Big ducks in the heart: Canard analysis can explain large early afterdepolarizations in cardiomyocytes

Early afterdepolarizations (EADs) are pathological voltage fluctuations that can occur in cardiac cells and are a potent source of potentially fatal arrhythmias. Recent works examining the mechanisms underlying EADs in minimal computational cardiac models have revealed that voltage-driven EADs are canard-induced mixed-mode oscillations whose properties are mediated by the rate at which these cells are paced. In this work, we analyze the mechanisms for the pacing-induced generation of different EAD behaviors in a reduced four-dimensional Luo-Rudy I model using slow-fast analysis. While previous explanations for EADs in this model have required manipulation of the underlying multitimescale structure, our approach does not and we find that the canard mechanism persists in generating EADs in this context. We also find that the canard mechanism gives a more complete explanation for the onset and properties of the EADs induced (e.g., EAD amplitude and number). In addition, we also find that the canards play an essential role in producing a richer set of behaviors than were seen in other minimal models, some of which have also been observed in experiments. These behaviors include pacing-induced termination of EADs, the periodic alternation of cardiac action potentials with and without EADs, as well as bistability between standard and EAD-containing action potentials at a fixed pacing rate. Finally, we show that this bistability can lead to hysteretic transitions between standard and arrhythmogenic action potentials under sufficiently slow oscillations in the pacing rate.