Characterizing sleep stages through the complexity-entropy plane in human intracranial data and in a whole-brain model

TL;DR

This work uses weighted permutation entropy $\mathrm{WPE}$ and statistical complexity $\mathrm{SCM}$ to map human sleep stages onto the complexity–entropy plane, revealing distinct regions for Wake, REM, N2, and N3 in intracranial EEG data. A data-driven analysis identifies an optimal embedding delay of $\tau = 10$ corresponding to $50\,\mathrm{ms}$ that maximizes separation between states, and findings are validated at global, subject, and single-channel levels. The authors introduce a whole-brain mean-field AdEx network constrained by human connectomes and neuromodulatory-adaptation dynamics, demonstrating that increasing adaptation from $40$ to $95$ pA reproduces the empirical transitions across sleep stages. An SVM classifier trained on windowed $\mathrm{WPE}$ and $\mathrm{SCM}$ achieves $92.25\%$ accuracy on empirical data and $88.79\%$ when generalized to simulated data, highlighting the practical potential for interpretable, data-driven sleep staging and clinical translation.

Abstract

Characterizing the brain dynamics during different cortical states can reveal valuable information about its patterns across various cognitive processes. In particular, studying the differences between awake and sleep stages can shed light on the understanding of brain processes essential for physical and mental well-being, such as memory consolidation, information processing, and fatigue recovery. Alterations in these patterns may indicate disorders and pathologies such as obstructive sleep apnea, narcolepsy, as well as Alzheimer's and Parkinson's diseases. Here, we analyze time series obtained from intracranial recordings of 106 patients, covering four sleep stages: Wake, N2, N3, and REM. Intracranial electroencephalography (iEEG), which can include electrocorticography (ECoG) and depth recordings, represents the state-of-the-art measurements of brain activity, offering unparalleled spatial and temporal resolution for investigating neural dynamics. We characterize the signals using Bandt and Pompe symbolic methodology to calculate the Weighted Permutation Entropy (WPE) and the Statistical Complexity Measure (SCM) based on the Jensen and Shannon disequilibrium. By mapping the data onto the complexity-entropy plane, we observe that each stage occupies a distinct region, revealing its own dynamic signature. We show that our empirical results can be reproduced by a whole-brain computational model, in which each cortical region is described by a mean-field formulation based on networks of Adaptive Exponential Integrate-and-Fire (AdEx) neurons, adjusting the adaptation parameter to simulate the different sleep stages. Finally, we show that a classification approach using Support Vector Machine (SVM) provides high accuracy in distinguishing between cortical states.

Figures (8)

• Figure 1: Illustration of the Bandt-Pompe methodology for transforming a time series into a probability distribution using a symbolic approach. (a) Representative time series. (b) Segmentation process for $D = 3$. (c) The six possible permutation patterns, where $N = D!$. (d) Probability distribution corresponding to the permutation patterns and their associated weights.
• Figure 2: Representative time series of sleep stages. (a) Five-second segment of the average signal across all channels, including the mean (solid line) and standard deviation (shaded area) for each of the four sleep stages. (b) Five-second segment showing the mean (solid line) and standard deviation (shaded area) of the electrical signals across all channels from a single participant (patient 47), also for the four studied stages. (c) Five-second segment of the signal from an individual channel (channel 297) across the same sleep stages, illustrating the similarity between the average and individual dynamics.
• Figure 3: Location of the 1,012 intracranial channels. The colors represent different brain lobes: occipital (light purple), parietal (light blue), insula (light orange), frontal (light green), and temporal (light red).
• Figure 4: Variation of (a) Weighted Permutation Entropy (WPE) and (b) Statistical Complexity Measure (SCM) as a function of the embedding delay $\tau$, reflecting different temporal resolutions of the mean iEEG signal obtained from the 1,012 recording channels. Values of $\tau$ range from 1 (5 ms) to 100 (500 ms). The four curves correspond to the canonical brain states—Wake, N2, N3, and REM. The dashed vertical line marks $\tau = 10$ (50 ms), the timescale at which the separation between brain states is maximal and used in subsequent analyses.
• Figure 5: Projection of brain states onto the complexity–entropy (SCM$\times$WPE) plane for $\tau = 10$. (a) Group-level projection based on the average signal across all 1,012 iEEG channels, showing that each sleep stage occupies a distinct region following the sequence Wake, REM, N2, and N3, with entropy decreasing and complexity increasing along the sleep–wake cycle. (b) Subject-level projection for the individual with the highest number of valid channels (subject 47), where the same ordered distribution of brain states is preserved, demonstrating the consistency of the pattern across subjects. (c) Projection for a representative single channel (channel 297), revealing that the same structured organization of brain states observed at the group and individual levels is maintained even at the local scale.