Curvature effects on activation speed and repolarization in an ionic model of cardiac myocytes.

Reentry is a major mechanism underlying the initiation and perpetuation of many cardiac arrhythmias. Stimulated ventricular myocytes give action potential characterized by a fast upstroke, a long-lasting plateau, and a late repolarization phase. The plateau phase determines the action potential duration (APD) during which the system remains refractory, a property essential to the synchronization of the heart cycle. The APD varies much with prematurity and this change has been shown to be the main determinant of the dynamics in models of paced cells and cable, and during reentry in the one-dimensional loop. Curvature has also been shown to be an important factor for propagation in experimental and theoretical cardiac extended tissue. The objective of this paper is to combine both curvature and prematurity effects in a kinematical model of propagation in cardiac tissue. First, an approximation of the ionic model is used to obtain the effects of curvature and prematurity on the speed of propagation, the APD, and the absolute refractory period. Two versions of the ionic model are studied that differ in their rate of excitability recovery. The functions are used in a kinematical model describing the propagation of period-1 solutions around an annulus.