Early afterdepolarizations with growing amplitudes via delayed subcritical hopf bifurcations and unstable manifolds of Saddle Foci in cardiac action potential dynamics

Abstract

Early after depolarizations (EADs) are pathological oscillations in cardiac action potentials during the repolarization phase and may be caused by drug side effects, ion channel disease or oxidative stress. The most widely observed EAD pattern is characterized by oscillations with growing amplitudes. So far, its occurence has been explained in terms of a supercritical Hopf bifurcation in the fast subsystem of the action potential dynamics from which stable limit cycles with growing amplitudes emerge. The novel contribution of this article is the introduction of two alternative explanations of EAD genesis with growing amplitudes that do not involve stable limit cycles in fast subsystems. In particular, we demonstrate that EAD patterns with growing amplitudes may alternatively arise due to a delayed subcritical Hopf bifurcation or an unstable manifold of a saddle focus fixed point in the full fast-slow system modelling the action potential. Our work extends the list of possible dynamical EAD mechanisms and may contribute to a classification of drug effects in preclinical cardiotoxicity testing.