Quantitative modelling of sleep dynamics

Investigating sleep, stress, and mood dynamics via temporal network analysis

OBJECTIVE/BACKGROUND

Prior research has emphasized the bidirectional relationships between sleep, stress, and affective states, such as depression. Given the inherent variability and fluctuations associated with sleep, assessing how sleep and affective variables function within a dynamic system may help further uncover possible causes and consequences of sleep disturbances, as well as find candidate targets for intervention. To this end, we examined dynamic relationships between self-reported stress, depressed mood, and clinically-relevant sleep parameters via temporal network analysis.

METHODS

Participants were 401 nurses (92% female, 78% White, Mage = 39.47 years) who completed 14 days of sleep diaries incorporating self-reported stress and depression, as well as total sleep time, sleep efficiency, sleep onset latency, and wake after sleep onset.

RESULTS AND CONCLUSIONS

Overall, total sleep time emerged as a highly influential variable in the context of "outstrength centrality," meaning total sleep time had numerous outward connections with other variables (e.g., stress and sleep efficiency). The high outstrength centrality of total sleep time suggests this variable is a source of activation within this dynamic system. Conversely, stress showed high "instrength centrality," suggesting this variable was highly impacted by other variables in the system, such as depressed mood and sleep efficiency. These findings emphasize the importance of assessing unfolding sleep processes within a naturalistic setting, and implicate the role of total sleep time in fueling depressed mood and stress. Discussion emphasizes implications of these results for understanding the connections between sleep, stress, and depression as well as clinical relevance of these findings.

Cortical waste clearance in normal and restricted sleep with potential runaway tau buildup in Alzheimer's disease

Accumulation of waste in cortical tissue and glymphatic waste clearance via extracellular voids partly drives the sleep-wake cycle and modeling has reproduced much of its dynamics. Here, new modeling incorporates higher void volume and clearance in sleep, multiple waste compounds, and clearance obstruction by waste. This model reproduces normal sleep-wake cycles, sleep deprivation effects, and performance decreases under chronic sleep restriction (CSR). Once fitted to calibration data, it successfully predicts dynamics in further experiments on sleep deprivation, intermittent CSR, and recovery after restricted sleep. The results imply a central role for waste products with lifetimes similar to tau protein. Strong tau buildup is predicted if pathologically enhanced production or impaired clearance occur, with runaway buildup above a critical threshold. Predicted tau accumulation has timescales consistent with the development of Alzheimer’s disease. The model unifies a wide sweep of phenomena, clarifying the role of glymphatic clearance and targets for interventions against waste buildup.

Dynamics of sleep: Exploring critical transitions and early warning signals

BACKGROUND AND OBJECTIVES

In standard practice, sleep is classified into distinct stages by human observers according to specific rules as for instance specified in the AASM manual. We here show proof of principle for a conceptualization of sleep stages as attractor states in a nonlinear dynamical system in order to develop new empirical criteria for sleep stages.

METHODS

EEG (single channel) of two healthy sleeping participants was used to demonstrate this conceptualization. Firstly, distinct EEG epochs were selected, both detected by a MLR classifier and through manual scoring. Secondly, change point analysis was used to identify abrupt changes in the EEG signal. Thirdly, these detected change points were evaluated on whether they were preceded by early warning signals.

RESULTS

Multiple change points were identified in the EEG signal, mostly in interplay with N2. The dynamics before these changes revealed, for a part of the change points, indicators of generic early warning signals, characteristic of complex systems (e.g., ecosystems, climate, epileptic seizures, global finance systems).

CONCLUSIONS

The sketched new framework for studying critical transitions in sleep EEG might benefit the understanding of individual and pathological differences in the dynamics of sleep stage transitions. Formalising sleep as a nonlinear dynamical system can be useful for definitions of sleep quality, i.e. stability and accessibility of an equilibrium state, and disrupted sleep, i.e. constant shifting between instable sleep states.

An electrophysiological marker of arousal level in humans

Deep non-rapid eye movement sleep (NREM) and general anesthesia with propofol are prominent states of reduced arousal linked to the occurrence of synchronized oscillations in the electroencephalogram (EEG). Although rapid eye movement (REM) sleep is also associated with diminished arousal levels, it is characterized by a desynchronized, 'wake-like' EEG. This observation implies that reduced arousal states are not necessarily only defined by synchronous oscillatory activity. Using intracranial and surface EEG recordings in four independent data sets, we demonstrate that the 1/f spectral slope of the electrophysiological power spectrum, which reflects the non-oscillatory, scale-free component of neural activity, delineates wakefulness from propofol anesthesia, NREM and REM sleep. Critically, the spectral slope discriminates wakefulness from REM sleep solely based on the neurophysiological brain state. Taken together, our findings describe a common electrophysiological marker that tracks states of reduced arousal, including different sleep stages as well as anesthesia in humans.

Pathway-Dependent Regulation of Sleep Dynamics in a Network Model of the Sleep-Wake Cycle

Sleep is a fundamental homeostatic process within the animal kingdom. Although various brain areas and cell types are involved in the regulation of the sleep-wake cycle, it is still unclear how different pathways between neural populations contribute to its regulation. Here we address this issue by investigating the behavior of a simplified network model upon synaptic weight manipulations. Our model consists of three neural populations connected by excitatory and inhibitory synapses. Activity in each population is described by a firing-rate model, which determines the state of the network. Namely wakefulness, rapid eye movement (REM) sleep or non-REM (NREM) sleep. By systematically manipulating the synaptic weight of every pathway, we show that even this simplified model exhibits non-trivial behaviors: for example, the wake-promoting population contributes not just to the induction and maintenance of wakefulness, but also to sleep induction. Although a recurrent excitatory connection of the REM-promoting population is essential for REM sleep genesis, this recurrent connection does not necessarily contribute to the maintenance of REM sleep. The duration of NREM sleep can be shortened or extended by changes in the synaptic strength of the pathways from the NREM-promoting population. In some cases, there is an optimal range of synaptic strengths that affect a particular state, implying that the amount of manipulations, not just direction (i.e., activation or inactivation), needs to be taken into account. These results demonstrate pathway-dependent regulation of sleep dynamics and highlight the importance of systems-level quantitative approaches for sleep-wake regulatory circuits.

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.

Mathematical modeling of circadian rhythms

Circadian rhythms are endogenous ~24-hr oscillations usually entrained to daily environmental cycles of light/dark. Many biological processes and physiological functions including mammalian body temperature, the cell cycle, sleep/wake cycles, neurobehavioral performance, and a wide range of diseases including metabolic, cardiovascular, and psychiatric disorders are impacted by these rhythms. Circadian clocks are present within individual cells and at tissue and organismal levels as emergent properties from the interaction of cellular oscillators. Mathematical models of circadian rhythms have been proposed to provide a better understanding of and to predict aspects of this complex physiological system. These models can be used to: (a) manipulate the system in silico with specificity that cannot be easily achieved using in vivo and in vitro experimental methods and at lower cost, (b) resolve apparently contradictory empirical results, (c) generate hypotheses, (d) design new experiments, and (e) to design interventions for altering circadian rhythms. Mathematical models differ in structure, the underlying assumptions, the number of parameters and variables, and constraints on variables. Models representing circadian rhythms at different physiologic scales and in different species are reviewed to promote understanding of these models and facilitate their use. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Circuit mechanisms and computational models of REM sleep

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REM sleep was discovered in the 1950s.

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Many hypothalamic and brainstem areas have been found to contribute to REM sleep.

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An up-to-date picture of REM-sleep-regulating circuits is reviewed.

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A brief overview of computational models for REM sleep regulation is provided.

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Outstanding issues for future studies are discussed.

Rapid eye movement (REM) sleep or paradoxical sleep is an elusive behavioral state. Since its discovery in the 1950s, our knowledge of the neuroanatomy, neurotransmitters and neuropeptides underlying REM sleep regulation has continually evolved in parallel with the development of novel technologies. Although the pons was initially discovered to be responsible for REM sleep, it has since been revealed that many components in the hypothalamus, midbrain, pons, and medulla also contribute to REM sleep. In this review, we first provide an up-to-date overview of REM sleep-regulating circuits in the brainstem and hypothalamus by summarizing experimental evidence from neuroanatomical, neurophysiological and gain- and loss-of-function studies. Second, because quantitative approaches are essential for understanding the complexity of REM sleep-regulating circuits and because mathematical models have provided valuable insights into the dynamics underlying REM sleep genesis and maintenance, we summarize computational studies of the sleep-wake cycle, with an emphasis on REM sleep regulation. Finally, we discuss outstanding issues for future studies.

Quantitative approaches to energy and glucose homeostasis: machine learning and modelling for precision understanding and prediction

Obesity is a major global public health problem. Understanding how energy homeostasis is regulated, and can become dysregulated, is crucial for developing new treatments for obesity. Detailed recording of individual behaviour and new imaging modalities offer the prospect of medically relevant models of energy homeostasis that are both understandable and individually predictive. The profusion of data from these sources has led to an interest in applying machine learning techniques to gain insight from these large, relatively unstructured datasets. We review both physiological models and machine learning results across a diverse range of applications in energy homeostasis, and highlight how modelling and machine learning can work together to improve predictive ability. We collect quantitative details in a comprehensive mathematical supplement. We also discuss the prospects of forecasting homeostatic behaviour and stress the importance of characterizing stochasticity within and between individuals in order to provide practical, tailored forecasts and guidance to combat the spread of obesity.

Multistability in the corticothalamic system

Neural field theory of the corticothalamic system is used to analyze the properties of its steady-state solutions, including their linear stability, in the parameter space of synaptic couplings for physiological parameter ranges representing normal arousal waking states in adult humans. The independent connections of the corticothalamic model define an eight-dimensional parameter space, while specific combinations of these connections parameterize intracortical, corticothalamic, and intrathalamic loops. Multistable regions are systematically identified and the existence of up to five steady-state solutions is confirmed, up to three of which are linearly stable. A key determinant for the existence of five steady states is found to be the number of nonzero connections. This finding had not been previously proposed as the determining factor of high multiplicities of multistability in mesoscopic models of the brain. In the corticothalamic model presented here, multistability occurs when the intrathalamic loop is present (i.e., the reticular nucleus inhibits the relay nuclei), and when the net synaptic effect of the intracortical loop is inhibitory. The signature of these additional waking states is an overall increased level of thalamic activity. It is argued that the additional steady states found may represent hyperarousal states which occur when the corticothalamic projections do not attenuate the activity of the cortex.

The pacemaker role of thalamic reticular nucleus in controlling spike-wave discharges and spindles

Absence epilepsy, characterized by 2-4 Hz spike-wave discharges (SWDs), can be caused by pathological interactions within the thalamocortical system. Cortical spindling oscillations are also demonstrated to involve the oscillatory thalamocortical rhythms generated by the synaptic circuitry of the thalamus and cortex. This implies that SWDs and spindling oscillations can share the common thalamocortical mechanism. Additionally, the thalamic reticular nucleus (RE) is hypothesized to regulate the onsets and propagations of both the epileptic SWDs and sleep spindles. Based on the proposed single-compartment thalamocortical neural field model, we firstly investigate the stimulation effect of RE on the initiations, terminations, and transitions of SWDs. It is shown that the activations and deactivations of RE triggered by single-pulse stimuli can drive the cortical subsystem to behave as the experimentally observed onsets and self-abatements of SWDs, as well as the transitions from 2-spike and wave discharges (2-SWDs) to SWDs. In particular, with increasing inhibition from RE to the specific relay nucleus (TC), rich transition behaviors in cortex can be obtained through the upstream projection path, RE→TC→Cortex. Although some of the complex dynamical patterns can be expected from the earlier single compartment thalamocortical model, the effect of brain network topology on the emergence of SWDs and spindles, as well as the transitions between them, has not been fully investigated. We thereby develop a spatially extended 3-compartment coupled network model with open-/closed-end connective configurations, to investigate the spatiotemporal effect of RE on the SWDs and spindles. Results show that the degrees of activations of RE₁ can induce the rich spatiotemporal evolution properties including the propagations from SWDs to spindles within different compartments and the transitions between them, through the RE₁→TC₁→Cortex₁ and Cortex₁→Cortex₂→Cortex₃ projecting paths, respectively. Overall, those results imply that RE possesses the pacemaker function in controlling SWDs and spindling oscillations, which computationally provide causal support for the involvement of RE in absence seizures and sleep spindles.

Cellular and neurochemical basis of sleep stages in the thalamocortical network

The link between the combined action of neuromodulators in the brain and global brain states remains a mystery. In this study, using biophysically realistic models of the thalamocortical network, we identified the critical intrinsic and synaptic mechanisms, associated with the putative action of acetylcholine (ACh), GABA and monoamines, which lead to transitions between primary brain vigilance states (waking, non-rapid eye movement sleep [NREM] and REM sleep) within an ultradian cycle. Using ECoG recordings from humans and LFP recordings from cats and mice, we found that during NREM sleep the power of spindle and delta oscillations is negatively correlated in humans and positively correlated in animal recordings. We explained this discrepancy by the differences in the relative level of ACh. Overall, our study revealed the critical intrinsic and synaptic mechanisms through which different neuromodulators acting in combination result in characteristic brain EEG rhythms and transitions between sleep stages.

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.

Multimodal antidepressant vortioxetine increases frontal cortical oscillations unlike escitalopram and duloxetine--a quantitative EEG study in rats

Background and Purpose

EEG studies show that 5-HT is involved in regulation of sleep–wake state and modulates cortical oscillations. Vortioxetine is a 5-HT₃, 5-HT₇, and 5-HT_1D receptor antagonist, 5-HT_1B partial agonist, 5-HT_1A agonist, and 5-HT transporter inhibitor. Preclinical (animal) and clinical studies with vortioxetine show positive impact on cognitive metrics involving cortical function. Here we assess vortioxetine's effect on cortical neuronal oscillations in actively awake rats.

Experimental Approach

Telemetric EEG recordings were obtained with the following treatments (mg·kg⁻¹, s.c.): vehicle, vortioxetine (0.1, 1.0, 3.0, 10), 5-HT_1A agonist flesinoxan (2.5), 5-HT₃ antagonist ondansetron (0.30), 5-HT₇ antagonist SB-269970-A (10), escitalopram (2.0), duloxetine (10) and vortioxetine plus flesinoxan. Target occupancies were determined by ex vivo autoradiography.

Key Results

Vortioxetine dose-dependently increased wakefulness. Flesinoxan, duloxetine, ondansetron, but not escitalopram or SB-269970-A increased wakefulness. Quantitative spectral analyses showed vortioxetine alone and with flesinoxan increased θ (4–8 Hz), α (8–12 Hz) and γ (30–50 Hz) power. Duloxetine had no effect on θ and γ, but decreased α power, while escitalopram produced no changes. Ondansetron and SB-269970 (≈31–35% occupancy) increased θ power. Flesinoxan (≈41% occupancy) increased θ and γ power.

Conclusions and Implications

Vortioxetine increased wakefulness and increased frontal cortical activity, most likely because of its 5-HT₇ and 5-HT₃ antagonism and 5-HT_1A agonism. Vortioxetine differs from escitalopram and duloxetine by increasing cortical θ, α and γ oscillations. These preclinical findings suggest a role of vortioxetine in modulating cortical circuits known to be recruited during cognitive behaviours and warrant further investigation as to their clinical impact.

Sleep-wake evaluation from whole-night non-contact audio recordings of breathing sounds

STUDY OBJECTIVES

To develop and validate a novel non-contact system for whole-night sleep evaluation using breathing sounds analysis (BSA).

DESIGN

Whole-night breathing sounds (using ambient microphone) and polysomnography (PSG) were simultaneously collected at a sleep laboratory (mean recording time 7.1 hours). A set of acoustic features quantifying breathing pattern were developed to distinguish between sleep and wake epochs (30 sec segments). Epochs (n = 59,108 design study and n = 68,560 validation study) were classified using AdaBoost classifier and validated epoch-by-epoch for sensitivity, specificity, positive and negative predictive values, accuracy, and Cohen's kappa. Sleep quality parameters were calculated based on the sleep/wake classifications and compared with PSG for validity.

SETTING

University affiliated sleep-wake disorder center and biomedical signal processing laboratory.

PATIENTS

One hundred and fifty patients (age 54.0±14.8 years, BMI 31.6±5.5 kg/m2, m/f 97/53) referred for PSG were prospectively and consecutively recruited. The system was trained (design study) on 80 subjects; validation study was blindly performed on the additional 70 subjects.

MEASUREMENTS AND RESULTS

Epoch-by-epoch accuracy rate for the validation study was 83.3% with sensitivity of 92.2% (sleep as sleep), specificity of 56.6% (awake as awake), and Cohen's kappa of 0.508. Comparing sleep quality parameters of BSA and PSG demonstrate average error of sleep latency, total sleep time, wake after sleep onset, and sleep efficiency of 16.6 min, 35.8 min, and 29.6 min, and 8%, respectively.

CONCLUSIONS

This study provides evidence that sleep-wake activity and sleep quality parameters can be reliably estimated solely using breathing sound analysis. This study highlights the potential of this innovative approach to measure sleep in research and clinical circumstances.

Characterization of K-complexes and slow wave activity in a neural mass model

NREM sleep is characterized by two hallmarks, namely K-complexes (KCs) during sleep stage N2 and cortical slow oscillations (SOs) during sleep stage N3. While the underlying dynamics on the neuronal level is well known and can be easily measured, the resulting behavior on the macroscopic population level remains unclear. On the basis of an extended neural mass model of the cortex, we suggest a new interpretation of the mechanisms responsible for the generation of KCs and SOs. As the cortex transitions from wake to deep sleep, in our model it approaches an oscillatory regime via a Hopf bifurcation. Importantly, there is a canard phenomenon arising from a homoclinic bifurcation, whose orbit determines the shape of large amplitude SOs. A KC corresponds to a single excursion along the homoclinic orbit, while SOs are noise-driven oscillations around a stable focus. The model generates both time series and spectra that strikingly resemble real electroencephalogram data and points out possible differences between the different stages of natural sleep.

Engineering a thalamo-cortico-thalamic circuit on SpiNNaker: a preliminary study toward modeling sleep and wakefulness

We present a preliminary study of a thalamo-cortico-thalamic (TCT) implementation on SpiNNaker (Spiking Neural Network architecture), a brain inspired hardware platform designed to incorporate the inherent biological properties of parallelism, fault tolerance and energy efficiency. These attributes make SpiNNaker an ideal platform for simulating biologically plausible computational models. Our focus in this work is to design a TCT framework that can be simulated on SpiNNaker to mimic dynamical behavior similar to Electroencephalogram (EEG) time and power-spectra signatures in sleep-wake transition. The scale of the model is minimized for simplicity in this proof-of-concept study; thus the total number of spiking neurons is ≈1000 and represents a "mini-column" of the thalamocortical tissue. All data on model structure, synaptic layout and parameters is inspired from previous studies and abstracted at a level that is appropriate to the aims of the current study as well as computationally suitable for model simulation on a small 4-chip SpiNNaker system. The initial results from selective deletion of synaptic connectivity parameters in the model show similarity with EEG power spectra characteristics of sleep and wakefulness. These observations provide a positive perspective and a basis for future implementation of a very large scale biologically plausible model of thalamo-cortico-thalamic interactivity-the essential brain circuit that regulates the biological sleep-wake cycle and associated EEG rhythms.

Coupled flip-flop model for REM sleep regulation in the rat

Recent experimental studies investigating the neuronal regulation of rapid eye movement (REM) sleep have identified mutually inhibitory synaptic projections among REM sleep-promoting (REM-on) and REM sleep-inhibiting (REM-off) neuronal populations that act to maintain the REM sleep state and control its onset and offset. The control mechanism of mutually inhibitory synaptic interactions mirrors the proposed flip-flop switch for sleep-wake regulation consisting of mutually inhibitory synaptic projections between wake- and sleep-promoting neuronal populations. While a number of synaptic projections have been identified between these REM-on/REM-off populations and wake/sleep-promoting populations, the specific interactions that govern behavioral state transitions have not been completely determined. Using a minimal mathematical model, we investigated behavioral state transition dynamics dictated by a system of coupled flip-flops, one to control transitions between wake and sleep states, and another to control transitions into and out of REM sleep. The model describes the neurotransmitter-mediated inhibitory interactions between a wake- and sleep-promoting population, and between a REM-on and REM-off population. We proposed interactions between the wake/sleep and REM-on/REM-off flip-flops to replicate the behavioral state statistics and probabilities of behavioral state transitions measured from experimental recordings of rat sleep under ad libitum conditions and after 24 h of REM sleep deprivation. Reliable transitions from REM sleep to wake, as dictated by the data, indicated the necessity of an excitatory projection from the REM-on population to the wake-promoting population. To replicate the increase in REM-wake-REM transitions observed after 24 h REM sleep deprivation required that this excitatory projection promote transient activation of the wake-promoting population. Obtaining the reliable wake-nonREM sleep transitions observed in the data required that activity of the wake-promoting population modulated the interaction between the REM-on and REM-off populations. This analysis suggests neuronal processes to be targeted in further experimental studies of the regulatory mechanisms of REM sleep.

Human turnover dynamics during sleep: statistical behavior and its modeling

Turnover is a typical intermittent body movement while asleep. Exploring its behavior may provide insights into the mechanisms and management of sleep. However, little is understood about the dynamic nature of turnover in healthy humans and how it can be modified in disease. Here we present a detailed analysis of turnover signals that are collected by accelerometry from healthy elderly subjects and age-matched patients with neurodegenerative disorders such as Parkinson's disease. In healthy subjects, the time intervals between consecutive turnover events exhibit a well-separated bimodal distribution with one mode at ⩽10 s and the other at ⩾100 s, whereas such bimodality tends to disappear in neurodegenerative patients. The discovery of bimodality and fine temporal structures (⩽10 s) is a contribution that is not revealed by conventional sleep recordings with less time resolution (≈30 s). Moreover, we estimate the scaling exponent of the interval fluctuations, which also shows a clear difference between healthy subjects and patients. We incorporate these experimental results into a computational model of human decision making. A decision is to be made at each simulation step between two choices: to keep on sleeping or to make a turnover, the selection of which is determined dynamically by comparing a pair of random numbers assigned to each choice. This decision is weighted by a single parameter that reflects the depth of sleep. The resulting simulated behavior accurately replicates many aspects of observed turnover patterns, including the appearance or disappearance of bimodality and leads to several predictions, suggesting that the depth parameter may be useful as a quantitative measure for differentiating between normal and pathological sleep. These findings have significant clinical implications and may pave the way for the development of practical sleep assessment technologies.

Physiologically-based modeling of sleep-wake regulatory networks

Mathematical modeling has played a significant role in building our understanding of sleep-wake and circadian behavior. Over the past 40 years, phenomenological models, including the two-process model and oscillator models, helped frame experimental results and guide progress in understanding the interaction of homeostatic and circadian influences on sleep and understanding the generation of rapid eye movement sleep cycling. Recent advances in the clarification of the neural anatomy and physiology involved in the regulation of sleep and circadian rhythms have motivated the development of more detailed and physiologically-based mathematical models that extend the approach introduced by the classical reciprocal-interaction model. Using mathematical formalisms developed in the field of computational neuroscience to model neuronal population activity, these models investigate the dynamics of proposed conceptual models of sleep-wake regulatory networks with a focus on generating appropriate sleep and wake state transition patterns as well as simulating disease states and experimental protocols. In this review, we discuss several recent physiologically-based mathematical models of sleep-wake regulatory networks. We identify common features among these models in their network structures, model dynamics and approaches for model validation. We describe how the model analysis technique of fast-slow decomposition, which exploits the naturally occurring multiple timescales of sleep-wake behavior, can be applied to understand model dynamics in these networks. Our purpose in identifying commonalities among these models is to propel understanding of both the mathematical models and their underlying conceptual models, and focus directions for future experimental and theoretical work.

Effects of Rotation Interval on Sleepiness and Circadian Dynamics on Forward Rotating 3-Shift Systems

A physiologically based mathematical model of sleep-wake cycles is used to examine the effects of shift rotation interval (RI) (i.e., the number of days spent on each shift) on sleepiness and circadian dynamics on forward rotating 3-shift schedules. The effects of the schedule start time on the mean shift sleepiness are also demonstrated but are weak compared to the effects of RI. The dynamics are studied for a parameter set adjusted to match a most common natural sleep pattern (i.e., sleep between 0000 and 0800) and for common light conditions (i.e., 350 lux of shift lighting, 200 lux of daylight, 100 lux of artificial lighting during nighttime, and 0 lux during sleep). Mean shift sleepiness on a rotating schedule is found to increase with RI, reach maximum at intermediate RI=6 d, and then decrease. Complete entrainment to shifts within the schedules is not achieved at RI≤10 d. However, circadian oscillations synchronize to the rotation cycles, with RI=1,2 d and RI≥6 d demonstrating regular periodic changes of the circadian rhythm. At rapid rotation, circadian phase stays within a small 4-h interval, whereas slow rotation leads to around-the-clock transitions of the circadian phase with constantly delayed sleep times. Schedules with RI=3-5 d are not able to entrain the circadian rhythms, even in the absence of external circadian disturbances like social commitments and days off. To understand the circadian dynamics on the rotating shift schedules, a shift response map is developed, showing the direction of circadian change (i.e., delay or advance) depending on the relation between the shift start time and actual circadian phase. The map predicts that the un-entrained dynamics come from multiple transitions between advance and delay behavior on the shifts in the schedules. These are primarily caused by the imbalance between the amount of delay and advance on the different shift types within the schedule. Finally, it is argued that shift response maps can aid in the development of shift schedules with desired circadian characteristics.

Mammalian rest/activity patterns explained by physiologically based modeling

Circadian rhythms are fundamental to life. In mammals, these rhythms are generated by pacemaker neurons in the suprachiasmatic nucleus (SCN) of the hypothalamus. The SCN is remarkably consistent in structure and function between species, yet mammalian rest/activity patterns are extremely diverse, including diurnal, nocturnal, and crepuscular behaviors. Two mechanisms have been proposed to account for this diversity: (i) modulation of SCN output by downstream nuclei, and (ii) direct effects of light on activity. These two mechanisms are difficult to disentangle experimentally and their respective roles remain unknown. To address this, we developed a computational model to simulate the two mechanisms and their influence on temporal niche. In our model, SCN output is relayed via the subparaventricular zone (SPZ) to the dorsomedial hypothalamus (DMH), and thence to ventrolateral preoptic nuclei (VLPO) and lateral hypothalamus (LHA). Using this model, we generated rich phenotypes that closely resemble experimental data. Modulation of SCN output at the SPZ was found to generate a full spectrum of diurnal-to-nocturnal phenotypes. Intriguingly, we also uncovered a novel mechanism for crepuscular behavior: if DMH/VLPO and DMH/LHA projections act cooperatively, daily activity is unimodal, but if they act competitively, activity can become bimodal. In addition, we successfully reproduced diurnal/nocturnal switching in the rodent Octodon degu using coordinated inversions in both masking and circadian modulation. Finally, the model correctly predicted the SCN lesion phenotype in squirrel monkeys: loss of circadian rhythmicity and emergence of ∼4-h sleep/wake cycles. In capturing these diverse phenotypes, the model provides a powerful new framework for understanding rest/activity patterns and relating them to underlying physiology. Given the ubiquitous effects of temporal organization on all aspects of animal behavior and physiology, this study sheds light on the physiological changes required to orchestrate adaptation to various temporal niches.

Modeling resting-state functional networks when the cortex falls asleep: local and global changes

The transition from wakefulness to sleep represents the most conspicuous change in behavior and the level of consciousness occurring in the healthy brain. It is accompanied by similarly conspicuous changes in neural dynamics, traditionally exemplified by the change from "desynchronized" electroencephalogram activity in wake to globally synchronized slow wave activity of early sleep. However, unit and local field recordings indicate that the transition is more gradual than it might appear: On one hand, local slow waves already appear during wake; on the other hand, slow sleep waves are only rarely global. Studies with functional magnetic resonance imaging also reveal changes in resting-state functional connectivity (FC) between wake and slow wave sleep. However, it remains unclear how resting-state networks may change during this transition period. Here, we employ large-scale modeling of the human cortico-cortical anatomical connectivity to evaluate changes in resting-state FC when the model "falls asleep" due to the progressive decrease in arousal-promoting neuromodulation. When cholinergic neuromodulation is parametrically decreased, local slow waves appear, while the overall organization of resting-state networks does not change. Furthermore, we show that these local slow waves are structured macroscopically in networks that resemble the resting-state networks. In contrast, when the neuromodulator decrease further to very low levels, slow waves become global and resting-state networks merge into a single undifferentiated, broadly synchronized network.

Implementing the cellular mechanisms of synaptic transmission in a neural mass model of the thalamo-cortical circuitry

A novel direction to existing neural mass modeling technique is proposed where the commonly used “alpha function” for representing synaptic transmission is replaced by a kinetic framework of neurotransmitter and receptor dynamics. The aim is to underpin neuro-transmission dynamics associated with abnormal brain rhythms commonly observed in neurological and psychiatric disorders. An existing thalamocortical neural mass model is modified by using the kinetic framework for modeling synaptic transmission mediated by glutamatergic and GABA (gamma-aminobutyric-acid)-ergic receptors. The model output is compared qualitatively with existing literature on in vitro experimental studies of ferret thalamic slices, as well as on single-neuron-level model based studies of neuro-receptor and transmitter dynamics in the thalamocortical tissue. The results are consistent with these studies: the activation of ligand-gated GABA receptors is essential for generation of spindle waves in the model, while blocking this pathway leads to low-frequency synchronized oscillations such as observed in slow-wave sleep; the frequency of spindle oscillations increase with increased levels of post-synaptic membrane conductance for AMPA (alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic-acid) receptors, and blocking this pathway effects a quiescent model output. In terms of computational efficiency, the simulation time is improved by a factor of 10 compared to a similar neural mass model based on alpha functions. This implies a dramatic improvement in computational resources for large-scale network simulation using this model. Thus, the model provides a platform for correlating high-level brain oscillatory activity with low-level synaptic attributes, and makes a significant contribution toward advancements in current neural mass modeling paradigm as a potential computational tool to better the understanding of brain oscillations in sickness and in health.

The sleeping brain as a complex system

'Complexity science' is a rapidly developing research direction with applications in a multitude of fields that study complex systems consisting of a number of nonlinear elements with interesting dynamics and mutual interactions. This Theme Issue 'The complexity of sleep' aims at fostering the application of complexity science to sleep research, because the brain in its different sleep stages adopts different global states that express distinct activity patterns in large and complex networks of neural circuits. This introduction discusses the contributions collected in the present Theme Issue. We highlight the potential and challenges of a complex systems approach to develop an understanding of the brain in general and the sleeping brain in particular. Basically, we focus on two topics: the complex networks approach to understand the changes in the functional connectivity of the brain during sleep, and the complex dynamics of sleep, including sleep regulation. We hope that this Theme Issue will stimulate and intensify the interdisciplinary communication to advance our understanding of the complex dynamics of the brain that underlies sleep and consciousness.

Towards a model-based integration of co-registered electroencephalography/functional magnetic resonance imaging data with realistic neural population meshes

Brain activity can be measured with several non-invasive neuroimaging modalities, but each modality has inherent limitations with respect to resolution, contrast and interpretability. It is hoped that multimodal integration will address these limitations by using the complementary features of already available data. However, purely statistical integration can prove problematic owing to the disparate signal sources. As an alternative, we propose here an advanced neural population model implemented on an anatomically sound cortical mesh with freely adjustable connectivity, which features proper signal expression through a realistic head model for the electroencephalogram (EEG), as well as a haemodynamic model for functional magnetic resonance imaging based on blood oxygen level dependent contrast (fMRI BOLD). It hence allows simultaneous and realistic predictions of EEG and fMRI BOLD from the same underlying model of neural activity. As proof of principle, we investigate here the influence on simulated brain activity of strengthening visual connectivity. In the future we plan to fit multimodal data with this neural population model. This promises novel, model-based insights into the brain's activity in sleep, rest and task conditions.

The multiple time scales of sleep dynamics as a challenge for modelling the sleeping brain

A particular property of the sleeping brain is that it exhibits dynamics on very different time scales ranging from the typical sleep oscillations such as sleep spindles and slow waves that can be observed in electroencephalogram (EEG) segments of several seconds duration over the transitions between the different sleep stages on a time scale of minutes to the dynamical processes involved in sleep regulation with typical time constants in the range of hours. There is an increasing body of work on mathematical and computational models addressing these different dynamics, however, usually considering only processes on a single time scale. In this paper, we review and present a new analysis of the dynamics of human sleep EEG at the different time scales and relate the findings to recent modelling efforts pointing out both the achievements and remaining challenges.