Bifurcation theory and cardiac arrhythmias

In this paper we review two types of dynamic behaviors defined by the bifurcation theory that are found to be particularly useful in describing two forms of cardiac electrical instabilities that are of considerable importance in cardiac arrhythmogenesis. The first is action potential duration (APD) alternans with an underlying dynamics consistent with the period doubling bifurcation theory. This form of electrical instability could lead to spatially discordant APD alternans leading to wavebreak and reentrant form of tachyarrhythmias. Factors that modulate the APD alternans are discussed. The second form of bifurcation of importance to cardiac arrhythmogenesis is the Hopf-homoclinic bifurcation that adequately describes the dynamics of the onset of early afterdepolarization (EAD)-mediated triggered activity (Hopf) that may cause ventricular tachycardia and ventricular fibrillation (VT/VF respectively). The self-termination of the triggered activity is compatible with the homoclinic bifurcation. Ionic and intracellular calcium dynamics underlying these dynamics are discussed using available experimental and simulation data. The dynamic analysis provides novel insights into the mechanisms of VT/VF, a major cause of sudden cardiac death in the US.