Department of
1Biomedical Engineering, 2Mathematics, 3Physics, and 4Center for Nonlinear and Complex Systems, Duke University
Cardiac arrhythmias can lead to sudden cardiac death, which is the number one cause of death in the United States. Cardiac alternans is recognized as a possible initiator of fatal arrhythmias. Cardiac alternans is characterized by long-short beat-to-beat alternation in action potential duration; it arises via period-doubling bifurcation in a myocardium paced at increasingly faster rates. Bifurcation theory indicates that a period-doubling bifurcation can occur via two different mechanisms: either through a classical period-doubling bifurcation as in return maps described by smooth functions or through a border-collision period-doubling bifurcation as in return maps described by piecewise smooth functions. To identify the true mechanism mediating cardiac alternans, this work investigates theoretically the differences between smooth and border-collision period-doubling bifurcations. Although, theoretically, bifurcation diagrams discriminate between the two bifurcations, we show that they may be hard to differentiate for discrete data and may even be misleading especially when decay of transient is too slow. We then show that alternating pacing, i.e., long-short beat-to-beat variation in pacing intervals, affords a more effective way to distinguish between the two bifurcations. Qualitative differences between the two bifurcations are significant\ and robust even in the presence of noise and other disturbances. Therefore, our theoretical findings provide an unambiguous technique that can be easily implemented in experiments to distinguish between smooth and border-collision period-doubling bifurcations.