Study objectives: To model sleep propensity (SP) as a continuous variable across 24 hours and to model the post-noon nap zone, or post-lunch dip in performance, and the early evening trough in SP.
Methods: The present model is a variant of the 2-process model with 2 major modifications. (1) The circadian threshold process was replaced by sleep drive R, derived from REM sleep propensity, which shows a strong circadian modulation. (2) The model is based on a multiplicative interaction between the 2 input variables S and R. The model parameters S and R were estimated from experimental data. Thus, SP is modeled by multiplicative interaction of 2 sleep drives, S and R, the former of homeostatic, the latter of circadian nature. In short: SP = S x R.
Results: Under the condition of normal phase and duration of nighttime sleep, SP across 24 hours displays 4 characteristics, (a) a major peak at nighttime, (b) a secondary increase, which peaks post-noon, (c) a first local minimum at sleep offset in the morning, and (d) a second local minimum in the early evening hours. Model simulations with either delayed or advanced sleep times suggest that the magnitude of the post-noon nap zone depends on the phase of the major sleep period within 24 hours. While the nap zone is attenuated or disappears when night sleep is delayed, SP increases during daytime when night sleep is advanced. In all conditions, the evening local minimum of SP remained stable.
Conclusions: SP can be modeled as a continuous variable, based on the multiplicative interaction of 2 basic sleep drives. The model predictions are in agreement with known variations of SP across 24 hours.