Unfolding homogenization method applied to physiological and phenomenological bidomain models in electrocardiology. (December 2019)

• Record Type: Journal Article
• Authors: Bendahmane, Mostafa; Mroue, Fatima; Saad, Mazen; Talhouk, Raafat
• Is Part Of: Nonlinear analysis. Volume 50(2019)
• Page Start: 413
• Page End: 447
• Publication Date: 2019-12
• Subjects: 35A01 -- 35A02 -- 35B27; Bidomain model -- Reaction–diffusion system -- Homogenization theory -- Unfolding method -- Convergence; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.05.006
• Languages: English
• ISSNs: 1468-1218

Abstract

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 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 L 2 -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.