Decoupled time-marching schemes in computational cardiac electrophysiology and ECG numerical simulation

Miguel Angel Fernández 1, * Nejib Zemzemi 1
* Corresponding author
1 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : This work considers the approximation of the cardiac bidomain equations, either isolated or coupled with the torso, via first order semi-implicit time-marching schemes involving a fully decoupled computation of the unknown fields (ionic state, transmembrane potential, extracellular and torso potentials). For the isolated bidomain system, we show that the Gauss-Seidel and Jacobi like splittings do not compromise energy stability; they simply alter the energy norm. Within the framework of the numerical simulation of electrocardiograms (ECG), these bidomain splittings are combined with an explicit Robin-Robin treatment of the heart-torso coupling conditions. We show that the resulting schemes allow a fully decoupled (energy) stable computation of the heart and torso fields, under an additional hyperbolic-CFL like condition. The accuracy and convergence rate of the considered schemes are investigated numerically with a series of numerical experiments.
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Miguel Angel Fernández, Nejib Zemzemi. Decoupled time-marching schemes in computational cardiac electrophysiology and ECG numerical simulation. Mathematical Biosciences, Elsevier, 2010, 226 (1), pp.58-75. ⟨10.1016/j.mbs.2010.04.003⟩. ⟨inria-00411510v3⟩

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