Dissociating the intensity and phase origins of sleepiness through a threshold-distance model of sleep-wake dynamics

Sleepiness is a leading proximate cause of drowsy-driving fatalities, medical errors and industrial accidents, yet it has resisted mechanistic prediction; although it arises from well-characterized sleep-wake physiology, it is experienced as a subjective state and has lacked a quantitative link to the underlying dynamics. We previously showed that subjective sleepiness maps linearly, with a protocol-invariant form, onto the signed distance H - H+ between the homeostatic pressure H and the circadian-modulated sleep-onset threshold H+. This single quantity predicts sleepiness accurately but is mechanistically ambiguous: the same value can arise either because H sits far from the boundary or because the threshold H+(t) has shifted with circadian phase, and these two origins call for entirely different interpretations and interventions. Here we resolve this ambiguity by decomposing H - H+ into two mechanistically separable axes-intensity and phase. The intensity axis is the time-averaged margin [<] H - H+[>], set by how far, on average, H sits from the sleep boundary: slowed homeostatic accumulation accounts for the paradoxically blunted sleepiness of older adults, and pharmacological suppression of H accounts for the dose-dependent alerting effect of caffeine. The phase axis is set by the circadian modulation of H+(t): under a forced-desynchrony protocol, in which the pacemaker free-runs and the homeostatic and circadian processes are experimentally decoupled, sleepiness tracks the circadian profile of H+(t) across all phases while the intensity mapping itself remains unchanged-a clean dissociation of the two axes. By resolving felt sleepiness into these two physiological degrees of freedom, this framework renders previously isolated phenomena-aging, caffeine and circadian misalignment-commensurable within a single theory and provides a physiologically interpretable basis for prospective fatigue-risk prediction. Author summaryWhy people feel sleepy after sleep loss, or at particular times of day, remains difficult to predict from physiology alone. Sleep and wake are shaped by two interacting processes: a daily circadian rhythm and a homeostatic pressure that builds during wakefulness. In earlier work, we linked subjective sleepiness ratings to a simple geometric quantity-how close sleep pressure sits to a circadian sleep-onset boundary. That link is useful, but ambiguous: the same distance can arise either because pressure itself has changed, or because the boundary has moved with circadian phase. Here we use a computational model of the sleep-wake switch, extended to include the wake-stabilizing orexin system, to separate these contributions into an intensity axis and a phase axis. We find that aging and caffeine mainly alter how large the average distance to the boundary becomes, whereas forced desynchrony mainly alters how that distance varies across circadian phase. This dissociation offers a compact way to interpret several otherwise separate observations within one quantitative picture, and a step toward more physiologically grounded fatigue-risk assessment.