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

Marie Dupraz, Simonetta Filippi, Alessio Gizzi, Alfio Quarteroni, Ricardo Ruiz-Baier

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1046-1058
Number of pages13
JournalMathematical Methods in the Applied Sciences
Volume38
Issue number6
DOIs
Publication statusPublished - 1 Apr 2015
Externally publishedYes

Keywords

  • cardiac alternans
  • finite element discretization
  • finite volume-element method
  • operator splitting
  • pseudo-ECG
  • reaction-diffusion system
  • spatio-temporal dynamics

Cite this