A coupled system of PDEs and ODEs arising in electrocardiograms modelling

Muriel Boulakia 1 Miguel Angel Fernández 1 Jean-Frédéric Gerbeau 1 Nejib Zemzemi 1
1 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
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 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.
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Rapport
[Research Report] RR-6352, INRIA. 2007, pp.24
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Muriel Boulakia, Miguel Angel Fernández, Jean-Frédéric Gerbeau, Nejib Zemzemi. A coupled system of PDEs and ODEs arising in electrocardiograms modelling. [Research Report] RR-6352, INRIA. 2007, pp.24. 〈inria-00186852v3〉

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