Mapping recovery from sleep deprivation

Abstract

Sleep timing is based on the interactions between circadian and homeostatic processes. However, sleep deprivation perturbs the time of sleep onset, and the timing and duration of the following recovery sleep may differ from that of baseline sleep. Here we show that the responses to 0–24 h of sleep deprivation can be approximated by a one-dimensional, discontinuous map computed from a physiologically-based ordinary differential equation model for human sleep-wake regulation. The map relates the circadian phase of sleep onset to the circadian phase of the previous sleep onset and reproduces sleep patterns seen in experimental data for the timing and duration of recovery sleep when sleep onset occurs 8 or 20 h after the usual sleep onset. In addition, the durations of recovery sleep predicted by the map for sleep deprivations of 0 to 24 h are consistent with numerical simulations of recovery sleep using the full (nonautonomous, 8-dimensional) model. Our results demonstrate that the circadian phase of sleep onset affects the duration of recovery sleep more strongly than the homeostatic sleep drive for most durations of sleep deprivation. In addition, the map establishes a lower bound for the length of recovery sleep. As a result, the map provides a computationally-efficient way of incorporating sleep dynamics into new technologies that allow users to predict the effects of sleep deprivation and identify optimal sleep schedules.