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At least 1,207 records · Page 67Linked to original sources

PubMed1999

Mathematical modelling of avascular-tumour growth. II: Modelling growth saturation.

We build on our earlier mathematical model (Ward & King, 1997, IMA J. Appl. Math Appl. Med. Biol., 14, 39-69) by incorporating two necrotic depletion mechanisms, which results in a model that can predict all the main phases of avascular-tumour growth and heterogeneity. The model assumes a continuum of live cells which, depending on the concentration of a generic nutrient, may reproduce or die, generating local volume changes and thus producing movement described by a velocity field. The necrotic material is viewed as basic cellular material (i.e. as a generic mix of proteins, DNA, etc.) which is able to diffuse and is utilized by living cells as raw material to construct new cells during mitosis. Numerical solution of the resulting system of partial differential equations shows that growth ultimately tends either to a steady-state (growth saturation) or becomes linear. Both the travelling-wave and steady-state limits of the model are therefore derived and studied. The analysis demonstrates that, except in a very special case, passage of cellular material across the tumour surface is necessary for growth saturation to occur. Using numerical techniques, the domains of existence of the large-time solutions are explored in parameter space. For a particular limit, asymptotic analysis makes explicit the main phases of growth and gives the location of the bifurcation between the long-time outcomes.

Models, Biological↗

PubMed2000

[Experimental hepatocarcinogenesis--evaluation of the significance of theoretical models. Contemporary models].

There are an increasing number of models for the study of liver cancer development with such agents as chemicals, hormones, and viruses. This process is almost always a multistep and during the long period of cancer development, discrete cells or cell populations acquire step-by step the various properties that go to make up a cancer. The hepatocarcinogenesis models are useful in identification and analysis of the preneoplastic and neoplastic alterations, as well HCC. This article presents a review of theoretical foundation and mechanisms of various models of experimental hepatocarcinogenesis as well contain a short presentation of animals practical in those experiments, principally rats. The remarkable similarities between many models with different carcinogens in animals and humans suggest the importance of such studies in understanding of molecular basis of liver cancer development.

Animals↗

PubMed2000

[Modeling asthma evolution by a multi-state model].

BACKGROUND: There are many scores for the evaluation of asthma. However, most do not take into account the evolutionary aspects of this illness. We propose a model for the clinical course of asthma by a homogeneous Markov model process based on data provided by the A.R.I.A. (Association de Recherche en Intelligence Artificielle dans le cadre de l'asthme et des maladies respiratoires). METHODS: The criterion used is the activity of the illness during the month before consultation. The activity is divided into three levels: light (state 1), mild (state 2) and severe (state 3). The model allows the evaluation of the strength of transition between states. RESULTS: We found that strong intensities were implicated towards state 2 (lambda(12) and lambda(32)), less towards state 1 (lambda(21) and lambda(31)), and minimum towards state 3 (lambda(23)). This results in an equilibrium distribution essentially divided between state 1 and 2 (44.6% and 51.0% respectively) with a small proportion in state 3 (4.4%). CONCLUSIONS: In the future, the increasing amount of available data should permit the introduction of covariables, the distinction of subgroups and the implementation of clinical studies. The interest of this model falls within the domain of the quantification of the illness as well as the representation allowed thereof, while offering a formal framework for the clinical notion of time and evolution.

Artificial Intelligence↗

PubMed2001

Model-free vs. model-based linkage analysis: a false dichotomy?

The aim of this article is to dispel some misunderstandings concerning the concepts of model-free or nonparametric linkage analysis (usually meaning affecteds-only analysis) and model-based or parametric analysis (usually meaning classical lod scores) and the implications of these concepts for the linkage analysis of complex genetic diseases. I review basic principles and then briefly indicate actual research findings. Readers may be surprised to learn that, technically, lod score analysis is also nonparametric. All this taken together indicates that classical lod score analysis, performed under a couple of different sets of genetic assumptions and corrected for multiple tests, is often actually superior to model-free analyses, even when the true genetic model is complex and unknown.

Computer Simulation↗

PubMedDate not supplied

[Modeling real eukaryotic control gene subnetworks based on generalized threshold models].

Mathematical and computational means are developed that take into consideration the specifics of control processes at the molecular level and allow one to obtain both qualitative and quantitative patterns of gene network dynamics. Using the method of generalized threshold models, models are constructed for the Arabidopsis thaliana flower morphogenesis control subsystem and gene subnetwork controlling the Drosophila melanogaster early ontogeny. The dynamics of these systems are investigated: kinetic curves are computed for molecular components (RNA, proteins), possible modes of functioning and steady states of the nets are revealed and biologically interpreted. The models are shown to be adequate to the real processes. The effectiveness of the generalized threshold model method is evaluated in the analysis of the actual eukaryotic gene networks.

Animals↗

PubMedDate not supplied

Geophysiological modeling: new ideas on modeling the evolution of ecosystems.

Living organisms evolve within ecological associations (from ecosystems to the biosphere) that are constituted by a biological component and a physico-chemical component. It is generally supposed that interactions such as competition and predation between the biological components of ecosystems are the main cause for the observed organization of ecosystems. We believe that in the search for a more comprehensive theory of evolution a much greater attention should be paid to the ways in which living organisms interact with the physico-chemical environment. To test our ideas, we develop a mathematical model to study the evolution of ecosystems, and we apply it to the study of hydrothermal vents. The model proposed is still a qualitative model. It tries to study, in a first approximation, the behaviours of the biological and chemical components. In the following we hope to develop and to improve it so to give a more realistic model.

Biological Evolution↗

PubMed2003

A new double-chamber model of ion channels. Beyond the Hodgkin and Huxley model.

This paper proposes a new double-chamber model (DCM) of ion channels. The model ion channel consists of a series of three pores alternating with two chambers. The chambers are net negatively charged. The chamber's electric charge originates from dissociated amino acid side chains and is pH dependent. The chamber's net negative charge is compensated by cations present inside the chamber and in a diffuse electric layer outside the chamber. The pore's permeability is constant independent of time. One pore of the sodium channel and one of the potassium channel is a voltage-sensing pore. Due to the channel's structure, ions flow through the pores and chambers in a time-dependent manner. The model reproduces experimental voltage clamp and action potential data. The current flowing through a single sodium channel is less then one femtoampere. The DCM is considerably simpler then the Hodgkin and Huxley model (HHM) used to describe the electrophysiological properties of an axon. Unlike the HHM, the DCM can explain refractoriness, anode break excitation, accommodation and the effect of pH and temperature on the channels without additional parameters. In the DCM, the axon membrane shows repetitive activity depending on the channel density, sodium to potassium channel ratio and external potassium concentration. In the DCM, the action potential starts from 'hot spot areas' of higher channel densities and a higher sodium to potassium channel ratio, and then propagates through the whole axon.

Action Potentials↗

PubMed2003

[Logistic regression model analysis on Bolton ratio of orthodontic extraction model].

OBJECTIVE: The purpose of this study was to evaluate the role of Angle's class, overall ratio and anterior ratio in the creation of tooth size discrepancies, and to determine whether any tooth extraction combinations create more severe discrepancies. METHODS: 166 dental casts of orthodontic patients were selected randomly. These models were classified according to angle's criterion. Mesio-distal dimensions of mandibular and maxillary teeth were measured before treatment, and subjected to Bolton's analysis. Hypothetical tooth extraction by the following combinations: all the first premolars, all the second premolars, upper first and lower second premolars, and upper second and lower first premolars, was performed on each patient. The measurement results were again subjected to Bolton's analysis to see whether any tooth-size discrepancy had been created. The results were evaluated statistically by means of Logistic regression model. RESULTS: Overall ratio, anterior ratio and extraction models affected mesio-distal tooth size ratio of both maxillary and mandibular teeth in the final stage of orthodontic treatment, Whereas, the results showed no significant difference among these groups of malocclusion. CONCLUSION: The results suggested that dentists should always keep in mind that each patient should be treated individually and should be aware of that other factors also played important roles in determining what teeth, if any, should be removed and the Bolton analyses of all kinds of extraction models should be carried out, as well as the general Bolton analysis.

Adolescent↗

PubMed2003

Modeling interindividual variation in physiological factors used in PBPK models of humans.

Modeling interindividual variation in internal doses in humans using PBPK models requires data on the variation in physiological parameters across the population of interest. These data should also reflect the correlations between the values of the various parameters in a person. In this project, we develop a source of data for human physiological parameters where (1) the parameter values for an individual are correlated with one another, and (2) values of parameters capture interindividual variation in populations of a specific gender, race, and age range. The parameters investigated in this project include: (1) volumes of selected organs and tissues; (2) blood flows for the organs and tissues; and (3) the total cardiac output under resting conditions and average daily inhalation rate. These parameters are expressed as records of correlated values for the approximately 30,000 individuals evaluated in the NHANES III survey. A computer program, Physiological Parameters for PBPK Modeling (P3M), is developed that allows records to be retrieved randomly from the database with specification of constraints on age, sex, and ethnicity. P3M is publicly available. The database and accompanying software provide a convenient tool for parameterizating models of interindividual variation in human pharmacokinetics.

Computer Simulation↗

PubMed2003

Calibration and inverse modelling of soil physical and biological parameters of a nitrate leaching model with the pest programme.

This paper reports on experiences with the use of the PEST (Parameter ESTimation) programme to calibrate the soil physical parameters of a nitrate leaching model (the Burns alpha model) and to determine the N mineralization rate by inverse modelling. Parameter estimation was much more efficient and accurate with the PEST programme than with a built in "trial and error" calibration module. The determination of the N mineralization rate by inverse modelling with PEST using measured nitrate concentrations was not possible, and several reasons for this are given. With more suitable experimental fields (lighter soil texture and/or deeper groundwater level), more replications in the nitrate measurements and a one-step calibration of the alpha parameter and the N mineralization rate, determination of the N mineralization rate may become possible.

Calibration↗

PubMed2004

The Rossby Centre Regional Atmospheric Climate Model part I: model climatology and performance for the present climate over Europe.

The Rossby Centre Atmospheric Regional Climate Model (RCA2) is described and simulation results, for the present climate over Europe, are evaluated against available observations. Systematic biases in the models mean climate and climate variability are documented and key parameterization weaknesses identified. The quality of near-surface parameters is investigated in some detail, particularly temperature, precipitation, the surface energy budget and cloud cover. The model simulates the recent, observed climate and variability with a high degree of realism. Compensating errors in the components of the surface radiation budget are highlighted and the fundamental causes of these biases are traced to the relevant aspects of the cloud, precipitation and radiation parameterizations. The model has a tendency to precipitate too frequently at small rates, this has a direct impact on the simulation of cloud-radiation interaction and surface temperatures. Great care must be taken in the use of observations to evaluate high resolution RCMs, when they are forced by analyzed boundary conditions. This is particularly true with respect to precipitation and cloudiness, where observational uncertainty is often larger than the RCM bias.

Atmosphere↗

PubMedDate not supplied

A continuous model studying T cell differentiation and lymphomagenesis and its distinction with discrete models.

The development of T-lymphocytes (T cells) constitute one of the basic and most vital processes in immunology. Conventional mathematical models, being based on the systems theory, fail to sufficiently distinguish the constituents of thymocytes and are thus of limited significance. On the basis of some well thought-out definitions and concepts, a continuous model was designed to describe T cell maturation in the thymus. A partial differential equation was first derived through the analysis of an infinitesimal element of the flow of thymocytes. A computation scheme was designed to determine the growth field in the thymus based upon available experimental data. The corresponding algorithm proved quite simple. A numerical example is given that focuses on the DN stage of the T cell development. The model opens a window for investigating the thymic microenvironment. The potential of the model in studying lymphomagenesis is discussed.

Animals↗

PubMed2004

Modelling carbon oxidation in pulp mill activated sludge systems: calibration of Activated Sludge Model No 3.

Activated Sludge Model No 3 (ASM3) was chosen to model an activated sludge system treating effluents from a mechanical pulp and paper mill. The high COD concentration and the high content of readily biodegradable substrates of the wastewater make this model appropriate for this system. ASM3 was calibrated based on batch respirometric tests using fresh wastewater and sludge from the treatment plant, and on analytical measurements of COD, TSS and VSS. The model, developed for municipal wastewater, was found suitable for fitting a variety of respirometric batch tests, performed at different temperatures and food to microorganism ratios (F/M). Therefore, a set of calibrated parameters, as well as the wastewater COD fractions, was estimated for this industrial wastewater. The majority of the calibrated parameters were in the range of those found in the literature.

Calibration↗

PubMed2003

Animal models of alcoholic liver disease--focus on the intragastric feeding model.

The use of animal models has contributed to greater understanding of how alcoholic liver disease (ALD) develops, and of how the severity of liver injury is influenced by factors other than alcohol, such as nutrition, oxygen deprivation (as occurs with sleep apnea or smoking), and gene regulation. This article focuses on the use of one animal model in particular, the intragastric feeding model in rats. This model allows scientists to rigorously control an animal's consumption of both alcohol and dietary nutrients and is providing important information on the mechanisms of injury of alcoholic liver disease.

Animals↗

PubMed1991

[A study of the simulation model of the lower urinary tract for urodynamics--(the first report)--theoretical evaluation of hydrodynamic model].

From the view point of urodynamics, the lower urinary tract might be able to be simulated by a hydrodynamic model, consisting of a spherical balloon corresponding to the bladder and a circular tube to the urethra. In this hydrodynamic model, the diameter of the tube corresponding to the posterior urethra was assumed to become smaller with increase of the prostatic pressure according to the development of BPH. On this assumption, Bernoulli's equation might be adopted. Because of the turbulent flow in the tube, the velocity of flow was expressed as a function of the invariants, which indicated the pressure in the balloon, the respective lengths and diameters of narrow tube and wide tube, coefficients due to pipe friction, pipe fitting and pipe enlargement. The findings suggested that the smaller the diameter of the narrow tube, the smaller the flow volume showed with the development of BPH. In conclusion the urodynamics in the lower urinary tract could be simulated quantitatively by this model. The study may lead to the development of the urodynamic simulation model for the lower urinary tract.

Humans↗

PubMed1991

Mathematical model of antiviral immune response regulation. II. Mathematical formalization of the modelled processes. Imitation of acute course of hepatitis B.

The mathematical formalization of the conceptual model for antiviral immune response regulation described in the preceding report was carried out. The mathematical model is presented as a system of 30 ordinary nonlinear differential equations with delays. The algorithm for numerical integration of the mathematical model is based on Gear's methods of variable step and variable order. Initial conditions and parameters, as well as intervals of plausible values for them, were chosen for adaptation of the model for description of acute hepatitis B.

Acute Disease↗

PubMed1991

Tests and model selection for the general growth curve model.

The model considered here is a generalized multivariate analysis of variance model useful especially for many types of growth curve problems including biological growth and technology substitution. It is defined as Yp x N = Xp x m tau m x r Ar x N + epsilon p x N, where tau is unknown, and X and A are known design matrices of ranks m less than p and r less than N, respectively. Furthermore, the columns of epsilon are independent p-variate normal with mean vector 0 and common covariance matrix sigma. In general, p is the number of time (or spatial) points observed on each of the N cases, (m - 1) is the degree of polynomial in time, and r is the number of groups. The main focus of this paper is the selection of models for the general growth curve model with regard to the covariance matrix sigma. Likelihood ratio tests and selection procedures based on sample reuse and predictions are proposed. Special emphasis is on the serial covariance structure for sigma, which has been shown to be quite important in the prediction of biological data and technology substitution data. One-population and K-population problems are considered. Some of the results are illustrated with two sets of biological data.

Animals↗

PubMed1988

Brain state and plasticity: an integration of the reciprocal interaction model of sleep cycle oscillation with attentional models of hippocampal function.

The present paper relates the reciprocal interaction model for sleep cycle oscillation (McCarley and Hobson, ref. 29) to an attentional model of hippocampal function (Schmajuk and Moore, ref. 44). We consider mechanisms by which the interaction between gigantocellular tegmental field (FTG) cells and locus coeruleus (LC) activity proposed by the sleep cycle model may differentially modulate the information processing carried out in the hippocampus as described by the attentional model. Our fundamental assumption is that learning about the relevancy of different stimuli is proportional to the level of LC activation. If the environment becomes unpredictable during waking, the FTG and LC are activated and the LC facilitates hippocampal learning about stimulus relevancy. In a predictable situation during waking, FTG cells discharge rarely because no novelty is detected, and LC neurons are moderately active. If the predictable situation lasts, LC cells also decrease their activity, and a sleep period might start. At sleep onset, LC inhibition decreases and FTG activity is low leading to slow sleep. As FTG activity increases and LC activity reaches its low point, REM sleep starts. Because LC activity is low during REM sleep, values of stimulus relevancy remain unchanged. Since during sleep the threshold for external stimuli is high, only internally generated novel stimuli (subjectively perceived as dream mentation) may activate the LC. LC renewed inhibitory influence on the FTG ends REM sleep.

Animals↗