Canards Underlie Both Electrical and Ca$^{2+}$-Induced Early Afterdepolarizations in a Model for Cardiac Myocytes

Abstract

Early afterdepolarizations (EADs) are voltage oscillations that can occur during the plateau phase of a cardiac action potential. EADs at the cellular level have been linked to potentially deadly tissue-level arrhythmias, and the mechanisms for their arisal are not fully understood. There is ongoing debate as to which is the predominant biophysical mechanism of EAD production: imbalanced interactions between voltage-gated transmembrane currents or overactive Ca$^{2+}$-dependent transmembrane currents brought about by pathological intracellular Ca$^{2+}$ release dynamics. In this article, we address this issue using a foundational 10-dimensional biophysical ventricular action potential model which contains both electrical and intracellular Ca$^{2+}$ components. Surprisingly, we find that the model can produce EADs through both biophysical mechanisms, which hints at a more fundamental dynamical mechanism for EAD production. Fast-slow analysis reveals EADs, in both cases, to be canard-induced mixed-mode oscillations. While the voltage-driven EADs arise from a fast-slow problem with two slow variables, the Ca$^{2+}$-driven EADs arise from the addition of a third slow variable. Hence, we adapt existing computational methods in order to compute 2D slow manifolds and 1D canard orbits in the reduced 7D model from which voltage-driven EADs arise. Further, we extend these computational methods in order to compute, for the first time, 2D sets of maximal canards which partition the 3D slow manifolds of the 8D problem from which Ca$^{2+}$-driven EADs arise. The canard viewpoint provides a unifying alternative to the voltage- or Ca$^{2+}$-driven viewpoints while also providing explanatory and predictive insights that cannot be obtained through the use of the traditional fast-slow approach.