Abstract
Sleep timing and sleep structure vary between and within individuals and are regulated by two main processes: sleep homeostasis and circadian rhythmicity. Homeostasis refers to the ability of an organism to maintain an internal biologic equilibrium through regulatory mechanisms. Homeostatic regulation of sleep has been demonstrated by driving the system away from a state of equilibrium through total, partial, and sleep stage specific deprivation and then monitoring the resultant changes in sleep. The homeostatic regulation of slow-wave activity has been quantified in detail but other aspects of sleep, such as sleep duration and REM sleep, are also under homeostatic control. All these aspects of sleep are also affected by circadian rhythmicity. The joint regulation of sleep timing by homeostasis and circadian rhythmicity has been formalised in the two-process model of sleep regulation. More recently, effects of light on the human circadian pacemaker have been incorporated in models of sleep regulation and other models developed to describe the ultradian NREM-REM cycle. Conceptual models of sleep regulation summarise accumulated knowledge and extract essential principles underlying empirical facts. Mathematical models can in addition test whether our understanding of phenomena as formulated in conceptual frameworks is sufficient to explain these phenomena quantitatively. Ultimately, models for sleep regulation should help us to understand sleep phenotypes, treat sleep disturbances, design physical and social environments to maximise the beneficial effects of sleep, and inform the development of policies to minimise the negative effects of insufficient and mistimed sleep.