A coupled system of PDEs and ODEs arising in electrocardiograms modeling

Abstract

We study the well-posedness of a coupled system of PDEs and ODEs arising in the numerical simulation of electrocardiograms. It consists of a system of degenerate reaction-diffusion equations, the so-called bidomain equations, governing the electrical activity of the heart, and a diffusion equation governing the potential in the surrounding tissues. Global existence of weak solutions is proved for an abstract class of ionic models including Mitchell-Schaeffer, FitzHugh-Nagumo, Aliev-Panfilov, and McCulloch. Uniqueness is proved in the case of the FitzHugh-Nagumo ionic model. The proof is based on a regularization argument with a Faedo-Galerkin/compactness procedure. © The Author 2008. Published by Oxford University Press.