Self-similarity and detrended fluctuation analysis of cardiovascular signals

Abstract

The beat-by-beat dynamics of several cardiovascular signals, including heart rate and arterial blood pressure, shows statistically self-similar properties. This means that shorter segments extracted from these signals may have the same structure of the whole time series, whenever the vertical axis is rescaled by a proper scale coefficient. A "self-similar" signal is thus analogous to a geometric fractal that can be split into small fragments, each containing the whole complexity of the original object. The self-similar dynamics reflects the nature of the complex system generating the signal. Therefore, in recent years a large body of research investigated the self-similar characteristics of cardiovascular signals by estimating their "self-similarity" scale coefficients for better understanding the mechanisms of cardiovascular regulation in health and disease, and for risk stratification. This chapter illustrates the main methods used in literature for assessing the selfsimilarity of cardiovascular time series, especially focusing on methods based on the popular Detrended Fluctuation Analysis (DFA) algorithm. In particular, it reviews applications of DFA that describe the cardiovascular time series in terms of fractal models, with one or more scale coefficients. Furthermore, it illustrates the more recent advancements of the DFA method for describing self-similarity as a continuous temporal spectrum of scale coefficients and for deriving multifractal spectra.