on the scaling relationship, we derive a grid site selection probability (SSP) function to consider the effect of a spatially varying temperature field. The SSP function is based on the differential MC step, which allows it to naturally consider time varying temperature fields too. We verify the model and compare the predictions to other existing formulations (Godfrey and Martin 1995 Phil. Mag. A 72 737-49 Radhakrishnan and Zacharia 1995 Metall. Mater. Trans. A 26 2123-30) in simple two-dimensional cases with only spatially varying temperature fields, where the predicted grain growth in regions of constant temperature are expected to be the same as for the isothermal case. We also test the model in a more realistic three-dimensional case with a temperature field varying in both space and time, modeling grain growth in the heat affected zone of a weld. We believe the newly proposed approach is promising for modeling grain growth in material manufacturing processes that involves time-dependent local temperature gradient.

  10. Minimal Model for Genome Evolution and Growth

    NASA Astrophysics Data System (ADS)

    Hsieh, Li-Ching; Luo, Liaofu; Ji, Fengmin; Lee, H. C.

    2003-01-01

    Textual analysis of typical microbial genomes reveals that they have the statistical characteristics of a DNA sequence of a much shorter length. This peculiar property supports an evolutionary model in which a genome evolves by random mutation but primarily grows by random segmental duplication. That genomes grew mostly by duplication is consistent with the observation that repeat sequences in all genomes are widespread and intragenomic and intergenomic homologous genes are preponderant across all life forms.

  11. Computational modeling of hypertensive growth in the human carotid artery

    PubMed Central

    Sáez, Pablo; Peña, Estefania; Martínez, Miguel Angel; Kuhl, Ellen

    2014-01-01

    Arterial hypertension is a chronic medical condition associated with an elevated blood pressure. Chronic arterial hypertension initiates a series of events, which are known to collectively initiate arterial wall thickening. However, the correlation between macrostructural mechanical loading, microstructural cellular changes, and macrostructural adaptation remains unclear. Here, we present a microstructurally motivated computational model for chronic arterial hypertension through smooth muscle cell growth. To model growth, we adopt a classical concept based on the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. Motivated by clinical observations, we assume that the driving force for growth is the stretch sensed by the smooth muscle cells. We embed our model into a finite element framework, where growth is stored locally as an internal variable. First, to demonstrate the features of our model, we investigate the effects of hypertensive growth in a real human carotid artery. Our results agree nicely with experimental data reported in the literature both qualitatively and quantitatively. PMID:25342868

  12. Modeling global organic aerosol formation and growth

    NASA Astrophysics Data System (ADS)

    Tsimpidi, Alexandra; Karydis, Vlasios; Pandis, Spyros; Lelieveld, Jos

    2014-05-01

    A computationally efficient framework for the description of organic aerosol (OA)-gas partitioning and chemical aging has been developed and implemented into the EMAC atmospheric chemistry-climate model. This model simulates the formation of primary (POA) and secondary organic aerosols (SOA) from semi-volatile (SVOC), intermediate-volatile (IVOC) and volatile organic compounds (VOC). POA are divided in two groups with saturation concentrations at 298 K 0.1, 10, 1000, 100000 µg m-3: OA from fossil fuel combustion and biomass burning. The first 2 surrogate species from each group represent the SVOC while the other surrogate species represent the IVOC. Photochemical reactions that change the volatility of the organics in the gas phase are taken into account. The oxidation products from each group of precursors (SVOC, IVOC, and VOC) are lumped into an additional set of oxidized surrogate species (S-SOA, I-SOA, and V-SOA, respectively) in order to track their source of origin. This model is used to i) estimate the relative contributions of SOA and POA to total OA, ii) determine how SOA concentrations are affected by biogenic and anthropogenic emissions, and iii) evaluate the effect of photochemical aging and long-range transport on OA budget over specific regions.

  13. Physcomitrella patens: a model for tip cell growth and differentiation.

    PubMed

    Vidali, Luis; Bezanilla, Magdalena

    2012-12-01

    The moss Physcomitrella patens has emerged as an excellent model system owing to its amenability to reverse genetics. The moss gametophyte has three filamentous tissues that grow by tip growth: chloronemata, caulonemata, and rhizoids. Because establishment of the moss plant relies on this form of growth, it is particularly suited for dissecting the molecular basis of tip growth. Recent studies demonstrate that a core set of actin cytoskeletal proteins is essential for tip growth. Additional actin cytoskeletal components are required for modulating growth to produce caulonemata and rhizoids. Differentiation into these cell types has previously been linked to auxin, light and nutrients. Recent studies have identified that core auxin signaling components as well as transcription factors that respond to auxin or nutrient levels are required for tip-growing cell differentiation. Future studies may establish a connection between the actin cytoskeleton and auxin or nutrient-induced cell differentiation. Copyright © 2012 Elsevier Ltd. All rights reserved.

  14. Simulating colonial growth of fungi with the Neighbour-Sensing model of hyphal growth.

    PubMed

    Meskauskas, Audrius; Fricker, Mark D; Moore, David

    2004-11-01

    The Neighbour-Sensing model brings together the basic essentials of hyphal growth kinetics into a vector-based mathematical model in which the growth vector of each virtual hyphal tip is calculated by reference to the surrounding virtual mycelium. The model predicts the growth pattern of many hyphae into three spatial dimensions and has been used to simulate complex fungal fruit body shapes. In this paper we show how the Neighbour-Sensing model can simulate growth in semi-solid substrata like agar or soil, enabling realistic simulation of mycelial colonies of filamentous fungi grown in 'Petri-dish style' experimental conditions. Newly implemented capabilities in the model include: a measurement and logging system within the program that maintains basic statistics about the mycelium it is simulating, this facilitates kinetic experimentation; inclusion of 'substrates' in the data space causing positive or negative tropisms for the growing mycelium; a horizontal plane tropism that provides a way of simulating colonies growing in or on a substratum like agar or soil by imposing a horizontal constraint on the data space the cyberhyphal tips can explore; three categories of hypha--standard hyphae are those that start the simulation, leading hyphae can emerge from the colony peripheral growth zone to take on a leading role, and secondary hyphae are branches that can arise late, far behind the peripheral growth zone, when mature hyphal segments resume branching to in-fill the older parts of the colony. We show how the model can be used to investigate hyphal growth kinetics in silico in experimental scenarios that would be difficult or impracticable in vivo. We also show that the Neighbour-Sensing model can generate sufficiently realistic cord-like structures to encourage the belief that this model is now sufficiently advanced for parameters to be defined that simulate specific in silico cyberfungi. The potential utility of these cyberspecies is that they provide a means to

  15. Model for the growth of the world airline network

    NASA Astrophysics Data System (ADS)

    Verma, T.; Araújo, N. A. M.; Nagler, J.; Andrade, J. S.; Herrmann, H. J.

    2016-06-01

    We propose a probabilistic growth model for transport networks which employs a balance between popularity of nodes and the physical distance between nodes. By comparing the degree of each node in the model network and the World Airline Network (WAN), we observe that the difference between the two is minimized for α≈2. Interestingly, this is the value obtained for the node-node correlation function in the WAN. This suggests that our model explains quite well the growth of airline networks.

  16. Mathematical Modeling of Tumor Cell Growth and Immune System Interactions

    NASA Astrophysics Data System (ADS)

    Rihan, Fathalla A.; Safan, Muntaser; Abdeen, Mohamed A.; Abdel-Rahman, Duaa H.

    In this paper, we provide a family of ordinary and delay differential equations to describe the dynamics of tumor-growth and immunotherapy interactions. We explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated. The possibility of clearing the tumor, with a strategy, is based on two parameters in the model: the rate of influx of the effector cells, and the rate of influx of IL2. The critical tumor-growth rate, below which endemic tumor does not exist, has been found. One can use the model to make predictions about tumor-dormancy.

  17. Modeling gas exchange in a closed plant growth chamber

    NASA Technical Reports Server (NTRS)

    Cornett, J. D.; Hendrix, J. E.; Wheeler, R. M.; Ross, C. W.; Sadeh, W. Z.

    1994-01-01

    Fluid transport models for fluxes of water vapor and CO2 have been developed for one crop of wheat and three crops of soybean grown in a closed plant growth chamber. Correspondence among these fluxes is discussed. Maximum fluxes of gases are provided for engineering design requirements of fluid recycling equipment in growth chambers. Furthermore, to investigate the feasibility of generalized crop models, dimensionless representations of water vapor fluxes are presented. The feasibility of such generalized models and the need for additional data are discussed.

  18. Modeling Gas Exchange in a Closed Plant Growth Chamber

    NASA Technical Reports Server (NTRS)

    Cornett, J. D.; Hendrix, J. E.; Wheeler, R. M.; Ross, C. W.; Sadeh, W. Z.

    1994-01-01

    Fluid transport models for fluxes of water vapor and CO2 have been developed for one crop of wheat and three crops of soybean grown in a closed plant a growth chamber. Correspondence among these fluxes is discussed. Maximum fluxes of gases are provided for engineering design requirements of fluid recycling equipment in growth chambers. Furthermore, to investigate the feasibility of generalized crop models, dimensionless representations of water vapor fluxes are presented. The feasibility of such generalized models and the need for additional data are discussed.

  19. Modelling volumetric growth in a thick walled fibre reinforced artery

    NASA Astrophysics Data System (ADS)

    Eriksson, T. S. E.; Watton, P. N.; Luo, X. Y.; Ventikos, Y.

    2014-12-01

    A novel framework for simulating growth and remodelling (G&R) of a fibre-reinforced artery, including volumetric adaption, is proposed. We show how to implement this model into a finite element framework and propose and examine two underlying assumptions for modelling growth, namely constant individual density (CID) or adaptive individual density (AID). Moreover, we formulate a novel approach which utilises a combination of both AID and CID to simulate volumetric G&R for a tissue composed of several different constituents. We consider a special case of the G&R of an artery subjected to prescribed elastin degradation and we theorise on the assumptions and suitability of CID, AID and the mixed approach for modelling arterial biology. For simulating the volumetric changes that occur during aneurysm enlargement, we observe that it is advantageous to describe the growth of collagen using CID whilst it is preferable to model the atrophy of elastin using AID.

  20. Testing the Testing: Validity of a State Growth Model

    ERIC Educational Resources Information Center

    Brown, Kim Trask

    2008-01-01

    Possible threats to the validity of North Carolina's accountability model used to predict academic growth were investigated in two ways: the state's regression equations were replicated but updated to utilize current testing data and not that from years past as in the state's current model; and the updated equations were expanded to include…

  1. Nonlinear mixed modeling of basal area growth for shortleaf pine

    Treesearch

    Chakra B. Budhathoki; Thomas B. Lynch; James M. Guldin

    2008-01-01

    Mixed model estimation methods were used to fit individual-tree basal area growth models to tree and stand-level measurements available from permanent plots established in naturally regenerated shortleaf pine (Pinus echinata Mill.) even-aged stands in western Arkansas and eastern Oklahoma in the USA. As a part of the development of a comprehensive...

  2. Nonlinear and Quasi-Simplex Patterns in Latent Growth Models

    ERIC Educational Resources Information Center

    Bianconcini, Silvia

    2012-01-01

    In the SEM literature, simplex and latent growth models have always been considered competing approaches for the analysis of longitudinal data, even if they are strongly connected and both of specific importance. General dynamic models, which simultaneously estimate autoregressive structures and latent curves, have been recently proposed in the…

  3. The Multigroup Multilevel Categorical Latent Growth Curve Models

    ERIC Educational Resources Information Center

    Hung, Lai-Fa

    2010-01-01

    Longitudinal data describe developmental patterns and enable predictions of individual changes beyond sampled time points. Major methodological issues in longitudinal data include modeling random effects, subject effects, growth curve parameters, and autoregressive residuals. This study embedded the longitudinal model within a multigroup…

  4. Practical Formulations of the Latent Growth Item Response Model

    ERIC Educational Resources Information Center

    McGuire, Leah Walker

    2010-01-01

    Growth modeling using longitudinal data seems to be a promising direction for improving the methodology associated with the accountability movement. Longitudinal modeling requires that the measurements of ability are comparable over time and on the same scale. One way to create the vertical scale is through concurrent estimation with…

  5. The Multigroup Multilevel Categorical Latent Growth Curve Models

    ERIC Educational Resources Information Center

    Hung, Lai-Fa

    2010-01-01

    Longitudinal data describe developmental patterns and enable predictions of individual changes beyond sampled time points. Major methodological issues in longitudinal data include modeling random effects, subject effects, growth curve parameters, and autoregressive residuals. This study embedded the longitudinal model within a multigroup…

  6. A Cautionary Note on Modeling Growth Trends in Longitudinal Data

    ERIC Educational Resources Information Center

    Kuljanin, Goran; Braun, Michael T.; DeShon, Richard P.

    2011-01-01

    Random coefficient and latent growth curve modeling are currently the dominant approaches to the analysis of longitudinal data in psychology. The application of these models to longitudinal data assumes that the data-generating mechanism behind the psychological process under investigation contains only a deterministic trend. However, if a…

  7. Growth-simulation model for lodgepole pine in central Oregon.

    Treesearch

    Walter G. Dahms

    1983-01-01

    A growth-simulation model for central Oregon lodgepole pine (Pinus contorta Dougl.) has been constructed by combining data from temporary and permanent sample plots. The model is similar to a conventional yield table with the added capacity for dealing with the stand-density variable. The simulator runs on a desk-top computer.

  8. Practical Formulations of the Latent Growth Item Response Model

    ERIC Educational Resources Information Center

    McGuire, Leah Walker

    2010-01-01

    Growth modeling using longitudinal data seems to be a promising direction for improving the methodology associated with the accountability movement. Longitudinal modeling requires that the measurements of ability are comparable over time and on the same scale. One way to create the vertical scale is through concurrent estimation with…

  9. Sensitivity of Fit Indices to Misspecification in Growth Curve Models

    ERIC Educational Resources Information Center

    Wu, Wei; West, Stephen G.

    2010-01-01

    This study investigated the sensitivity of fit indices to model misspecification in within-individual covariance structure, between-individual covariance structure, and marginal mean structure in growth curve models. Five commonly used fit indices were examined, including the likelihood ratio test statistic, root mean square error of…

  10. A Cautionary Note on Modeling Growth Trends in Longitudinal Data

    ERIC Educational Resources Information Center

    Kuljanin, Goran; Braun, Michael T.; DeShon, Richard P.

    2011-01-01

    Random coefficient and latent growth curve modeling are currently the dominant approaches to the analysis of longitudinal data in psychology. The application of these models to longitudinal data assumes that the data-generating mechanism behind the psychological process under investigation contains only a deterministic trend. However, if a…

  11. Phase field modeling of grain growth in porous polycrystalline solids

    NASA Astrophysics Data System (ADS)

    Ahmed, Karim E.

    The concurrent evolution of grain size and porosity in porous polycrystalline solids is a technically important problem. All the physical properties of such materials depend strongly on pore fraction and pore and grain sizes and distributions. Theoretical models for the pore-grain boundary interactions during grain growth usually employ restrictive, unrealistic assumptions on the pore and grain shapes and motions to render the problem tractable. However, these assumptions limit the models to be only of qualitative nature and hence cannot be used for predictions. This has motivated us to develop a novel phase field model to investigate the process of grain growth in porous polycrystalline solids. Based on a dynamical system of coupled Cahn-Hilliard and All en-Cahn equations, the model couples the curvature-driven grain boundary motion and the migration of pores via surface diffusion. As such, the model accounts for all possible interactions between the pore and grain boundary, which highly influence the grain growth kinetics. Through a formal asymptotic analysis, the current work demonstrates that the phase field model recovers the corresponding sharp-interface dynamics of the co-evolution of grain boundaries and pores; this analysis also fixes the model kinetic parameters in terms of real materials properties. The model was used to investigate the effect of porosity on the kinetics of grain growth in UO2 and CeO2 in 2D and 3D. It is shown that the model captures the phenomenon of pore breakaway often observed in experiments. Pores on three- and four- grain junctions were found to transform to edge pores (pores on two-grain junction) before complete separation. The simulations demonstrated that inhomogeneous distribution of pores and pore breakaway lead to abnormal grain growth. The simulations also showed that grain growth kinetics in these materials changes from boundary-controlled to pore-controlled as the amount of porosity increases. The kinetic growth

  12. A diameter growth model for the SRS FIA

    Treesearch

    David. Gartner

    2015-01-01

    Changes in the national Forest Inventory and Analysis (FIA) processing system required the Southern Research Station’s FIA unit to create a diameter growth model to estimate the growth of trees that could not be measured at both ends of a measurement interval. Examples of such trees are trees that have died or been harvested, and trees that grow over the minimum...

  13. Modelling grain growth in the framework of Rational Extended Thermodynamics

    NASA Astrophysics Data System (ADS)

    Kertsch, Lukas; Helm, Dirk

    2016-05-01

    Grain growth is a significant phenomenon for the thermomechanical processing of metals. Since the mobility of the grain boundaries is thermally activated and energy stored in the grain boundaries is released during their motion, a mutual interaction with the process conditions occurs. To model such phenomena, a thermodynamic framework for the representation of thermomechanical coupling phenomena in metals including a microstructure description is required. For this purpose, Rational Extended Thermodynamics appears to be a useful tool. We apply an entropy principle to derive a thermodynamically consistent model for grain coarsening due to the growth and shrinkage of individual grains. Despite the rather different approaches applied, we obtain a grain growth model which is similar to existing ones and can be regarded as a thermodynamic extension of that by Hillert (1965) to more general systems. To demonstrate the applicability of the model, we compare our simulation results to grain growth experiments in pure copper by different authors, which we are able to reproduce very accurately. Finally, we study the implications of the energy release due to grain growth on the energy balance. The present unified approach combining a microstructure description and continuum mechanics is ready to be further used to develop more elaborate material models for complex thermo-chemo-mechanical coupling phenomena.

  14. Modeling of the metabolic energy dissipation for restricted tumor growth.

    PubMed

    Pajic-Lijakovic, Ivana; Milivojevic, Milan

    2017-08-29

    Energy dissipation mostly represents unwanted outcome but in the biochemical processes it may alter the biochemical pathways. However, it is rarely considered in the literature although energy dissipation and its alteration due to the changes in cell microenvironment may improve methods for guiding chemical and biochemical processes in the desired directions. Deeper insight into the changes of metabolic activity of tumor cells exposed to osmotic stress or irradiation may offer the possibility of tumor growth reduction. In this work effects of the osmotic stress and irradiation on the thermodynamical affinity of tumor cells and their damping effects on metabolic energy dissipation were investigated and modeled. Although many various models were applied to consider the tumor restrictive growth they have not considered the metabolic energy dissipation. In this work a pseudo rheological model in the form of "the metabolic spring-pot element" is formulated to describe theoretically the metabolic susceptibility of tumor spheroid. This analog model relates the thermodynamical affinity of cell growth with the volume expansion of tumor spheroid under isotropic loading conditions. Spheroid relaxation induces anomalous nature of the metabolic energy dissipation which causes the damping effects on cell growth. The proposed model can be used for determining the metabolic energy "structure" in the context of restrictive cell growth as well as for predicting optimal doses for cancer curing in order to tailor the clinical treatment for each person and each type of cancer.

  15. Human growth and body weight dynamics: an integrative systems model.

    PubMed

    Rahmandad, Hazhir

    2014-01-01

    Quantifying human weight and height dynamics due to growth, aging, and energy balance can inform clinical practice and policy analysis. This paper presents the first mechanism-based model spanning full individual life and capturing changes in body weight, composition and height. Integrating previous empirical and modeling findings and validated against several additional empirical studies, the model replicates key trends in human growth including A) Changes in energy requirements from birth to old ages. B) Short and long-term dynamics of body weight and composition. C) Stunted growth with chronic malnutrition and potential for catch up growth. From obesity policy analysis to treating malnutrition and tracking growth trajectories, the model can address diverse policy questions. For example I find that even without further rise in obesity, the gap between healthy and actual Body Mass Indexes (BMIs) has embedded, for different population groups, a surplus of 14%-24% in energy intake which will be a source of significant inertia in obesity trends. In another analysis, energy deficit percentage needed to reduce BMI by one unit is found to be relatively constant across ages. Accompanying documented and freely available simulation model facilitates diverse applications customized to different sub-populations.

  16. Quantitative model of the growth of floodplains by vertical accretion

    USGS Publications Warehouse

    Moody, J.A.; Troutman, B.M.

    2000-01-01

    A simple one-dimensional model is developed to quantitatively predict the change in elevation, over a period of decades, for vertically accreting floodplains. This unsteady model approximates the monotonic growth of a floodplain as an incremental but constant increase of net sediment deposition per flood for those floods of a partial duration series that exceed a threshold discharge corresponding to the elevation of the floodplain. Sediment deposition from each flood increases the elevation of the floodplain and consequently the magnitude of the threshold discharge resulting in a decrease in the number of floods and growth rate of the floodplain. Floodplain growth curves predicted by this model are compared to empirical growth curves based on dendrochronology and to direct field measurements at five floodplain sites. The model was used to predict the value of net sediment deposition per flood which best fits (in a least squares sense) the empirical and field measurements; these values fall within the range of independent estimates of the net sediment deposition per flood based on empirical equations. These empirical equations permit the application of the model to estimate of floodplain growth for other floodplains throughout the world which do not have detailed data of sediment deposition during individual floods. Copyright (C) 2000 John Wiley and Sons, Ltd.

  17. Human Growth and Body Weight Dynamics: An Integrative Systems Model

    PubMed Central

    Rahmandad, Hazhir

    2014-01-01

    Quantifying human weight and height dynamics due to growth, aging, and energy balance can inform clinical practice and policy analysis. This paper presents the first mechanism-based model spanning full individual life and capturing changes in body weight, composition and height. Integrating previous empirical and modeling findings and validated against several additional empirical studies, the model replicates key trends in human growth including A) Changes in energy requirements from birth to old ages. B) Short and long-term dynamics of body weight and composition. C) Stunted growth with chronic malnutrition and potential for catch up growth. From obesity policy analysis to treating malnutrition and tracking growth trajectories, the model can address diverse policy questions. For example I find that even without further rise in obesity, the gap between healthy and actual Body Mass Indexes (BMIs) has embedded, for different population groups, a surplus of 14%–24% in energy intake which will be a source of significant inertia in obesity trends. In another analysis, energy deficit percentage needed to reduce BMI by one unit is found to be relatively constant across ages. Accompanying documented and freely available simulation model facilitates diverse applications customized to different sub-populations. PMID:25479101

  18. Growth mechanism of carbon nanotubes: a nano Czochralski model

    NASA Astrophysics Data System (ADS)

    Lu, Jingyu; Miao, Jianmin

    2012-07-01

    Carbon nanotubes (CNTs) have been under intense investigations during the past two decades due to their unique physical and chemical properties; however, there is still no commonly accepted growth mechanism to describe the growth behavior of CNTs. Here, we propose a nano Czochralski (CZ) model which regards the catalytic growth of a CNT as a CZ process taking place on the nano scale. The main idea is that, during the CNT growth, each catalyst particle acts as a nano crucible to nucleate and maintain the CNT growth, and the extruding CNT rotates relative to the nano crucible, leading to a chirality-dependent growth rate. In this case, the structural quality gradually changes along the CNT due to the dynamic generation-reconstruction-diffusion of defects during the CNT growth. The nano CZ mechanism may also apply to the catalytic growth of many other one-dimensional (1D) nanostructures (including various nanotubes and nanowires), thus further efforts will be stimulated in the quality and property control, as well as application explorations of these 1D nanomaterials.

  19. Growth mechanism of carbon nanotubes: a nano Czochralski model

    PubMed Central

    2012-01-01

    Carbon nanotubes (CNTs) have been under intense investigations during the past two decades due to their unique physical and chemical properties; however, there is still no commonly accepted growth mechanism to describe the growth behavior of CNTs. Here, we propose a nano Czochralski (CZ) model which regards the catalytic growth of a CNT as a CZ process taking place on the nano scale. The main idea is that, during the CNT growth, each catalyst particle acts as a nano crucible to nucleate and maintain the CNT growth, and the extruding CNT rotates relative to the nano crucible, leading to a chirality-dependent growth rate. In this case, the structural quality gradually changes along the CNT due to the dynamic generation-reconstruction-diffusion of defects during the CNT growth. The nano CZ mechanism may also apply to the catalytic growth of many other one-dimensional (1D) nanostructures (including various nanotubes and nanowires), thus further efforts will be stimulated in the quality and property control, as well as application explorations of these 1D nanomaterials. PMID:22747835

  20. Potts-model grain growth simulations: Parallel algorithms and applications

    SciTech Connect

    Wright, S.A.; Plimpton, S.J.; Swiler, T.P.

    1997-08-01

    Microstructural morphology and grain boundary properties often control the service properties of engineered materials. This report uses the Potts-model to simulate the development of microstructures in realistic materials. Three areas of microstructural morphology simulations were studied. They include the development of massively parallel algorithms for Potts-model grain grow simulations, modeling of mass transport via diffusion in these simulated microstructures, and the development of a gradient-dependent Hamiltonian to simulate columnar grain growth. Potts grain growth models for massively parallel supercomputers were developed for the conventional Potts-model in both two and three dimensions. Simulations using these parallel codes showed self similar grain growth and no finite size effects for previously unapproachable large scale problems. In addition, new enhancements to the conventional Metropolis algorithm used in the Potts-model were developed to accelerate the calculations. These techniques enable both the sequential and parallel algorithms to run faster and use essentially an infinite number of grain orientation values to avoid non-physical grain coalescence events. Mass transport phenomena in polycrystalline materials were studied in two dimensions using numerical diffusion techniques on microstructures generated using the Potts-model. The results of the mass transport modeling showed excellent quantitative agreement with one dimensional diffusion problems, however the results also suggest that transient multi-dimension diffusion effects cannot be parameterized as the product of the grain boundary diffusion coefficient and the grain boundary width. Instead, both properties are required. Gradient-dependent grain growth mechanisms were included in the Potts-model by adding an extra term to the Hamiltonian. Under normal grain growth, the primary driving term is the curvature of the grain boundary, which is included in the standard Potts-model Hamiltonian.

  1. A Model for Tetragonal Lysozyme Crystal Nucleation and Growth

    NASA Technical Reports Server (NTRS)

    Pusey, Marc L.; Curreri, Peter A. (Technical Monitor)

    2002-01-01

    Macromolecular crystallization is a complex process, involving a system that typically has 5 or more components (macromolecule, water, buffer + counter ion, and precipitant). Whereas small molecules have only a few contacts in the crystal lattice, macromolecules generally have 10's or even 100's of contacts between molecules. These can range from hydrogen bonds (direct or water-mediated), through van der Waals, hydrophobic, salt bridges, and ion-mediated contacts. The latter interactions are stronger and require some specificity in the molecular alignment, while the others are weaker, more prevalent, and more promiscuous, i.e., can be readily broken and reformed between other sites. Formation of a consistent, ordered, 3D structure may be difficult or impossible in the absence of any or presence of too many strong interactions. Further complicating the process is the inherent structural asymmetry of monomeric (single chain) macromolecules. The process of crystal nucleation and growth involves the ordered assembly of growth units into a defined 3D lattice. We suggest that for many macromolecules, particularly those that are monomeric, this involves a preliminary solution-phase assembly process into a growth unit having some symmetry prior to addition to the lattice, recapitulating the initial stages of the nucleation process. If this model is correct then fluids and crystal growth models assuming a strictly monodisperse nutrient solution need to be revised. This model has been developed from experimental evidence based upon face growth rate, AFM, and fluorescence energy transfer data for the nucleation and growth of tetragonal lysozyme crystals.

  2. A Model for Tetragonal Lysozyme Crystal Nucleation and Growth

    NASA Technical Reports Server (NTRS)

    Pusey, Marc L.; Curreri, Peter A. (Technical Monitor)

    2002-01-01

    Macromolecular crystallization is a complex process, involving a system that typically has 5 or more components (macromolecule, water, buffer + counter ion, and precipitant). Whereas small molecules have only a few contacts in the crystal lattice, macromolecules generally have 10's or even 100's of contacts between molecules. These can range from hydrogen bonds (direct or water-mediated), through van der Waals, hydrophobic, salt bridges, and ion-mediated contacts. The latter interactions are stronger and require some specificity in the molecular alignment, while the others are weaker, more prevalent, and more promiscuous, i.e., can be readily broken and reformed between other sites. Formation of a consistent, ordered, 3D structure may be difficult or impossible in the absence of any or presence of too many strong interactions. Further complicating the process is the inherent structural asymmetry of monomeric (single chain) macromolecules. The process of crystal nucleation and growth involves the ordered assembly of growth units into a defined 3D lattice. We suggest that for many macromolecules, particularly those that are monomeric, this involves a preliminary solution-phase assembly process into a growth unit having some symmetry prior to addition to the lattice, recapitulating the initial stages of the nucleation process. If this model is correct then fluids and crystal growth models assuming a strictly monodisperse nutrient solution need to be revised. This model has been developed from experimental evidence based upon face growth rate, AFM, and fluorescence energy transfer data for the nucleation and growth of tetragonal lysozyme crystals.

  3. Biologically-motivated system identification: application to microbial growth modeling.

    PubMed

    Yan, Jinyao; Deller, J R

    2014-01-01

    This paper presents a new method for identification of system models that are linear in parametric structure, but arbitrarily nonlinear in signal operations. The strategy blends traditional system identification methods with three modeling strategies that are not commonly employed in signal processing: linear-time-invariant-in-parameters models, set-based parameter identification, and evolutionary selection of the model structure. This paper reports recent advances in the theoretical foundation of the methods, then focuses on the operation and performance of the approach, particularly the evolutionary model determination. The method is applied to the modeling of microbial growth by Monod Kinetics.

  4. Differential Growth Trajectories for Achievement Among Children Retained in First Grade: A Growth Mixture Model

    PubMed Central

    Chen, Qi; Hughes, Jan N.; Kwok, Oi-Man

    2013-01-01

    The authors investigated the differential effect of retention on the development of academic achievement from grade one to five on children retained in first grade over six years. Growth Mixture Model (GMM) analyses supported the existence of two distinct trajectory groups of retained children for both reading and math among 125 ethnically and linguistically diverse retained children. For each achievement domain, a low intercept/higher growth group (Class 1) and a high intercept/slower growth group (Class 2) were identified. Furthermore, Class 1 children were found to score lower on several measures of learning related skills (LRS) variables and were characterized by having poorer self-regulation and less prosocial behaviors, compared to the other group. Findings suggest that some children appear to benefit more from retention, in terms of higher reading and math growth, than others. Study findings have implications for selecting children into retention intervention and early intervention. PMID:24771882

  5. A Dynamic, Architectural Plant Model Simulating Resource‐dependent Growth

    PubMed Central

    YAN, HONG‐PING; KANG, MENG ZHEN; DE REFFYE, PHILIPPE; DINGKUHN, MICHAEL

    2004-01-01

    • Background and Aims Physiological and architectural plant models have originally been developed for different purposes and therefore have little in common, thus making combined applications difficult. There is, however, an increasing demand for crop models that simulate the genetic and resource‐dependent variability of plant geometry and architecture, because man is increasingly able to transform plant production systems through combined genetic and environmental engineering. • Model GREENLAB is presented, a mathematical plant model that simulates interactions between plant structure and function. Dual‐scale automaton is used to simulate plant organogenesis from germination to maturity on the basis of organogenetic growth cycles that have constant thermal time. Plant fresh biomass production is computed from transpiration, assuming transpiration efficiency to be constant and atmospheric demand to be the driving force, under non‐limiting water supply. The fresh biomass is then distributed among expanding organs according to their relative demand. Demand for organ growth is estimated from allometric relationships (e.g. leaf surface to weight ratios) and kinetics of potential growth rate for each organ type. These are obtained through parameter optimization against empirical, morphological data sets by running the model in inverted mode. Potential growth rates are then used as estimates of relative sink strength in the model. These and other ‘hidden’ plant parameters are calibrated using the non‐linear, least‐square method. • Key Results and Conclusions The model reproduced accurately the dynamics of plant growth, architecture and geometry of various annual and woody plants, enabling 3D visualization. It was also able to simulate the variability of leaf size on the plant and compensatory growth following pruning, as a result of internal competition for resources. The potential of the model’s underlying concepts to predict the plant

  6. Forest evaporation models: relationships between stand growth and evaporation

    NASA Astrophysics Data System (ADS)

    Le Maitre, D. C.; Versfeld, D. B.

    1997-06-01

    The relationships between forest stand structure, growth and evaporation were analysed to determine whether forest evaporation can be estimated from stand growth data. This approach permits rapid assessment of the potential impacts of afforestation on the water regime. The basis for this approach is (a) that growth rates are determined by water availability and limited by the maximum water extraction potential, and (b) that stand evaporation is proportional to biomass and biomass increment. The relationships between stand growth and evaporation were modelled for a set of catchment experiments where estimates of both growth and evaporation were available. The predicted mean evaporation, over periods of several years, was generally within 10% of the measured mean annual evaporation (rainfall minus streamflow) when the model from one catchment was applied to other catchments planted with the same species. The residual evaporation, after fitting the models, was correlated with rainfall: above-average rainfall resulted in above-average evaporation. This relationship could be used to derive estimates for dry and wet years. Analyses using the models provide additional evidence that Eucalyptus grandis may be depleting groundwater reserves in catchments where its roots can reach the water table. The models are designed to be integrated into a plantation management system which uses a geographic information system for spatial analysis and modelling. The use of readily available growth parameters as predictor variables may reduce our dependence on intricate process-based models. This is seen as an efficient way of extrapolating existing catchment data — reflecting the impacts of forestry on water supplies across a range of sites, climatic zones and species. This approach has the potential for further development, especially in dealing with low flows and faster growing species.

  7. Growth curves and age-related changes in carcass characteristics, organs, serum parameters, and intestinal transporter gene expression in domestic pigeon (Columba livia).

    PubMed

    Gao, C Q; Yang, J X; Chen, M X; Yan, H C; Wang, X Q

    2016-04-01

    Two experiments were conducted to fit growth curves, and determine age-related changes in carcass characteristics, organs, serum biochemical parameters, and gene expression of intestinal nutrient transporters in domestic pigeon (Columba livia). In experiment 1, body weight (BW) of 30 pigeons was respectively determined at 1, 3, 7, 14, 21, 28, and 35 days old to fit growth curves and to describe the growth of pigeons. In experiment 2, eighty-four 1-day-old squabs were grouped by weight into 7 groups. On d 1, 3, 7, 14, 21, 28, and 35, twelve birds from each group were randomly selected for slaughter and post-slaughter analysis. The results showed that BW of pigeons increased rapidly from d 1 to d 28 (a 25.7-fold increase), and then had little change until d 35. The Logistic, Gompertz, and Von Bertalanffy functions can all be well fitted with the growth curve of domestic pigeons (R2>0.90) and the Gompertz model showed the highest R2value among the models (R2=0.9997). The equation of Gompertz model was Y=507.72×e-(3.76exp(-0.17t))(Y=BW of pigeon (g); t=time (day)). In addition, breast meat yield (%) increased with age throughout the experiment, whereas the leg meat yield (%) reached to the peak on d 14. Serum total protein, albumin, globulin, and glucose concentration were increased with age, whereas serum uric acid concentration was decreased (P<0.05). Furthermore, the gene expressions of nutrient transporters (y+LAT2, LAT1, B0AT1, PepT1, and NHE2) in jejunum of pigeon were increased with age. The results of correlation analysis showed the gene expressions of B0AT1, PepT1, and NHE2 had positive correlations with BW (0.73

  8. Plant growth and architectural modelling and its applications

    PubMed Central

    Guo, Yan; Fourcaud, Thierry; Jaeger, Marc; Zhang, Xiaopeng; Li, Baoguo

    2011-01-01

    Over the last decade, a growing number of scientists around the world have invested in research on plant growth and architectural modelling and applications (often abbreviated to plant modelling and applications, PMA). By combining physical and biological processes, spatially explicit models have shown their ability to help in understanding plant–environment interactions. This Special Issue on plant growth modelling presents new information within this topic, which are summarized in this preface. Research results for a variety of plant species growing in the field, in greenhouses and in natural environments are presented. Various models and simulation platforms are developed in this field of research, opening new features to a wider community of researchers and end users. New modelling technologies relating to the structure and function of plant shoots and root systems are explored from the cellular to the whole-plant and plant-community levels. PMID:21638797

  9. Power of Latent Growth Modeling for Detecting Linear Growth: Number of Measurements and Comparison with Other Analytic Approaches

    ERIC Educational Resources Information Center

    Fan, Xitao; Fan, Xiaotao

    2005-01-01

    The authors investigated 2 issues concerning the power of latent growth modeling (LGM) in detecting linear growth: the effect of the number of repeated measurements on LGM's power in detecting linear growth and the comparison between LGM and some other approaches in terms of power for detecting linear growth. A Monte Carlo simulation design was…

  10. Power of Latent Growth Modeling for Detecting Linear Growth: Number of Measurements and Comparison with Other Analytic Approaches

    ERIC Educational Resources Information Center

    Fan, Xitao; Fan, Xiaotao

    2005-01-01

    The authors investigated 2 issues concerning the power of latent growth modeling (LGM) in detecting linear growth: the effect of the number of repeated measurements on LGM's power in detecting linear growth and the comparison between LGM and some other approaches in terms of power for detecting linear growth. A Monte Carlo simulation design was…

  11. Growth modeling of Listeria monocytogenes in pasteurized liquid egg.

    PubMed

    Ohkochi, Miho; Koseki, Shigenobu; Kunou, Masaaki; Sugiura, Katsuaki; Tsubone, Hirokazu

    2013-09-01

    The growth kinetics of Listeria monocytogenes and natural flora in commercially produced pasteurized liquid egg was examined at 4.1 to 19.4°C, and a growth simulation model that can estimate the range of the number of L. monocytogenes bacteria was developed. The experimental kinetic data were fitted to the Baranyi model, and growth parameters, such as maximum specific growth rate (μ(max)), maximum population density (N(max)), and lag time (λ), were estimated. As a result of estimating these parameters, we found that L. monocytogenes can grow without spoilage below 12.2°C, and we then focused on storage temperatures below 12.2°C in developing our secondary models. The temperature dependency of the μ(max) was described by Ratkowsky's square root model. The N(max) of L. monocytogenes was modeled as a function of temperature, because the N(max) of L. monocytogenes decreased as storage temperature increased. A tertiary model of L. monocytogenes was developed using the Baranyi model and μ(max) and N(max) secondary models. The ranges of the numbers of L. monocytogenes bacteria were simulated using Monte Carlo simulations with an assumption that these parameters have variations that follow a normal distribution. Predictive simulations under both constant and fluctuating temperature conditions demonstrated a high accuracy, represented by root mean square errors of 0.44 and 0.34, respectively. The predicted ranges also seemed to show a reasonably good estimation, with 55.8 and 51.5% of observed values falling into the prediction range of the 25th to 75th percentile, respectively. These results suggest that the model developed here can be used to estimate the kinetics and range of L. monocytogenes growth in pasteurized liquid egg under refrigerated temperature.

  12. Modeling Bacterial Population Growth from Stochastic Single-Cell Dynamics

    PubMed Central

    Molina, Ignacio; Theodoropoulos, Constantinos

    2014-01-01

    A few bacterial cells may be sufficient to produce a food-borne illness outbreak, provided that they are capable of adapting and proliferating on a food matrix. This is why any quantitative health risk assessment policy must incorporate methods to accurately predict the growth of bacterial populations from a small number of pathogens. In this aim, mathematical models have become a powerful tool. Unfortunately, at low cell concentrations, standard deterministic models fail to predict the fate of the population, essentially because the heterogeneity between individuals becomes relevant. In this work, a stochastic differential equation (SDE) model is proposed to describe variability within single-cell growth and division and to simulate population growth from a given initial number of individuals. We provide evidence of the model ability to explain the observed distributions of times to division, including the lag time produced by the adaptation to the environment, by comparing model predictions with experiments from the literature for Escherichia coli, Listeria innocua, and Salmonella enterica. The model is shown to accurately predict experimental growth population dynamics for both small and large microbial populations. The use of stochastic models for the estimation of parameters to successfully fit experimental data is a particularly challenging problem. For instance, if Monte Carlo methods are employed to model the required distributions of times to division, the parameter estimation problem can become numerically intractable. We overcame this limitation by converting the stochastic description to a partial differential equation (backward Kolmogorov) instead, which relates to the distribution of division times. Contrary to previous stochastic formulations based on random parameters, the present model is capable of explaining the variability observed in populations that result from the growth of a small number of initial cells as well as the lack of it compared to

  13. Modeling bacterial population growth from stochastic single-cell dynamics.

    PubMed

    Alonso, Antonio A; Molina, Ignacio; Theodoropoulos, Constantinos

    2014-09-01

    A few bacterial cells may be sufficient to produce a food-borne illness outbreak, provided that they are capable of adapting and proliferating on a food matrix. This is why any quantitative health risk assessment policy must incorporate methods to accurately predict the growth of bacterial populations from a small number of pathogens. In this aim, mathematical models have become a powerful tool. Unfortunately, at low cell concentrations, standard deterministic models fail to predict the fate of the population, essentially because the heterogeneity between individuals becomes relevant. In this work, a stochastic differential equation (SDE) model is proposed to describe variability within single-cell growth and division and to simulate population growth from a given initial number of individuals. We provide evidence of the model ability to explain the observed distributions of times to division, including the lag time produced by the adaptation to the environment, by comparing model predictions with experiments from the literature for Escherichia coli, Listeria innocua, and Salmonella enterica. The model is shown to accurately predict experimental growth population dynamics for both small and large microbial populations. The use of stochastic models for the estimation of parameters to successfully fit experimental data is a particularly challenging problem. For instance, if Monte Carlo methods are employed to model the required distributions of times to division, the parameter estimation problem can become numerically intractable. We overcame this limitation by converting the stochastic description to a partial differential equation (backward Kolmogorov) instead, which relates to the distribution of division times. Contrary to previous stochastic formulations based on random parameters, the present model is capable of explaining the variability observed in populations that result from the growth of a small number of initial cells as well as the lack of it compared to

  14. SEM++: A particle model of cellular growth, signaling and migration

    NASA Astrophysics Data System (ADS)

    Milde, Florian; Tauriello, Gerardo; Haberkern, Hannah; Koumoutsakos, Petros

    2014-06-01

    We present a discrete particle method to model biological processes from the sub-cellular to the inter-cellular level. Particles interact through a parametrized force field to model cell mechanical properties, cytoskeleton remodeling, growth and proliferation as well as signaling between cells. We discuss the guiding design principles for the selection of the force field and the validation of the particle model using experimental data. The proposed method is integrated into a multiscale particle framework for the simulation of biological systems.

  15. Growth of Byssochlamys Nivea in Pineapple Juice Under the Effect of Water Activity and Ascospore Age

    PubMed Central

    Zimmermann, M.; Miorelli, S.; Massaguer, P.R.; Aragão, G.M.F.

    2011-01-01

    The study of thermal resistant mould, including Byssochlamys nivea, is of extreme importance since it has been associated with fruit and fruit products. The aim of this work is to analyze the influence of water activity (aw) and ascospore age (I) on the growth of Byssochlamys nivea in pineapple juice. Mold growth was carried out under different conditions of water activity (aw) (0.99, 0.96, 0.95, 0.93, 0.90) and ascospore age (I) (30, 51, 60, 69, 90 days). Growth parameters as length of adaptation phase (λ), maximum specific growth rate (µmax) and maximum diameter reached by the colony (A) were obtained through the fit of the Modified Gompertz model to experimental data (measuring radial colony diameter). Statistica 6.0 was used for statistical analyses (significance level α = 0.05). The results obtained clearly showed that water activity is statistically significant and that it influences all growth parameters, while ascospore age does not have any statistically significant influence on growth parameters. Also, these data showed that by increasing aw from 0.90 to 0.99, the λ value substantially decreased, while µmax and A values rose. The data contributed for the understanding of the behavior of B. nivea in pineapple juice. Therefore, it provided mathematical models that can well predict growth parameters, also helping on microbiological control and products’ shelf life determination. PMID:24031622

  16. Modeling of thin film GaAs growth

    NASA Technical Reports Server (NTRS)

    Heinbockel, J. H.

    1982-01-01

    A potential scaling Monte Carlo model of crystal growth is developed. The model is a modification of the solid-on-solid method for studying crystal growth in that potentials at surface sites are continuously updated on a time scale reflecting the surface events of migration, incorporation and evaporation. The model allows for B on A type of crystal growth and lattice disregistry by the assignment of potential values at various surface sites. The surface adatoms are periodically assigned a random energy from a Boltzmann distribution and this energy determines whether the adatoms evaporate, migrate or remain stationary during the sampling interval. For each addition or migration of an adatom, the surface potentials are adjusted to reflect the adsorption, migration or desorption potential changes.

  17. Phase transitions in tumor growth: II prostate cancer cell lines

    NASA Astrophysics Data System (ADS)

    Llanos-Pérez, J. A.; Betancourt-Mar, A.; De Miguel, M. P.; Izquierdo-Kulich, E.; Royuela-García, M.; Tejera, E.; Nieto-Villar, J. M.

    2015-05-01

    We propose a mechanism for prostate cancer cell lines growth, LNCaP and PC3 based on a Gompertz dynamics. This growth exhibits a multifractal behavior and a "second order" phase transition. Finally, it was found that the cellular line PC3 exhibits a higher value of entropy production rate compared to LNCaP, which is indicative of the robustness of PC3, over to LNCaP and may be a quantitative index of metastatic potential tumors.

  18. Toward Multiscale Models of Cyanobacterial Growth: A Modular Approach

    PubMed Central

    Westermark, Stefanie; Steuer, Ralf

    2016-01-01

    Oxygenic photosynthesis dominates global primary productivity ever since its evolution more than three billion years ago. While many aspects of phototrophic growth are well understood, it remains a considerable challenge to elucidate the manifold dependencies and interconnections between the diverse cellular processes that together facilitate the synthesis of new cells. Phototrophic growth involves the coordinated action of several layers of cellular functioning, ranging from the photosynthetic light reactions and the electron transport chain, to carbon-concentrating mechanisms and the assimilation of inorganic carbon. It requires the synthesis of new building blocks by cellular metabolism, protection against excessive light, as well as diurnal regulation by a circadian clock and the orchestration of gene expression and cell division. Computational modeling allows us to quantitatively describe these cellular functions and processes relevant for phototrophic growth. As yet, however, computational models are mostly confined to the inner workings of individual cellular processes, rather than describing the manifold interactions between them in the context of a living cell. Using cyanobacteria as model organisms, this contribution seeks to summarize existing computational models that are relevant to describe phototrophic growth and seeks to outline their interactions and dependencies. Our ultimate aim is to understand cellular functioning and growth as the outcome of a coordinated operation of diverse yet interconnected cellular processes. PMID:28083530

  19. Plant growth modeling at the JSC variable pressure growth chamber - An application of experimental design

    NASA Technical Reports Server (NTRS)

    Miller, Adam M.; Edeen, Marybeth; Sirko, Robert J.

    1992-01-01

    This paper describes the approach and results of an effort to characterize plant growth under various environmental conditions at the Johnson Space Center variable pressure growth chamber. Using a field of applied mathematics and statistics known as design of experiments (DOE), we developed a test plan for varying environmental parameters during a lettuce growth experiment. The test plan was developed using a Box-Behnken approach to DOE. As a result of the experimental runs, we have developed empirical models of both the transpiration process and carbon dioxide assimilation for Waldman's Green lettuce over specified ranges of environmental parameters including carbon dioxide concentration, light intensity, dew-point temperature, and air velocity. This model also predicts transpiration and carbon dioxide assimilation for different ages of the plant canopy.

  20. Plant growth modeling at the JSC variable pressure growth chamber - An application of experimental design

    NASA Technical Reports Server (NTRS)

    Miller, Adam M.; Edeen, Marybeth; Sirko, Robert J.

    1992-01-01

    This paper describes the approach and results of an effort to characterize plant growth under various environmental conditions at the Johnson Space Center variable pressure growth chamber. Using a field of applied mathematics and statistics known as design of experiments (DOE), we developed a test plan for varying environmental parameters during a lettuce growth experiment. The test plan was developed using a Box-Behnken approach to DOE. As a result of the experimental runs, we have developed empirical models of both the transpiration process and carbon dioxide assimilation for Waldman's Green lettuce over specified ranges of environmental parameters including carbon dioxide concentration, light intensity, dew-point temperature, and air velocity. This model also predicts transpiration and carbon dioxide assimilation for different ages of the plant canopy.

  1. Numerical solution of the Penna model of biological aging with age-modified mutation rate

    NASA Astrophysics Data System (ADS)

    Magdoń-Maksymowicz, M. S.; Maksymowicz, A. Z.

    2009-06-01

    In this paper we present results of numerical calculation of the Penna bit-string model of biological aging, modified for the case of a -dependent mutation rate m(a) , where a is the parent’s age. The mutation rate m(a) is the probability per bit of an extra bad mutation introduced in offspring inherited genome. We assume that m(a) increases with age a . As compared with the reference case of the standard Penna model based on a constant mutation rate m , the dynamics of the population growth shows distinct changes in age distribution of the population. Here we concentrate on mortality q(a) , a fraction of items eliminated from the population when we go from age (a) to (a+1) in simulated transition from time (t) to next time (t+1) . The experimentally observed q(a) dependence essentially follows the Gompertz exponential law for a above the minimum reproduction age. Deviation from the Gompertz law is however observed for the very old items, close to the maximal age. This effect may also result from an increase in mutation rate m with age a discussed in this paper. The numerical calculations are based on analytical solution of the Penna model, presented in a series of papers by Coe [J. B. Coe, Y. Mao, and M. E. Cates, Phys. Rev. Lett. 89, 288103 (2002)]. Results of the numerical calculations are supported by the data obtained from computer simulation based on the solution by Coe

  2. Fast Bayesian parameter estimation for stochastic logistic growth models.

    PubMed

    Heydari, Jonathan; Lawless, Conor; Lydall, David A; Wilkinson, Darren J

    2014-08-01

    The transition density of a stochastic, logistic population growth model with multiplicative intrinsic noise is analytically intractable. Inferring model parameter values by fitting such stochastic differential equation (SDE) models to data therefore requires relatively slow numerical simulation. Where such simulation is prohibitively slow, an alternative is to use model approximations which do have an analytically tractable transition density, enabling fast inference. We introduce two such approximations, with either multiplicative or additive intrinsic noise, each derived from the linear noise approximation (LNA) of a logistic growth SDE. After Bayesian inference we find that our fast LNA models, using Kalman filter recursion for computation of marginal likelihoods, give similar posterior distributions to slow, arbitrarily exact models. We also demonstrate that simulations from our LNA models better describe the characteristics of the stochastic logistic growth models than a related approach. Finally, we demonstrate that our LNA model with additive intrinsic noise and measurement error best describes an example set of longitudinal observations of microbial population size taken from a typical, genome-wide screening experiment. Copyright © 2014 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

  3. Modeling Intrinsic Heterogeneity and Growth of Cancer Cells

    PubMed Central

    Greene, James M.; Levy, Doron; Fung, King L.; Silva de Souza, Paloma; Gottesman, Michael M.; Lavi, Orit

    2014-01-01

    Intratumoral heterogeneity has been found to be a major cause of drug resistance. Cell-to-cell variation increases as a result of cancer-related alterations, which are acquired by stochastic events and further induced by environmental signals. However, most cellular mechanisms include natural fluctuations that are closely regulated, and thus lead to asynchronization of the cells, which causes intrinsic heterogeneity in a given population. Here, we derive two novel mathematical models, a stochastic agent-based model and an integro-differential equation model, each of which describes the growth of cancer cells as a dynamic transition between proliferative and quiescent states. These models are designed to predict variations in growth as a function of the intrinsic heterogeneity emerging from the durations of the cell-cycle and apoptosis, and also include cellular density dependencies. By examining the role all parameters play in the evolution of intrinsic tumor heterogeneity, and the sensitivity of the population growth to parameter values, we show that the cell-cycle length has the most significant effect on the growth dynamics. In addition, we demonstrate that the agent-based model can be approximated well by the more computationally efficient integro-differential equations when the number of cells is large. This essential step in cancer growth modeling will allow us to revisit the mechanisms of multi-drug resistance by examining spatiotemporal differences of cell growth while administering a drug among the different sub-populations in a single tumor, as well as the evolution of those mechanisms as a function of the resistance level. PMID:25457229

  4. Modeling intrinsic heterogeneity and growth of cancer cells.

    PubMed

    Greene, James M; Levy, Doron; Fung, King Leung; Souza, Paloma S; Gottesman, Michael M; Lavi, Orit

    2015-02-21

    Intratumoral heterogeneity has been found to be a major cause of drug resistance. Cell-to-cell variation increases as a result of cancer-related alterations, which are acquired by stochastic events and further induced by environmental signals. However, most cellular mechanisms include natural fluctuations that are closely regulated, and thus lead to asynchronization of the cells, which causes intrinsic heterogeneity in a given population. Here, we derive two novel mathematical models, a stochastic agent-based model and an integro-differential equation model, each of which describes the growth of cancer cells as a dynamic transition between proliferative and quiescent states. These models are designed to predict variations in growth as a function of the intrinsic heterogeneity emerging from the durations of the cell-cycle and apoptosis, and also include cellular density dependencies. By examining the role all parameters play in the evolution of intrinsic tumor heterogeneity, and the sensitivity of the population growth to parameter values, we show that the cell-cycle length has the most significant effect on the growth dynamics. In addition, we demonstrate that the agent-based model can be approximated well by the more computationally efficient integro-differential equations when the number of cells is large. This essential step in cancer growth modeling will allow us to revisit the mechanisms of multidrug resistance by examining spatiotemporal differences of cell growth while administering a drug among the different sub-populations in a single tumor, as well as the evolution of those mechanisms as a function of the resistance level.

  5. Testing fault growth models with low-temperature thermochronology

    NASA Astrophysics Data System (ADS)

    Curry, Magdalena; Barnes, Jason; Colgan, Joseph

    2017-04-01

    Common fault-growth models diverge in predicting how faults accumulate displacement and lengthen through time. A paucity of field-based data documenting the lateral component of fault growth hinders our ability to test these models and fully understand how natural fault systems evolve. We outline a framework for using apatite (U-Th)/He thermochronology (AHe) to quantify the along-strike growth of faults. We test our framework in the normal-fault bounded Pine Forest Range from the U.S. Basin and Range Province. We combine new and existing cross-sections with 18 new and 16 existing AHe cooling ages to determine the spatiotemporal variability in footwall exhumation and evaluate models for fault growth. Three age-elevation transects in the Pine Forest Range show rapid exhumation began along the range-front fault between ca. 15-11 Ma at rates of 0.2-0.4 km/m.y., ultimately exhuming ca. 1.5-5 km. The ages of onset of rapid exhumation identified at each sample transect lie within data uncertainty, indicating concomitant onset of faulting along strike. We show that even in the case of growth by fault-segment linkage, the fault would achieve its modern >40 km length within 3-4 m.y. of onset. A constant fault-length growth model is the best explanation for our thermochronology results. We advocate that low-temperature thermochronology can be further utilized to better understand and quantify fault growth with broader implications for seismic hazard assessments and the coevolution of faulting and topography.

  6. Fatigue crack growth with single overload - Measurement and modeling

    NASA Technical Reports Server (NTRS)

    Davidson, D. L.; Hudak, S. J., Jr.; Dexter, R. J.

    1987-01-01

    This paper compares experiments with an analytical model of fatigue crack growth under variable amplitude. The stereoimaging technique was used to measure displacements near the tips of fatigue cracks undergoing simple variations in load amplitude-single overloads and overload/underload combinations. Measured displacements were used to compute strains, and stresses were determined from the strains. Local values of crack driving force (Delta-K effective) were determined using both locally measured opening loads and crack tip opening displacements. Experimental results were compared with simulations made for the same load variation conditions using Newman's FAST-2 model. Residual stresses caused by overloads, crack opening loads, and growth retardation periods were compared.

  7. Deterministic versus stochastic aspects of superexponential population growth models

    NASA Astrophysics Data System (ADS)

    Grosjean, Nicolas; Huillet, Thierry

    2016-08-01

    Deterministic population growth models with power-law rates can exhibit a large variety of growth behaviors, ranging from algebraic, exponential to hyperexponential (finite time explosion). In this setup, selfsimilarity considerations play a key role, together with two time substitutions. Two stochastic versions of such models are investigated, showing a much richer variety of behaviors. One is the Lamperti construction of selfsimilar positive stochastic processes based on the exponentiation of spectrally positive processes, followed by an appropriate time change. The other one is based on stable continuous-state branching processes, given by another Lamperti time substitution applied to stable spectrally positive processes.

  8. Kinetic model for microbial growth and desulphurisation with Enterobacter sp.

    PubMed

    Liu, Long; Guo, Zhiguo; Lu, Jianjiang; Xu, Xiaolin

    2015-02-01

    Biodesulphurisation was investigated by using Enterobacter sp. D4, which can selectively desulphurise and convert dibenzothiophene into 2-hydroxybiphenyl (2-HBP). The experimental values of growth, substrate consumption and product generation were obtained at 95 % confidence level of the fitted values using three models: Hinshelwood equation, Luedeking-Piret and Luedeking-Piret-like equations. The average error values between experimental values and fitted values were less than 10 %. These kinetic models describe all the experimental data with good statistical parameters. The production of 2-HBP in Enterobacter sp. was by "coupled growth".

  9. Kinetic model of particle-inhibited grain growth

    NASA Astrophysics Data System (ADS)

    Thompson, Gary Scott

    The effects of second phase particles on matrix grain growth kinetics were investigated using Al2O3-SiC as a model system. In particular, the validity of the conclusion drawn from a previous kinetic analysis that the kinetics of particle-inhibited grain growth in Al2 O3-SiC samples with an intermediate volume fraction of second phase could be well quantified by a modified-Zener model was investigated. A critical analysis of assumptions made during the previous kinetic analysis revealed oversimplifications which affect the validity of the conclusion. Specifically, the degree of interaction between particles and grain boundaries was assumed to be independent of the mean second phase particle size and size distribution. In contrast, current measurements indicate that the degree of interaction in Al2O3-SiC is dependent on these parameters. An improved kinetic model for particle-inhibited grain growth in Al 2O3-SiC was developed using a modified-Zener approach. The comparison of model predictions with experimental grain growth data indicated that significant discrepancies (as much as 4--5 orders of magnitude) existed. Based on this, it was concluded that particles had a much more significant effect on grain growth kinetics than that caused by a simple reduction of the boundary driving force due to the removal of boundary area. Consequently, it was also concluded that the conclusion drawn from the earlier kinetic analysis regarding the validity of a modified-Zener model was incorrect. Discrepancies between model and experiment were found to be the result of a significant decrease in experimental growth rate constant not predicted by the model. Possible physical mechanisms for such a decrease were investigated. The investigation of a small amount of SiO2 on grain growth in Al2O3 indicated that the decrease was not the result of a decrease in grain boundary mobility due to impurity contamination by particles. By process of elimination and based on previous observations

  10. MODELING GROWTH OF AU-CU NANOCRYSTALLIINE COATINGS

    SciTech Connect

    Jankowski, A F

    2005-09-22

    The electrodeposition process parameters of current density, pulse duration, and cell potential affect both the structure and composition of the foils. The mechanism for nucleation and growth as determined from current transients yield relationships for nucleus density and nucleation rate. To develop an understanding of the role of the process parameters on grain size--as a design structural parameter to control strength, for example, a formulation is presented to model the affects of the deposition energetics on grain size and morphology. An activation energy for the deposition process is modeled that reveals different growth mechanisms, wherein nucleation and diffusion effects are each dominant as dependent upon pulse duration. A diffusion coefficient common for each of the pulsed growth modes demarcates an observed transition in growth from smooth to rough surfaces. Empirical relationships are developed that relate the parameters of the deposition process to the morphology and grain size at the nanoscale. Regimes for nanocrystalline growth include a short and long pulse mode, each with distinct activation energies. The long pulse has the additional contribution of bulk-like diffusion whereas the short pulse is limited to surface diffusion and nucleation. For either pulse condition, a transition from a rough (or nodular) growth to a smooth surface results with an increase in the kinetics of diffusion.

  11. Modeling of a compost biofilter incorporating microbial growth

    SciTech Connect

    Morgenroth, E.; Schroeder, E.D.; Chang, D.P.Y.; Scow, K.M.

    1995-11-01

    Biofiltration of air streams is gaining acceptance as an air pollution control technology. Biofilters are advantageous because of low operating costs and low energy requirements. Biofilters are advantageous for the removal of biodegradable pollutants at low concentrations. In this paper steady state and dynamic models for biofilters are presented. Analytical steady state models are useful for design purposes. The effects of changing operating conditions on removal efficiency and elimination capacity can be predicted. Dynamic models give a better representation of processes in a biofilter. A dynamic biofilter model incorporating microbial growth was developed. The dynamic model accounts for higher organism density at the inlet due to higher substrate concentrations.

  12. Modeling of bacterial growth as a function of temperature.

    PubMed Central

    Zwietering, M H; de Koos, J T; Hasenack, B E; de Witt, J C; van't Riet, K

    1991-01-01

    The temperature of chilled foods is a very important variable for microbial safety in a production and distribution chain. To predict the number of organisms as a function of temperature and time, it is essential to model the lag time, specific growth rate, and asymptote (growth yield) as a function of temperature. The objective of this research was to determine the suitability and usefulness of different models, either available from the literature or newly developed. The models were compared by using an F test, by which the lack of fit of the models was compared with the measuring error. From the results, a hyperbolic model was selected for the description of the lag time as a function of temperature. Modified forms of the Ratkowsky model were selected as the most suitable model for both the growth rate and the asymptote as a function of temperature. The selected models could be used to predict experimentally determined numbers of organisms as a function of temperature and time. PMID:2059034

  13. Photorealistic Modeling of the Growth of Filamentous Specimens

    NASA Astrophysics Data System (ADS)

    Sedlář, Jiří; Flusser, Jan; Sedlářová, Michaela

    2007-12-01

    We present a new method for modeling the development of settled specimens with filamentous growth patterns, such as fungi and oomycetes. In phytopathology, the growth parameters of such microorganisms are frequently examined. Their development is documented repeatedly, in a defined time sequence, leaving the growth pattern incomplete. This restriction can be overcome by reconstructing the missing images from the images acquired at consecutive observation sessions. Image warping is a convenient tool for such purposes. In the proposed method, the parameters of the geometric transformation are estimated by means of the growth tracking based on the morphological skeleton. The result is a sequence of photorealistic artificial images that show the development of the specimen within the interval between observations.

  14. Platelet leukocyte gel facilitates bone substitute growth and autologous bone growth in a goat model.

    PubMed

    Everts, Peter A M; Delawi, Diyar; Mahoney, Christine Brown; van Erp, Albert; Overdevest, Eddy P; van Zundert, André; Knape, Johannes T A; Dhert, Wouter J A

    2010-02-01

    The aim of this study is to evaluate multiple conditions on the formation of bone growth in a goat model. We prepared from a unit of whole blood, platelet-leukocyte gel (PLG) to stimulate bone formation, based on the release of platelet growth factors. Two 3-compartment cages containing autologous bone, calcium phosphate, and trabecular metal were implanted onto goat spinal transverse processes. One cage was treated with PLG, prepared according to a standardized protocol. An untreated cage served as a control. To monitor bone formation overtime, fluorochrome markers were administered at 2, 3, and 5 weeks. Animals were sacrificed at 9 weeks after implantation. Bone growth in these 3-compartments cages was examined by histology and histomorphometry of nondecalcified sections using traditional light and epifluorescent microscopy. Compared to the control samples, bone growth in the PLG-treated autologous bone and calcium phosphate samples was significantly more. Fairly little bone growth was seen in PLG treated or untreated trabecular metal scaffolds. The results obtained from this goat model suggest a potential role for the application of autologous PLG during surgeries in which autologous bone grafts or calcium phosphate scaffolds are used.

  15. Reserve growth in oil pools of Alberta: Model and forecast

    USGS Publications Warehouse

    Verma, M.; Cook, T.

    2010-01-01

    Reserve growth is recognized as a major component of additions to reserves in most oil provinces around the world, particularly in mature provinces. It takes place as a result of the discovery of new pools/reservoirs and extensions of known pools within existing fields, improved knowledge of reservoirs over time leading to a change in estimates of original oil-in-place, and improvement in recovery factor through the application of new technology, such as enhanced oil recovery methods, horizontal/multilateral drilling, and 4D seismic. A reserve growth study was conducted on oil pools in Alberta, Canada, with the following objectives: 1) evaluate historical oil reserve data in order to assess the potential for future reserve growth; 2) develop reserve growth models/ functions to help forecast hydrocarbon volumes; 3) study reserve growth sensitivity to various parameters (for example, pool size, porosity, and oil gravity); and 4) compare reserve growth in oil pools and fields in Alberta with those from other large petroleum provinces around the world. The reported known recoverable oil exclusive of Athabasca oil sands in Alberta increased from 4.5 billion barrels of oil (BBO) in 1960 to 17 BBO in 2005. Some of the pools that were included in the existing database were excluded from the present study for lack of adequate data. Therefore, the known recoverable oil increased from 4.2 to 13.9 BBO over the period from 1960 through 2005, with new discoveries contributing 3.7 BBO and reserve growth adding 6 BBO. This reserve growth took place mostly in pools with more than 125,000 barrels of known recoverable oil. Pools with light oil accounted for most of the total known oil volume, therefore reflecting the overall pool growth. Smaller pools, in contrast, shrank in their total recoverable volumes over the years. Pools with heavy oil (gravity less than 20o API) make up only a small share (3.8 percent) of the total recoverable oil; they showed a 23-fold growth compared to

  16. Modeling fatigue crack growth for life-extending control

    NASA Astrophysics Data System (ADS)

    Patankar, Ravindra Prakash

    1999-12-01

    This dissertation presents a nonlinear dynamic model of fatigue crack growth in the state-space setting under variable amplitude cyclic load. The model is especially suited to the needs of real-time decision-making for life-extending control. The state variables are crack length and crack opening stress. The model is capable of capturing the effects of a single-cycle overload, block loads, random loads, and irregular sequences through a fading memory algorithm. Model predictions are in good agreement with experimental data on 7075-T6 and 2024-T3 aluminum alloys. Compiled results also demonstrate that the proposed model compares well with one of the most comprehensive models, FASTRAN-II that is used by the aircraft industry. Specifically, the state-space model recursively computes the crack opening stress via a simple functional relationship based on the principle of fading memory and does not require the storage of the stress history for its execution. Therefore, savings in both computation time and memory requirements are significant. The need for a reliable damage model for life-extending control is addressed with reference to the colossal inaccuracies that could occur in controller synthesis for a reusable rocket engine if a simplistic damage model is used under variable-amplitude load conditions. The seemingly counter-intuitive notion of overload injection could be gainfully utilized for life-extending optimization. The proof of this concept is demonstrated on a laboratory test apparatus by life-extension of test specimens with intentionally injected overload pulses at specific intervals. A stochastic model of fatigue crack growth under variable-amplitude load is proposed using the framework of the state-space model. The stochastic model is validated with four sets of constant-amplitude load test data and a set under variable-amplitude load test. The crack growth process is observed to be nearly deterministic for a cyclic load applied to a given specimen

  17. Thermal-capillary model for Czochralski growth of semiconductor materials

    NASA Technical Reports Server (NTRS)

    Derby, J. J.; Brown, R. A.

    1985-01-01

    The success of efficiently calculating the temperature field, crystal radius, melt mensicus, and melt/solid interface in the Czochralski crystal growth system by full finite-element solution of the government thermal-capillary model is demonstrated. The model predicts realistic response to changes in pull rate, melt volume, and the thermal field. The experimentally observed phenomena of interface flipping, bumping, and the difficulty maintaining steady-state growth as the melt depth decreases are explained by model results. These calculations will form the basis for the first quantitative picture of Cz crystal growth. The accurate depiction of the melt meniscus is important in calculating the crystal radius and solidification interface. The sensitivity of the results to the equilibrium growth angle place doubt on less sophisticated attempts to model the process without inclusion of the meniscus. Quantitative comparison with experiments should be possible once more representation of the radiation and view factors in the thermal system and the crucible are included. Extensions of the model in these directions are underway.

  18. A full lifespan model of vertebrate lens growth.

    PubMed

    Šikić, Hrvoje; Shi, Yanrong; Lubura, Snježana; Bassnett, Steven

    2017-01-01

    The mathematical determinants of vertebrate organ growth have yet to be elucidated fully. Here, we utilized empirical measurements and a dynamic branching process-based model to examine the growth of a simple organ system, the mouse lens, from E14.5 until the end of life. Our stochastic model used difference equations to model immigration and emigration between zones of the lens epithelium and included some deterministic elements, such as cellular footprint area. We found that the epithelial cell cycle was shortened significantly in the embryo, facilitating the rapid growth that marks early lens development. As development progressed, epithelial cell division becomes non-uniform and four zones, each with a characteristic proliferation rate, could be discerned. Adjustment of two model parameters, proliferation rate and rate of change in cellular footprint area, was sufficient to specify all growth trajectories. Modelling suggested that the direction of cellular migration across zonal boundaries was sensitive to footprint area, a phenomenon that may isolate specific cell populations. Model runs consisted of more than 1000 iterations, in each of which the stochastic behaviour of thousands of cells was followed. Nevertheless, sequential runs were almost superimposable. This remarkable degree of precision was attributed, in part, to the presence of non-mitotic flanking regions, which constituted a path by which epithelial cells could escape the growth process. Spatial modelling suggested that clonal clusters of about 50 cells are produced during migration and that transit times lengthen significantly at later stages, findings with implications for the formation of certain types of cataract.

  19. A full lifespan model of vertebrate lens growth

    PubMed Central

    Šikić, Hrvoje; Shi, Yanrong; Lubura, Snježana

    2017-01-01

    The mathematical determinants of vertebrate organ growth have yet to be elucidated fully. Here, we utilized empirical measurements and a dynamic branching process-based model to examine the growth of a simple organ system, the mouse lens, from E14.5 until the end of life. Our stochastic model used difference equations to model immigration and emigration between zones of the lens epithelium and included some deterministic elements, such as cellular footprint area. We found that the epithelial cell cycle was shortened significantly in the embryo, facilitating the rapid growth that marks early lens development. As development progressed, epithelial cell division becomes non-uniform and four zones, each with a characteristic proliferation rate, could be discerned. Adjustment of two model parameters, proliferation rate and rate of change in cellular footprint area, was sufficient to specify all growth trajectories. Modelling suggested that the direction of cellular migration across zonal boundaries was sensitive to footprint area, a phenomenon that may isolate specific cell populations. Model runs consisted of more than 1000 iterations, in each of which the stochastic behaviour of thousands of cells was followed. Nevertheless, sequential runs were almost superimposable. This remarkable degree of precision was attributed, in part, to the presence of non-mitotic flanking regions, which constituted a path by which epithelial cells could escape the growth process. Spatial modelling suggested that clonal clusters of about 50 cells are produced during migration and that transit times lengthen significantly at later stages, findings with implications for the formation of certain types of cataract. PMID:28280571

  20. Probabilistic Model of Microbial Cell Growth, Division, and Mortality ▿

    PubMed Central

    Horowitz, Joseph; Normand, Mark D.; Corradini, Maria G.; Peleg, Micha

    2010-01-01

    After a short time interval of length δt during microbial growth, an individual cell can be found to be divided with probability Pd(t)δt, dead with probability Pm(t)δt, or alive but undivided with the probability 1 − [Pd(t) + Pm(t)]δt, where t is time, Pd(t) expresses the probability of division for an individual cell per unit of time, and Pm(t) expresses the probability of mortality per unit of time. These probabilities may change with the state of the population and the habitat's properties and are therefore functions of time. This scenario translates into a model that is presented in stochastic and deterministic versions. The first, a stochastic process model, monitors the fates of individual cells and determines cell numbers. It is particularly suitable for small populations such as those that may exist in the case of casual contamination of a food by a pathogen. The second, which can be regarded as a large-population limit of the stochastic model, is a continuous mathematical expression that describes the population's size as a function of time. It is suitable for large microbial populations such as those present in unprocessed foods. Exponential or logistic growth with or without lag, inactivation with or without a “shoulder,” and transitions between growth and inactivation are all manifestations of the underlying probability structure of the model. With temperature-dependent parameters, the model can be used to simulate nonisothermal growth and inactivation patterns. The same concept applies to other factors that promote or inhibit microorganisms, such as pH and the presence of antimicrobials, etc. With Pd(t) and Pm(t) in the form of logistic functions, the model can simulate all commonly observed growth/mortality patterns. Estimates of the changing probability parameters can be obtained with both the stochastic and deterministic versions of the model, as demonstrated with simulated data. PMID:19915038