Microscopic tridomain model of electrical activity in the heart with dynamical gap junctions. Part 2 – Derivation of the macroscopic tridomain model by unfolding homogenization method - Archive ouverte HAL Access content directly
Journal Articles Asymptotic Analysis Year : 2022

Microscopic tridomain model of electrical activity in the heart with dynamical gap junctions. Part 2 – Derivation of the macroscopic tridomain model by unfolding homogenization method

Abstract

We study the homogenization of a novel microscopic tridomain system, allowing for a more detailed analysis of the properties of cardiac conduction than the classical bidomain and monodomain models. In (Acta Appl.Math. 179 (2022) 1–35), we detail this model in which gap junctions are considered as the connections between adjacent cells in cardiac muscle and could serve as alternative or supporting pathways for cell-to-cell electrical signal propagation. Departing from this microscopic cellular model, we apply the periodic unfolding method to derive the macroscopic tridomain model. Several difficulties prevent the application of unfolding homogenization results, including the degenerate temporal structure of the tridomain equations and a nonlinear dynamic boundary condition on the cellular membrane. To prove the convergence of the nonlinear terms, especially those defined on the microscopic interface, we use the boundary unfolding operator and a Kolmogorov–Riesz compactness’s result.
Fichier principal
Vignette du fichier
Article Trid Part 2.pdf (2.15 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03776998 , version 1 (14-09-2022)

Identifiers

Cite

Fakhrielddine Bader, Mostafa Bendahmane, Mazen Saad, Raafat Talhouk. Microscopic tridomain model of electrical activity in the heart with dynamical gap junctions. Part 2 – Derivation of the macroscopic tridomain model by unfolding homogenization method. Asymptotic Analysis, 2022, pp.1-32. ⟨10.3233/ASY-221804⟩. ⟨hal-03776998⟩
46 View
22 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More