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

hal.structure.identifierDynamiques de populations multi-échelles pour des systèmes physiologiques [MUSCA]
hal.structure.identifierMathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] [MaIAGE]
dc.contributor.authorDARRIGADE, Léo
hal.structure.identifierPleiade, from patterns to models in computational biodiversity and biotechnology [PLEIADE]
hal.structure.identifierBiodiversité, Gènes & Communautés [BioGeCo]
hal.structure.identifierMathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] [MaIAGE]
dc.contributor.authorLABARTHE, Simon
hal.structure.identifierDynamiques de populations multi-échelles pour des systèmes physiologiques [MUSCA]
hal.structure.identifierMathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] [MaIAGE]
dc.contributor.authorLAROCHE, Béatrice
dc.date.issued2023-12-11
dc.description.abstractEnMathematical 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.
dc.language.isoen
dc.rights.urihttp://creativecommons.org/licenses/by/
dc.subject.enbiological tissue model
dc.subject.enindividual-based model (IBM)
dc.subject.enlarge population asymptotics
dc.title.enDeterministic limit of a PDMP model of epithelial tissue interacting with diffusing chemicals and application to the intestinal crypt
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]
dc.subject.halSciences du Vivant [q-bio]
hal.identifierhal-04336174
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-04336174v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2023-12-11&rft.au=DARRIGADE,%20L%C3%A9o&LABARTHE,%20Simon&LAROCHE,%20B%C3%A9atrice&rft.genre=preprint


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