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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-di usion 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 di usivities, we prove existence of weak solutions to the underlying coupled reaction-di usion 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.
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https://hal.archives-ouvertes.fr/hal-01256811
Contributor : Mostafa Bendahmane <>
Submitted on : Tuesday, January 19, 2016 - 10:38:54 PM
Last modification on : Tuesday, February 18, 2020 - 3:02:43 PM
Document(s) archivé(s) le : Friday, November 11, 2016 - 7:40:16 AM

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Boris Andreianov, Mostafa Bendahmane, Alfio Quarteroni, Ricardo Ruiz-Baier. Solvability analysis and numerical approximation of linearized cardiac electromechanics. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2015, ⟨10.1142/S0218202515500244⟩. ⟨hal-01256811⟩

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