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Unfolding homogenization method applied to physiological and phenomenological bidomain models in electrocardiology

By Mostafa Bendahmane, Fatima Mroue, Mazen Saad and Raafat Talhouk

Abstract

International audienceIn this paper, we apply a rigorous homogenization method based on unfolding operators to a microscopic bidomain model representing the electrical activity of the heart at a cellular level. The heart is represented by an arbitrary open bounded connected domain with smooth boundary and the cardiac cells’ (myocytes) domain is viewed as a periodic region. We start by proving the well posedness of the microscopic problem by using Faedo–Galerkin method and -compactness argument on the membrane surface without any restrictive assumptions on the conductivity matrices. Using the unfolding method in homogenization, we show that the sequence of solutions constructed in the microscopic model converges to the solution of the macroscopic bidomain model. Because of the nonlinear ionic function, the proof is based on the surface unfolding method and Kolmogorov compactness argument

Topics: Convergence, Bidomain model, Reaction–diffusion system, Homogenization theory, Unfolding method, MSC : 35A01;35A02;35B27, [MATH]Mathematics [math], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], [NLIN]Nonlinear Sciences [physics], [SDV]Life Sciences [q-bio], [SDV.BC]Life Sciences [q-bio]/Cellular Biology
Publisher: 'Elsevier BV'
Year: 2019
DOI identifier: 10.1016/j.nonrwa.2019.05.006
OAI identifier: oai:HAL:hal-02142028v1
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