A Mathematical Model of the Human Sleep Cycle

Michael Rempe
Mathematical Biosciences Institute (MBI), The Ohio State University

(December 11, 2008 2:30 PM - 3:30 PM)

A Mathematical Model of the Human Sleep Cycle

Abstract

Sleep is not a simple process but instead is the result of a dynamic interplay between several different brain regions. As such, mathematical and computational modeling are useful in understanding how interactions between different neuron groups give rise to observed sleep and wake states. Recent experiments have shown that the brain contains mutually inhibitory connections between sleep-active and wake-active regions. I will present a biologically-based mathematical model of these brain regions consistent with this mutual inhibition concept. The model is able to account for several features of the human sleep/wake cycle including the timing of sleep and wakefulness under normal and sleep-deprived conditions, rapid eye movement (REM) rhythms, and the circadian dependence of several sleep characteristics. Additionally, if the input from the neuropeptide orexin is removed, the system exhibits more frequent switching between sleep and wakefulness, consistent with the sleep disorder narcolepsy. Our model demonstrates that the mutual inhibition concept, with the addition of a sleep homeostat and circadian rhythm, is sufficient to account for several features of the sleep/wake cycle. Phase-plane analysis of the model gives insight into the mechanisms of sleep transitions, as well as what might be going wrong in certain sleep disorders.