Spatial discordance and phase reversals during alternate pacing in discrete-time kinematic and cardiomyocyte ionic models.

Alternans, a beat-to-beat alternation in the cardiac action potential duration (APD), is a dynamical instability linked with the initiation of arrhythmias and sudden cardiac death, and arises via a period-doubling bifurcation when myocytes are stimulated at fast rates. In this study, we analyze the stability of a propagating electrical wave in a one-dimensional cardiac myocyte model in response to an arrhythmogenic rhythm known as alternate pacing. Using a discrete-time kinematic model and complex frequency (Z) domain analysis, we derive analytical expressions to predict phase reversals and spatial discordance in the interbeat interval (IBI) and APD, which, importantly, cannot be predicted with a model that neglects the influence of cell coupling on repolarization. We identify key dimensionless parameters that determine the transition from spatial concordance to discordance. Finally, we show that the theoretical predictions agree closely with numerical simulations of an ionic myocyte model, over a wide range of parameters, including variable IBI, altered ionic current gating, and reduced cell coupling. We demonstrate a novel approach to predict instability in cardiac tissue during alternate pacing and further illustrate how this approach can be generalized to more detail models of myocyte dynamics.