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Mathematical analysis of cardiac electromechanics with physiological ionic model

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 diffu-sivities. 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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https://hal.inria.fr/hal-01680593
Contributor : Mostafa Bendahmane <>
Submitted on : Tuesday, October 30, 2018 - 11:20:53 PM
Last modification on : Friday, January 10, 2020 - 1:40:49 AM

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Mostafa Bendahmane, Fatima Mroue, Mazen Saad, Raafat Talhouk. Mathematical analysis of cardiac electromechanics with physiological ionic model. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2019, 24 (9), pp.34. ⟨hal-01680593⟩

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