Synchronization of the Processes of Autonomic Control of Blood Circulation in Humans Is Different in the Awake State and in Sleep Stages

FIGURE 1. A simplified schematic illustration of the study.

FIGURE 2. Schematic illustration of the method for estimating the total percentage S of phase synchronization. (A) ECG signal; (B) RR-intervals. Dots show experimental values of RR-intervals, interpolation by cubic β-splines is shown by a line; (C) the BP signal; (D) the power spectrum of the RR-interval signal; (E) power spectrum of the blood pressure signal. The bandwidth of the bandpass filters is marked in pink and blue on the power spectra graphs; (F) signals of RR-intervals and blood pressure filtered in the LF-band and normalized to unity amplitude; (G) instantaneous phases of the filtered signals of RR-intervals and blood pressure; (H) the instantaneous phases difference of the signals and an illustration of the automatic procedure for finding the epochs of synchronization. Orange bracket marks a window sliding along the time series Δϕ(t) with a shift of 1 discrete sample. w is the sliding window width. The orange line is a linear approximation of the time series Δϕ(t) in every sliding window. αi is the slope of the approximating line in ith sliding window. α0 is the method parameter, maximum slope angle, dj is the length of jth epoch of synchronization. Parameter L has the meaning…

FIGURE 3. Experimental signals, their Fourier power spectra and the difference of instantaneous phases for the subject No. 1 (No. C04Z1N2) in the awake state (first column), NREM sleep (second column), and REM sleep (third column). (A–C) ECG signals; (D–F) RR-intervals. Experimental values are shown with dots and interpolation by cubic β-splines is shown with line; (G–I) BP signals; (J–L) Fourier power spectra of RR-intervals; (M–O) Fourier power spectra of BP signals. The bandpass of filtering is shown in the power spectra plots in pink and blue; (P–R) Phase differences. Epochs of phase synchronization are shown in yellow.

FIGURE 4. (A) S values in the awake state, NREM sleep, and REM sleep for each of the subjects. Statistically insignificant S values are shown with white squares and white triangles. (B) Distribution function for S. (C) Box-and-whisker diagrams for S values in the awake state, NREM sleep, and REM sleep. The box boundaries are the first and third quartiles, the horizontal line is the median, the whiskers are the minimum and maximum values. Figures (B,C) include only statistically significant S values (p < 0.05). The asterisks in panel (C) correspond to the p-level of intergroup differences, assessed using the Mann-Whitney U-test: p= 0.01 for “*” and “**” and p< 0.01 for “***”.

FIGURE 5. ROC curves for classifying the awake state and sleep stages. TPR is true positive rate and FPR is false positive rate. (A) REM and awake state. (B) REM and NREM. (C) NREM and awake state. The diagonal line is shown with black dashed line. Put off point is marked with colored dots.