Statistical physics and physiology: Monofractal and multifractal approaches

• Published in: Physica A Vol. 270; no. 1; pp. 309 - 324
• Main Authors: Stanley, H.E., Amaral, L.A.N., Goldberger, A.L., Havlin, S., Ivanov, P.Ch, Peng, C.-K.
• Format: Journal Article
• Language: English
• Published: Legacy CDMS Elsevier B.V 01.08.1999
• Subjects: Biophysical Phenomena; Biophysics; Death, Sudden, Cardiac; Fractals; Heart Diseases - physiopathology; Heart Failure; Heart Rate - physiology; Homeostasis; Humans; Life Sciences (General); Models, Cardiovascular; Models, Statistical; Nonlinear Dynamics; Physiology; Stochastic Processes; Heart Diseases/physiopathology; Human; Nasa Discipline Cardiopulmonary; Heart Rate/physiology; Models, Cardiovascular; Non-Nasa Center; Homeostasis; Fractals; Biophysics; Models, Statistical; Heart Failure, Congestive; Death, Sudden, Cardiac; Stochastic Processes; Nonlinear Dynamics; NASA Discipline Cardiopulmonary; Non-NASA Center
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/S0378-4371(99)00230-7

Even under healthy, basal conditions, physiologic systems show erratic fluctuations resembling those found in dynamical systems driven away from a single equilibrium state. Do such “nonequilibrium” fluctuations simply reflect the fact that physiologic systems are being constantly perturbed by external and intrinsic noise? Or, do these fluctuations actually contain useful, “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 – sufficient 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 than that of diseased subjects.