Theory of the development of alternans in the heart during controlled diastolic interval pacing

The beat-to-beat alternation in action potential durations (APDs) in the heart, called APD alternans, has been linked to the development of serious cardiac rhythm disorders, including ventricular tachycardia and fibrillation. The length of the period between action potentials, called the diastolic interval (DI), is a key dynamical variable in the standard theory of alternans development. Thus, methods that control the DI may be useful in preventing dangerous cardiac rhythms. In this study, we examine the dynamics of alternans during controlled-DI pacing using a series of single-cell and one-dimensional (1D) fiber models of alternans dynamics. We find that a model that combines a so-called memory model with a calcium cycling model can reasonably explain two key experimental results: the possibility of alternans during constant-DI pacing and the phase lag of APDs behind DIs during sinusoidal-DI pacing. We also find that these results can be replicated by incorporating the memory model into an amplitude equation description of a 1D fiber. The 1D fiber result is potentially concerning because it seems to suggest that constant-DI control of alternans can only be effective over only a limited region in space.