Section: New Results

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

Authors: Annabelle Collin, Sébastien Imperiale. Paper published in Mathematical Models and Methods in Applied Sciences. https://hal.inria.fr/hal-01759914

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.