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Solvability analysis and numerical approximation of linearized cardiac electromechanics
Abstract : 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.
https://hal.archives-ouvertes.fr/hal-00865585
Contributor : Ricardo Ruiz Baier Connect in order to contact the contributor
Submitted on : Tuesday, September 29, 2015 - 1:55:15 PM
Last modification on : Thursday, January 13, 2022 - 12:00:02 PM
Long-term archiving on: : Wednesday, December 30, 2015 - 10:14:09 AM
Contributor : Ricardo Ruiz Baier Connect in order to contact the contributor
Submitted on : Tuesday, September 29, 2015 - 1:55:15 PM
Last modification on : Thursday, January 13, 2022 - 12:00:02 PM
Long-term archiving on: : Wednesday, December 30, 2015 - 10:14:09 AM
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