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

TL;DR

This paper introduces a detailed microscopic model of cardiac electrical activity incorporating dynamical gap junctions, establishing the existence and uniqueness of solutions using advanced mathematical techniques.

Contribution

It presents a novel tridomain PDE-ODE model for cardiac tissue with dynamical gap junctions and proves its well-posedness, advancing understanding of cardiac electrophysiology modeling.

Findings

Proved global existence and uniqueness of weak solutions.

Developed an approximate non-degenerate system for analysis.

Applied Faedo-Galerkin method and compactness arguments.

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.