Microscopic Tridomain Model of Electrical Activity in the Heart with Dynamical Gap Junctions. Part 1 – Modeling and Well-Posedness - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Acta Applicandae Mathematicae Year : 2022

Microscopic Tridomain Model of Electrical Activity in the Heart with Dynamical Gap Junctions. Part 1 – Modeling and Well-Posedness

Abstract

We present a novel microscopic tridomain model describing the electrical activity in cardiac tissue with dynamical gap junctions. The microscopic tridomain system consists of three PDEs modeling the tissue electrical conduction in the intra-and extra-cellular domains, supplemented by a nonlinear ODE system for the dynamics of the ion channels and the gap junctions. We establish the global existence and uniqueness of the weak solutions to our microscopic tridomain model. The global existence of solution, which constitutes the main result of this paper, is proved by means of an approximate non-degenerate system, the Faedo-Galerkin method, and an appropriate compactness argument.
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Dates and versions

hal-03682214 , version 1 (30-05-2022)

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Fakhrielddine Bader, Mostafa Bendahmane, Mazen Saad, Raafat Talhouk. Microscopic Tridomain Model of Electrical Activity in the Heart with Dynamical Gap Junctions. Part 1 – Modeling and Well-Posedness. Acta Applicandae Mathematicae, 2022, 179 (11), ⟨10.1007/s10440-022-00498-7⟩. ⟨hal-03682214⟩
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