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

doi:10.1142/S0218202515500244

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

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

QUARTERONI, Alfio
Modeling and Scientific Computing [Milano] [MOX]
Chair of Modelling and Scientific Computing [CMCS]
Institut de Mathématiques de Bordeaux [IMB]

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Mathematical Models and Methods in Applied Sciences. 2015

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-diusion 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 diusivities, we prove existence of weak solutions to the underlying coupled reaction-diusion 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

Weak solutions

Active deformation

Electro-mechanical coupling

Bidomain equations

Weak compactness method

Weak-strong uniqueness

Finite element approximation

Convergence of approximations

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Solvability analysis and numerical approximation of linearized cardiac electromechanics

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