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Vinogradova

Research of Cell Population Dynamics with Two Arbitrary Mutations
Engineering Education # 11, November 2015
DOI: 10.7463/1115.0815502
pp. 559-578

Engineering Bulletin # 12, December 2014
УДК: 519.71
Analysing Scenarios of Cell Population System Development
Engineering Education # 11, November 2014
DOI: 10.7463/1114.0735732
pp. 607-622
A dynamic model of a cell population system
Engineering Education # 12, December 2013
DOI: 10.7463/1213.0646463
This paper deals with development of a mathematical model of population dynamics of human stem cells being cultured in vitro. This investigation was inspired by intensive development of stem cell transplantation. The authors investigated formation processes of a cell population with chromosome abnormalities in a population of normal cells along with co-development of these populations in vitro. In this paper a refined continuous dynamic model of an isolated population system consisting of a population of normal stem cells and a population of cells with chromosomal abnormalities was proposed. An essential feature of this model is a necessity for biological characteristics of processes that occur in a cell population system for its creation. These characteristics are:  a portion of cells divided within a specified time, a portion of dead cells and a portion of cells passed into a population of abnormal cells from normal cell populations. This approach allows to provide a more detailed analysis of the impact of different "primary" parameters on dynamics of a population system. Parametric analysis of the model was carried out; the main scenarios of its development were described. The proposed model allows to simulate correctly the main evolution scenarios of a population system which are known from experimental investigations.
Construction of marginal probability density function of model parameters of cell population
Engineering Education # 12, December 2012
DOI: 10.7463/1212.0500575
The author considers a mathematical model describing dynamics of the population of stem cells in standard laboratory culture conditions without food restrictions. For this model, point estimates of parameters and expression for their joint probability density function are known. They are derived on the basis of the Bayesian approach and Jeffreys invariat theory with limited samples of experimental data on values ​​of the state vector. The author found marginal functions of probability density parameters of the mathematical model and interval estimates for these parameters.
Parametrical identification of a model of cooperating cellular populations on the basis of Bayesian approach
Engineering Education # 11, November 2012
DOI: 10.7463/1112.0490900
Algorithm, which allows one to obtain point estimations of a model’s parameters by using a limited sample of experimental data on the state vector’s values, was developed for a mathematical model that describes the dynamics of selective reproduction of clone-forming population of abnormal cells in the culture of human stem cells under standard laboratory conditions of cultivation without dietary restrictions. Bayesian approach was briefly described along with Jeffreys’ invariance theory. Probability density functions of specified mathematical model’s parameters were obtained with the use of these theories.
77-30569/251409 Quality analysis of interacting cell populations’ functional model
Engineering Education # 11, November 2011
Mathematical model of selective replication dynamics of clone forming population of abnormal cells in the culture of human stem cells in the laboratory (in vitro), considering the influence of density factor on cells multiplication. Model is a system of second order ordinary differential equations with polynomial special right member. All stationary points of this model with non-negative coordiantes with at least one zero coordinate were found; stability analysis for these points was carried out with different values of model parameters. It was shown that system couldn’t have more than two points with both positive coordinates. The results of numerical simulation were included in the article.
 
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