## 4 Discussion and Conclusions  
In the work of this paper, we investigated the statistical properties of the overnight EEG data in obstructive apnea patients. One of the main findings is that the brain activity asymmetry intends to get worse with the severity of sleep-disordered breathing for obstructive sleep apnea patients. Some \begin{table}
\begin{tabular}{c c} \hline \hline
**Factors** & \(p\) \\ \hline Sleep Stages & 0.0012 \\ Groups & 0.0006 \\ Sleep Stages \({}^{*}\)Groups & 0.1106 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Test of two-way ANOVA. Figure 7: Boxplot of switching rate for three Groups. interpretations of this finding include that sleep-disordered breathing is always accompanied by neural injuries, and this kind of damage is preferentially unilateral. Injured structures include brain regions involved in hormone release and major neurotransmitter activity. This damage is reflected in a series of structural magnetic resonance procedures and also as a functional distortion of the evoked activity in the brain that regulates important autonomic and respiratory functions [46]. Besides, another finding implies that the fuzzy entropy features during wake state are much bigger than the other three sleep stages, and deep sleep shows the smallest fuzzy entropy while light sleep is only smaller than that of wake state. In addition, in terms of the four sleep stages, REM shows the highest mean switching rate while deep sleep shows the lowest. Existing work reported that the REM stage showed close coordination of the electrical manifestations of activity of the two hemispheres [47]. The REM stage is a kind of heterogeneous sleep because it is very similar to the wake state. Although the body is paralyzed, the brain is somewhat awake in some respects. EEG during the REM stage often shows faster neural oscillations that are different from Delta waves in deep sleep, more similar to patterns in wake state. During the REM stage, the neuronal state of the cerebral cortex and thalamus is more depolarized than other sleep stages, which means that it is more likely to be excited. As a result, the switching between the left and right hemispheres of the brain during REM sleep will be more. Similar study was presented in [48], they reported that switching was found in all sleep stages, and variation in left-right switch rate (Hz) was observed during W (0.076-0.084), light sleep (0.073-0.088), deep sleep (0.082-0.094) and REM sleep (0.082-0.090). In comparison, our results showed more distinct differences among sleep stages and thus could be used for stage scoring. At the same time, we should also point out the main limitation of this study, which we will focus on improving in the future. Since there is only 1 healthy subject (ucddb018, AHI = 2) in the applied database, we simply included it in group A, i.e., mild obstructive sleep apnea, and thus there is no control group in this study. Still, the current conclusions were still trustworthy because we mainly focus on interhemispheric switching correlates with the severity of sleep-disordered breathing which gets worse from Group A to Group C. In our future work, on the one hand, we would include a control group of adequate healthy subjects, and on the other hand, bipolar montage C3/C4 would be applied instead of unipolar C3 and C4, since relative changes may provide better reliability for characterizing the differences, and laterality analysis. As a conclusion, alternating interhemispheric brain activity during sleep is investigated for obstructive sleep apnea patients. Our main work focuses on characterising inter-individual variation in brain switching activity, examining the relationship between such switching activity and subjects' apnoea-hypopnoea index (AHI), and exploring the differences in brain switching in subjects with sleep-disordered breathing during different sleep states.