Homogenization of a modified bidomain model involving imperfect transmission

Micol Amar; Daniele Andreucci; Claudia Timofte

doi:10.3934/cpaa.2021040

Article Contents

2021, Volume 20, Issue 5: 1755-1782. Doi: 10.3934/cpaa.2021040

This issue Previous Article Next Article Partial regularity for parabolic systems with VMO-coefficients

Homogenization of a modified bidomain model involving imperfect transmission

1.
Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza - Università di Roma, Via A. Scarpa 16, 00161 Roma, Italy
2.
University of Bucharest, Faculty of Physics, 405, Atomistilor, 077125 Bucharest-Magurele, Romania

^* Corresponding author
^* Corresponding author

Received: August 31, 2020

Revised: December 31, 2020

Early access: March 2021

Published: May 2021

The first author is member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The second author is member of the Gruppo Nazionale per la Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM)

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Abstract

We study, by means of the periodic unfolding technique, the homogenization of a modified bidomain model, which describes the propagation of the action potential in the cardiac electrophysiology. Such a model, allowing the presence of pathological zones in the heart, involves various geometries and non-standard transmission conditions on the interface between the healthy and the damaged part of the cardiac muscle.

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Mathematics Subject Classification: Primary: 35B27; Secondary: 35Q92, 35K20.

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Figure 1. ${Left}$: the periodic cell $ Y $. $ E^{ \rm{D}} $ is the shaded region and $ E^{ \rm{B}} $ is the white region.${Right}$: the region $ \varOmega $

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Figure 2. The periodic cell $ Y $. $ E^{ \rm{D}} $ is the shaded region and $ E^{ \rm{B}} $ is the white region

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