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Mathematical analysis and 2-scale convergence of a heterogeneous microscopic bidomain model

Annabelle Collin 1 Sébastien Imperiale 2, 3
1 MONC - Modélisation Mathématique pour l'Oncologie
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest, Institut Bergonié - CRLCC Bordeaux
2 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
LMS - Laboratoire de mécanique des solides, Inria Saclay - Ile de France
Abstract : The aim of this paper is to provide a complete mathematical analysis of the periodic homogenization procedure that leads to the macroscopic bidomain model in cardiac elec-trophysiology. We consider space-dependent and tensorial electric conductivities as well as space-dependent physiological and phenomenological non-linear ionic models. We provide the nondimensionalization of the bidomain equations and derive uniform estimates of the solutions. The homogenization procedure is done using 2-scale convergence theory which enables us to study the behavior of the non-linear ionic models in the homogenization process .
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Submitted on : Friday, April 6, 2018 - 4:10:56 PM
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Annabelle Collin, Sébastien Imperiale. Mathematical analysis and 2-scale convergence of a heterogeneous microscopic bidomain model. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2018, ⟨10.1142/S0218202518500264⟩. ⟨hal-01759914⟩

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