Numerical simulations of electrocardiograms

International audienceThis chapter presents a concise overview of various mathematical and numerical problems raised by the simulation of electrocardiograms (ECGs). A model for the propagation of the electrical activation in the heart and in the torso is proposed. Some of its mathematical properties are analyzed. This model is not aimed at reproducing the complex phenomena taking place at the microscopic level. It has been devised to produce realistic healthy ECGs, and some pathological ones, with a reasonable level of complexity. It relies on various assumptions that are carefully discussed through their impact on the ECGs. The coupling between the heart and the torso is a critical numerical issue which is addressed. In particular efficient coupling strategies based on explicit algorithms are presented and analyzed. The chapter ends with some preliminary results of a reduced order model based on the Proper Orthogonal Decomposition (POD) method