Mathematical Model of Network Dynamics Governing Mouse Sleep–Wake Behavior

Abstract

Recent work in experimental neurophysiology has identified distinct neuronal populations in the rodent brain stem and hypothalamus that selectively promote wake and sleep. Mutual inhibition between these cell groups has suggested the conceptual model of a sleep-wake switch that controls transitions between wake and sleep while minimizing time spent in intermediate states. By combining wake- and sleep-active populations with populations governing transitions between different stages of sleep, a "sleep-wake network" of neuronal populations may be defined. To better understand the dynamics inherent in this network, we created a model sleep-wake network composed of coupled relaxation oscillation equations. Mathematical analysis of the deterministic model provides insight into the dynamics underlying state transitions and predicts mechanisms for each transition type. With the addition of noise, the simulated sleep-wake behavior generated by the model reproduces many qualitative and quantitative features of mouse sleep-wake behavior. In particular, the existence of simulated brief awakenings is a unique feature of the model. In addition to capturing the experimentally observed qualitative difference between brief and sustained wake bouts, the model suggests distinct network mechanisms for the two types of wakefulness. Because circadian and other factors alter the fine architecture of sleep-wake behavior, this model provides a novel framework to explore dynamical principles that may underlie normal and pathologic sleep-wake physiology.

Current Approaches and Challenges to Development of an Individualized Sleep and Performance Prediction Model~!2009-03-22~!2010-05-11~!2010-07-15~!

“…We note that there are other mathematical models of sleep/wake cycles motivated, in part, by the hypothalamic sleep switch [18,31,32]. In particular, Behn et al [32] model the activity of wake-and sleep-promoting cell groups as relaxation oscillators, as is done here. Their model has the ability to produce polyphasic sleep rhythms with frequent brief awakenings, features more prominent in the sleep of mice than of humans.…”

“…To examine this issue, data were used from a study involving 21 healthy adults (10 males and 11 females; ages [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. As part of a larger protocol [48,49], these subjects underwent 36 hours of total sleep deprivation in a controlled laboratory environment.…”

Modelling changes in sleep timing and duration across the lifespan: Changes in circadian rhythmicity or sleep homeostasis?

“…This has resulted in several physiology-based models of the sleep-wake cycle [80,81,82] that focus on the principle groups of neurons believed to promote wake and sleep states and link them to homeostatic and circadian processes. In particular, the Phillips-Robinson model and its extensions have been extensively tested against human data and used to describe: the response to impulsive auditory stimuli [83]; measures of sleepiness during sleep deprivation experiments [84,85]; the effects of caffeine [86]; spontaneous internal desynchrony [87], and the effects of non-rotating and rotating shift schedules [88,89].…”

Quantitative modelling of sleep dynamics

“…The widely known two-process model is of the latter form, and includes circadian and homeostatic influences [23]. The relatively recent advances in sleep neurophysiology have enabled the development of physiologically based models [24][25][26], and here we use NMT to model the dynamics of the AAS nuclei, following Phillips & Robinson [19], who argued that (i) since the system spends little time in transitions, the generation rate of H has just two values, one for wake and one for sleep, (ii) the clearance rate of H is proportional to H with a characteristic time scale c, and (iii) the production rate of H is mQ m , where m is a constant and Q m serves as a proxy for arousal state. These steps yield equations for H and the mean soma voltages V a in the MA group (a = m) and VLPO (a = v):…”