Timing of sleep modelling: Circadian modulation of the homeostatic process

Abstract Some basic assumptions of the two‐process model (somnostat; Daan et al. 1984) were used to develop a more general model called the rhythmostat. It addresses the timing mechanisms underlying the sleep‐wake cycle (somnostat). One of the two main features of rhythmostatic regulation is illustrated by a mathematical model of the relay thermostat. Like the time course of room temperature is representing the process of heat regulation in the relay thermostat, slow‐wave activity is representing sleep‐regulating processes in the somnostat. The observed alternations of reverse‐exponential and exponential phases in the day‐ and nighttime course of slow‐wave activity reflect the deviations of a regulated process around a set‐point level. These oscillations may result from time delays in the process of sleep regulation. However, unlike the parameters in the relay thermostat model, the parameters of the regulated process in the somnostat (e.g. set‐point and time constants for reverse‐exponential and exponential phases) are modulated by the circadian pacemaker. To account for the second main feature of the rhythmostatic regulation, a circadian term (a sine function with 24‐h period) was incorporated in the mathematical model describing the time course of slow‐wave activity. The data of sleep deprivation experiments of Dijk et al. (1987b, 1990, 1991), and Äkerstedt and Gillberg (1981, 1986) were used to estimate the human somnostat parameters. The simulations of these data offer explanations for some phenomena which can not be explained by the model of Daan et al. (1984).