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

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