Effects of thermoregulation on human sleep patterns: A mathematical model of sleep-wake cycles with REM-NREM subcircuit

In this paper we construct a mathematical model of human sleep/wake regulation with thermoregulation and temperature e ects. Simulations of this model show features previously presented in experimental data such as elongation of duration and number of REM bouts across the night as well as the appearance of awakenings due to deviations in body temperature from thermoneutrality. This model helps to demonstrate the importance of temperature in the sleep cycle. Further modi cations of the model to include more temperature e ects on other aspects of sleep regulation such as sleep and REM latency are discussedPostprint (author's final draft

Assessing day-to-day regularity of sleep-wake patterns: theoretical and practical implications of available metrics

Background. Day-to-day changes in sleep-wake patterns are important to quantify because they can result in circadian disruption, a risk factor for health outcomes. Traditionally, sleep regularity has been assessed by comparing each day to the average sleep-wake pattern, using metrics such as standard deviation (StDev) and Interdaily Stability (IS). Recently, metrics have been proposed to instead capture variability between consecutive days: the Sleep Regularity Index (SRI) and the Composite Phase Deviation (CPD). Here, we systematically compared these metrics across a range of sources of day-to-day variability, including naps, awakenings, and missing data. Methods. Sleep-wake patterns were synthetically generated over 2-28 days with a weekdayweekend structure. Daily sleep variability was introduced by randomly drawing daily midsleeps and/or sleep durations from a normal distribution with standard deviation ranging from 0- 120min. Average estimates and 95% confidence intervals (CIs) were calculated for each metric under the following scenarios: (1) ‘scrambling’ the order of days, (2) fragmented sleep (i.e. naps, wake after sleep onset (WASO), and all-nighters), (3) varying number of days, and (4) randomly vs. non-randomly (i.e. very early/late sleep more likely to be missing) missing data. Results. (1) Scrambling did not affect IS and StDev values but did affect SRI and CPD values, showing that the metrics measure sleep regularity on different time scales: global vs. circadian. (2) SRI and IS behaved similarly for naps and WASO but differed for all-nighters: SRI values increased (more regular) when all-nighters exceeded 50% of nights, whereas IS yielded monotonically lower (less regular) scores. (3) When based on £ 7 days, StDev and IS overestimated how regular patterns were by up to 40% whereas SRI and CPD were more stable, yet with wider CIs requiring up to 40% larger samples. (4) All metrics were highly sensitive to non-randomly missing data but remarkably stable for up to 50% randomly missing data. Conclusions. All examined metrics have been used for quantifying sleep regularity, yet they measure different aspects and should be seen as complementary rather than redundant. Studies should consider including more than one metric and examining mechanistic links between circadian disruption and sleep regularity

Assessing day-to-day regularity of sleep: theoretical and practical implications of available metrics

Objectives Sleep regularity has emerged as an important factor for health in recent years. Metrics differ in their approach to quantifying sleep regularity: Interdaily Stability (IS), Social Jet Lag (SJL), and Standard Deviation (SD) assess variability relative to the mean, whereas the more recent metrics Composite Phase Deviation (CPD) and Sleep Regularity Index (SRI) capture variability on a circadian timescale (i.e., between consecutive days). We systematically assessed and compared these metrics using a range of simulations. Methods Daily sleep patterns were generated for 8 weeks, with later and longer sleep on weekends (0:00-9:00) than weekdays (23:00-6:00). Random variation in sleep timing was systematically increased from 0 min to 360 min in 30-min steps. Mean values and 95% confidence intervals (CIs) were calculated across 10,000 iterations for IS, SJL, SD, CPD, and SRI. Missing data were generated by removing 24h entries, either randomly or non-randomly (e.g., 50% earliest/latest sleep onsets). Results With increasing variation in sleep onset time, all metrics reflected higher irregularity, except SJL, which is sensitive to weekly but not daily changes in sleep timing. As expected, 95% CIs were generally wider for consecutive metrics CPD and SRI than for overall metrics IS and SD. Over the first 14 days, average estimates of IS changed as much as 50% while CPD and SRI remained stable, indicating that IS tends to overestimate how regular sleep patterns are when based on relatively few days. For missing data, 95% CIs were generally wider for consecutive than overall metrics, while their average estimates were more stable, especially for 50% of missing data. The amount of tolerable missing data (e.g., not affecting mean estimates) decreased substantially with increasing non-randomly missing data or variation in sleep timing. Conclusions Overall metrics require relatively many days for an accurate estimate, whereas consecutive metrics such as CPD and SRI are sensitive to daily changes and can better reflect the regularity of patterns that are based on only a few sleep episodes. The right choice of metric may depend on study length, anticipated regularity of the study population, likelihood and distribution of missing data as well as whether the outcome of interest is local vs. global (i.e., accident vs. chronic illness). Future work will examine the metrics’ sensitivity to shift work, nights with no sleep, naps, and fragmented sleep patterns

Measuring sleep regularity: Theoretical properties and practical usage of existing metrics

Study Objectives: Sleep regularity predicts many health-related outcomes. Currently, however, there is no systematic approach to measuring sleep regularity. Traditionally, metrics have assessed deviations in sleep patterns from an individual’s average. Traditional metrics include intra-individual standard deviation (StDev), Interdaily Stability (IS), and Social Jet Lag (SJL). Two metrics were recently proposed that instead measure variability between consecutive days: Composite Phase Deviation (CPD) and Sleep Regularity Index (SRI). Using large-scale simulations, we investigated the theoretical properties of these five metrics. Methods: Multiple sleep-wake patterns were systematically simulated, including variability in daily sleep timing and/or duration. Average estimates and 95% confidence intervals were calculated for six scenarios that affect measurement of sleep regularity: ‘scrambling’ the order of days; daily vs. weekly variation; naps; awakenings; ‘all-nighters’; and length of study. Results: SJL measured weekly but not daily changes. Scrambling did not affect StDev or IS, but did affect CPD and SRI; these metrics, therefore, measure sleep regularity on multi-day and day-to-day timescales, respectively. StDev and CPD did not capture sleep fragmentation. IS and SRI behaved similarly in response to naps and awakenings but differed markedly for all-nighters. StDev and IS required over a week of sleep-wake data for unbiased estimates, whereas CPD and SRI required larger sample sizes to detect group differences. Conclusions: Deciding which sleep regularity metric is most appropriate for a given study depends on a combination of the type of data gathered, the study length and sample size, and which aspects of sleep regularity are most pertinent to the research question

Anwendung eines bio-mathematischen Modells zur Vorhersage von Schlaf und Schläfrigkeit in der Luftfahrt

Einleitung: Schläfrigkeit am Arbeitsplatz ist speziell in der Luftfahrt von besonderem Interesse für die Sicherheit von Personal und Passagieren. Sehr frühe und späte Dienstzeiten sowie Nachtarbeit gehen mit erhöhter Schläfrigkeit einher, nicht zuletzt durch einen damit verbundenen Schlafmangel. Adenosin ist eine neurochemische Substanz im Gehirn, die sich während des Wachseins ansammelt und während des Schlafes wieder abgebaut wird. Erhöhte Adenosinkonzentrationen können sich negativ auf das Leistungsvermögen und somit die Sicherheit im Luftverkehr auswirken. Ein validiertes bio-mathematisches Modell baut auf diesem Adenosin-System auf, um akkurate Vorhersagen zu Schläfrigkeit und Leistungsvermögen in verschiedenen Arbeitsmodellen (z.B. Anzahl und Verteilung von Früh-/Nachtdiensten sowie freier Tage) zu treffen. Fragestellung: Vergleich der Auswirkung verschiedener (Schicht-)Arbeitspläne der kommerziellen Luftfahrt auf Schlaf und Schläfrigkeit unter Anwendung eines bio-mathematischen Adenosin-Modells. Methodik: Ein validiertes mathematisches Modell des Adenosin-Systems im menschlichen Gehirn wird angewandt zur Vorhersage von Schlaf (Dauer, Zeitpunkt) und Schläfrigkeit. Schläfrigkeit wird hierbei quantifiziert als das Ausbleiben einer Reaktion im sog. Psychomotorischen Vigilanztest (PVT), einem validierten Instrument zur Erfassung der Schläfrigkeit. Reale Dienstpläne von Piloten und Kabinenpersonal werden als Modellinput herangezogen und deren Auswirkungen auf Schlaf und Schläfrigkeit verglichen. Ergebnisse: Dienstpläne von Piloten und Kabinenpersonal werden derzeit über Auskünfte von Airlines sowie in der Literatur veröffentlichte Daten gesammelt und anschließend in das vorhandene Modell eingespeist. Schlussfolgerungen: Ein validiertes Modell zur Vorhersage der Schläfrigkeit von Piloten und Kabinenpersonal kann eingesetzt werden, um Dienstpläne hinsichtlich Schlaf und Aufmerksamkeit zu optimieren und mit Schläfrigkeit verbundene Sicherheitsrisiken zu minimieren

Light sensitivity as a physiological factor that promotes irregular sleep/wake patterns: a model-based investigation

Introduction: Irregular sleep is a health risk factor. However, we currently have a poor understanding of physiological factors that contribute to individuals having irregular sleep/wake patterns. We used a validated mathematical model of sleep-wake and circadian physiology to systematically examine the influence of circadian, sleep homeostatic, and light sensitivity parameters on sleep regularity. Materials and Methods: Sleep-wake patterns were generated by a computational model, assuming a 5-day work schedule with enforced wakefulness from 7:00 to 19:00. We introduced daily random variation σ in the model’s sleep-onset threshold to mimic observed intra-individual variability in sleep/wake patterns. The Sleep Regularity Index (SRI) was calculated, ranging from 0 (random pattern) to 100 (perfectly regular pattern). Eight model parameters were varied to determine their effects on SRI: circadian period (τ); circadian amplitude (νvc); sleep homeostatic time constant (χ); and five light sensitivity parameters: delay bias of the phase response curve (b), sensitivity of the dose response curve (p), retinal output strength (G), photoreceptor recovery rate (β), and photoreceptor activation rate (α0). Results: Sleep regularity was meaningfully affected by six of the eight parameters. Responses occurred in three clusters: (1) light sensitivity parameters G and β had no effect on SRI; (2) circadian amplitude νvc modulated the effect of σ, such that weaker amplitude resulted in lower SRI (less regular patterns) for the same σ; and (3) the remaining five parameters τ, χ, b, p, and α0 all generated maximal SRI scores (most regular patterns) for default parameter values, with lower SRI scores when parameters deviated from default values. Conclusions: This is the first study to systematically investigate potential mechanisms of irregular sleep using mathematical modeling. Our findings suggest that irregular sleep can result from individual differences in the sensitivity to the timing and intensity of light exposure, as well as differences in circadian and sleep homeostatic parameters

Modeling neurocognitive decline and recovery during repeated cycles of extended sleep and chronic sleep deficiency

Study Objectives: Intraindividual night-to-night sleep duration is often insufficient and variable. Here we report the effects of such chronic variable sleep deficiency on neurobehavioral performance and the ability of state-of-the-art models to predict these changes. Methods: Eight healthy males (mean age ± SD: 23.9 ± 2.4 years) studied at our inpatient intensive physiologic monitoring unit completed an 11-day protocol with a baseline 10-hour sleep opportunity and three cycles of two 3-hour time-in-bed (TIB) and one 10-hour TIB sleep opportunities. Participants received one of three polychromatic white light interventions (200 lux 4100K, 200 or 400 lux 17000K) for 3.5 hours on the morning following the second 3-hour TIB opportunity each cycle. Neurocognitive performance was assessed using the psychomotor vigilance test (PVT) administered every 1-2 hours. PVT data were compared to predictions of five group-average mathematical models that incorporate chronic sleep loss functions. Results: While PVT performance deteriorated cumulatively following each cycle of two 3-hour sleep opportunities, and improved following each 10-hour sleep opportunity, performance declined cumulatively throughout the protocol at a more accelerated rate than predicted by state-of-the-art group-average mathematical models. Subjective sleepiness did not reflect performance. The light interventions had minimal effect. Conclusions: Despite apparent recovery following each extended sleep opportunity, residual performance impairment remained and deteriorated rapidly when rechallenged with subsequent sleep loss. None of the group-average models were capable of predicting both the build-up in impairment and recovery profile of performance observed at the group or individual level, raising concerns regarding their use in real-world settings to predict performance and improve safety

High sensitivity and interindividual variability in the response of the human circadian system to evening light

Before the invention of electric lighting, humans were primarily exposed to intense (>300 lux) or dim (<30 lux) environmental light�stimuli at extreme ends of the circadian system�s dose�response curve to light. Today, humans spend hours per day exposed to intermediate light intensities (30�300 lux), particularly in the evening. Interindividual differences in sensitivity to evening light in this intensity range could therefore represent a source of vulnerability to circadian disruption by modern lighting. We characterized individual-level dose�response curves to light-induced melatonin suppression using a within-subjects protocol. Fifty-five participants (aged 18�30) were exposed to a dim control (<1 lux) and a range of experimental light levels (10�2,000 lux for 5 h) in the evening. Melatonin suppression was determined for each light level, and the effective dose for 50% suppression (ED50) was computed at individual and group levels. The group-level fitted ED50 was 24.60 lux, indicating that the circadian system is highly sensitive to evening light at typical indoor levels. Light intensities of 10, 30, and 50 lux resulted in later apparent melatonin onsets by 22, 77, and 109 min, respectively. Individual-level ED50 values ranged by over an order of magnitude (6 lux in the most sensitive individual, 350 lux in the least sensitive individual), with a 26% coefficient of variation. These findings demonstrate that the same evening-light environment is registered by the circadian system very differently between individuals. This interindividual variability may be an important factor for determining the circadian clock�s role in human health and disease. © 2019 National Academy of Sciences. All rights reserved

Increased sensitivity of the circadian system to light in delayed sleep–wake phase disorder

Patients with delayed sleep�wake phase disorder (DSWPD) exhibit delayed sleep�wake behaviour relative to desired bedtime, often leading to chronic sleep restriction and daytime dysfunction. The majority of DSWPD patients also display delayed circadian timing in the melatonin rhythm. Hypersensitivity of the circadian system to phase-delaying light is a plausible physiological basis for DSWPD vulnerability. We compared the phase shifting response to a 6.5 h light exposure (~150 lux) between male patients with diagnosed DSWPD (n = 10; aged 20.8 ± 2.3 years) and male healthy controls (n = 11; aged 22.4 ± 3.3 years). Salivary dim light melatonin onset (DLMO) was measured under controlled conditions in dim light (<3 lux) before and after light exposure. Correcting for the circadian time of the light exposure, DSWPD patients exhibited 31.5% greater phase delay shifts than healthy controls. In both groups, a later initial melatonin phase was associated with a greater magnitude phase shift, indicating that increased circadian sensitivity to light may be a factor that contributes to delayed phase, even in non-clinical groups. DSWPD patients also had reduced pupil size following the light exposure, and showed a trend towards increased melatonin suppression during light exposure. These findings indicate that, for patients with DSWPD, assessment of light sensitivity may be an important factor that can inform behavioural therapy, including minimization of exposure to phase-delaying night-time light. © 2018 The Authors. The Journal of Physiology and 2018 The Physiological Society

Irregular sleep and event schedules are associated with poorer self-reported well-being in US college students

Study Objectives: Sleep regularity, in addition to duration and timing, is predictive of daily variations in well-being. One possible contributor to changes in these sleep dimensions are early morning scheduled events. We applied a composite metric—the Composite Phase Deviation (CPD)—to assess mistiming and irregularity of both sleep and event schedules to examine their relationship with self-reported well-being in US college students. Methods: Daily well-being, actigraphy, and timing of sleep and first scheduled events (academic/exercise/other) were collected for approximately 30 days from 223 US college students (37% females) between 2013 and 2016. Participants rated well-being daily upon awakening on five scales: Sleepy–Alert, Sad–Happy, Sluggish–Energetic, Sick–Healthy, and Stressed–Calm. A longitudinal growth model with time-varying covariates was used to assess relationships between sleep variables (i.e. CPDSleep, sleep duration, and midsleep time) and daily and average well-being. Cluster analysis was used to examine relationships between CPD for sleep vs. event schedules. Results: CPD for sleep was a significant predictor of average well-being (e.g. Stressed–Calm: b = -6.3, p < 0.01), whereas sleep duration was a significant predictor of daily well-being (Stressed–Calm, b = 1.0, p < 0.001). Although cluster analysis revealed no systematic relationship between CPD for sleep vs. event schedules (i.e. more mistimed/irregular events were not associated with more mistimed/irregular sleep), they interacted upon well-being: the poorest well-being was reported by students for whom both sleep and event schedules were mistimed and irregular. Conclusions: Sleep regularity and duration may be risk factors for lower well-being in college students. Stabilizing sleep and/or event schedules may help improve well-being