Fundamentals of sleep regulation: Model and benchmark values for fractal and oscillatory neurodynamics.

Homeostatic, circadian and ultradian mechanisms play crucial roles in the regulation of sleep. Evidence suggests that ratios of low-to-high frequency power in the electroencephalogram (EEG) spectrum indicate the instantaneous level of sleep pressure, influenced by factors such as individual sleep-wake history, current sleep stage, age-related differences and brain topography characteristics. These effects are well captured and reflected in the spectral exponent, a composite measure of the constant low-to-high frequency ratio in the periodogram, which is scale-free and exhibits lower interindividual variability compared to slow wave activity, potentially serving as a suitable standardization and reference measure. Here we propose an index of sleep homeostasis based on the spectral exponent, reflecting the level of membrane hyperpolarization and/or network bistability in the central nervous system in humans. In addition, we advance the idea that the U-shaped overnight deceleration of oscillatory slow and fast sleep spindle frequencies marks the biological night, providing somnologists with an EEG-index of circadian sleep regulation. Evidence supporting this assertion comes from studies based on sleep replacement, forced desynchrony protocols and high-resolution analyses of sleep spindles. Finally, ultradian sleep regulatory mechanisms are indicated by the recurrent, abrupt shifts in dominant oscillatory frequencies, with spindle ranges signifying non-rapid eye movement and non-spindle oscillations - rapid eye movement phases of the sleep cycles. Reconsidering the indicators of fundamental sleep regulatory processes in the framework of the new Fractal and Oscillatory Adjustment Model (FOAM) offers an appealing opportunity to bridge the gap between the two-process model of sleep regulation and clinical somnology.

Scale-free and oscillatory spectral measures of sleep stages in humans.

Power spectra of sleep electroencephalograms (EEG) comprise two main components: a decaying power-law corresponding to the aperiodic neural background activity, and spectral peaks present due to neural oscillations. "Traditional" band-based spectral methods ignore this fundamental structure of the EEG spectra and thus are susceptible to misrepresenting the underlying phenomena. A fitting method that attempts to separate and parameterize the aperiodic and periodic spectral components called "fitting oscillations and one over f" (FOOOF) was applied to a set of annotated whole-night sleep EEG recordings of 251 subjects from a wide age range (4-69 years). Most of the extracted parameters exhibited sleep stage sensitivity; significant main effects and interactions of sleep stage, age, sex, and brain region were found. The spectral slope (describing the steepness of the aperiodic component) showed especially large and consistent variability between sleep stages (and low variability between subjects), making it a candidate indicator of sleep states. The limitations and arisen problems of the FOOOF method are also discussed, possible solutions for some of them are suggested.

A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks.

The combination of network sciences, nonlinear dynamics and time series analysis provides novel insights and analogies between the different approaches to complex systems. By combining the considerations behind the Lyapunov exponent of dynamical systems and the average entropy of transition probabilities for Markov chains, we introduce a network measure for characterizing the dynamics on state-transition networks with special focus on differentiating between chaotic and cyclic modes. One important property of this Lyapunov measure consists of its non-monotonous dependence on the cylicity of the dynamics. Motivated by providing proper use cases for studying the new measure, we also lay out a method for mapping time series to state transition networks by phase space coarse graining. Using both discrete time and continuous time dynamical systems the Lyapunov measure extracted from the corresponding state-transition networks exhibits similar behavior to that of the Lyapunov exponent. In addition, it demonstrates a strong sensitivity to boundary crisis suggesting applicability in predicting the collapse of chaos.