Mathematical models for sleep-wake dynamics: comparison of the two-process model and a mutual inhibition neuronal model

Sleep is essential for the maintenance of the brain and the body, yet many features of sleep are poorly understood and mathematical models are an important tool for probing proposed biological mechanisms. The most well-known mathematical model of sleep regulation, the two-process model, models the sleep-wake cycle by two oscillators: a circadian oscillator and a homeostatic oscillator. An alternative, more recent, model considers the mutual inhibition of sleep promoting neurons and the ascending arousal system regulated by homeostatic and circadian processes. Here we show there are fundamental similarities between these two models. The implications are illustrated with two important sleep-wake phenomena. Firstly, we show that in the two-process model, transitions between different numbers of daily sleep episodes occur at grazing bifurcations.This provides the theoretical underpinning for numerical results showing that the sleep patterns of many mammals can be explained by the mutual inhibition model. Secondly, we show that when sleep deprivation disrupts the sleep-wake cycle, ostensibly different measures of sleepiness in the two models are closely related. The demonstration of the mathematical similarities of the two models is valuable because not only does it allow some features of the two-process model to be interpreted physiologically but it also means that knowledge gained from study of the two-process model can be used to inform understanding of the mutual inhibition model. This is important because the mutual inhibition model and its extensions are increasingly being used as a tool to understand a diverse range of sleep-wake phenomena such as the design of optimal shift-patterns, yet the values it uses for parameters associated with the circadian and homeostatic processes are very different from those that have been experimentally measured in the context of the two-process model

Neuroimaging the effects of light on non-visual brain functions

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Circadian regulation of slow waves in human sleep:Topographical aspects

Slow waves (SWs, 0.5-4Hz) in field potentials during sleep reflect synchronized alternations between bursts of action potentials and periods of membrane hyperpolarization of cortical neurons. SWs decline during sleep and this is thought to be related to a reduction of synaptic strength in cortical networks and to be central to sleep's role in maintaining brain function. A central assumption in current concepts of sleep function is that SWs during sleep, and associated recovery processes, are independent of circadian rhythmicity. We tested this hypothesis by quantifying all SWs from 12 EEG derivations in 34 participants in whom 231 sleep periods were scheduled across the circadian cycle in a 10-day forced-desynchrony protocol which allowed estimation of the separate circadian and sleep-dependent modulation of SWs. Circadian rhythmicity significantly modulated the incidence, amplitude, frequency and the slope of the SWs such that the peaks of the circadian rhythms in these slow-wave parameters were located during the biological day. Topographical analyses demonstrated that the sleep-dependent modulation of SW characteristics was most prominent in frontal brain areas whereas the circadian effect was similar to or greater than the sleep-dependent modulation over the central and posterior brain regions. The data demonstrate that circadian rhythmicity directly modulates characteristics of SWs thought to be related to synaptic plasticity and that this modulation depends on topography. These findings have implications for the understanding of local sleep regulation and conditions such as ageing, depression, and neurodegeneration which are associated with changes in SWs, neural plasticity and circadian rhythmicity

Infraslow oscillations in human sleep spindle activity

Background: It has previously been reported that EEG sigma (10-15 Hz) activity during sleep exhibits infraslow oscillations (ISO) with a period of 50 seconds. However, a detailed analysis of the ISO of individually identified sleep spindles is not available. New Method: We investigated basic properties of ISO during baseline sleep of 34 healthy young human participants using a new and established methods. The analyses focused on fast sleep spindle and sigma activity (13-15 Hz) in NREM stage 2 and slow wave sleep (SWS). To describe ISO in sigma activity we analysed power of power of the EEG signal. For the study of ISO in sleep spindle activity we applied a new method in which the EEG signal was reduced to a spindle on/off binary square signal. Its spectral properties were contrasted to that of a square signal wherein the same spindles and also the inter spindle intervals were permutated randomly. This approach was validated using surrogate data with imposed ISO modulation. Results: We confirm the existence of ISO in sigma activity albeit with a frequency below the previously reported 0.02 Hz. These ISO are most prominent in the high sigma band and over the centro-parieto-occipital regions. A similar modulation is present in spindle activity. ISO in sleep spindles are most prominent in the centro-parieto-occipital regions, left hemisphere and second half of the night independent of the number of spindles. Conclusions: The comparison of spectral properties of binary event signals and permutated event signals is effective in detecting slow oscillatory phenomena

Sleep Timing in Late Autumn and Late Spring Associates With Light Exposure Rather Than Sun Time in College Students

Timing of the human sleep-wake cycle is determined by social constraints, biological processes (sleep homeostasis and circadian rhythmicity) and environmental factors, particularly natural and electrical light exposure. To what extent seasonal changes in the light-dark cycle affect sleep timing and how this varies between weekdays and weekends has not been firmly established. We examined sleep and activity patterns during weekdays and weekends in late autumn (standard time, ST) and late spring (daylight saving time, DST), and expressed their timing in relation to three environmental reference points: clock-time, solar noon (SN) which occurs one clock hour later during DST than ST, and the midpoint of accumulated light exposure (50% LE). Observed sleep timing data were compared to simulated data from a mathematical model for the effects of light on the circadian and homeostatic regulation of sleep. A total of 715 days of sleep timing and light exposure were recorded in 19 undergraduates in a repeated-measures observational study. During each three-week assessment, light and activity were monitored, and self-reported bed and wake times were collected. Light exposure was higher in spring than in autumn. 50% LE did not vary across season, but occurred later on weekends compared to weekdays. Relative to clock-time, bedtime, wake-time, mid-sleep, and midpoint of activity were later on weekends but did not differ across seasons. Relative to SN, sleep and activity measures were earlier in spring than in autumn. Relative to 50% LE, only wake-time and mid-sleep were later on weekends, with no seasonal differences. Individual differences in mid-sleep did not correlate with SN but correlated with 50% LE. Individuals with different habitual bedtimes responded similarly to seasonal changes. Model simulations showed that light exposure patterns are sufficient to explain sleep timing in spring but less so in autumn. The findings indicate that during autumn and spring, the timing of sleep associates with actual light exposure rather than sun time as indexed by SN