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

doi:10.3934/dcdsb.2019035

Métadonnées

Licence d’utilisation du document

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

MROUE, Fatima
Département de Mathématiques et Informatique - Université de Nantes
Laboratoire de Mathématiques Jean Leray [LMJL]

SAAD, Mazen
École Centrale de Nantes [ECN]
Laboratoire de Mathématiques Jean Leray [LMJL]

Langue

Article de revue

Ce document a été publié dans

Discrete and Continuous Dynamical Systems - Series B. 2019, vol. 24, n° 9, p. 34

American Institute of Mathematical Sciences

Résumé en anglais

This paper is concerned with the mathematical analysis of a coupled elliptic-parabolic system modeling the interaction between the propagation of electric potential coupled with general physiological ionic models and subsequent deformation of the cardiac tissue. A prototype system belonging to this class is provided by the electromechanical bidomain model, which is frequently used to study and simulate electrophysiological waves in cardiac tissue. The coupling between muscle contraction, biochemical reactions and electric activity is introduced with a so-called active strain decomposition framework, where the material gradient of deformation is split into an active (electrophysiology-dependent) part and an elastic (passive) one. We prove existence of weak solutions to the underlying coupled electromechanical bidomain model under the assumption of linearized elastic behavior and a truncation of the updated nonlinear diffu-sivities. The proof of the existence result, which constitutes the main thrust of this paper, is proved by means of a non-degenerate approximation system, the Faedo-Galerkin method, and the compactness method.< Réduire

Mots clés en anglais

Weak solutions

Bidomain equations

Electro-mechanical coupling

Weak compactness method

Active deformation

URI

https://oskar-bordeaux.fr/handle/20.500.12278/193181

DOI

http://dx.doi.org/10.3934/dcdsb.2019035

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