Our study presents the results of investigating the synchronization of brain activity in two groups of volunteers: control group (Group I) consisting of healthy participants of different ages and Group II including OSA patients. Standard high-quality PSG records were selected from the SIESTA database46,47. Test subjects were chosen to minimize the impact of comorbid diseases and complications related to physical and mental distress. The database included two PSG records for each participant, which made it possible to assess not only intraindividual, but also interindividual robustness in patterns of brain activity.
Staging of nocturnal sleep in the first and second records
The assessment of \(\Delta {\tau }^{SS}\) changes in the duration of sleep stages in patients revealed no statistically significant differences between groups I and II (Fig. 1). At the second monitoring session, Group I patients increased the duration of their N3 stage of deep sleep; whereas in patients of Group II, on average, the duration of all sleep stages slightly increased. Besides, Group II patients were waking up less frequently on the second overnight monitoring. Also, we observed the highest variability of N2 stage in patients with sleep apnea.
(a, b) \(\Delta {\tau }^{SS}\)—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.
Figure 2 presents the statistical characteristics of the relative durations of each stage, \(\left. {\left\{ {\tau^{AW} ;\;\tau^{N1} ;\;\tau^{N2} ;\;\tau^{N3} ;\;\tau^{REM} } \right\}} \right|_{R1 + R2}\), defined in the first and second PSG records. It is clearly seen that the duration of sleep stages and of nocturnal wakefulness for Groups I and II are quite homogeneous and do not differ statistically from each other. Overall, the sleep structure in patients of both groups is similar.
Statistical characteristics of the relative durations of each stage,\({\left.\left\{{\tau }^{AW}; {\tau }^{N1}; {\tau }^{N2}; {\tau }^{N3}; {\tau }^{REM}\right\}\right|}_{R1+R2}\), 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.
Based on comparable dynamics and statistically similar distributions of nocturnal stage durations during the first and second PSG monitoring sessions, we will further analyze the connectivity characteristics of brain activity without dividing them between the first and second nights.
EEG connectivity strength distribution
The distributions of interhemispheric connections, \(\rho \left({\mathrm{WB}}_{{\mathrm{EEG}}_{i},{\mathrm{EEG}}_{j}}^{{\Delta f}_{k}}\right)\), are described by a complex structure of the connection strength dynamics during the first and second nights of monitoring sessions. Furthermore, they are described by the distribution range rather than only by the mean\median and maximum values. Figure 3 shows typical shapes of such distributions for the interhemispheric connectivity strength. The distributions \(\rho \left({\mathrm{WB}}_{i,j}^{{\Delta f}_{1}}\right),\) lined up by the ordinal numbers of the subjects, demonstrate a high degree of robustness of the functional connectivity for the first and second PSG monitoring sessions of each participant. In addition, the average level of \(\rho \left({\mathrm{WB}}_{i,j}^{{\Delta f}_{1}}\right)\) for the interhemispheric connections significantly increases in apparently healthy individuals against the background of patients with apnea (on the right of the diagrams in Fig. 3).
Distributions of the interhemispheric connectivity strength, \(\rho \left({\mathrm{WB}}_{{\mathrm{EEG}}_{i},{\mathrm{EEG}}_{j}}^{{\Delta f}_{1}}\right),\) for the frequency band \({\Delta f}_{1}\): (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 channels, a scale of connection strength values is given. At the bottom, alternating black and gray arrows I and II indicate the first and second PSG monitoring sessions for each patient. At the top of the graphs, the serial numbers of patients are shown. Group I patients are coded in blue, while Group II subjects are listed in red.
Similar distributions of the connectivity strength, \(\rho \left({\mathrm{WB}}_{{\mathrm{EEG}}_{i},{\mathrm{EEG}}_{j}}^{{\Delta f}_{k}}\right)\), for various intrahemispheric pairs of EEG channels are shown in Fig. 4. The structure of the distributions seems stationary. The maximum level of connection strength and the distribution range for nearly every patient are repeated on the first and second nights of sleep. Moreover, the general shape of probability distributions is robust for all pairs of channels in the considered frequency bands.
Distributions of the intrahemispheric connectivity strength, \(\rho \left({\mathrm{WB}}_{{\mathrm{EEG}}_{i},{\mathrm{EEG}}_{j}}^{{\Delta f}_{k}}\right)\): (a) EEG channels Fp1 and C3, \(\Delta {f}_{3}\); (b) EEG channels Fp1 and O1, \(\Delta {f}_{4}\); (c) EEG channels Fp1 and O1, \(\Delta {f}_{5}\); (d) EEG channels C3 and O1, \(\Delta {f}_{1}\), (e) EEG channels C3 and O1, \(\Delta {f}_{2}\); (f) EEG channels Fp2 and C4, \(\Delta {f}_{3}\); (g) EEG channels Fp2 and C4, \(\Delta {f}_{4}\); (h) EEG channels Fp2 and C4, \(\Delta {f}_{5}\); (i) EEG channels C4 and O2, \(\Delta {f}_{1}\); (j) EEG channels C4 and O2, \(\Delta {f}_{2}\). 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 channels, a scale of connection strength values is given. At the bottom, alternating black and gray arrows I and II indicate the first and second PSG monitoring sessions for each patient. At the top of the graphs, the serial numbers of patients are shown. Group I patients are coded in blue, while Group II subjects are listed in red.
At the same time, in patients Nos. 18 and 20, the results of the synchronization assessment between the occipital channels, show significant differences for some frequency bands, when comparing the first and second PSG records, as seen in Fig. 4d, e, i, j. This situation is typical in the analysis of biomedical signals generated by living systems; it could be caused by as technical issues regarding the recording procedure on the first and second nights of a study subject sleep, as certain individual circumstances of patients.
The graphical representation of distributions of the connectivity strength, \(\rho \left({\mathrm{WB}}_{{\mathrm{EEG}}_{i},{\mathrm{EEG}}_{j}}^{{\Delta f}_{k}}\right)\), is cumbersome and redundant. Besides, examination of the synchronization distribution does not allow a direct statistical assessment of the differences in the characteristics of the first and second nocturnal sleep sessions between Groups I (virtually healthy participants)) and II (OSA patients).
Changes of EEG connectivity strength between the first and second records
To assess the robustness of the EEG connectivity characteristics, we calculated the mean values of connectivity strength, \(\left\langle {{\text{WB}}_{{{\text{EEG}}_{i} ,{\text{EEG}}_{j} }}^{{\Delta f_{k} }} } \right\rangle_{1,2}\), over the entire duration of the first and second PSG sessions.
The results of statistical analysis of the connectivity change in EEG records, \(\left. {\Delta \left( {\left\langle {{\text{WB}}_{{{\text{EEG}}_{i} ,{\text{EEG}}_{j} }}^{{\Delta f_{k} }} } \right\rangle } \right)} \right|_{1 – 2}\), are shown in Fig. 5, the diagrams on which demonstrate the following general trends. First, the differences in the average synchronization from night to night tend to 0 without exceeding 0.1 in absolute value (i.e., they are minimal). Second, the distributions of the calculated values are close to normal, and their mean also tends to zero. Finally, outliers up to 0.2–0.3 in some frequency bands occur in the records of only one or two patients and can be due to either typical errors in the registration of biomedical signals or high individual variability within the population.
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.
The performed estimates imply a high stationarity, stability and steadiness in the oscillational structure of brain activity. This structure remains almost unchanged when analyzing two independent records of nocturnal sleep. Thus, it seems possible to pool together two PSG records in order to increase the reliability of the results.
Changes of EEG connectivity strength at different stages of polysomnography
Next, we assessed the structural robustness of electroencephalographic connectivity in brain activity directly during PSG, i.e., taking into account the resulting hypnogram and structuring the entire duration of sleep into standard stages of NREM sleep (N1, N2, N3), REM sleep, and arousal wakefulness.
For each pair of EEG channels, recorded in each study participant, we measured a changes in the connectivity strength at a certain PSG stage, relative to the average overnight connectivity strength, \(\left\langle {{\text{WB}}_{{{\text{EEG}}_{i} ,{\text{EEG}}_{j} }}^{{\Delta f_{k} }} } \right\rangle_{{1,2}}\). Figure 6 presents statistical estimates of differences, \(\left. {\Delta \left( {\left\langle {{\text{WB}}_{{{\text{EEG}}_{i} ,{\text{EEG}}_{j} }}^{{\Delta f_{k} }} } \right\rangle } \right)} \right|_{{{\text{stage}} – 1,2}}\), calculated for some pairs of EEG channels at each stage of a hypnogram for patients in Groups I and II. Similar difference diagrams for the remaining pairs of channels are presented in Appendix I.
Distribution diagrams for \(\left. {\Delta \left( {\left\langle {{\text{WB}}_{{{\text{EEG}}_{i} ,{\text{EEG}}_{j} }}^{{\Delta f_{k} }} } \right\rangle } \right)} \right|_{{{\text{stage}} – 1,2}}\) 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.
First, the analysis of the presented diagrams allowed observing that the range of values of \(\left. {\Delta \left( {\left\langle {{\text{WB}}_{{{\text{EEG}}_{i} ,{\text{EEG}}_{j} }}^{{\Delta f_{k} }} } \right\rangle } \right)} \right|_{{{\text{N}}1,{\text{N}}2, {\text{N}}3 – 1,2}}\) for stages N1–N3 of NREM sleep was minimal, and their means belonged to the interval of [−0.05; 0.05]. Outliers of variability in N3 deep sleep were associated with a random increase in the level of variability in one study participant, while the shape of the distribution was indicative of its normality.
Then, the stage of REM sleep slightly increased the variability of the functional connectivity in electroencephalographic activity. The increase in the value of \(\left. {\Delta \left( {\left\langle {{\text{WB}}_{{{\text{EEG}}_{i} ,{\text{EEG}}_{j} }}^{{\Delta f_{k} }} } \right\rangle } \right)} \right|_{{{\text{REM}} – 1,2}}\) was more pronounced for interhemispheric connections, as seen in Fig. 6a–c. In low frequency bands, \(\left. {\Delta \left( {\left\langle {{\text{WB}}_{{{\text{EEG}}_{i} ,{\text{EEG}}_{j} }}^{{\Delta f_{k} }} } \right\rangle } \right)} \right|_{{{\text{REM}} – 1,2}}\) prevailed in OSA patients (Group II), while in high frequency bands, the effect was more noticeable in apparently healthy study participants (Group I). However, the overall variability remained low. The average values of \(\left. {\Delta \left( {\left\langle {{\text{WB}}_{{{\text{EEG}}_{i} ,{\text{EEG}}_{j} }}^{{\Delta f_{k} }} } \right\rangle } \right)} \right|_{{{\text{REM}} – 1,2}}\) did not go beyond the interval of [−0.1; 0.1].
Finally, the maximum variability was associated with arousal wakefulness. Of course, this aspect of the results was not unexpected, since the processes of enhancing participants’ response to the environment, along with activation of cognitive functions and self-awareness per se, increased individual variability in the EEG functional structure.
At the same time, the main changes in stage of arousal wakefulness were observed only in the low-frequency bands of delta and theta oscillations. For all considered pairs of EEG channels, we observed only slight changes of the distributions and means in the range of [−0.2; 0.2], while outliers did not exceed 0.35–0.39. So, a very interesting and surprising phenomenon was the EEG functional connectivity robustness during awakenings.
The performed analysis of changes in the EEG connectivity strength between the stages of hypnograms allows proposing that the main structure of functional connectivity in study participants at different stages of sleep remains very similar. The analysis of changes in the strength of EEG connectivity between the stages of hypnograms allows us to observe that the main structure of functional connectivity in the participants of the study at different stages of sleep remains practically unchanged. Deviations of connection strengths in each sleep stage relative to the nightly average connection strength are insignificant, mainly being in the range [−0.1; 1.0]. In other words, at any stage of sleep, deviations in the measure of synchronization, calculated from the average measure for the night, usually do not exceed 10%. Therefore, averaging the measure of synchronization over the entire duration of nocturnal sleep is not the extreme oversimplification of the situation and may be a quite adequate method for estimating the strength of connectivity between pairs of EEG channels. Consequently, the approach of pairwise estimates of EEG connectivity strength calculated over the entire duration of nocturnal sleep does not contradict results, described in this Section.
Statistical estimates of EEG connectivity strength
The calculated \(\left\langle {{\text{WB}}_{{{\text{EEG}}_{i} , {\text{EEG}}_{j} }}^{{\Delta f_{k} }} } \right\rangle\) connectivity strength means for groups I and II for all pairs of EEG channels are presented in Fig. 7. EEG activity demonstrates maximum connectivity in interhemispheric symmetrical connections (Fp1–Fp2, C3–C4, O1–O2) for the slowest oscillations (∆f1). In general, the average strength of associations in OSA patients varies more or less in all frequency bands, compared with the control group.
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.
Next, we consider in detail the statistical characteristics of changes in EEG connectivity for the Groups I and II. The consideration begins with the analysis of interhemispheric connectivity presented in Fig. 8. The strength of bilateral connections between the symmetrical channels (O1–O2, C3–C4, Fp1–Fp2) in healthy patients (Group I, shown in blue in Figs. 8, 9, 10, 11) is significantly higher than in patients with apnea (Group II, shown in red in Figs. 8, 9, 10, 11). However, the group of apparently healthy patients exhibits significant individual differences in the strength of the connectivity, and the characteristics of bilateral connections in patients with apnea are surprisingly homogeneous (i. e., they are characterized by a very small variation range), a detailed numerical analysis of which is presented in Appendix II. The values of the observed bilateral connections between Groups I and II are the highest for oscillatory processes in frequency bands \({\Delta f}_{1-5}\). They become less pronounced for the fastest processes (\({\Delta f}_{6})\).
(a–c) Distributions of connectivity strength, \(\left\langle {{\text{WB}}_{i,j}^{{\Delta f_{k} }} } \right\rangle^{{{\text{I}},{\text{ II}}}}\), 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.
(a–d) Distributions of connectivity strength, \(\left\langle {{\text{WB}}_{i,j}^{{\Delta f_{k} }} } \right\rangle^{{{\text{I}},{\text{ II}}}}\), 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.
(a–d) Distributions of connectivity strength, \(\left\langle {{\text{WB}}_{i,j}^{{\Delta f_{k} }} } \right\rangle^{{{\text{I}},{\text{ II}}}}\), 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.
(a–d) Distributions of connectivity strength, \(\left\langle {{\text{WB}}_{i,j}^{{\Delta f_{k} }} } \right\rangle^{{{\text{I}},{\text{ II}}}}\), 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.
In Fig. 9, the interaction of processes between the left occipital channel (O1) and the central channels (C3 and C4) could also be described as significantly different between the studied groups. Within one hemisphere, the strength of connectivity in the presence of apnea syndrome increases significantly, compared with apparently healthy subjects. When considering interhemispheric interaction, i.e., between channels O1 and C4, the slowest oscillatory processes in the frequency band \({\Delta f}_{1}\) are more synchronized in apparently healthy participants of Group I, and the synchronization degree of fast oscillations (\({\Delta f}_{5-6}\)) is higher in patients with apnea. The pattern of symmetrical interactions between the right occipital channel (O2) and the central channels is less diverse. In case of interhemispheric interactions (O2–C3) in the band \({\Delta f}_{1}\) in patients with apnea (Group II), the degree of synchronization decreases; however, there are no differences in the connectivity strength for higher frequencies. At the same time, within the right hemisphere, the strength of interaction (O2–C4) in Group II significantly exceeds that in Group I for all frequency bands.
As seen in Fig. 10, for the farthest distances, corresponding to the connections between the left/right occipital channels (O1/O2) and the frontal channels (Fp1/Fp2), the strength of connectivity increases with the speed of the oscillatory processes, reaching maximum values in band \({\Delta f}_{4}\). When considering the interaction of oscillatory processes in both occipital channels and the left frontal channel (Fp1), the results of the analysis of the groups do not differ statistically. For the EEG of the right frontal lead (Fp2), the values of connectivity with the signals of the occipital channels for Group II significantly exceed those for Group I in bands \({\Delta f}_{2-6}\), differing to the maximum in bands \({\Delta f}_{4-5}\).
As seen in Fig. 11, in the left hemisphere, the strengths of interaction between the oscillatory processes of the frontal lead (Fp1) and the central channel (C3) do not differ between the study participants of two groups. At the same time, when analyzing symmetrical activity in the right hemisphere (Fp2 and C4), observed in Group II (patients with apnea), the strength of interaction significantly exceeds the observed connectivity in apparently healthy participants for oscillatory processes in bands \({\Delta f}_{2-5}\). When analyzing the synchronization of interhemispheric EEG activity recorded in Fp1 and C4, as well as in Fp2 and C3, the strength of the connectivity between slow oscillatory processes in frequency bands \({\Delta f}_{1-4}\) decreases in Group II vs. Group I.