Unfolding homogenization method applied to physiological and phenomenological bidomain models in electrocardiology
TALHOUK, Raafat
الجامعة اللبنانية [بيروت] = Lebanese University [Beirut] = Université libanaise [Beyrouth] [LU / ULB]
< Reduce
الجامعة اللبنانية [بيروت] = Lebanese University [Beirut] = Université libanaise [Beyrouth] [LU / ULB]
Language
en
Article de revue
This item was published in
Nonlinear Analysis: Real World Applications. 2019-12, vol. 50, p. 413-447
Elsevier
English Abstract
In 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 ...Read more >
In 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.Read less <
English Keywords
Bidomain model
Reaction–diffusion system
Homogenization theory
Unfolding method
Convergence
ANR Project
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
Origin
Hal imported