Statistical methods for estimating doubling time in in vitro cell growth

Summary Doubling time has been widely used to represent the growth pattern of cells. A traditional method for finding the doubling time is to apply gray-scaled cells, where the logarithmic transformed scale is used. As an alternative statistical method, the log-linear model was recently proposed, for which actual cell numbers are used instead of the transformed gray-scaled cells. In this paper, I extend the log-linear model and propose the extended log-linear model. This model is designed for extra-Poisson variation, where the log-linear model produces the less appropriate estimate of the doubling time. Moreover, I compare statistical properties of the gray-scaled method, the log-linear model, and the extended log-linear model. For this purpose, I perform a Monte Carlo simulation study with three data-generating models: the additive error model, the multiplicative error model, and the overdispersed Poisson model. From the simulation study, I found that the gray-scaled method highly depends on the normality assumption of the gray-scaled cells; hence, this method is appropriate when the error model is multiplicative with the log-normally distributed errors. However, it is less efficient for other types of error distributions, especially when the error model is additive or the errors follow the Poisson distribution. The estimated standard error for the doubling time is not accurate in this case. The log-linear model was found to be efficient when the errors follow the Poisson distribution or nearly Poisson distribution. The efficiency of the log-linear model was decreased accordingly as the overdispersion increased, compared to the extended log-linear model. When the error model is additive or multiplicative with Gamma-distributed errors, the log-linear model is more efficient than the gray-scaled method. The extended log-linear model performs well overall for all three data-generating models. The loss of efficiency of the extended log-linear model is observed only when the error model is multiplicative with log-normally distributed errors, where the gray-scaled method is appropriate. However, the extended log-linear model is more efficient than the log-linear model in this case.     

Reliability Analysis of the Groundwater Conceptual Model

The hydrologic model is the foundation of water resource management and planning. Conceptual model is the essential component of groundwater model. Due to limited understanding of natural hydrogeological conditions, the conceptual model is always constructed incompletely. Therefore, the uncertainty in the model's output is evitable when natural groundwater field is simulated by a single groundwater model. A synthetic groundwater model is built and regarded as the true model, and three alternative conceptual models are constructed by considering incomplete hydrogeological conditions. The outputs (groundwater budget terms from boundary conditions) of these groundwater models are analyzed statistically. The results show that when the conceptual model is closer to the true hydrogeological conditions, the distributions of outputs of the groundwater model are more concentrated on the true outputs. Therefore, the more reliable the structure of the conceptual model is, the more reliable the output of the groundwater model is. Moreover, the uncertainty caused by the conceptual model cannot be compensated by parameter uncertainty.     

A modified mathematical model of the anatomy of the cardiac left ventricle

A modification of the mathematical model of the shape and fiber direction field of the left cardiac ventricle is presented. The model was developed based on the idea of nested spiral surfaces. The ventricle is composed of surfaces that model myocardial layers. Each layer is filled with curves corresponding to myocardial fibers. The tangents to these curves form the myofiber direction field. A modified spherical coordinate system is linked with the model left ventricle, where the ventricular boundaries are coordinate surfaces. The model is based on echocardiographic, computed-tomography, or magnetic-resonance-imaging data. For this purpose, four-chamber and two-chamber echocardiography views or sections along the long axis of the left ventricle from these tomographic data in several positions are approximated with a model profile. To construct a 3D model, we then interpolate model parameters by periodic cubic splines and the vector field of the tangents to the model fibers is calculated. For verification of the model, we used diffusion-tensor magneticresonance-imaging data of the human heart.     

Age-dependent predation is not a simple process. II. Wolves,ungulates, and a discrete time model for predation on juveniles with a stabilizing tail

A discrete time model for a predator-prey model, where the predator eats only juvenile prey is developed. The model is developed to capture some of the behavior of wolf-ungulate systems. Age-dependent predation is shown to be a stabilizing influence. The behavior of the model depends critically on the age of senescence of the prey—an extremely small number of old prey individuals represent a very powerful stabilizing factor. The model behaves in a similar fashion to, but is less stable than, an age structured Ricker model.     

Escherichia coil growth dynamics: A three-pool biochemically based description

A three-pool growth model of an individual Escherichia coli cell is described herein. The model is based on a previously developed chemically structured complex single cell growth model. The reduction in model complexity and the identification of the essential modes of motion, over the time scale of growth, is achieved by temporal decomposition and analysis of hierarchy in relaxation times. The three-pool model faithfully simulates the changes in cell size, cell shape, cell macromolecular composition, DNA initiation and termination periods, and the dependence of cell growth under abiotic glucose limitation. The predictions made by the reduced model compare favorably with both the experimental data and those of the full single cell model (SCM) without any parameter adjustments. The three-pool model has very few significant parameters and has the potential to find immediate practical use in bioreactor design and process control strategies. The model development illustrates the use of modal analysis to yield reduced physiologically realistic dynamic model of complex microbial system such as E. coll.     

Multiple limit cycles in the chemostat with variable yield

The global asymptotic behavior of solutions of the variable yield model is determined. The model generalizes the classical Monod model and it assumes that the yield is an increasing function of the nutrient concentration. In contrast to the Monod model, it is demonstrated that the variable yield model exhibits sustained oscillations. Moreover, it is shown that the variable yield model may undergo a subcritical Hopf bifurcation and feature at least two distinct limit cycles. Implications for the coexistence of competing populations are discussed.     

Modeling of antibiotics production in magneto three-phase airlift fermenter

A mathematical model is developed to describe the performance of a three-phase airlift reactor utilizing a transverse magnetic field. The model is based on the complete mixing model for the bulk of liquid phase and on the Michaelis-Menten kinetics. The model equations are solved by the explicit finite difference method from transient to steady state conditions. The results of the numerical simulation indicate that the magnetic field increases the degree of bioconversion. The mathematical model is experimentally verified in a three-phase airlift reactor with P. chrysogenum immobilized on magnetic beads. The experimental results are well described by the developed model when the reactor operates in the stabilized regime. At relatively high magnetic field intensities a certain discrepancy in the model solution was observed when the model over estimates the product concentration.     

Model of the spreading dynamics of a hospital infection

The article deals with the epidemiological model and the corresponding mathematical model of the spread of hospital infection. The mathematical apparatus of Markov's heterogeneous chain is used. The model may be used for the analysis and planning of antiepidemic measures, as well as for the evaluation of their effectiveness. The conditions for the possibility of the application of the newly developed mathematical model have been formulated. The method for calculating the parameters of the model on the basis of data on morbidity in different forms of hospital infection is presented. An example of using the above model for the analysis of the data of observation is considered in detail.     

Noninteracting local-structure model of folding and unfolding transition in globular proteins. II. Application to two-dimensional lattice proteins

The noninteracting local-structure model of the folding and unfolding transition in globular proteins, the formulation of which was given in the preceding paper, is applied to the analysis of the two-dimensional lattice model of proteins. The lattice model of proteins is a theoretical tool designed to study the statistical-mechanical aspect of the folding and unfolding transition. Its dynamics have been studied by a method of Monte Carlo simulation. The noninteracting local-structure model reproduces the equilibrium properties of the lattice model obtained previously by computer simulation remarkably well, when the specificity of the long-range interactions is strong. This observation indicates that the basic assumption of the noninteracting local-structure model is equivalent to the assumption of strong specificity of intramolecular interactions. It is argued that by assuming this strong specificity, we can emphasize the correct main paths of folding and unfolding transition. The way local structures grow and/or merge along the most probable path of folding in the lattice model is discussed by the noninteracting local-structure model.     

选择方向强化学习的神经网络模型

提出了神经网络模型的一种选择方向强化学习规则,定义并导出了新模型与Hopfield模型两种不同的筛选曲线,由此表明新模型对相关图样的分辨力优于Hopfield模型。在微机上模拟了由100个神经元构成的网络,结果显示新模型具有重复记忆这一神经生理学特点。定义并分行了记忆强度因子,模拟结果表明记忆强度因子愈大的记忆态,联想性能愈好,学习周期愈短。     

用光合-蒸散耦合模型模拟冬小麦CO2通量的日变化

根据SPAC理论建立了一个冬小麦光合和蒸散的耦合模型.冬小麦CO2通量包括冠层光合、呼吸和土壤呼吸.冠层光合采用了Farquhar光合作用生化模型,并通过冠层阻力的参数化将光合作用与蒸腾作用耦合起来.用涡度相关方法观测了CO2通量,对模型进行了验证,结果显示模型可以较好地模拟CO2通量日变化过程.对模型的敏感性分析发现日间CO2通量最敏感的参数是初始量子效率.其次,CO2通量对光响应曲线凸度、CO2补偿点、凋萎点和叶面积指数的变化也有着较强的敏感性;夜间CO2通量敏感的参数是最适温度下Rubisco催化能力和暗呼吸参数.     

A Multiplicative Model Imposed More Restrictions on the Quasi-Symmetry Model for the Analysis of Square Contingency Tables

For the analysis of square contingency tables, this note proposes a multiplicative model imposed more restrictions on CAUSSINUS ' (1965) quasi-symmetry (QS) model. The model is not so strict as in the quasi-double symmetry model considered by TOMIZAWA (1985b). The proposed model has the structure of the QS about the main diagonal plus an extended QS about the reverse diagonal of the square contingency table. The model is applied to the data on unaided vision of students in a university in Japan.     

Simulation of bracken cover in forested areas in Victoria in response to season,overstorey and fire conditions

Abstract A computer-based model is presented that brings together the existing knowledge about the dynamics of bracken in eucalypt forests in south-eastern Australia. The average length of the growing season, the timing and extent of logging, and the timing and severity of fire are major inputs to the model. The model is predominantly deterministic, but has a stochastic environmental component. The model is validated with four independent sets of data. The model successfully predicts the trends in the data. The interactions between bracken, other understorey species and eucalypt regeneration are explored with the model. The likely effect of different silvicultural and fire management practices on the cover of bracken are investigated using the model. Year to year variation can mask the effects of disturbance if bracken cover is viewed in any one year in isolation. Bracken cover trends can only be seen over a period of 10 years or more. The model reinforces the importance of site productivity as measured by length of growing season and the degree of tree removal on bracken cover.     

Component inertia modeling of segmental wobbling and rigid masses

A modification to an existing mathematical model is described, which permits the determination of subject-specific inertia parameters for wobbling and rigid masses of female body segments. The model comprises segment-specific soft tissue, bone, and lung components. A total of 59 geometric solids (40 soft tissue, 17 bone, 2 lung) were used to represent the body components. Ninety-five anthropometric measurements were collected from 7 female participants and were used to develop and evaluate the model. The success of the model is evaluated using predicted mass and mass distribution. The overall absolute accuracy in predicted whole body mass was better than 3.0%, with a maximum error of 4.9%. The appropriateness of the cadaver-based density values used in the model is addressed and the accuracy of the component inertia model in relation to uniform density models is discussed. The model offers a novel approach for determining component inertia parameters, which have been used successfully in a wobbling mass model to produce realistic kinetic analyses of drop-landings.     

A Model of the Peripheral Auditory System Responding to Low-Frequency Tones

A model of the peripheral auditory system responding to low-frequency tone stimulation is given. The model is of the type previously introduced by Weiss (1966). It includes three interconnected parts: a linear model of the ear's mechanical system, a model of the cochlear transducer, and a stochastic model of an auditory nerve fiber. The output of the model accurately mimics many characteristics of the output of some auditory nerve neurons responding to sinusoidal stimuli but is unable to successfully match all reported aspects of data obtained from other of these neurons. Characteristics of the model neurons are discussed.     

Modelling wind driven circulation One Tree Reef,Southern Great Barrier Reef

A vertically integrated numerical model of wind-driven circulation at One Tree Reef is presented. The model is the numerical model SURGE developed originally to study tropical cyclone surge. Current data collected in the reef lagoon and over the reef flats is used to test the model's applicability. The reef topography has been modelled explicitly, rather than using an assumed reef shape, with a grid spacing of 150 m. The model corresponds well to the measured current behaviour. The greatest drawback to use of the model is that, at low tide, currents reverse with depth due to lagoon enclosure and a depth integrated model cannot produce water velocity depth profiles. The model can be used to predict current behaviour in strong wind conditions, such as during a cyclone, and to estimate net flows into and out of the lagoon.     

用光合-蒸散耦合模型模拟冬小麦CO2通量的日变化

根据 SPAC理论建立了一个冬小麦光合和蒸散的耦合模型。冬小麦 CO2 通量包括冠层光合、呼吸和土壤呼吸。冠层光合采用了 Farquhar光合作用生化模型 ,并通过冠层阻力的参数化将光合作用与蒸腾作用耦合起来。用涡度相关方法观测了 CO2通量 ,对模型进行了验证 ,结果显示模型可以较好地模拟 CO2 通量日变化过程。对模型的敏感性分析发现日间 CO2 通量最敏感的参数是初始量子效率。其次 ,CO2 通量对光响应曲线凸度、CO2 补偿点、凋萎点和叶面积指数的变化也有着较强的敏感性 ;夜间 CO2 通量敏感的参数是最适温度下 Rubisco催化能力和暗呼吸参数     

Linear quadratic and tumour control probability modelling in external beam radiotherapy

The standard linear-quadratic (LQ) survival model for external beam radiotherapy is reviewed with particular emphasis on studying how different schedules of radiation treatment planning may be affected by different tumour repopulation kinetics. The LQ model is further examined in the context of tumour control probability (TCP) models. The application of the Zaider and Minerbo non-Poissonian TCP model incorporating the effect of cellular repopulation is reviewed. In particular the recent development of a cell cycle model within the original Zaider and Minerbo TCP formalism is highlighted. Application of this TCP cell-cycle model in clinical treatment plans is explored and analysed.