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. 2021 Sep 14;24(10):103129. doi: 10.1016/j.isci.2021.103129

Figure 2.

Figure 2

Sleep episodes are categorized as either circadian sufficient or circadian insufficient with a physiologically based mathematical model of sleep-wake cycles

(A) In the mathematical model, the homeostatic sleep pressure (black line) dissipates during sleep and increases during wake. When it becomes higher than the circadian sleep threshold (yellow solid line), a transition from wake to sleep occurs (i). When the model would naturally fall asleep in the sleep region (gray region), forced wakefulness is needed to simulate wakefulness (ii). On the other hand, when homeostatic sleep pressure falls below the circadian sleep threshold and thus the model is in the potential wake region (white region), wakefulness can be simulated without forced wakefulness (iii). When the homeostatic sleep pressure falls below the circadian wake threshold (yellow dotted line), a transition from sleep to wake actively occurs (iv). In this case, forced sleep is required to simulate sleep (v). See Figures S2–S5 for details. Gray and yellow shades on top indicate the night (22:00-6:00 h) and the day (6:00-22:00 h), respectively.

(B and C) The computational package based on the mathematical model simulated homeostatic sleep pressure (black line; C) according to sleep-wake patterns (blue shade; B), which were estimated by measured activity (black vertical lines; B). It also simulated the circadian variation of the sleep threshold (yellow line; C) by estimating the light signal reaching the circadian clock based on measured light exposure (yellow line; B). Then, the minimum sleep duration required to wake-up specifically in the potential wake region (i.e., the circadian necessary sleep; gray striped bars; C) was calculated for each sleep episode. Compared with circadian necessary sleep, longer or shorter sleep episodes (black bars; C) are referred to as circadian sufficient or circadian insufficient sleep, respectively. Gray and yellow shades on top of (B) indicate the night (22:00-6:00 h) and the day (6:00-22:00 h), respectively.

See also Figures S2–S5.