Finite element and finite volume-element simulation of pseudo-ECGs and cardiac alternans

• Published in: Mathematical methods in the applied sciences Vol. 38; no. 6; pp. 1046 - 1058
• Main Authors: Dupraz, Marie, Filippi, Simonetta, Gizzi, Alessio, Quarteroni, Alfio, Ruiz-Baier, Ricardo
• Format: Journal Article
• Language: English
• Published: Freiburg Blackwell Publishing Ltd 01.04.2015; Wiley Subscription Services, Inc
• Subjects: Alternan; Anisotropy; cardiac alternans; Discretization; Dynamical systems; finite element discretization; Finite element method; finite volume-element method; Mathematical analysis; Mathematical models; Nonlinear dynamics; operator splitting; pseudo-ECG; reaction-diffusion system; spatio-temporal dynamics
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.3127

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.