Spatial heterogeneity of restitution properties and the onset of alternans.

Traditionally, it was believed that cardiac rhythm stability was governed by the slope of the restitution curve (RC), which relates the duration of an action potential to the preceding diastolic interval. However, a single RC does not exist; rate-dependence leads to multiple distinct RCs. We measure spatial differences in the steady-state action potential duration (APD), as well as in three different RCs: the S1-S2 (SRC), constant-basic-cycle-length (BRC), and dynamic (DRC), and correlate these differences with the tissue's propensity to develop alternans.

Control of electrical alternans in simulations of paced myocardium using extended time-delay autosynchronization.

Experimental studies have linked alternans, an abnormal beat-to-beat alternation of cardiac action potential duration, to the genesis of lethal arrhythmias such as ventricular fibrillation. Prior studies have considered various closed-loop feedback control algorithms for perturbing interstimulus intervals in such a way that alternans is suppressed. However, some experimental cases are restricted in that the controller's stimuli must preempt those of the existing waves that are propagating in the tissue, and therefore only shortening perturbations to the underlying pacing are allowed.

Period-doubling bifurcation to alternans in paced cardiac tissue: crossover from smooth to border-collision characteristics.

We investigate, both experimentally and theoretically, the period-doubling bifurcation to alternans in heart tissue. Previously, this phenomenon has been modeled with either smooth or border-collision dynamics. Using a modification of existing experimental techniques, we find a hybrid behavior: Very close to the bifurcation point, the dynamics is smooth, whereas further away it is border-collision-like.

Small-Signal Amplification of Period-Doubling Bifurcations in Smooth Iterated Maps.

Various authors have shown that, near the onset of a period-doubling bifurcation, small perturbations in the control parameter may result in much larger disturbances in the response of the dynamical system. Such amplification of small signals can be measured by a gain defined as the magnitude of the disturbance in the response divided by the perturbation amplitude. In this paper, the perturbed response is studied using normal forms based on the most general assumptions of iterated maps.