The role of short term memory and conduction velocity restitution in alternans formation

Alternans is the periodic beat-to-beat short-long alternation in action potential duration (APD), which is considered to be a precursor of ventricular arrhythmias and sudden cardiac death. In extended cardiac tissue, electrical alternans can be either spatially concordant (SCA, all cells oscillate in phase) or spatially discordant (SDA, cells in different regions oscillate out of phase). SDA gives rise to an increase in the spatial dispersion of repolarization, which is thought to be proarrhythmic. In this paper, we investigated the effect of two aspects of short term memory (STM) (α, τ) and their interplay with conduction velocity (CV) restitution on alternans formation using numerical simulations of a mapping model with two beats of memory. Here, α quantifies the dependence of APD restitution on pacing history and τ characterizes APD accommodation, which is an exponential change of APD over time once basic cycle length (BCL) changes. Our main findings are as follows: In both single cell and spatially coupled homogeneous cable, the interplay between α and τ affects the dynamical behaviors of the system. For the case of large APD accommodation (τ ≥ 290 ms), increase in α leads to suppression of alternans. However, if APD accommodation is small (τ ≤ 250 ms), increase in α leads to appearance of additional alternans region. On the other hand, the slope of CV restitution does not change the regions of alternans in the cable. However, steep CV restitution leads to more complicated dynamical behaviors of the system. Specifically, SDA instead of SCA are observed. In addition, for steep CV restitution and sufficiently large τ, we observed formations of type II conduction block (CB2), transition from type I conduction block (CB1) to CB2, and unstable nodes.