Compensatory mechanisms of reduced interhemispheric EEG connectivity during sleep in patients with apnea

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  Figure 1. (a, b) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {\tau }^{SS}$$\end{document}ΔτSS—changes of relative time durations τ for each stage of PSG monitoring from the first to the second recording session of patients in Groups I and II, respectively. The following states are shown: AW—staying awake; sleep stages N1, N2, N3 and REM. Changes are shown as a percentage. The diagrams depict the following statistical characteristics of numerical indicators: the first and third quartiles (25–75%, inside the box); the median and the mean (transverse line and point inside the box, respectively); 1.5 interquartile ranges (shown by whiskers); and outliers represented by asterisks.

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  Figure 2. Statistical characteristics of the relative durations of each stage,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\left.\left\{{\tau }^{AW}; {\tau }^{N1}; {\tau }^{N2}; {\tau }^{N3}; {\tau }^{REM}\right\}\right|}_{R1+R2}$$\end{document}τAW;τN1;τN2;τN3;τREMR1+R2, defined for the first and second PSG records, averaged for Groups I (apparently healthy test subjects, in blue) and II (OSA patients, in red). Relative durations of stages are shown as a percentage of the total duration of the corresponding record. The diagrams depict the following statistical characteristics of numerical indicators: the first and third quartiles (25–75%, inside the box); the median and the mean (transverse line and point inside the box, respectively); 1.5 interquartile ranges (denoted by whiskers); and outliers represented by asterisks.

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  Figure 3. Distributions of the interhemispheric connectivity strength, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho \left({\mathrm{WB}}_{{\mathrm{EEG}}_{i},{\mathrm{EEG}}_{j}}^{{\Delta f}_{1}}\right),$$\end{document}ρWBEEGi,EEGjΔf1, for the frequency band \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta f}_{1}$$\end{document}Δf1: (a) EEG channels O1 and O2, (b) EEG channels C3 and C4, (c) EEG channels Fp1 and Fp2. The y-axis corresponds to the magnitude of the connection strength from zero to one. The surface color corresponds to the value of the frequency of occurrence of each of the values of the connection strength between the corresponding EEG channels, where the red color corresponds to the maximum value of the WB distribution density, while the dark blue color corresponds to the minimum value. For each pair of…

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  Figure 4. Distributions of the intrahemispheric connectivity strength, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho \left({\mathrm{WB}}_{{\mathrm{EEG}}_{i},{\mathrm{EEG}}_{j}}^{{\Delta f}_{k}}\right)$$\end{document}ρWBEEGi,EEGjΔfk: (a) EEG channels Fp1 and C3, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {f}_{3}$$\end{document}Δf3; (b) EEG channels Fp1 and O1, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {f}_{4}$$\end{document}Δf4; (c) EEG channels Fp1 and O1, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

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  Figure 5. Diagrams of differences in synchronization levels for the frequency bands ∆f1–∆f7 assessed during the first and second nights of PSG records. Each set of diagrams is presented for a specific pair of EEG channels, the standard notations of which are indicated on the top. The gray background shows the range of differences in synchronization estimates for the first and second nights within [−0.1; 0.1]. Diagrams in blue and red represent calculation results for Groups I and II, correspondingly.

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  Figure 6. Distribution diagrams for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left. {\Delta \left( {\left\langle {{\text{WB}}_{{{\text{EEG}}_{i} ,{\text{EEG}}_{j} }}^{{\Delta f_{k} }} } \right\rangle } \right)} \right|_{{{\text{stage}} - 1,2}}$$\end{document}ΔWBEEGi,EEGjΔfkstage-1,2 calculated for stages of NREM sleep (N1, N2, N3), REM sleep, and arousal wakefulness. For each set of diagrams, a pair of channels for which the calculation was performed is indicated. The gray background depicts the range of differences in synchronization estimates for the first and second nights within [−0.1; 0.1]. The calculation results for Groups I and II are coded in blue and red, respectively.

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  Figure 7. Graphical diagrams of mean connectivity strength values between various EEG channels. The connectivity strength is color-coded according to the legend on the right. The frequency bands ∆f1–∆f7 are labeled in the middle of the figure against a gray background. The connectivity patterns in the groups of healthy participants and OSA patients are shown above and below, respectively.

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  Figure 8. (a–c) Distributions of connectivity strength, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\langle {{\text{WB}}_{i,j}^{{\Delta f_{k} }} } \right\rangle^{{{\text{I}},{\text{ II}}}}$$\end{document}WBi,jΔfkI,II, in Groups I (blue) and II (red) for interhemispheric connections: among frontal leads (Fp1 and Fp2), central leads (C3 and C4), and occipital leads (O1 and O2), respectively. (d) Arrangement of EEG channels and interhemispheric connections. Interpretation of the symbols used in diagrams.

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  Figure 9. (a–d) Distributions of connectivity strength, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\langle {{\text{WB}}_{i,j}^{{\Delta f_{k} }} } \right\rangle^{{{\text{I}},{\text{ II}}}}$$\end{document}WBi,jΔfkI,II, in Groups I (blue) and II (red) for interactions between EEG channels (O1 and C3, O1 and C4, O2 and C3, O2 and C4, respectively). (e) Arrangement of EEG channels and interhemispheric connections. Interpretation of the symbols used in diagrams.

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  Figure 10. (a–d) Distributions of connectivity strength, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\langle {{\text{WB}}_{i,j}^{{\Delta f_{k} }} } \right\rangle^{{{\text{I}},{\text{ II}}}}$$\end{document}WBi,jΔfkI,II, in Groups I (blue) and II (red) for interactions between EEG channels O1 and Fp1, O1 and Fp2, O2 and Fp1, O2 and Fp2, respectively. (e) Arrangement of EEG channels and interhemispheric connections. Interpretation of the symbols used in diagrams.

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  Figure 11. (a–d) Distributions of connectivity strength, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\langle {{\text{WB}}_{i,j}^{{\Delta f_{k} }} } \right\rangle^{{{\text{I}},{\text{ II}}}}$$\end{document}WBi,jΔfkI,II, in Groups I (blue) and II (red) for interactions between EEG channels C3 and Fp1, C3 and Fp2, C4 and Fp1, C4 and Fp2, respectively. (e) Arrangement of EEG channels and interhemispheric connections. Interpretation of the symbols used in diagrams.

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  Figure 12. Scheme of identified patterns in connectivity changes in Group II (OSA patients) vs. control group (Group I). Connections for which the synchronization has decreased are depicted in red. Connections with an increased synchronization are shown in blue. Connections with unchanged synchronization are marked in green. (a) Change in symmetrical interhemispheric connections; (b) change in intrahemispheric connections; (c) asymmetric interhemispheric short-distance connections; (d) asymmetric interhemispheric long-distance connections. Coupled connections in panel (c) between channels C3–O2 and C4–O1 correspond to two patterns of dynamics: a reduction in the connectivity strength in the frequency band \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta f}_{1}$$\end{document}Δf1 and stable/increased connectivity in the bands \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…