Geometric Singular Perturbation Analysis of Early Afterdepolarizations in Cardiac Myocytes

Early afterdepolarizations (EADs) are pathological voltage fluctuations that can occur during an action potential in cardiac cells and are a potent source of potentially fatal arrhythmia. As such, there are long-running experimental and computational efforts to characterize the biophysical conditions which promote the occurrence of EADs. Some of these efforts aim to uncover and analyze the common mechanisms underlying the occurrence of EADs across biophysical conditions. Only recently have dynamical systems techniques been used to advance such efforts. Geometric singular perturbation (fast-slow) analysis has proven to be a powerful tool in this vein. The classic fast-slow approach, which treats the dynamical variable with slowest evolution rate as a parameter, posits that EAD initiation and termination are due to dynamic bifurcations of the remaining (fast) subsystem. Yet, a more recent fast-slow approach, which frames EADs as canard-induced mixed-mode oscillations, provides sharper explanatory and predictive insights. Both approaches provide mechanistic explanations for EAD behavior beyond what can be obtained through experiments and numerical simulation alone. However, we show that the canard-based approach, with its growing suite of associated computational tools, is capable of extending these sharp explanatory and predictive insights beyond the domain of idealized minimal models and into the domain of complex biophysical models which contain a richer set of interacting components as well as of disparate timescales. Over the course of three projects, we show that canards persist in biophysical models as the most informative EAD generating mechanism, that the canards we uncover provide remarkable power in explaining long-standing experimental observations and in making falsifiable experimentally testable predictions, and that canards provide an alternative framing of a major debate about the dominant source of EADs in cardiac cells.