BADER, Fakhrielddine; BENDAHMANE, Mostafa; SAAD, Mazen; TALHOUK, Raafat

doi:10.3233/ASY-221804

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BADER, Fakhrielddine
Institut de Recherche Mathématique de Rennes [IRMAR]

BENDAHMANE, Mostafa
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
Institut de Mathématiques de Bordeaux [IMB]

SAAD, Mazen
Laboratoire de Mathématiques Jean Leray [LMJL]

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Article de revue

Ce document a été publié dans

Asymptotic Analysis. 2022-09-08p. 1-32

IOS Press

Résumé en anglais

We study the homogenization of a novel microscopic tridomain system, allowing for a more detailed analysis of the properties of cardiac conduction than the classical bidomain and monodomain models. In (Acta Appl.Math. 179 (2022) 1–35), we detail this model in which gap junctions are considered as the connections between adjacent cells in cardiac muscle and could serve as alternative or supporting pathways for cell-to-cell electrical signal propagation. Departing from this microscopic cellular model, we apply the periodic unfolding method to derive the macroscopic tridomain model. Several difficulties prevent the application of unfolding homogenization results, including the degenerate temporal structure of the tridomain equations and a nonlinear dynamic boundary condition on the cellular membrane. To prove the convergence of the nonlinear terms, especially those defined on the microscopic interface, we use the boundary unfolding operator and a Kolmogorov–Riesz compactness’s result.< Réduire

Mots clés en anglais

Tridomain model

reaction-diffusion system

homogenization theory

time-periodic unfolding method

gap junctions

cardiac electric field

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191070

DOI

http://dx.doi.org/10.3233/ASY-221804

Project ANR

Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251