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Journal Articles Discrete and Continuous Dynamical Systems - Series S Year : 2019

Modified bidomain model with passive periodic heterogeneities

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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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Dates and versions

hal-02363470 , version 1 (14-11-2019)

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Yves Coudière, Anđela Davidović, Clair Poignard. Modified bidomain model with passive periodic heterogeneities. Discrete and Continuous Dynamical Systems - Series S, 2019, ⟨10.3934/dcdss.2020126⟩. ⟨hal-02363470⟩
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