Existence of a $T$-periodic solution for the monodomain model corresponding to an isolated ventricle due to ionic-diffusive relations

TL;DR

This paper establishes conditions linking ionic and diffusion parameters to guarantee the existence of periodic solutions in a heart electrical activity model, aiding understanding of rhythm disorders.

Contribution

It introduces specific ionic-diffusive relations that ensure periodic solutions in the monodomain heart model, using Faedo-Galerkin approximation methods.

Findings

Identifies sufficient ionic-diffusive relations for periodic solutions

Proves existence of weak periodic solutions in the monodomain model

Provides insights into rhythm disorder mechanisms

Abstract

In this paper, we find relations between the ionic parameters and the diffusion parameters which are sufficient to ensure the existence of a periodic solution for a well-known monodomain model in a weak sense. We make use of the method of approximation of Faedo-Galerkin to prove the existence of weak periodic solutions of the monodomain model for the electrical activity of the heart assuming that it is periodically activated in its boundaries. Actually, this periodic solution has the same period of activation. Finally, we reflect on how these ionic-diffusive relations are useful to explain the pathophysiology of some rhythm disorders.