Scaling differences of heartbeat excursions between wake and sleep periods

We study the statistical properties of excursions in heart interbeat time series. An excursion is defined as the time employed by a walker to return to its mean value. We consider the homeostatic property of the heartbeat dynamics as a departing point to characterize the dynamics of excursions in beat-to-beat fluctuations. Scaling properties of excursions during wake and sleep periods from two groups are compared: 16 healthy subjects and 11 patients with congestive heart failure (CHF). We find that the cumulative distributions of excursions for both groups follow stretched exponential functions given by g(τ)~e(-aτ(b)) with different fitting parameters a and b, leading to different decaying rates. Our results show that the average characteristic scale associated with the excursion distributions is greater for healthy data compared to CHF patients whereas sleep-wake transitions are more significant for healthy data. Next, we explore changes in the distributions of excursions when considering (i) a shifted mean value to define an excursion and (ii) the sum of the kth excursion successor. Besides, the presence of temporal correlations in the excursions sequences is evaluated by means of the detrended fluctuation analysis. We observe the presence of long-range correlations for healthy subjects, whereas for the CHF group, correlations are described by two regimes; over short scales the fluctuations are close to uncorrelated noise, and for large scales the fluctuations reveal long-range correlations. Finally, we apply a stability analysis of excursions based on the Allan variance which reveals that healthy dynamics is more stable than heart failure excursions.