Clinical diagnosis and basic investigations are critically dependent on the ability to record and analyze physiologic signals. Examples include heart rate recordings of patients at high risk of sudden death (Fig. 1), electroencephalographic (EEG) recordings in epilepsy and other disorders, and fluctuations of hormone and other molecular signal messengers in neuroendocrine dynamics. However, the traditional bedside and laboratory analyses of these signals have not kept pace with major advances in technology that allow for recording and storage of massive datasets of continuously fluctuating signals. Surprisingly, although these typically complex signals have recently been shown to represent processes that are nonlinear, nonstationary, and nonequilibrium in nature, the tools to analyze such data often still assume linearity, stationarity, and equilibrium-like conditions. Such conventional techniques include analysis of means, standard deviations and other features of histograms, along with classical power spectrum analysis.
An exciting recent finding is that such complex datasets may contain hidden information, defined here as information not extractable with conventional methods of analysis. Such information promises to be of clinical value (forecasting sudden cardiac death in ambulatory patients, or cardiopulmonary catastrophes during surgical procedures), as well as to relate to basic mechanisms of healthy and pathologic function. Fractal analysis is one of the most promising new approaches for extracting such hidden information from physiologic time series. This is partly due to the fact that the absence of characteristic temporal (or spatial) scales--the hallmark of fractal behavior--may confer important biological advantages, related to the adaptability of response [2, 4, 1, 5, 3, 6].
In this chapter, we present some recent progress in applying fractal analysis to human physiology. We begin with a definition of fractal dynamics, followed by an introduction to some special problems posed by physiological time series. We then discuss the analysis of the output from two model systems: (1) human heartbeat regulation, which is under involuntary (neuroautonomic) control; and (2) human gait regulation, which is under the voluntary control of the central nervous system. We focus on the analysis of the output of these two systems in health and disease.
Figure: Representative complex physiological fluctuations. Heart rate (normal sinus rhythm) time series of 30 min from (a) a healthy subject at sea level, (b) a subject with congestive heart failure, (c) a subject with obstructive sleep apnea, and (d) a sudden cardiac death subject who sustained a cardiac arrest with ventricular fibrillation (VF). Note the highly nonstationary and ``noisy'' appearance of the healthy variability which is related in part to fractal (scale-free) dynamics. In contrast, pathologic states may be associated with the emergence of periodic oscillations, indicating the emergence of a characteristic time scale.