Mathematical analysis of cardiac electromechanics with physiological ionic model

Mostafa Bendahmane; Fatima Mroue; Mazen Saad; Raafat Talhouk

doi:10.3934/dcdsb.2019035

Article Contents

2019, Volume 24, Issue 9: 4863-4897. Doi: 10.3934/dcdsb.2019035

This issue Previous Article Birth of an arbitrary number of T-singularities in 3D piecewise smooth vector fields Next Article Upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations

Mathematical analysis of cardiac electromechanics with physiological ionic model

1.
Institut de mathématiques de Bordeaux (IMB), Institut de rythmologie et modélisation cardiaque (Liryc), Université de Bordeaux and INRIA-Carmen Bordeaux Sud-Ouest, France
2.
Mathematics Laboratory, Doctoral School of Sciences and Technologies, Lebanese University, Hadat, Lebanon
3.
Département d'informatique et mathématiques, Centrale Nantes, Laboratoire de Mathématiques Jean Leray, France
4.
Mathematics Laboratory, Doctoral School of Sciences and Technologies, Lebanese University, Hadat, Lebanon

^* Corresponding author: Mostafa Bendahmane
^* Corresponding author: Mostafa Bendahmane

Received: March 2018

Revised: September 2018

Early access: February 2019

Published: July 2019

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Abstract

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 diffusivities. 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.

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Mathematics Subject Classification: 74F99, 35K57, 92C10, 35A01.

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