  Early afterdepolarizations (EADs) are pathological voltage oscillations in
cardiomyocytes that have been observed in response to a number of
pharmacological agents and disease conditions. EADs are small voltage
fluctuations that occur during the plateau of an action potential. Although a
single-cell behavior, EADs can lead to tissue-level arrhythmias, including
ventricular tachycardia. Much is currently known about the biophysical
mechanisms (i.e., the roles of ion channels and intracellular calcium stores)
for 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 3D model to demonstrate that the phase-2 EADs are
canards that are formed in the neighborhood of a folded node singularity. This
knowledge allows us to determine the number of EADs that can be produced for a
given parameter set without performing computer simulations, and provides
guidance on parameter changes that can facilitate or inhibit EAD production.
With this approach, we demonstrate why periodic stimulation, as would occur in
an 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 stimulation. These revelations fall out naturally from
an understanding of folded node singularities, but are hard or impossible to
glean from a knowledge of the biophysical mechanism for EADs alone. Therefore,
an understanding of the canard mechanism is a useful complement to an
understanding of the biophysical mechanism that has been developed over years
of experimental and computational investigations.
