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Journal Articles Mathematical Models and Methods in Applied Sciences Year : 2018

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

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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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hal-01759914 , version 1 (06-04-2018)

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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, 2018, ⟨10.1142/S0218202518500264⟩. ⟨hal-01759914⟩
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