BENDAHMANE, Mostafa; MROUE, Fatima; SAAD, Mazen; TALHOUK, Raafat

doi:10.1016/j.nonrwa.2019.05.006

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http://creativecommons.org/licenses/by-nc/

BENDAHMANE, Mostafa
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]

MROUE, Fatima
Département de Mathématiques et Informatique - Université de Nantes

SAAD, Mazen
Laboratoire de Mathématiques Jean Leray [LMJL]

Langue

Article de revue

Ce document a été publié dans

Nonlinear Analysis: Real World Applications. 2019-12, vol. 50, p. 413-447

Elsevier

Résumé en anglais

In this paper, we apply a rigorous homogenization method based on unfolding operators to a microscopic bidomain model representing the electrical activity of the heart at a cellular level. The heart is represented by an arbitrary open bounded connected domain with smooth boundary and the cardiac cells’ (myocytes) domain is viewed as a periodic region. We start by proving the well posedness of the microscopic problem by using Faedo–Galerkin method and -compactness argument on the membrane surface without any restrictive assumptions on the conductivity matrices. Using the unfolding method in homogenization, we show that the sequence of solutions constructed in the microscopic model converges to the solution of the macroscopic bidomain model. Because of the nonlinear ionic function, the proof is based on the surface unfolding method and Kolmogorov compactness argument.< Réduire

Mots clés en anglais

Bidomain model

Reaction–diffusion system

Homogenization theory

Unfolding method

Convergence

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191417

DOI

http://dx.doi.org/10.1016/j.nonrwa.2019.05.006

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