COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics


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Colloquium:Managing Sleep to Sustain Performance


4:10 p.m. Neill Hall 5W

Gregory Belenky, M.D.

Acute total sleep deprivation and chronic partial sleep restriction produce a sleep-dose-dependent degradation in performance (1). The key to effectively managing sleep to sustain performance is a mathematical model that accurately predicts individual performance on the basis of sleep/wake history. The existing models used to predict alertness and performance from sleep/wake history involve two processes - the sleep homeostatic process and the circadian process. In the sleep homeostatic process, a notional quantity increases during sleep by a function akin to battery charging (rapid at first, heeling over and approaching an asymptote toward the end of the night of sleep) restoring performance and this same notional quantity decreases during waking by a simple linear function degrading performance. In the circadian process, an actual quantity, body temperature, gradually increases over the course of the day peaking at 2000 hrs (8:00 PM) and thereafter declines reaching a nadir between 0400 and 0600 hrs (4:00-6:00 AM). Performance lags temperature, peaking at 2200 hrs and reaching its minimum between 0600 and 0800 hrs. This temperature and performance circadian rhythm modulates the expression of the sleep homeostat, effectively yielding stable performance during the day. In both acute, total sleep deprivation and chronic, partial sleep restriction, there are large individual differences in their effects on performance. These differences are a persistent individual trait, stable on retest months later. The two-process model accurately predicts the average effects of acute, total sleep deprivation on performance and subsequent recovery. The two-process model does not accurately predict the average effects of chronic, partial sleep restriction on performance and subsequent recovery. Further, no existing model has been successfully individualized to predict a specific persons performance based on that persons sleep/wake history.