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P.E. McSharry and B.D. Malamud (2005) Quantifying Self-Similarity in Cardiac Inter-Beat Interval Time Series Computers in Cardiology 32: 459-462

Abstract

Five techniques to quantify scaling and long-range persistence in cardiac inter-beat interval time series are examined. These time series reflect the control mechanisms that are essential for the healthy functioning of the cardiovascular system. Power spectral analyses are first used to examine the long-range persistence (long memory) of values in the time domain, or whether values have a tendency to cluster together in a self-similar manner. This power-law scaling in the frequency domain implies that each value of the time series is correlated with all other values. One way of defining long-range persistence is if the power spectral density, S(f), is proportional to the frequency, f, raised to the power -beta. A white noise (beta = 0) has equal contribution at all frequencies and has no correlations between values in the series, compared to a Brownian motion (beta = 2), which has strong long-range persistence. For cardiac inter-beat interval time series, at long time scales the power-spectral analysis gives beta = 1 (pink noise), or a 1/f noise process. There are many methods for examining long-range persistence in time series, including semivariograms, rescaled-range, wavelet and detrended fluctuation analysis. In the past, DFA has been used extensively in the literature to examine cardiac time series. Its scaling exponent, alpha, is related to the power-spectral analysis beta through beta = 2 alpha-1. Recent DFA research has suggested that the value of alpha estimated from long recordings may be used to distinguish between healthy subjects and those suffering from cardiac disorders and to detect the effect of ageing. To compare the applicability of DFA to power-spectral analysis, semivariograms, and wavelets, synthetic datasets were generated with known levels of long-range persistence satisfying -3