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

Data-driven mathematical modeling of sleep consolidation in early childhood

Across early childhood development, sleep behavior transitions from a biphasic pattern (a daytime nap and nighttime sleep) to a monophasic pattern (only nighttime sleep). The transition to consolidated nighttime sleep, which occurs in most children between 2- and 5-years-old, is a major developmental milestone and reflects interactions between the developing homeostatic sleep drive and circadian system. Using a physiologically-based mathematical model of the sleep-wake regulatory network constrained by observational and experimental data from preschool-aged participants, we analyze how developmentally-mediated changes in the homeostatic sleep drive may contribute to the transition from napping to non-napping sleep patterns. We establish baseline behavior by identifying parameter sets that model typical 2-year-old napping behavior and 5-year-old non-napping behavior. Then we vary six model parameters associated with the dynamics of and sensitivity to the homeostatic sleep drive between the 2-year-old and 5-year-old parameter values to induce the transition from biphasic to monophasic sleep. We analyze the individual contributions of these parameters to sleep patterning by independently varying their age-dependent developmental trajectories. Parameters vary according to distinct evolution curves and produce bifurcation sequences representing various ages of transition onset, transition durations, and transitional sleep patterns. Finally, we consider the ability of napping and non-napping light schedules to reinforce napping or promote a transition to consolidated sleep, respectively. These modeling results provide insight into the role of the homeostatic sleep drive in promoting interindividual variability in developmentally-mediated transitions in sleep behavior and lay foundations for the identification of light- or behavior-based interventions that promote healthy sleep consolidation in early childhood.

Sleep and circadian rhythmicity as entangled processes serving homeostasis

Sleep is considered essential for the brain and body. A predominant concept is that sleep is regulated by circadian rhythmicity and sleep homeostasis, processes that were posited to be functionally and mechanistically separate. Here we review and re-evaluate this concept and its assumptions using findings from recent human and rodent studies. Alterations in genes that are central to circadian rhythmicity affect not only sleep timing but also putative markers of sleep homeostasis such as electroencephalogram slow-wave activity (SWA). Perturbations of sleep change the rhythmicity in the expression of core clock genes in tissues outside the central clock. The dynamics of recovery from sleep loss vary across sleep variables: SWA and immediate early genes show an early response, but the recovery of non-rapid eye movement and rapid eye movement sleep follows slower time courses. Changes in the expression of many genes in response to sleep perturbations outlast the effects on SWA and time spent asleep. These findings are difficult to reconcile with the notion that circadian- and sleep-wake-driven processes are mutually independent and that the dynamics of sleep homeostasis are reflected in a single variable. Further understanding of how both sleep and circadian rhythmicity contribute to the homeostasis of essential physiological variables may benefit from the assessment of multiple sleep and molecular variables over longer time scales.

A real-time, personalized sleep intervention using mathematical modeling and wearable devices

The prevalence of artificial light exposure has enabled us to be active any time of the day or night, leading to the need for high alertness outside of traditional daytime hours. To address this need, we developed a personalized sleep intervention framework that analyzes real-world sleep-wake patterns obtained from wearable devices to maximize alertness during specific target periods. Our framework utilizes a mathematical model that tracks the dynamic sleep pressure and circadian rhythm based on the user's sleep history. In this way, the model accurately predicts real-time alertness, even for shift workers with complex sleep and work schedules (N = 71, t = 13~21 days). This allowed us to discover a new sleep-wake pattern called the adaptive circadian split sleep, which incorporates a main sleep period and a late nap to enable high alertness during both work and non-work periods of shift workers. We further developed a mobile application that integrates this framework to recommend practical, personalized sleep schedules for individual users to maximize their alertness during a targeted activity time based on their desired sleep onset and available sleep duration. This can reduce the risk of errors for those who require high alertness during nontraditional activity times and improve the health and quality of life for those leading shift work-like lifestyles.

Modeling homeostatic and circadian modulation of human pain sensitivity

Introduction

Mathematical modeling has played a significant role in understanding how homeostatic sleep pressure and the circadian rhythm interact to influence sleep-wake behavior. Pain sensitivity is also affected by these processes, and recent experimental results have measured the circadian and homeostatic components of the 24 h rhythm of thermal pain sensitivity in humans. To analyze how rhythms in pain sensitivity are affected by disruptions in sleep behavior and shifts in circadian rhythms, we introduce a dynamic mathematical model for circadian and homeostatic regulation of sleep-wake states and pain intensity.

Methods

The model consists of a biophysically based, sleep-wake regulation network model coupled to data-driven functions for the circadian and homeostatic modulation of pain sensitivity. This coupled sleep-wake-pain sensitivity model is validated by comparison to thermal pain intensities in adult humans measured across a 34 h sleep deprivation protocol.

Results

We use the model to predict dysregulation of pain sensitivity rhythms across different scenarios of sleep deprivation and circadian rhythm shifts, including entrainment to new environmental light and activity timing as occurs with jet lag and chronic sleep restriction. Model results show that increases in pain sensitivity occur under conditions of increased homeostatic sleep drive with nonlinear modulation by the circadian rhythm, leading to unexpected decreased pain sensitivity in some scenarios.

Discussion

This model provides a useful tool for pain management by predicting alterations in pain sensitivity due to varying or disrupted sleep schedules.

NREM-REM alternation complicates transitions from napping to non-napping behavior in a three-state model of sleep-wake regulation

The temporal structure of human sleep changes across development as it consolidates from the polyphasic sleep of infants to the single nighttime sleep episode typical in adults. Experimental studies have shown that changes in the dynamics of sleep need may mediate this developmental transition in sleep patterning, however, it is unknown how sleep architecture interacts with these changes. We employ a physiologically-based mathematical model that generates wake, rapid eye movement (REM) and non-REM (NREM) sleep states to investigate how NREM-REM alternation affects the transition in sleep patterns as the dynamics of the homeostatic sleep drive are varied. To study the mechanisms producing these transitions, we analyze the bifurcations of numerically-computed circle maps that represent key dynamics of the full sleep-wake network model by tracking the evolution of sleep onsets across different circadian (∼ 24 h) phases. The maps are non-monotonic and discontinuous, being composed of branches that correspond to sleep-wake cycles containing distinct numbers of REM bouts. As the rates of accumulation and decay of the homeostatic sleep drive are varied, we identify the bifurcations that disrupt a period-adding-like behavior of sleep patterns in the transition between biphasic and monophasic sleep. These bifurcations include border collision and saddle-node bifurcations that initiate new sleep patterns, period-doubling bifurcations leading to higher-order patterns of NREM-REM alternation, and intervals of bistability of sleep patterns with different NREM-REM alternations. Furthermore, patterns of NREM-REM alternation exhibit variable behaviors in different regimes of constant sleep-wake patterns. Overall, the sequence of sleep-wake behaviors, and underlying bifurcations, in the transition from biphasic to monophasic sleep in this three-state model is more complex than behavior observed in models of sleep-wake regulation that do not consider the dynamics of NREM-REM alternation. These results suggest that interactions between the dynamics of the homeostatic sleep drive and the dynamics of NREM-REM alternation may contribute to the wide interindividual variation observed when young children transition from napping to non-napping behavior.

Timing is everything: Circadian rhythms and their role in the control of sleep

Sleep and the circadian clock are intertwined and have persisted throughout history. The suprachiasmatic nucleus (SCN) orchestrates sleep by controlling circadian (Process C) and homeostatic (Process S) activities. As a "hand" on the endogenous circadian clock, melatonin is critical for sleep regulation. Light serves as a cue for sleep/wake control by activating retino-recipient cells in the SCN and subsequently suppressing melatonin. Clock genes are the molecular timekeepers that keep the 24 h cycle in place. Two main sleep and behavioural disorder diagnostic manuals have now officially recognised the importance of these processes for human health and well-being. The body's ability to respond to daily demands with the least amount of effort is maximised by carefully timing and integrating all components of sleep and waking. In the brain, the organization of timing is essential for optimal brain physiology.

Human Alertness Optimization with a Three-Process Dynamic Model

Circadian rhythm is an important biological process for humans as it modulates a wide range of physiological processes, including body temperature, sleep-wake cycle, and cognitive performance. As the most powerful external stimulus of circadian rhythm, light has been studied as a zeitgeber to regulate the circadian phase and sleep. This paper addresses the human alertness optimization problem, by optimizing light exposure and sleep schedules to relieve fatigue and cognitive impairment, in cases of night-shift workers and subjects with certain mission periods based on dynamics of the circadian rhythm system. A three-process hybrid dynamic model is used for simulating the circadian rhythm and predicting subjective alertness and sleepiness. Based on interindividual difference in sleep type and living habits, we propose a tunable sleep schedule in the alertness optimization problem, which allows the appropriate tuning of sleep and wake times based on sleep propensity. Variational calculus is applied to evaluate the impacts of light and sleep schedules on the alertness and a gradient descent algorithm is proposed to determine the optimal solutions to maximize the alertness level in various cases. Numerical simulation results demonstrate that the cognitive performance during certain periods can be significantly improved by optimizing the light input and tuning sleep/wake times compared to empirical data.

Personalized On-Device E-health Analytics with Decentralized Block Coordinate Descent

Actuated by the growing attention to personal healthcare and the pandemic, the popularity of E-health is proliferating. Nowadays, enhancement on medical diagnosis via machine learning models has been highly effective in many aspects of e-health analytics. Nevertheless, in the classic cloud-based/centralized e-health paradigms, all the data will be centrally stored on the server to facilitate model training, which inevitably incurs privacy concerns and high time delay. Distributed solutions like Decentralized Stochastic Gradient Descent (D-SGD) are proposed to provide safe and timely diagnostic results based on personal devices. However, methods like D-SGD are subject to the gradient vanishing issue and usually proceed slowly at the early training stage, thereby impeding the effectiveness and efficiency of training. In addition, existing methods are prone to learning models that are biased towards users with dense data, compromising the fairness when providing E-health analytics for minority groups. In this paper, we propose a Decentralized Block Coordinate Descent (D-BCD) learning framework that can better optimize deep neural network-based models distributed on decentralized devices for E-health analytics. As a gradient-free optimization method, Block Coordinate Descent (BCD) mitigates the gradient vanishing issue and converges faster at the early stage compared with the conventional gradient-based optimization. To overcome the potential data scarcity issues for users local data, we propose similarity-based model aggregation that allows each on-device model to leverage knowledge from similar neighbor models, so as to achieve both personalization and high accuracy for the learned models. Benchmarking experiments on three real-world datasets illustrate the effectiveness and practicality of our proposed DBCD, where additional simulation study showcases the strong applicability of D-BCD in real-life E-health scenarios.

Prediction of shiftworker alertness, sleep, and circadian phase using a model of arousal dynamics constrained by shift schedules and light exposure

STUDY OBJECTIVES

The study aimed to, for the first time, (1) compare sleep, circadian phase, and alertness of intensive care unit (ICU) nurses working rotating shifts with those predicted by a model of arousal dynamics; and (2) investigate how different environmental constraints affect predictions and agreement with data.

METHODS

The model was used to simulate individual sleep-wake cycles, urinary 6-sulphatoxymelatonin (aMT6s) profiles, subjective sleepiness on the Karolinska Sleepiness Scale (KSS), and performance on a Psychomotor Vigilance Task (PVT) of 21 ICU nurses working day, evening, and night shifts. Combinations of individual shift schedules, forced wake time before/after work and lighting, were used as inputs to the model. Predictions were compared to empirical data. Simulations with self-reported sleep as an input were performed for comparison.

RESULTS

All input constraints produced similar prediction for KSS, with 56%-60% of KSS scores predicted within ±1 on a day and 48%-52% on a night shift. Accurate prediction of an individual's circadian phase required individualized light input. Combinations including light information predicted aMT6s acrophase within ±1 h of the study data for 65% and 35%-47% of nurses on diurnal and nocturnal schedules. Minute-by-minute sleep-wake state overlap between the model and the data was between 81 ± 6% and 87 ± 5% depending on choice of input constraint.

CONCLUSIONS

The use of individualized environmental constraints in the model of arousal dynamics allowed for accurate prediction of alertness, circadian phase, and sleep for more than half of the nurses. Individual differences in physiological parameters will need to be accounted for in the future to further improve predictions.

Addressing fatigue in medical residents with biomathematical fatigue modeling

Fatigue in resident physicians has been identified as a factor that contributes to burnout and a decline in overall wellbeing. Fatigue risk exists because of poor sleep habits and demanding work schedules that have only increased due to the COVID‐19 pandemic. At this time, it is important not to lose sight of how fatigue can impact residents and how fatigue risk can be mitigated. While fatigue mitigation is currently addressed by duty hour restrictions and education about fatigue, Fatigue Risk Management Systems (FRMSs) offer a more comprehensive strategy for addressing these issues. An important component of FRMS in other shiftwork industries, such as aviation and trucking, is the use of biomathematical models to prospectively identify fatigue risk in work schedules. Such an approach incorporates decades of knowledge of sleep and circadian rhythm research into shift schedules, taking into account not just duty hour restrictions but the temporal placement of work schedules. Recent research has shown that biomathematical models of fatigue can be adapted to a resident physician population and can help address fatigue risk. Such models do not require subject matter experts and can be applied in graduate medical education program shift scheduling. It is important for graduate medical education program providers to consider these alternative methods of fatigue mitigation. These tools can help reduce fatigue risk and may improve wellness as they allow for a more precise fatigue management strategy without reducing overall work hours.

Creation of discontinuities in circle maps

Circle maps frequently arise in mathematical models of physical or biological systems. Motivated by Cherry flows and ‘threshold’ systems such as integrate and fire neuronal models, models of cardiac arrhythmias, and models of sleep/wake regulation, we consider how structural transitions in circle maps occur. In particular, we describe how maps evolve near the creation of a discontinuity. We show that the natural way to create discontinuities in the maps associated with both threshold systems and Cherry flows results in a singularity in the derivative of the map as the discontinuity is approached from either one or both sides. For the threshold systems, the associated maps have square root singularities and we analyse the generic properties of such maps with gaps, showing how border collisions and saddle-node bifurcations are interspersed. This highlights how the Arnold tongue picture for tongues bordered by saddle-node bifurcations is amended once gaps are present. We also show that a loss of injectivity naturally results in the creation of multiple gaps giving rise to a novel codimension two bifurcation.

Optimization of light exposure and sleep schedule for circadian rhythm entrainment

The circadian rhythm, called Process C, regulates a wide range of biological processes in humans including sleep, metabolism, body temperature, and hormone secretion. Light is the dominant synchronizer of the circadian rhythm-it has been used to regulate the circadian phase to cope with jet-lag, shift work, and sleep disorder. The homeostatic oscillation of the sleep drive is called Process S. Process C and Process S together determine the sleep-wake cycle in what is known as the two-process model. This paper addresses the regulation of both Process C and Process S by scheduling light exposure and sleep based on numerical simulations of circadian rhythm and sleep mathematical models. This is a significant step beyond the existing literature that only considers the entrainment of Process C. Regulation of the two-process model poses several unique features and challenges: 1. Process S is non-smooth, i.e., the homeostatic dynamics are different in the sleep and wake regimes; 2. Light only indirectly affects Process S through Process C; 3. Light does not affect Process C during sleep. We consider two scenarios: optimizing light intensity as the control input with spontaneous (i.e., unscheduled) sleep/wake times and jointly optimizing the light intensity and the sleep/wake times, which allows limited delayed sleep and early waking as part of the decision variables. We solve the time-optimal entrainment problem for the two-process model for both scenarios using an extension of the gradient descent algorithm to non-smooth systems. To illustrate the efficacy of our time-optimal entrainment strategies, we consider two common use cases: transmeridian travelers and shift workers. For transmeridian travelers, joint optimization of the two-process model avoids the unrealistic long wake duration when only Process C is considered. The entrainment time also decreases when both the light input and the sleep schedule are optimized compared to when only the light input is optimized. For shift workers, we show that the entrainment time is significantly shortened by optimizing the night shift working light.

Sleepiness is a signal to go to bed: data and model simulations

Study Objectives

Assess the validity of a subjective measure of sleepiness as an indicator of sleep drive by quantifying associations between intraindividual variation in evening sleepiness and bedtime, sleep duration, and next morning and subsequent evening sleepiness, in young adults.

Methods

Sleep timing and sleepiness were assessed in 19 students in late autumn and late spring on a total of 771 days. Karolinska Sleepiness Scales (KSS) were completed at half-hourly intervals at fixed clock times starting 4 h prior to participants’ habitual bedtime, and in the morning. Associations between sleepiness and sleep timing were evaluated by mixed model and nonparametric approaches and simulated with a mathematical model for the homeostatic and circadian regulation of sleepiness.

Results

Intraindividual variation in evening sleepiness was very large, covering four or five points on the 9-point KSS scale, and was significantly associated with subsequent sleep timing. On average, a one point higher KSS value was followed by 20 min earlier bedtime, which led to 11 min longer sleep, which correlated with lower sleepiness next morning and the following evening. Associations between sleepiness and sleep timing were stronger in early compared to late sleepers. Model simulations indicated that the directions of associations between sleepiness and sleep timing are in accordance with their homeostatic and circadian regulation, even though much of the variance in evening sleepiness and details of its time course remain unexplained by the model.

Conclusion

Subjective sleepiness is a valid indicator of the drive for sleep which, if acted upon, can reduce insufficient sleep.

Circadian Chimeric Mice Reveal an Interplay Between the Suprachiasmatic Nucleus and Local Brain Clocks in the Control of Sleep and Memory

Sleep is regulated by circadian and homeostatic processes. Whereas the suprachiasmatic nucleus (SCN) is viewed as the principal mediator of circadian control, the contributions of sub-ordinate local circadian clocks distributed across the brain are unknown. To test whether the SCN and local brain clocks interact to regulate sleep, we used intersectional genetics to create temporally chimeric CK1ε Tau mice, in which dopamine 1a receptor (Drd1a)-expressing cells, a powerful pacemaking sub-population of the SCN, had a cell-autonomous circadian period of 24 h whereas the rest of the SCN and the brain had intrinsic periods of 20 h. We compared these mice with non-chimeric 24 h wild-types (WT) and 20 h CK1ε Tau mutants. The periods of the SCN ex vivo and the in vivo circadian behavior of chimeric mice were 24 h, as with WT, whereas other tissues in the chimeras had ex vivo periods of 20 h, as did all tissues from Tau mice. Nevertheless, the chimeric SCN imposed its 24 h period on the circadian patterning of sleep. When compared to 24 h WT and 20 h Tau mice, however, the sleep/wake cycle of chimeric mice under free-running conditions was disrupted, with more fragmented sleep and an increased number of short NREMS and REMS episodes. Even though the chimeras could entrain to 20 h light:dark cycles, the onset of activity and wakefulness was delayed, suggesting that SCN Drd1a-Cre cells regulate the sleep/wake transition. Chimeric mice also displayed a blunted homeostatic response to 6 h sleep deprivation (SD) with an impaired ability to recover lost sleep. Furthermore, sleep-dependent memory was compromised in chimeras, which performed significantly worse than 24 h WT and 20 h Tau mice. These results demonstrate a central role for the circadian clocks of SCN Drd1a cells in circadian sleep regulation, but they also indicate a role for extra-SCN clocks. In circumstances where the SCN and sub-ordinate local clocks are temporally mis-aligned, the SCN can maintain overall circadian control, but sleep consolidation and recovery from SD are compromised. The importance of temporal alignment between SCN and extra-SCN clocks for maintaining vigilance state, restorative sleep and memory may have relevance to circadian misalignment in humans, with environmental (e.g., shift work) causes.

Overcoming Compensatory Mechanisms toward Chronic Drug Administration to Ensure Long-Term, Sustainable Beneficial Effects

Chronic administration of drugs leads to the activation of compensatory mechanisms that may inhibit some of their activity and induce unwanted toxicity. These mechanisms are an obstacle for maintaining a sustainable effect for many chronic medications. Pathways that adapt to the burden induced by chronic drugs, whether or not related to the underlying disease, can lead to a partial or complete loss of effect. Variability characterizes many biological systems and manifests itself as large intra- and inter-individual differences in the response to drugs. Circadian rhythm-based chronotherapy is further associated with variability in responses noted among patients. This paper reviews current knowledge regarding the loss of effect of chronic medications and the range of variabilities that have been described in responses and loss of responses. Establishment of a personalized platform for overcoming these prohibitive mechanisms is presented as a model for ensuring long-term sustained medication effects. This novel platform implements personalized variability signatures and individualized circadian rhythms for preventing and opposing the prohibitive effect of the compensatory mechanisms induced by chronic drug administration.

Hidden Markov models for monitoring circadian rhythmicity in telemetric activity data

Wearable computing devices allow collection of densely sampled real-time information on movement enabling researchers and medical experts to obtain objective and non-obtrusive records of actual activity of a subject in the real world over many days. Our interest here is motivated by the use of activity data for evaluating and monitoring the circadian rhythmicity of subjects for research in chronobiology and chronotherapeutic healthcare. In order to translate the information from such high-volume data arising we propose the use of a Markov modelling approach which (i) naturally captures the notable square wave form observed in activity data along with heterogeneous ultradian variances over the circadian cycle of human activity, (ii) thresholds activity into different states in a probabilistic way while respecting time dependence and (iii) gives rise to circadian rhythm parameter estimates, based on probabilities of transitions between rest and activity, that are interpretable and of interest to circadian research.

Sleep Modelling across Physiological Levels

Sleep and circadian rhythms are regulated across multiple functional, spatial and temporal levels: from genes to networks of coupled neurons and glial cells, to large scale brain dynamics and behaviour. The dynamics at each of these levels are complex and the interaction between the levels is even more so, so research have mostly focused on interactions within the levels to understand the underlying mechanisms—the so-called reductionist approach. Mathematical models were developed to test theories of sleep regulation and guide new experiments at each of these levels and have become an integral part of the field. The advantage of modelling, however, is that it allows us to simulate and test the dynamics of complex biological systems and thus provides a tool to investigate the connections between the different levels and study the system as a whole. In this paper I review key models of sleep developed at different physiological levels and discuss the potential for an integrated systems biology approach for sleep regulation across these levels. I also highlight the necessity of building mechanistic connections between models of sleep and circadian rhythms across these levels.

Interacting circadian and homeostatic processes with opportunity cost: A mathematical model of sleep with application to two mammalian species

This paper introduces a new model of sleep for mammals. It extends the classic ‘two-process’ model of sleep to account for differences in external circumstances. We apply this model to previously-collected data on elephants and sloths, comparing sleep patterns in the wild with sleep patterns in captivity. We find that the model does very well in explaining sleeping patterns for both types of animals, in both the captive state and in the wild state.

Mathematical Models of Sleep and Circadian Rhythms: A Case for Using the 2-Process Model in Neuroscience Nursing

Acute and chronic neurological disorders impair sleep. Despite the availability of theoretical/mathematical frameworks about sleep, the nursing profession rarely incorporates these models. The purpose of this article was to analyze the 2-process model of sleep regulation using Fawcett and DeSanto-Madeya's method, a systematic approach for determining whether a theory is relevant to nursing. The 2-process model has 3 concepts: process S (sleep-dependent process), process C (circadian-timing-dependent process), and total sleep propensity (summation of processes S and C). Nonnursing theories do not explicitly incorporate nursing metaparadigm concepts-person, health, environment, and nursing-but the 2-process model is congruent with nursing's philosophy. The model guided studies quantifying sleep and circadian patterns in other fields, and nurses could use this framework to measure the impact of nursing interventions. Strengths of the 2-process model include parsimony (conciseness without oversimplification) and the ability to empirically test propositions related to processes S and C. The 2-process model is relevant to neuroscience nursing-by measuring sleep/circadian-related variables (electroencephalogram, core body temperature, salivary melatonin). Nurses have opportunities to design, test, and use interventions that improve sleep in patients with neurological conditions.

Sleep-wake detection using recurrence quantification analysis

Actigraphy is a method for monitoring the movements of the nondominant arm, and the technology has found applications ranging from clinical devices to smart wristbands. Time series obtained from actigraphy data is used in chronobiology to define the sleep-wake cycle, as well as in sleep medicine to evaluate an individual's sleep quality. In the study described in this paper, an algorithm based on recurrence quantification analysis (RQA) was applied to a time series obtained from a commercial actigraph, which was used to collect raw data alongside polysomnography (PSG), generally considered as the gold standard for assessing sleep quality. The central hypothesis is that transitions between sleep and wakefulness are not purely random events, but are strongly influenced by two internal processes: the homeostatic pressure and the circadian cycle. On the basis of this premise, application of RQA to time series as an estimator of this system should lead to improved results and allow more reliable investigations than a purely empirical approach. To compare the results from the RQA algorithm and those from PSG, we present a detailed statistical analysis involving a bias evaluation of the two methods following an approach suggested by Bland and Altman, a comparison of data processed using the kappa coefficient, and a comparison of consolidated sleep quality data using the p -value.

Achieving Accurate Automatic Sleep Staging on Manually Pre-processed EEG Data Through Synchronization Feature Extraction and Graph Metrics

Sleep staging, the process of assigning labels to epochs of sleep, depending on the stage of sleep they belong, is an arduous, time consuming and error prone process as the initial recordings are quite often polluted by noise from different sources. To properly analyze such data and extract clinical knowledge, noise components must be removed or alleviated. In this paper a pre-processing and subsequent sleep staging pipeline for the sleep analysis of electroencephalographic signals is described. Two novel methods of functional connectivity estimation (Synchronization Likelihood/SL and Relative Wavelet Entropy/RWE) are comparatively investigated for automatic sleep staging through manually pre-processed electroencephalographic recordings. A multi-step process that renders signals suitable for further analysis is initially described. Then, two methods that rely on extracting synchronization features from electroencephalographic recordings to achieve computerized sleep staging are proposed, based on bivariate features which provide a functional overview of the brain network, contrary to most proposed methods that rely on extracting univariate time and frequency features. Annotation of sleep epochs is achieved through the presented feature extraction methods by training classifiers, which are in turn able to accurately classify new epochs. Analysis of data from sleep experiments on a randomized, controlled bed-rest study, which was organized by the European Space Agency and was conducted in the "ENVIHAB" facility of the Institute of Aerospace Medicine at the German Aerospace Center (DLR) in Cologne, Germany attains high accuracy rates, over 90% based on ground truth that resulted from manual sleep staging by two experienced sleep experts. Therefore, it can be concluded that the above feature extraction methods are suitable for semi-automatic sleep staging.

Reentrainment of the circadian pacemaker during jet lag: East-west asymmetry and the effects of north-south travel

The normal alignment of circadian rhythms with the 24-h light-dark cycle is disrupted after rapid travel between home and destination time zones, leading to sleep problems, indigestion, and other symptoms collectively known as jet lag. Using mathematical and computational analysis, we study the process of reentrainment to the light-dark cycle of the destination time zone in a model of the human circadian pacemaker. We calculate the reentrainment time for travel between any two points on the globe at any time of the day and year. We construct one-dimensional entrainment maps to explain several properties of jet lag, such as why most people experience worse jet lag after traveling east than west. We show that this east-west asymmetry depends on the endogenous period of the traveler's circadian clock as well as daylength. Thus the critical factor is not simply whether the endogenous period is greater than or less than 24 h as is commonly assumed. We show that the unstable fixed point of an entrainment map determines whether a traveler reentrains through phase advances or phase delays, providing an understanding of the threshold that separates orthodromic and antidromic modes of reentrainment. Contrary to the conventional wisdom that jet lag only occurs after east-west travel across multiple time zones, we predict that the change in daylength encountered during north-south travel can cause jet lag even when no time zones are crossed. Our techniques could be used to provide advice to travelers on how to minimize jet lag on trips involving multiple destinations and a combination of transmeridian and translatitudinal travel.

Lhx6-positive GABA-releasing neurons of the zona incerta promote sleep

Multiple populations of wake-promoting neurons have been characterized in mammals, but few sleep-promoting neurons have been identified. Wake-promoting cell types include hypocretin and GABA (γ-aminobutyric-acid)-releasing neurons of the lateral hypothalamus, which promote the transition to wakefulness from non-rapid eye movement (NREM) and rapid eye movement (REM) sleep. Here we show that a subset of GABAergic neurons in the mouse ventral zona incerta, which express the LIM homeodomain factor Lhx6 and are activated by sleep pressure, both directly inhibit wake-active hypocretin and GABAergic cells in the lateral hypothalamus and receive inputs from multiple sleep-wake-regulating neurons. Conditional deletion of Lhx6 from the developing diencephalon leads to decreases in both NREM and REM sleep. Furthermore, selective activation and inhibition of Lhx6-positive neurons in the ventral zona incerta bidirectionally regulate sleep time in adult mice, in part through hypocretin-dependent mechanisms. These studies identify a GABAergic subpopulation of neurons in the ventral zona incerta that promote sleep.

Cognitive brain responses during circadian wake-promotion: evidence for sleep-pressure-dependent hypothalamic activations

The two-process model of sleep-wake regulation posits that sleep-wake-dependent homeostatic processes interact with the circadian timing system to affect human behavior. The circadian timing system is fundamental to maintaining stable cognitive performance, as it counteracts growing homeostatic sleep pressure during daytime. Using magnetic resonance imaging, we explored brain responses underlying working memory performance during the time of maximal circadian wake-promotion under varying sleep pressure conditions. Circadian wake-promoting strength was derived from the ability to sleep during an evening nap. Hypothalamic BOLD activity was positively linked to circadian wake-promoting strength under normal, but not under disproportionally high or low sleep pressure levels. Furthermore, higher hypothalamic activity under normal sleep pressure levels predicted better performance under sleep loss. Our results reappraise the two-process model by revealing a homeostatic-dose-dependent association between circadian wake-promotion and cognition-related hypothalamic activity.

The effects of self-selected light-dark cycles and social constraints on human sleep and circadian timing: a modeling approach

Why do we go to sleep late and struggle to wake up on time? Historically, light-dark cycles were dictated by the solar day, but now humans can extend light exposure by switching on artificial lights. We use a mathematical model incorporating effects of light, circadian rhythmicity and sleep homeostasis to provide a quantitative theoretical framework to understand effects of modern patterns of light consumption on the human circadian system. The model shows that without artificial light humans wakeup at dawn. Artificial light delays circadian rhythmicity and preferred sleep timing and compromises synchronisation to the solar day when wake-times are not enforced. When wake-times are enforced by social constraints, such as work or school, artificial light induces a mismatch between sleep timing and circadian rhythmicity ('social jet-lag'). The model implies that developmental changes in sleep homeostasis and circadian amplitude make adolescents particularly sensitive to effects of light consumption. The model predicts that ameliorating social jet-lag is more effectively achieved by reducing evening light consumption than by delaying social constraints, particularly in individuals with slow circadian clocks or when imposed wake-times occur after sunrise. These theory-informed predictions may aid design of interventions to prevent and treat circadian rhythm-sleep disorders and social jet-lag.

High metabolic demand in neural tissues: Information and control theory perspectives on the synergism between rate and stability

Evolutionary process has been selected for inherently unstable systems in higher animals that can react swiftly to changing patterns of threat or opportunity, for example blood pressure, the immune response, and gene expression. However, these require continual strict regulation: uncontrolled blood pressure is fatal, immune cells can attack 'self' tissues, and improper gene expression triggers developmental disorders. Consciousness in particular demands high rates of metabolic free energy to both operate and regulate the fundamental biological machinery: both the 'stream of consciousness' and the 'riverbanks' that confine it to useful realms are constructed and reconstructed moment-by-moment in response to highly dynamic internal and environmental circumstances. We develop powerful necessary conditions models for such phenomena based on the Data Rate Theorem linking control and information theories in the context of inherent instability. The synergism between conscious action and its regulation underlies the ten-fold higher rate of metabolic energy consumption in human neural tissues and implies a close, culturally modulated relation between sleep disorders and certain psychopathologies.

Wake-sleep transition as a noisy bifurcation

A recent physiologically based model of the ascending arousal system is used to analyze the dynamics near the transition from wake to sleep, which corresponds to a saddle-node bifurcation at a critical point. A normal form is derived by approximating the dynamics by those of a particle in a parabolic potential well with dissipation. This mechanical analog is used to calculate the power spectrum of fluctuations in response to a white noise drive, and the scalings of fluctuation variance and spectral width are derived versus distance from the critical point. The predicted scalings are quantitatively confirmed by numerical simulations, which show that the variance increases and the spectrum undergoes critical slowing, both in accord with theory. These signals can thus serve as potential precursors to indicate imminent wake-sleep transition, with potential application to safety-critical occupations in transport, air-traffic control, medicine, and heavy industry.

A Neurophysiological Approach for Evaluating Noise-Induced Sleep Disturbance: Calculating the Time Constant of the Dynamic Characteristics in the Brainstem

Chronic sleep disturbance induced by traffic noise is considered to cause environmental sleep disorder, which increases the risk of cardiovascular disease, stroke, diabetes and other stress-related diseases. However, noise indices for the evaluation of sleep disturbance are not based on the neurophysiological process of awakening regulated by the brainstem. In this study, through the neurophysiological approach, we attempted (1) to investigate the thresholds of awakening due to external stimuli in the brainstem; (2) to evaluate the dynamic characteristics in the brainstem and (3) to verify the validity of existing noise indices. Using the mathematical Phillips-Robinson model, we obtained thresholds of awakening in the brainstem for different durations of external stimuli. The analysis revealed that the brainstem seemed insensitive to short stimuli and that the response to external stimuli in the brainstem could be approximated by a first-order lag system with a time constant of 10-100 s. These results suggest that the brainstem did not integrate sound energy as external stimuli, but neuroelectrical signals from auditory nerve. To understand the awakening risk accumulated in the brainstem, we introduced a new concept of "awakening potential" instead of sound energy.

Exponential state transition dynamics in the rest-activity architecture of patients with bipolar disorder

OBJECTIVE

Our goal was to model the temporal dynamics of sleep-wake transitions, represented by transitions between rest and activity obtained from actigraphic data, in patients with bipolar disorder using a probabilistic state transition approach.

METHODS

We collected actigraphic data for 14 days from 20 euthymic patients with bipolar disorder, who had been characterized clinically, demographically, and with respect to their circadian preferences (chronotype). We processed each activity record to generate a series of transitions in both directions between the states of rest (R) and activity (A) and plotted the estimated transition probabilities (pRA and pAR). Each 24-hour period was also divided into a rest phase consisting of the eight consecutive least active hours in each day and an active phase consisting of the 16 consecutive most active hours in each day. We then calculated separate transition probabilities for each of these phases for each participant. We subsequently modeled the rest phase data to find the best fit for rest-activity transitions using maximum likelihood estimation. We also examined the association of transition probabilities with clinical and demographic variables.

RESULTS

The best-fit model for rest-activity transitions during the rest phase was a mixture (bimodal) of exponential functions. Of those patients with rapid cycling, 75% had an evening-type chronotype. Patients with bipolar II disorder taking antidepressants had a lower probability of transitioning back to rest than those not on antidepressants [mean ± SD = 0.050 ± 0.006 versus 0.141 ± 0.058, F(1,15) = 3.40, p < 0.05].

CONCLUSIONS

The dynamics of transitions between rest and activity in bipolar disorder can be accounted for by a mixture (bimodal) of exponential functions. Patients taking antidepressants had a reduced probability of sustaining and returning to sleep.