A Combinatorial Algorithm to Detect Higher-Order Dynamics in Cardiac Signals

Repolarization alternans is one of the mainstays of theoretical cardiac electrophysiology and provides a link between cellular dynamics and fibrillation. Action potential duration (APD) alternans is the simplest manifestation of repolarization dynamics. However, excitation-contraction coupling can generate higher-order periodicities that are precursors to chaotic rhythms. Higher-order periods have been experimentally elusive and only detected in a few cases. We detect higher-order periods using a combinatorial algorithm. The key idea of the algorithm is to set up a weighted-directed graph, where the vertices correspond to the beats, and the links are assigned according to the distance metric function between the beats. The shortest path between the first and last beats in the graph determines the optimal periodicity of each beat. We applied the algorithm to optical-mapping signals recorded using voltage-sensitive fluorescent dyes to six human heart transplantation recipients. We detected periods 4, 6, and 8, and higher (chaotic areas) with heterogeneous spatial distribution. Our graph-based algorithm is a valuable tool to probe the complex dynamics of cardiac tissue by looking beyond classic alternans, especially at fast rates and before the transition to chaotic fibrillation.