A model-based interpretation of the biphasic daily pattern of sleepiness

We developed a thermoregulatory model of sleep control based on the hypothesis that non-rapid eye-movement sleep participates in homeostatic thermoregulation. This model successfully reproduced several qualitative features of human sleep/wake cycles during entrained as well as the internally desynchronized states. Among the reproduced features, generation mechanisms of the biphasic sleepiness distribution are studied here in the light of the model structure. Harmonic analysis is employed for this purpose. Through linearizations and confining the harmonics of the masking process to the fundamental component, a simplified representation of sleepiness is obtained. The simplified sleepiness is constructed with the fundamental circadian, the second harmonic components, and the constant (DC). The bimodality of the sleepiness is shown to be made by the second harmonic which is added to the fundamental component. The behavior of their amplitudes and phase positions are investigated under the varied sleep/wake durations and phase differences between the oscillators. Since the sleepiness generated by our model is roughly mimicked by the simplified representation under diverse conditions, this simplification can be regarded as adequate. From the behavior of the constituents of respective harmonic components, the fundamental component is shown to originate from the sleep/wake masking process and the circadian oscillators; the second harmonic from the multiplicative interactions between the circadian oscillators and the sleep/wake masking process. These results indicate that the rhythmic processes are principal constituents of the sleepiness, at least in the steady state.