Properties of Asymmetric Detrended Fluctuation Analysis in the time series of RR intervals

Heart rate asymmetry is a phenomenon by which the accelerations and decelerations of heart rate behave differently, and this difference is consistent and unidirectional, i.e. in most of the analyzed recordings the inequalities have the same directions. So far, it has been established for variance and runs based types of descriptors of RR intervals time series. In this paper we apply the newly developed method of Asymmetric Detrended Fluctuation Analysis, which so far has mainly been used with economic time series, to the set of 420 stationary 30 min time series of RR intervals from young, healthy individuals aged between 20 and 40. This asymmetric approach introduces separate scaling exponents for rising and falling trends. We systematically study the presence of asymmetry in both global and local versions of this method. In this study global means “applying to the whole time series” and local means “applying to windows jumping along the recording”. It is found that the correlation structure of the fluctuations left over after detrending in physiological time series shows strong asymmetric features in both magnitude, with α+<α−, where α+ is related to heart rate decelerations and α− to heart rate accelerations, and the proportion of the signal in which the above inequality holds. A very similar effect is observed if asymmetric noise is added to a symmetric self-affine function. No such phenomena are observed in the same physiological data after shuffling or with a group of symmetric synthetic time series.