Abstract
In clinical practice, human sleep is classified into stages, each associated with different levels of muscular activity and marked by characteristic patterns in the EEG signals. It is however unclear whether this subdivision into discrete stages with sharply defined boundaries is truly reflecting the dynamics of human sleep. To address this question, we consider one-channel EEG signals as heterogeneous random walks: stochastic processes controlled by hyper-parameters that are themselves time-dependent. We first demonstrate the heterogeneity of the random process by showing that each sleep stage has a characteristic distribution and temporal correlation function of the raw EEG signals. Next, we perform a super-statistical analysis by computing hyper-parameters, such as the standard deviation, kurtosis, and skewness of the raw signal distributions, within subsequent 30-second epochs. It turns out that also the hyper-parameters have characteristic, sleep-stage-dependent distributions, which can be exploited for a simple Bayesian sleep stage detection. Moreover, we find that the hyper-parameters are not piece-wise constant, as the traditional hypnograms would suggest, but show rising or falling trends within and across sleep stages, pointing to an underlying continuous rather than sub-divided process that controls human sleep. Based on the hyper-parameters, we finally perform a pairwise similarity analysis between the different sleep stages, using a quantitative measure for the separability of data clusters in multi-dimensional spaces.
Highlights
In clinical practice, human sleep is classified into stages, each associated with different levels of muscular activity and marked by characteristic patterns in the EEG signals
We find that the amplitude distributions ps(y) are non-Gaussian and clearly leptocurtic for all sleep stages—an anomaly that is frequently found in complex systems with super-statistical parameter changes[18]
In contrast to a stationary, temporally homogeneous random walk, where the parameter STE could be regarded as fixed, we find in our case rather wide distributions that clearly differ between the sleep stages
Summary
Human sleep is classified into stages, each associated with different levels of muscular activity and marked by characteristic patterns in the EEG signals. In simple physical systems, state variables fluctuate around a fixed mean value and with a fixed variance (as in the case of local pressure variations in a gas at equilibrium), complex systems often have multiple dynamical attractors[4], i.e., a set of qualitatively different modes of behavior, between which the system will occasionally switch. Such transitions typically show up in the time series by a sudden (or gradual) change of the statistical properties of the fluctuating state variables. The momentary amplitudes of an N-channel EEG recording represent a point in an N-dimensional state space and the ongoing time series of vectorial amplitudes defines a random walk within this high-dimensional space
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
