Statistical properties and memory of excursions in heartbeat intervals

We study the statistics of excursions, defined as the number of beats to return to a local mean value in heartbeat interval time series from healthy subjects and patients with congestive heart failure (CHF). We find that the cumulative distributions of excursions (of size τ) are consistent with a stretched exponential function of the form G(τ) ~ e^(aτb) with a and b constants. Also, we study the statistics of return intervals between long excursions above certain threshold q for both groups to explore the possibility of memory in the time organization of the extreme-size excursions. The correlation method applied to the return intervals shows a weak correlation for both groups with changes as the threshold q increases. The DFA analysis confirms the presence of correlations with scaling exponents higher than the uncorrelated value (α = 0.5).