Predicting the Onset of Alternating Rhythms in Noisy Cardiac Systems

Abstract

Predicting the onset of transitions in the qualitative dynamics of complex systems has relevance in diverse fields, including ecology, climate change, finance, and medicine. Alternating rhythms represent beat-to-beat variations in the response of the heart, and can precede the onset of fatal arrhythmias, including ventricular fibrillation. Treating spontaneously beating aggregates of embryonic chick cardiac cells with a potassium channel blocker induces alternating rhythms through a mathematical instability, termed a period-doubling bifurcation. Theory predicts that in the neighborhood of period-doubling bifurcations, the system's noise amplifies and oscillations emerge in the autocorrelation function. By examining the aggregates’ inter-beat intervals, we demonstrate that noise amplification and oscillations in the autocorrelation function emerge near the bifurcation [1]. We also examine return maps, plots that functionally relate the following inter-beat interval with the previous inter-beat interval, and develop a quantitative measure that detects exactly how close the system is to the bifurcation point. Our work suggests that it may be possible to predict the onset of potentially dangerous alternating rhythms.[1] Quail T., Shrier A., and Glass L. (2015) Predicting the onset of period-doubling bifurcations in noisy cardiac systems. Proc. Natl. Acad. Sci. USA. 112: 9358-9363.