A coupled system of PDEs and ODEs arising in electrocardiograms modelling

Muriel Boulakia (1, 2) , Miguel Angel Fernández (1) , Jean-Frédéric Gerbeau (1) , Nejib Zemzemi (1)

1 REO - Numerical simulation of biological flows
2 LJLL - Laboratoire Jacques-Louis Lions

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 MacCulloch. Uniqueness is proved in the case of the FitzHugh-Nagumo ionic model. The proof is based on a regularisation argument with a Faedo-Galerkin/compactness procedure.

Domaines: Analyse numérique [math.NA]

Muriel Boulakia, Miguel Angel Fernández, Jean-Frédéric Gerbeau, Nejib Zemzemi. A coupled system of PDEs and ODEs arising in electrocardiograms modelling. Applied Mathematics Research eXpress, 2008, 2008, pp.abn002. ⟨10.1093/amrx/abn002⟩. ⟨hal-00701786⟩