A biomathematical model of the restoring effects of caffeine on cognitive performance during sleep deprivation

J Theor Biol. 2013 Feb 21:319:23-33. doi: 10.1016/j.jtbi.2012.11.015. Epub 2012 Nov 23.


Rationale: While caffeine is widely used as a countermeasure to sleep loss, mathematical models are lacking.

Objective: Develop a biomathematical model for the performance-restoring effects of caffeine in sleep-deprived subjects.

Methods: We hypothesized that caffeine has a multiplicative effect on performance during sleep loss. Accordingly, we first used a phenomenological two-process model of sleep regulation to estimate performance in the absence of caffeine, and then multiplied a caffeine-effect factor, which relates the pharmacokinetic-pharmacodynamic effects through the Hill equation, to estimate the performance-restoring effects of caffeine.

Results: We validated the model on psychomotor vigilance test data from two studies involving 12 subjects each: (1) single caffeine dose of 600mg after 64.5h of wakefulness and (2) repeated doses of 200mg after 20, 22, and 24h of wakefulness. Individualized caffeine models produced overall errors that were 19% and 42% lower than their population-average counterparts for the two studies. Had we not accounted for the effects of caffeine, the individualized model errors would have been 117% and 201% larger, respectively.

Conclusions: The presented model captured the performance-enhancing effects of caffeine for most subjects in the single- and repeated-dose studies, suggesting that the proposed multiplicative factor is a feasible solution.

Publication types

  • Clinical Trial
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Adult
  • Caffeine / administration & dosage*
  • Caffeine / pharmacokinetics*
  • Central Nervous System Stimulants / administration & dosage*
  • Central Nervous System Stimulants / pharmacokinetics*
  • Cognition / drug effects*
  • Female
  • Humans
  • Male
  • Sleep Deprivation / metabolism
  • Sleep Deprivation / pathology
  • Sleep Deprivation / physiopathology*
  • Time Factors


  • Central Nervous System Stimulants
  • Caffeine