Scaling properties of excursions in heartbeat dynamics

¹  Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional Av. IPN No. 2580, L. Ticomán, México D.F. 07340, México
²  Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional - Edif. No. 9 U.P. Zacatenco, México D.F., 07738, México

Corresponding author: lguzmanv@ipn.mx

Received: 6 October 2009
Accepted: 19 January 2010

Abstract

In this work we study the 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). First, we apply the segmentation procedure proposed by Bernaola-Galván et al. (Phys. Rev. Lett., 87 (2001) 168105), to nonstationary heartbeat time series to identify stationary segments with a local mean value. Next, we identify local excursions around the local mean value and construct the distributions to analyze the time organization and memory in the excursions sequences from the whole time series. We find that the cumulative distributions of excursions are consistent with a stretched exponential function given by g(x) ~ , with a = 1.09±0.15 (mean value±SD) and b = 0.91±0.11 for healthy subjects and a = 1.31±0.23 and b = 0.77±0.13 for CHF patients. The cumulative conditional probability is considered to evaluate if depends on a given interval , that is, to evaluate the memory effect in excursion sequences. We find that the memory in excursions sequences under healthy conditions is characterized by the presence of clusters related to the fact that large excursions are more likely to be followed by large ones whereas for CHF data we do not observe this behavior. The presence of correlations in healthy data is confirmed by means of the detrended fluctuation analysis (DFA) while for CHF records the scaling exponent is characterized by a crossover, indicating that for short scales the sequences resemble uncorrelated noise.