Modelación del proceso de maduración de las células madre mediante ecuaciones diferenciales estocásticas
Fecha
2018-06-24
Autores
Lumpuy Obregón, Dennis
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Editor
Universidad Central “Marta Abreu” de Las Villas
Resumen
En el presente trabajo se realiza un estudio del proceso de maduración celular modelado mediante ecuaciones diferenciales estocásticas. Partiendo de las hipótesis biológicas, se plantean los modelos deterministas que representan dicho proceso y se escoge el caso a estudiar, a partir del cual se presenta el modelo probabilístico que posee la influencia del ruido como nuevo termino a analizar. El modelo probabilístico planteado se resuelve para los casos de dos, seis y ocho compartimientos, se llega a conclusiones sobre los efectos de la representación estocástica a partir de su representación mediante el software Wolfram Mathematica y se comparan los resultados con los presentes en la bibliografía consultada. Se realiza además de una interpretación biológica de los resultados matemáticos obtenidos en la resolución de los sistemas estocásticos planteados y se realiza una interpretación biológica del parámetro ruido estocástico introducido en los diferentes modelos multicompartimientos de subpoblaciones de células madre
In the present work, a study of the cell maturation process modeling by stochastics differentials equations is performed. Starting from the biological hypothesis, the deterministic models that represent this process are presented and the case to be studied is chosen, from which the probabilistic model that has the influence of noise as a new term to analyze is presented. The proposed probabilistic model is solved for the cases of two, six and eight compartments, conclusions are reached about the effects of stochastic representation from its representation using Wolfram Mathematica software and the results are compared with those present in the consulted bibliography. In addition to a biological interpretation of the mathematical results obtained in the resolution of the stochastic systems and a biological interpretation of the stochastic noise parameter introduced in the different multicompartment models of stem cell subpopulations is made.
In the present work, a study of the cell maturation process modeling by stochastics differentials equations is performed. Starting from the biological hypothesis, the deterministic models that represent this process are presented and the case to be studied is chosen, from which the probabilistic model that has the influence of noise as a new term to analyze is presented. The proposed probabilistic model is solved for the cases of two, six and eight compartments, conclusions are reached about the effects of stochastic representation from its representation using Wolfram Mathematica software and the results are compared with those present in the consulted bibliography. In addition to a biological interpretation of the mathematical results obtained in the resolution of the stochastic systems and a biological interpretation of the stochastic noise parameter introduced in the different multicompartment models of stem cell subpopulations is made.
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Palabras clave
Modelación, Proceso de Maduración, Células Madre, Ecuaciones Diferenciales Estocásticas