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Modified bidomain model with passive periodic heterogeneities

Yves Coudière 1, 2, 3 Anđela Davidović 1, 2, 3, 4, * Clair Poignard 5, 2
* Corresponding author
1 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest, IHU-LIRYC
5 MONC - Modélisation Mathématique pour l'Oncologie
IMB - Institut de Mathématiques de Bordeaux, Institut Bergonié [Bordeaux], Inria Bordeaux - Sud-Ouest
Abstract : In this paper we study how mesoscopic heterogeneities affect electrical signal propagation in cardiac tissue. The standard model used in cardiac electrophysiology is a bidomain model-a system of degenerate parabolic PDEs, coupled with a set of ODEs, representing the ionic behviour of the cardiac cells. We assume that the heterogeneities in the tissue are periodically distributed diffusive regions, that are significantly larger than a cardiac cell. These regions represent the fibrotic tissue, collagen or fat, that is electrically passive. We give a mathematical setting of the model. Using semigroup theory we prove that such model has a uniformly bounded solution. Finally, we use two-scale convergence to find the limit problem that represents the average behviour of the electrical signal in this setting.
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https://hal.inria.fr/hal-02363470
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Submitted on : Thursday, November 14, 2019 - 2:15:44 PM
Last modification on : Thursday, June 11, 2020 - 3:21:03 AM
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Yves Coudière, Anđela Davidović, Clair Poignard. Modified bidomain model with passive periodic heterogeneities. Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2019, ⟨10.3934/dcdss.2020126⟩. ⟨hal-02363470⟩

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