Modeling fatigue over sleep deprivation, circadian rhythm, and caffeine with a minimal performance inhibitor model

Sleep loss, as well as concomitant fatigue and risk, is ubiquitous in today's fast-paced society. A biomathematical model that succeeds in describing performance during extended wakefulness would have practical utility in operational environments and could help elucidate the physiological basis of sleep loss effects. Eighteen subjects (14 males, 4 females; age 25.8 +/- 4.3 years) with low levels of habitual caffeine consumption (<300 mg/day) participated. On night 1, subjects slept for 8 h (2300-0700 h), followed by 77 h of continuous wakefulness. They were assigned randomly to receive placebo or caffeine (200 mg, i.e., two sticks of Stay Alert gum) at 0100, 0300, 0500, and 0700 during nights 2, 3, and 4. The psychomotor vigilance test (PVT) was administered periodically over the 77-h period of continuous wakefulness. Statistical analysis reveals lognormality in each PVT, allowing for closed-form median calculation. An iterative parameter estimation algorithm, which takes advantage of MatLab's (R2007a) least-squares nonlinear regression, is used to estimate model parameters from subjects' PVT medians over time awake. In the model, daily periodicity is accounted for with a four-component Fourier series, and a simplified binding function describes asymptotic fatigue. The model highlights patterns in data that suggest (1) the presence of a performance inhibitor that increases and saturates over the period of continuous wakefulness, (2) competitive inhibition of this inhibitor by caffeine, (3) the persistence of an internally driven circadian rhythm of alertness, and (4) a multiplicative relationship between circadian rhythm and performance inhibition. The present inhibitor-based minimal model describes performance data in a manner consistent with known biochemical processes.