The statistical self-similarity of heart rate variability

Abstract

Even under healthy, basal conditions, the time series of heart rate variability shows erratic fluctuations and possess no characteristics time scale, resembling those found in dynamical systems driven away from a single equilibrium state. The heart rate regulation systems are dynamical systems under neuroautonomic regulation and exhibit temporal structures that are similar under certain conditions. The classical methods based on auto correlation, thresholds derivatives, time domain analysis and frequency domain analysis gives a coarse quantification of variability, without distinguishing between short-term and long-term correlation found in heart rate control mechanisms. In this paper we propose a wavelet based method to analyse the fractal behaviour of heart rate variability. Estimation of the self-similarity features in heart rate variability reveals some of the mysteries of the heart rate regulation systems, by completely characterizing the scaling relationship for the entire process. The wavelet transform uniquely well suited to analyse a process which is essentially a scale invariant process. For small number of samples this method outperforms the traditional DFA method.