Bifurcation of Spatiotemporal Cardiac Alternans

Cardiac alternans is an initiator of ventricular fibrillation, a fatal heart rhythm disorder that kills hundreds of thousands people in the US each year. Alternans manifests as a pattern with beat-to-beat long-short variations in action potential duration. In an isolated cardiac cell, alternans arises as a supercritical period-doubling bifurcation. In cardiac tissue (coupled cells), propagation effect leads to more complicated bifurcation structures. Specifically, there may coexist multiple spatiotemporal patterns of alternans in tissue due to the interaction between electrotonic coupling and intrinsic instability in the dynamics of action potential. In this work, we carry out a detailed bifurcation analysis to illustrate the mechanism that leads to this phenomenon. The results on this analysis may shed light on the onset and control of the dreadful instability of cardiac alternans.