Effect of nonlinearity on coupling estimations between oscillators using partial directed coherence approach

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The aim of this study is to compare experimental data on sleep dynamics in healthy volunteers with the results of mathematical modeling of circadian rhythm and sleep cycles, and also to examine the variability of certain characteristics of sleep cycles across different chronotypes. Methods. The study analyzed nocturnal polysomnographic recordings of 103 healthy volunteers divided into early, intermediate, and late chronotype groups. The recording included 19 EEG channels according to the 10–20 system, ECG, photoplethysmogram, electrooculogram, electromyogram, and respiratory signals. Sleep staging was performed by a certified somnologist; sleep cycles with an average duration of 90–110 min were identified within the recordings. To analyze oscillatory EEG activity, a continuous wavelet transform based on the Morlet wavelet was used, and normalized instantaneous energy was calculated in frequency bands corresponding to δ, θ, μ, α, β1, β2 and γ rhythms. NREM sleep intensity was assessed by the power of slow oscillatory EEG activity, while REM density was assessed by the average number of saccades in 10-s intervals. Heart rate variability was assessed from ECG/PPG using a continuous rhythm estimation method based on skeleton analysis of the wavelet transform. Statistical differences were assessed using the Mann–Whitney test with Bonferroni correction for three groups. The mathematical model described AWAKE/NREM/REM state transitions based on the dynamics of a Duffing oscillator under external noise, the intensity of which was modulated by the degree of phase synchronization of coupled Rossler systems. Results. Time-frequency EEG analysis revealed statistically significant differences between early and late chronotypes in the pre-awakening sleep cycle for low-frequency bands: δ oscillation intensity was less than 0.05 in the early chronotype and more than 0,05 in the late chronotype; a similar pattern persisted for the 4–8, 8–12, and 12–20 Hz bands. NREM sleep intensity decreased from the first cycle to the last, while REM intensity increased. In individuals with the early chronotype, a decrease in NREM intensity in the pre-awakening hours was noted compared with the late chronotype. Maximum heart rate variability was observed in the first cycle in the early chronotype, and in the intermediate chronotype in the third cycle. The mathematical model allows phenomenological reproduction of reference hypnograms, AWAKE/NREM/REM transitions, and the characteristic decrease in NREM duration and increase in REM before awakening. Conclusion. The proposed nonlinear dynamic model reproduces key patterns of sleep dynamics. The observed inter-chronotype differences can be interpreted through synchronization and noise parameters. The obtained results can be used for personalized assessment of the state of sleep regulatory systems and further improvement of mathematical models of the wake–sleep cycle.