Why pacing frequency affects the production of early afterdepolarizations in cardiomyocytes: An explanation revealed by slow-fast analysis of a minimal model.

Early afterdepolarizations (EADs) are pathological voltage oscillations in cardiomyocytes that have been observed in response to a number of pharmacological agents and disease conditions. Phase-2 EADs consist of small voltage fluctuations during the plateau of an action potential, typically under conditions in which the action potential is elongated. Although a single-cell behavior, EADs can lead to tissue-level arrhythmias. Much is currently known about the biophysical mechanisms (i.e., the roles of ion channels and intracellular Ca^{2+} stores) for the various forms of EADs, due partially to the development and analysis of mathematical models. This includes the application of slow-fast analysis, which takes advantage of timescale separation inherent in the system to simplify its analysis. We take this further, using a minimal three-dimensional model to demonstrate that phase-2 EADs are canards formed in the neighborhood of a folded node singularity. This allows us to predict the number of EADs that can be produced for a given parameter set, and provides guidance on parameter changes that facilitate or inhibit EAD production. With this approach, we demonstrate why periodic stimulation, as occurs in intact heart, preferentially facilitates EAD production when applied at low frequencies. We also explain the origin of complex alternan dynamics that can occur with intermediate-frequency stimulation, in which varying numbers of EADs are produced with each pulse. These revelations fall out naturally from an understanding of folded node singularities, but are difficult to glean from knowledge of the biophysical mechanism for EADs alone. Therefore, understanding the canard mechanism is a useful complement to understanding of the biophysical mechanism that has been developed over years of experimental and computational investigations.