title: Decoupled time-marching schemes in computational cardiac electrophysiology and ECG numerical simulation.
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.
authors.affiliation: INRIA, CRI Paris-Rocquencourt, F-78153 Le Chesnay Cedex, France. miguel.fernandez@inria.fr
authors.forename: Miguel A
authors.initials: MA
authors.lastname: Fernández
authors.forename: Nejib
authors.initials: N
authors.lastname: Zemzemi
mesh_terms: D018780:Body Surface Potential Mapping / Q000706:statistics & numerical data; D003198:Computer Simulation; D004562:Electrocardiography / Q000706:statistics & numerical data*; D055724:Electrophysiological Phenomena; D056966:Excitation Contraction Coupling / Q000502:physiology; D006321:Heart / Q000033:anatomy & histology / Q000502:physiology*; D006801:Humans; D021621:Imaging, Three-Dimensional; D066298:In Vitro Techniques; D008953:Models, Anatomic; D008955:Models, Cardiovascular; D015233:Models, Statistical; D013997:Time Factors