ANDREIANOV, Boris; BENDAHMANE, Mostafa; QUARTERONI, Alfio; RUIZ BAIER, Ricardo

doi:10.1142/S0218202515500244

Métadonnées

Licence d’utilisation du document

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

ANDREIANOV, Boris
Laboratoire de Mathématiques et Physique Théorique [LMPT]
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]

BENDAHMANE, Mostafa
Institut de Mathématiques de Bordeaux [IMB]

QUARTERONI, Alfio
Chair of Modelling and Scientific Computing [CMCS]
Modeling and Scientific Computing [Milano] [MOX]

Langue

Article de revue

Ce document a été publié dans

Mathematical Models and Methods in Applied Sciences. 2015, vol. 25, p. 959-993

World Scientific Publishing

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 and subsequent deformation of the cardiac tissue. The problem consists in a reaction-diffusion system governing the dynamics of ionic quantities, intra and extra-cellular potentials, and the linearized elasticity equations are adopted to describe the motion of an incompressible material. 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. Under the assumption of linearized elastic behavior and a truncation of the updated nonlinear diffusivities, we prove existence of weak solutions to the underlying coupled reaction-diffusion system and uniqueness of regular solutions. The proof of existence is based on a combination of parabolic regularization, the Faedo-Galerkin method, and the monotonicity-compactness method of J.L. Lions. A finite element formulation is also introduced, for which we establish existence of discrete solutions and show convergence to a weak solution of the original problem. We close with a numerical example illustrating the convergence of the method and some features of the model.< Réduire

Mots clés en anglais

Finite element approximation

Weak compactness method

Weak-strong uniqueness

Electro--mechanical coupling

Bidomain equations

Active deformation

Weak solutions

Convergence of approximations

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194310

DOI

http://dx.doi.org/10.1142/S0218202515500244

Projet Européen

ERC-2008-AdG 227058, MATHCARD: Mathematical Modelling and Simulation of the Cardiovascular System

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251