A proposed mathematical model for sleep patterning

The simple model of a ramp, intersecting a triangular waveform, yields results which conform with seven generalized observations of sleep patterning; including the progressive lengthening of 'rapid-eye-movement' (REM) sleep periods within near-constant REM/nonREM cycle periods. Predicted values of REM sleep time, and of Stage 3/4 nonREM sleep time, can be computed using the observed values of other parameters. The distributions of the actual REM and Stage 3/4 times relative to the predicted values were closer to normal than the distributions relative to simple 'best line' fits. It was found that sleep onset tends to occur at a particular moment in the individual subject's '90-min cycle' (the use of a solar time-scale masks this effect), which could account for a subject with a naturally short sleep/wake cycle synchronizing to a 24-h rhythm. A combined 'sleep control system' model offers quantitative simulation of the sleep patterning of endogenous depressives and, with a different perturbation, qualitative simulation of the symptoms of narcolepsy.