Monofractal and multifractal approaches to complex biomedical signals
Stanley, HE, Amaral, LAN, Goldberger, AL, Havlin, S, Ivanov, PC, Peng, CKAIP CONF PROC 502, 133 - 145 (2000)
Abstract
Even under healthy, basal conditions, physiologic systems show erratic fluctuations resembling those found in dynamical systems driven away from an equilibrium state. Do such “nonequilibrium” fluctuations simply reflect the fact that physiologic systems are being constantly perturbed by external and intrinsic uncorrelated noise? Or, do these fluctuations actually contain “hidden” information about the underlying nonequilibrium control mechanisms? We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. Specifically, we focus on interbeat interval variability as an important quantity to help elucidate possibly nonhomeostatic physiologic Variability because (i) the heart rate is under direct neuroautonomic control, (ii) interbeat interval variability is readily measured by noninvasive means, and (iii) analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. The analytic tools we discuss may be used on a wider range of physiologic signals. We first review recent progress using two analysis methods-detrended fluctuation analysis and wavelets-appropriate for quantifying monofractal structures. We then describe very recent work that quantifies multifractal features of interbeat interval series, and the discovery that the multifractal structure of healthy subjects is different from that of diseased subjects. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the scaling exponent alpha is smaller during sleep periods compared to wake periods.