Extremes of fractional noises: A model for the timings of arrhythmic heart beats in post-infarction patients.

We have analyzed symbol sequences of heart beat annotations obtained from 24-h electrocardiogram recordings of 184 post-infarction patients (from the Cardiac Arrhythmia Suppression Trial database, CAST). In the symbol sequences, each heart beat was coded as an arrhythmic or as a normal beat. The symbol sequences were analyzed with a model-based approach which relies on two-parametric peaks over the threshold (POT) model, interpreting each premature ventricular contraction (PVC) as an extreme event. For the POT model, we explored (i) the Shannon entropy which was estimated in terms of the Lempel-Ziv complexity, (ii) the shape parameter of the Weibull distribution that best fits the PVC return times, and (iii) the strength of long-range correlations quantified by detrended fluctuation analysis (DFA) for the two-dimensional parameter space. We have found that in the frame of our model the Lempel-Ziv complexity is functionally related to the shape parameter of the Weibull distribution. Thus, two complementary measures (entropy and strength of long-range correlations) are sufficient to characterize realizations of the two-parametric model. For the CAST data, we have found evidence for an intermediate strength of long-range correlations in the PVC timings, which are correlated to the age of the patient: younger post-infarction patients have higher strength of long-range correlations than older patients. The normalized Shannon entropy has values in the range 0.5