Sleep Stage-Based Threshold Circles

Long sleep deprivation may cause brain sleep or hallucinations while a person seems awake. In such cases, drowsiness can instantly lead the human brain through various sleep stages (Craik et al., 2019; Ko et al., 2020). Moreover, in such a condition of drowsiness, if the brain is being forced to focus, then it can result in frequent state changeovers between wakefulness and sleep stages, for example, repetitively nodding off while driving in a drowsy state. Drowsiness is interrelated with sleep in terms of physical symptoms and effects on human brain hemodynamics. Sleep stages are NREM sleep and rapid eye movement (REM) sleep. NREM has further three stages: N1, N2, and N3 representing light sleep, medium sleep, and deep sleep, respectively (Ahn et al., 2016; Oniz et al., 2019). The sleep cycle starts when wakefulness is followed by NREM stages and REM sleep (Van Wyk et al., 2019; Chi et al., 2020). The main feature of drowsiness is slow rolling eye movements (SREM), which are associated with the N1 stage or light sleep. fNIRS studies have investigated brain hemodynamics during various sleep stages and discussed CORE dynamics related to sleep (Oniz et al., 2019). It is conceived that there is a relationship between hemodynamics of sleep stages and W. If CORE dynamics of W is known, then CORE of sleep stages can be deduced from it according to a somewhat fixed relationship as shown in (10). Mean CORE status during W of any subject can be accessed by collecting |R| of fNIRS brain signal for a specific duration and taking its mean. Mean |R| of NREM sleep stages can be deduced from mean |R| of W stage according to the following relationships.

where |RK|¯ represents |RW|¯,|RN⁢1|¯,|RN⁢2|¯,|RN⁢3|¯, which are the sample means of phase diagram vectors’ magnitude for W, N1, N2, and N3, stages, respectively; and n is the number of samples used for mean values computation from the respective sample spaces.

Eqs. (9, 10) give the radii of threshold circles for W and NREM stages in the vector phase diagram as shown in Figure 4. These threshold circles along with the VPA diagram are employed to detect drowsiness activity when the fNIRS brain signal trajectory follows a specific pattern according to CORE states. Eq. (9) is evaluated for all eight channels of right DPFC for each subject with sample space spanning over 5 min of W state. Once |RW|¯ is obtained, Eq. (10) is evaluated for all channels of each subject to obtain |RN⁢1|¯,|RN⁢2|¯,|RN⁢3|¯.

Threshold circles of wakefulness and non-rapid eye movement (NREM) sleep stages employed for drowsiness detection and sleep stage classification, obtained from Eqs. (9, 10).