Random walk model simulates the increased drowsiness of children with obstructive sleep apnea

Obstructive sleep apnea (OSA) is a common sleep disorder, which is particularly harmful to children as it may lead to learning deficits, attention deficit hyperactivity disorder (ADHD) and growth retardation. Furthermore, OSA alters the dynamics of sleep-stage transitions and in particular increases the transition time from being awake to falling asleep ("drowsiness"). In this letter, we show that sleep bout durations during this transient state can be described by an exponential distribution with a longer characteristic time scale for OSA compared to healthy children. This finding can be simulated and better understood by using a random walk model of the integrated neuronal voltage of wake-promoting neurons, and by introducing a new concept of a light sleep threshold parameter L that distinguishes between drowsiness and deeper forms of light sleep. Our analysis also shows that the value of L correlates well with OSA severity. Moreover, we find that after OSA treatment, the parameter L returns to normal values similar to those we detected for healthy children. We anticipate that our methodology can help in better understanding and modeling sleep dynamics, and may improve diagnostics and treatment monitoring of OSA.