Is Human Atrial Fibrillation Stochastic or Deterministic?

A reason why the mechanism that maintains human atrial fibrillation (AF) remain unclear may derive from the stochasticity of cardiac dynamics. Using forbidden ordinal patterns (FOP) with Bandt-Pompe symbolization, we characterize the intracardiac bipolar electrograms of AF from 15 patients. We calculate normalized Shannon entropy and Jansen-Shannon statistical complexity. We compare the results with stochastic time series as well as simulated bipolar spiral waves with different levels of white Gaussian noise. For all series, we construct surrogate data with the same frequency spectrum and autocorrelation, and estimate the ratio of FOP decay in the first 6,000 timepoints. Human AF exhibit a median of 460 FOP (range 357-525) which is significantly higher from surrogate data (range 0-103, p<0.05) and all stochastic series (range 0-5, p<0.05). The ratio of FOP decay in time series over surrogate data is significantly lower in AF compared to any stochastic series. On the causal entropy-complexity plane, human AF is of lower entropy, higher complexity than stochastic series, and of higher entropy, higher complexity than simulated spiral waves. We conclude that, although human AF is quantitatively different from simulated spiral waves, it has little evidence to suggest stochasticity.