P. Colli Franzone, L.F. Pavarino and B. Taccardi,  Simulating patterns of excitation, repolarization and action potential duration with cardiac Bidomain and Monodomain models, Mathematical Biosciences, Volume 197, Issue 1, September 2005, Pages 35-66.

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Abstract

Parallel numerical simulations of excitation and recovery in three-dimensional myocardial domains are presented. The simulations are based on the anisotropic Bidomain and Monodomain models, including intramural fiber rotation and orthotropic or axisymmetric anisotropy of the intra- and extra-cellular conductivity tensors. The Bidomain model consist of a system of two reaction–diffusion equations, while the Monodomain model consists of one reaction–diffusion equation. Both models are coupled with the phase I Luo–Rudy membrane model describing the ionic currents. Simulations of excitation and repolarization sequences on myocardial slabs of different sizes show how the distribution of the action potential durations (APD) is influenced by both the anisotropic electrical conduction and the fiber rotation. This influence occurs in spite of the homogeneous intrinsic properties of the cell membrane. The APD dispersion patterns are closely correlated to the anisotropic curvature of the excitation wavefront.

Keywords: Cardiac Bidomain and Monodomain models; Myocardial anisotropy; Excitation and repolarization processes; Action potential duration; Reaction–diffusion equations; Numerical simulations