There is evidence that physiological signals under healthy conditions may have a fractal temporal structure. Here we investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their scaling properties. We report on evidence for multifractality in a biological dynamical system, the healthy human heartbeat, and show that the multifractal character and nonlinear properties of the healthy heart rate are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure.

We describe the nature of human behavioral organization, specifically how resting and active periods are interwoven throughout daily life. Active period durations with physical activity count successively above a predefined threshold, when rescaled with individual means, follow a universal stretched exponential (gamma-type) cumulative distribution with characteristic time, both in healthy individuals and in patients with major depressive disorder. On the other hand, resting period durations below the threshold for both groups obey a scale-free power-law cumulative distribution over two decades, with significantly lower scaling exponents in the patients. We thus find universal distribution laws governing human behavioral organization, with a parameter altered in depression.

We explore the degree to which concepts developed in statistical physics can be usefully applied to physiological signals. We illustrate the problems related to physiologic signal analysis with representative examples of human heartbeat dynamics under healthy and pathologic conditions. We first review recent progress based on two analysis methods, power spectrum and detrended fluctuation analysis, used to quantify long-range power-law correlations in noisy heartbeat fluctuations. The finding of power-law correlations indicates presence of scale-invariant, fractal structures in the human heartbeat. These fractal structures are represented by self-affine cascades of beat-to-beat fluctuations revealed by wavelet decomposition at different time scales. We then describe very recent work that quantifies multifractal features in these cascades, and the discovery that the multifractal structure of healthy dynamics is lost with congestive heart failure. The analytic tools we discuss may be used on a wide range of physiologic signals.

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Mental or cognitive brain functions, and the effect on them of abnormal psychiatric diseases, are difficult to approach through molecular biological techniques due to the lack of appropriate assay systems with objective measures. We therefore study laws of behavioral organization, specifically how resting and active periods are interwoven throughout daily life, using objective criteria, and first discover that identical laws hold both for healthy humans subject to the full complexity of daily life, and wild-type mice subject to maximum environmental constraints. We find that active period durations with physical activity counts successively above a predefined threshold, when rescaled with individual means, follow a universal stretched exponential (gamma-type) cumulative distribution, while resting period durations below the threshold obey a universal power-law cumulative distribution with identical parameter values for both of the mammalian species. Further, by analyzing the behavioral organization of mice with a circadian clock gene (Period2) eliminated, and humans suffering from major depressive disorders, we find significantly lower parameter values (power-law scaling exponents) for the resting period durations in both these cases. Such a universality and breakdown of the behavioral organization of mice and humans, revealed through objective measures, is expected to facilitate the understanding of the molecular basis of the pathophysiology of neurobehavioral diseases, including depression, and lay the foundations for formulating a range of neuropsychiatric behavioral disorder models.