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Modeling and analysis of cell population dynamics : application to the early development of ovarian follicles

Abstract : This thesis aims to design and analyze population dynamics models dedicated to the dynamics of somatic cells during the early stages of ovarian follicle growth. The model behaviors are analyzed through theoretical and numerical approaches, and the calibration of parameters is performed by proposing maximum likelihood strategies adapted to our specific dataset. A non-linear stochastic model, that accounts for the joint dynamics of two cell types (precursors and proliferative), is dedicated to the activation of follicular growth. In particular, we compute the extinction time of precursor cells. A rigorous finite state projection approach is implemented to characterize the system state at extinction. A linear multitype age-structured model for the proliferative cell population is dedicated to the early follicle growth. The different types correspond here to the spatial cell positions. This model is of decomposable kind; the transitions are unidirectional from the first to the last spatial type. We prove the long-term convergence for both the stochastic Bellman-Harris model and the multi-type McKendrick-VonFoerster equation. We adapt existing results in a context where the Perron-Frobenius theorem does not apply, and obtain explicit analytical formulas for the asymptotic moments of cell numbers and stable age distribution. We also study the well-posedness of the inverse problem associated with the deterministic model.
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Submitted on : Friday, November 20, 2020 - 6:01:08 PM
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Frédérique Robin. Modeling and analysis of cell population dynamics : application to the early development of ovarian follicles. Probability [math.PR]. Sorbonne Université, 2019. English. ⟨NNT : 2019SORUS344⟩. ⟨tel-03017273⟩

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