Stability and bifurcation in an integral-delay model of cardiac reentry including spatial coupling in repolarization.
We present the bifurcation analysis of a revised version of the integral-delay model [Courtemanche et al., Siam J. Appl. Math. 56, 119 (1996)] of reentry in a one-dimensional ring that includes a spatial coupling in the calculation of the action potential duration. This coupling is meant to reproduce the modulation of repolarization by the diffusive current flowing through the intercellular resistance. We show that coupling modifies the criterion for the stability of the period-1 solution, which is no longer uniquely related to the action potential restitution curve, but depends also on the degree of coupling between cells and on the dispersion relation of the velocity. Coupling also changes the scenario from an infinite-dimension Hopf bifurcation to a finite sequence of Hopf bifurcations that take place at different ring lengths.
Comtois
Philippe
P
Institute of Biomedical Engineering, Université de Montréal and Research Centre, Hôpital du Sacré-Coeur, 5400 Gouin W., Montréal (Québec), Canada H4J 1C5.
Vinet
Alain
A
D000200:Action Potentials; D000818:Animals; D055592:Biophysical Phenomena; D001703:Biophysics; D003198:Computer Simulation; D004058:Diffusion; D004594:Electrophysiology; D006329:Heart Conduction System; D006339:Heart Rate; D008955:Models, Cardiovascular; D008962:Models, Theoretical; D009200:Myocardial Contraction