Bifurcation and chaos in a model of cardiac early afterdepolarizations.

Complex oscillatory behaviors, such as spiking and bursting dynamics in pancreatic β-cells [1], neurons [1–5], and optical lasers [6], are common phenomena in excitable systems. These complex dynamics are generally described by systems with fast and slow time scales, where the full system behavior can be described by slow dynamics evolving the fast subsystem through a series of bifurcations [1,2]. Cardiac myocytes can exhibit pathological excitations called early afterdepolarizations (EADs), which are voltage oscillations during the repolarizing phase of the action potential (AP). They have been implicated as a cause of lethal cardiac arrhythmias [7–9] and have been widely investigated in experiments [8,10–12] and also in simulations [13–16]. It is commonly agreed that EADs occur when inward (depolarizing) currents are increased and/or outward (repolarizing) currents are decreased. But many such changes do not produce EADs, and the general underlying dynamical mechanism still remains unknown. In single myocytes, EADs typically occur irregularly [10–12], which is generally attributed to random fluctuations of the underlying ion channels [13]. In a recent study [16], we presented evidence from isolated myocyte experiments and computational simulations that irregular EAD behavior is not random, but rather dynamical chaos, and gives rise to novel tissue scale dynamics. EADs have typically been studied in computational simulations using highly detailed AP models making dynamical analysis difficult [13–16]. In this study, we show that EADs can occur in a simple AP model and the Poincare-Andronov-Hopf (“Hopf”) and homoclinic bifurcations are responsible for the genesis of EADs. We also show that due to the homoclinic bifurcation, EAD chaos can be readily induced during periodic pacing, providing a mechanistic explanation for the irregular EAD dynamics widely observed in cardiac experiments [10–12].