Finite element and finite volume‐element simulation of pseudo‐ECGs and cardiac alternans |
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| Authors: | Marie Dupraz Simonetta Filippi Alessio Gizzi Alfio Quarteroni Ricardo Ruiz‐Baier |
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| Institution: | 1. Modeling and Scientific Computing, MATHICSE, école Polytechnique Fédérale de Lausanne, CH‐1015 Lausanne, Switzerland;2. Nonlinear Physics and Mathematical Modeling Lab, University Campus Bio‐Medico of Rome, I‐00128 Rome, Italy;3. MOX ‐ Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milano, Italy;4. Institute of Earth Sciences, FGSE, University of Lausanne, CH‐1015 Lausanne, Switzerland |
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| Abstract: | In this paper, we are interested in the spatio‐temporal dynamics of the transmembrane potential in paced isotropic and anisotropic cardiac tissues. In particular, we observe a specific precursor of cardiac arrhythmias that is the presence of alternans in the action potential duration. The underlying mathematical model consists of a reaction–diffusion system describing the propagation of the electric potential and the nonlinear interaction with ionic gating variables. Either conforming piecewise continuous finite elements or a finite volume‐element scheme are employed for the spatial discretization of all fields, whereas operator splitting strategies of first and second order are used for the time integration. We also describe an efficient mechanism to compute pseudo‐ECG signals, and we analyze restitution curves and alternans patterns for physiological and pathological cardiac rhythms. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | finite element discretization finite volume‐element method reaction– diffusion system operator splitting cardiac alternans pseudo‐ECG spatio‐temporal dynamics |
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