P. Ch. Ivanov

Sleep-wake differences in scaling behavior of the human heartbeat: Analysis of terrestrial and long-term space flight data

We compare scaling properties of the cardiac dynamics during sleep and wake periods for healthy individuals, cosmonauts during orbital flight, and subjects with severe heart disease. For all three groups, we find a greater degree of anticorrelation in the heartbeat fluctuations during sleep compared to wake periods. The sleep-wake difference in the scaling exponents for the three groups is comparable to the difference between healthy and diseased individuals. The observed scaling differences are not accounted for simply by different levels of activity, but appear related to intrinsic changes in the neuroautonomic control of the heartbeat.

Dynamics of sleep-wake transitions during sleep

We study the dynamics of the awakening during the night for healthy subjects and find that the wake and the sleep periods exhibit completely different behavior: the durations of wake periods are characterized by a scale-free power law distribution, while the durations of sleep periods have an exponential distribution with a characteristic time scale. We find that the characteristic time scale of sleep periods changes throughout the night. In contrast, there is no measurable variation in the power law behavior for the durations of wake periods. We develop a stochastic model which agrees with the data and suggests that the difference in the dynamics of sleep and wake states arises from the constraints on the number of microstates in the sleep-wake system.

Application of statistical physics to heartbeat diagnosis

We present several recent studies based on statistical physics concepts that can be used as diagnostic tools for heart failure. We describe the scaling exponent characterizing the long-range correlations in heartbeat time series as well as the multifractal features recently discovered in heartbeat rhythm. It is found that both features, the long-range correlations and the multifractility, are weaker in cases of heart failure.

Scale invariance and universality: organizing principles in complex systems

This paper is a brief summary of a talk that was designed to address the question of whether two of the pillars of the field of phase transitions and critical phenomena – scale invariance and universality – can be useful in guiding research on a broad class of complex phenomena. We shall see that while scale invariance has been tested for many years, universality is relatively more rarely discussed. In particular, we shall develop a heuristic argument that serves to make more plausible the universality hypothesis in both thermal critical phenomena and percolation phenomena, and suggest that this argument could be developed into a possible coherent approach to understanding the ubiquity of scale invariance and universality in a wide range of complex systems.

Steady-State Visual Evoked Potentials and Phase Synchronization in Migraine Patients

We investigate phase synchronization in EEG recordings from migraine patients. We use the analytic signal technique, based on the Hilbert transform, and find that migraine brains are characterized by enhanced alpha band phase synchronization in the presence of visual stimuli. Our findings show that migraine patients have an overactive regulatory mechanism that renders them more sensitive to external stimuli.

The suprachiasmatic nucleus functions beyond circadian rhythm generation.

We recently discovered that human activity possesses a complex temporal organization characterized by scale-invariant/self-similar fluctuations from seconds to approximately 4 h-(statistical properties of fluctuations remain the same at different time scales). Here, we show that scale-invariant activity patterns are essentially identical in humans and rats, and exist for up to approximately 24 h: six-times longer than previously reported. Theoretically, such scale-invariant patterns can be produced by a neural network of interacting control nodes-system components with feedback loops-operating at different time scales. However such control nodes have not yet been identified in any neurophysiological model of scale invariance/self-similarity in mammals. Here we demonstrate that the endogenous circadian pacemaker (suprachiasmatic nucleus; SCN), known to modulate locomotor activity with a periodicity of approximately 24 h, also acts as a major neural control node responsible for the generation of scale-invariant locomotor patterns over a broad range of time scales from minutes to at least 24 h (rather than solely at approximately 24 h). Remarkably, we found that SCN lesion in rats completely abolished the scale-invariant locomotor patterns between 4 and 24 h and significantly altered the patterns at time scales <4 h. Identification of the control nodes of a neural network responsible for scale invariance is the critical first step in understanding the neurophysiological origin of scale invariance/self-similarity.

Scaling and universality in heart rate variability distributions

We find that a universal homogeneous scaling form describes the distribution of cardiac variations for a group of healthy subjects, which is stable over a wide range of time scales. However, a similar scaling function does not exist for a group with a common cardiopulmonary instability associated with sleep apnea. Subtle differences in the distributions for the day- and night-phase dynamics for healthy subjects are detected.

Scaling in nature: from DNA through heartbeats to weather

The purpose of this report is to describe some recent progress in applying scaling concepts to various systems in nature. We review several systems characterized by scaling laws such as DNA sequences, heartbeat rates and weather variations. We discuss the finding that the exponent alpha quantifying the scaling in DNA in smaller for coding than for noncoding sequences. 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. We also discuss the recent findings that suggest a universal scaling exponent characterizing the weather fluctuations.

Stratification Pattern of Static and Scale-Invariant Dynamic Measures of Heartbeat Fluctuations Across Sleep Stages in Young and Elderly

Cardiac dynamics exhibit complex variability characterized by scale-invariant and nonlinear temporal organization related to the mechanism of neuroautonomic control, which changes with physiologic states and pathologic conditions. Changes in sleep regulation during sleep stages are also related to fluctuations in autonomic nervous activity. However, the interaction between sleep regulation and cardiac autonomic control remains not well understood. Even less is known how this interaction changes with age, as aspects of both cardiac dynamics and sleep regulation differ in healthy elderly compared to young subjects. We hypothesize that because of the neuroautonomic responsiveness in young subjects, fractal and nonlinear features of cardiac dynamics exhibit a pronounced stratification pattern across sleep stages, while in elderly these features will remain unchanged due to age-related loss of cardiac variability and decline of neuroautonomic responsiveness. We analyze the variability and the temporal fractal organization of heartbeat fluctuations across sleep stages in both young and elderly. We find that independent linear and nonlinear measures of cardiac control consistently exhibit the same ordering in their values across sleep stages, forming a robust stratification pattern. Despite changes in sleep architecture and reduced heart rate variability in elderly subjects, this stratification surprisingly does not break down with advanced age. Moreover, the difference between sleep stages for some linear, fractal, and nonlinear measures exceeds the difference between young and elderly, suggesting that the effect of sleep regulation on cardiac dynamics is significantly stronger than the effect of healthy aging. Quantifying changes in this stratification pattern may provide insights into how alterations in sleep regulation contribute to increased cardiac risk.

Scale-invariant truncated Lévy process

We develop a scale-invariant truncated Levy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits Levy stability for the distribution, and hence shows scaling properties as commonly observed in empirical data; it has the advantage that all moments are finite and so accounts for the empirical scaling of the moments. To test the potential utility of the STL process, we analyze financial data.