Deterministic limit of a PDMP model of epithelial tissue interacting with diffusing chemicals and application to the intestinal crypt - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2023

Deterministic limit of a PDMP model of epithelial tissue interacting with diffusing chemicals and application to the intestinal crypt

Abstract

Mathematical models of biological tissues are a promising tool for multi-scale data integration, computational experiments and system biology approaches. While some data and insights are rooted at the cellular level, macroscopic mechanisms emerge and are observed at the tissue scale, rendering tissue modeling an inherently multi-scale process. As a consequence, tissue models can be broadly categorized as either individual-based or continuous population-based. In this paper, we first introduce a generic individual-based model of epithelial tissue including the main regulation processes such as cell division, differentiation, migration and death, together with cell-cell mechanical interactions. The coupling with diffusing molecules is also considered. This model is a measure-valuedpiecewise-deterministic Markov processes, coupled with reaction-diffusion PDEs. The well-posedness of the model is assessed and large population deterministic limit is rigorously derived. Finally, numerical experiments are conducted: this model is applied to the context of epithelial tissues in the intestinal crypt and the convergence towards the deterministic model are numerically illustrated.
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Dates and versions

hal-04336174 , version 1 (11-12-2023)
hal-04336174 , version 2 (13-12-2023)

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  • HAL Id : hal-04336174 , version 2

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Léo Darrigade, Simon Labarthe, Béatrice Laroche. Deterministic limit of a PDMP model of epithelial tissue interacting with diffusing chemicals and application to the intestinal crypt. 2023. ⟨hal-04336174v2⟩
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