Sleep Workshop: New Approaches to Modeling Sleep/Wake Dynamics and Cognitive Performance - sponsored by AFOSR

(October 26,2006 - October 27,2006 )

Organizers


Janet Best
David Terman
MBI, The Ohio State University
Hans Van Dongen
Sleep and Performance Research Center, Washington State University

This workshop will address several important aspects of sleep/wake modeling, including interactions between the homeostatic and circadian processes; the link between sleep/wake dynamics, cognitive capabilities and performance; and how individual differences should be incorporated into the models. Although these questions have received previous study, earlier models have been largely phenomenological and thus far have not accounted for many important aspects such as the cumulative effects of chronic sleep restriction. Recent progress in understanding the neuronal and neurochemical substrates underlying the sleep/wake cycle, as well as the development of theoretical tools for analyzing complex biologically inspired models, makes this an auspicious time to forge new modeling approaches. The workshop will bring together a diverse and highly accomplished group of researchers across the spectrum from experimentation to mathematics. The workshop will focus on the link between sleep/wake regulation and human cognitive performance. It will provide a unique opportunity to exchange points of view, forge new collaborations and develop new approaches to modeling these important issues.

The workshop will address three primary themes:

  1. Modeling the homeostatic system and how it interacts with the circadian system: Most current models for sleep/wake regulation and for interactions between the circadian and homeostatic processes are directly or indirectly based on the seminal two-process model of sleep regulation. The two-process model has been successful in accounting for the effects of acute sleep deprivation on sleep and performance; however, the model has been less successful in accounting for experiments involving chronic sleep restriction and subsequent recovery sleep periods. This may be because the two-process model assumes that recovery during sleep occurs in an exponential manner; moreover the model assumes that the homeostatic and circadian processes are additive. More detailed models are needed to better describe the homeostatic process and account for the chronic sleep restriction experiments.
  2. Modeling the link between sleep/wake dynamics and cognitive/psychomotor capabilities: Most current models estimate the general trend of performance decline under conditions of sleep loss and/or circadian misalignment. There is evidence that sleep/wake alterations have differential effects depending on the nature of the performance task-which is not accounted for in contemporary models. Furthermore, time on task effects have thus far not been included. There is a need to develop models in which parameters have specific physiological and/or neuropsychological correlates, so that the behavior of the model may be interpreted biologically and interventions may be incorporated appropriately.
  3. Modeling individual differences: Sleep/wake and performance modeling thus far has focused on describing and predicting group-average responses. However, there is accumulating evidence for trait-like individual differences in responses to sleep and circadian challenges. Such systematic individual differences tend to represent a considerable portion of the variance and therefore need to be accounted for. It remains to be determined whether capturing individual differences would require variations in model structure or could be handled with subject-specific parameter settings. New modeling strategies are needed to address these important issues.

Accepted Speakers

Peter Achermann
Institute of Pharmacology and Toxicology, University of Zurich
Domien Beersma
Chronobiology, Rijksuniversiteit te Groningen
Mark Blumberg
Psychology, University of Iowa
Derk-Jan Dijk
Biomedical and Molecular Sciences, University of Surrey
David Dinges
Psychiatry, University of Pennsylvania
Glenn Gunzelmann
Air Force Research Laboratory
Sean Hill
Blue Brain Project, Brain Mind Institute, Lausanne Switzerland
Jen-Kuang Huang
Mechanical Engineering, Old Dominion University
Christopher Mott
V.P. Engineering, Pulsar Informatics Inc
Erik Olofsen
Department of Anesthesiology P5Q , Rijksuniversiteit te Leiden
Clifford Saper
Neurology, Harvard Medical School
Giulio Tononi
Psychiatry, School of Medicine, University of Wisconsin
Thursday, October 26, 2006
Time Session
09:00 AM
10:00 AM
Peter Achermann - The Two-process Model of Sleep Regulation: Background and future directions

The two-process model of sleep regulation posits that the timing of sleep and waking is generated by the interaction of its two constituent processes, the sleep-wake dependent homeostatic Process S and the circadian Process C. In addition to the timing of sleep, the interaction of the two processes accounts for changes in daytime vigilance. The attractiveness of the model derives from its physiological basis and its mathematical simplicity. The time course of Process S was derived from a physiological variable, EEG slow-wave activity (SWA). The two-process model offers a conceptual framework for the analysis of existing and new data and stimulated the establishment of various models of neurobehavioral functions. The major of these models have already inspired a considerable number of experiments.


The background of the two-process model will be reviewed and discussed in the light of new findings. The following topics will be addressed: determination of the parameters of Process S; inter-individual differences; relationship between SWA and Process S in case of disturbed sleep; markers of sleep homeostasis in the waking and sleep EEG; regional and use-dependent aspects of sleep homeostasis; topographical differences in the dynamics of Process S and its consequences for modeling sleep regulation; synaptic plasticity and how slow oscillations (< 1 Hz) contribute to sleep homeostasis ; which additional processes are needed for modeling neurobehavioral functions; and whether the interaction of homeostatic and circadian processes is linear or non-linear.

10:15 AM
10:45 AM
Clifford Saper - Modeling Sleep and Wakefulness: The flip-flop model

Transitions between sleep and wakefulness are controlled by precise synaptic circuitry in the brain, and much of this has been mapped out in the past decade. Current models are based upon mutually inhibitory interactions between a master sleep switch, the ventrolateral preoptic nucleus, on the one hand, and a series of wake-promoting cell groups in the brainstem and hypothalamus, on the other hand. These interactions produce a flip-flop switch, and may account for the rapid and complete transitions between behavioral states that are seen in all animals.


The transitions between Rapid Eye Movement (REM) and non-REM sleep appear to be due to a second flip-flop switch in the brainstem. This switch is composed of mutually inhibitory neurons in distinct REM-off and REM-on areas of the pons. The REM switch appears under normal circumstances to be subsidiary to the wake-sleep switch, as transitions into REM states from wakefulness do not occur except under specific pathological conditions. One of those conditions is the loss of the orexin/hypocretin neurons in the lateral hypothalamus. These neurons appear to stabilize both the wake-sleep and the REM-nonREM switches.


The transitions between sleep and wake states also oscillate and appear to be under both homeostatic and circadian controls. The homeostatic input is thought to be regulated by buildup of substances in the brain during wakefulness, such as excess adenosine, that inhibit arousal systems, and activate sleep systems. Lesions of the ventrolateral preoptic nucleus prevent the homeostatic system from increasing sleep after sleep deprivation, suggesting that the action of the homeostatic system on this component of the sleep switch are critical.


Circadian drive for sleep and wakefulness appears to be mediated by the dorsomedial nucleus of the hypothalamus. This cell group normally comes under the influence of the brain's master biological clock, the suprachiasmatic nucleus. However, under some circumstances, e.g., when food is available only during the normal sleep period, it can take over (even in the absence of a suprachiasmatic nucleus) and remodel circadian influences to cause wakefulness to co-ordinate with the food availability. The outputs from the dorsomedial nucleus to the ventrolateral preoptic nucleus and to the orexin neurons may explain much of this influence.


These synaptic connections, most of which have been discovered only in the last few years, provide a solid basis for structuring mathematical models of the regulation of sleep and wakefulness.

10:45 AM
11:15 AM
Mark Blumberg - Tracking the Developmental Dynamics of Sleep and Wakefulness

Difficulties inherent in the measurement of sleep in early infancy have given rise to significant disagreements concerning the nature of infant sleep, its neural control, and its continuity with sleep in adults. By combining measures of nuchal and extraocular EMG during early development in rats, as well as neocortical EEG when possible, we have shown that infant sleep is neither undifferentiated nor primitive, as has been argued in the past. Moreover, the development of techniques for recording neurophysiological activity in infants has demonstrated that neural structures in the medulla, midbrain, and forebrain are involved in the regulation and modulation of behavioral states at ages before state-dependent EEG activity is detectable. Indeed, measurement of muscle tone alone provides surprisingly valuable information for defining infant sleep and for describing pronounced quantitative and qualitative changes in the statistical structure of sleep and wake bouts across development. These insights, gleaned from experiments in normal infant rats, have been extended to orexin knockout mice to suggest a surprising and counterintuitive interpretation of the relationship between fragmented states in adult narcoleptics and normal infants. Finally, our methods are allowing us to detect circadian rhythms of sleep and wakefulness near the time of birth and to track the relationship between circadian and ultradian rhythms across development. All together, these approaches and findings provide a rich foundation for the development of computational models that can account for the dynamics of sleep and wakefulness across the lifespan.

11:30 AM
12:00 PM
Domien Beersma - Mapping NREM Sleep Regulation across the Brain: Process S revisited

The regulation of the timing of sleep is thought to be linked to the temporal dynamics of slow-wave activity (SWA, EEG spectral power in ~0.75-4.5 Hz range) in the cortical NREM sleep EEG. In the two process model of sleep regulation, SWA was used as a direct indication of sleep debt. Originally, this was done in a gross way, by quantifying average SWA across NREM-REM sleep cycles. Later studies demonstrated that SWA could hardly be a direct reflection of S, but that SWA was proportional to the instantaneous decay rate of S. Following up on this, an extended model of SWA dynamics was developed, in which consequences of intrusions of REM sleep and wakefulness were incorporated. For each subject, a 'gain constant' value could be estimated quantifying the efficacy of SWA in dissipating S. Since the course of SWA is variable across cortical locations, local differences are likely to exist in the speed of discharge of Process S, eventually leading to different levels of S in different cortical regions. This disparity is in obvious contradiction with the concept of S in the two process model, because this would induce unambiguity in the regulation of sleep onset and termination. In this study we quantified the extent of local differences of SWA regulation on the basis of the extended model of SWA dynamics, for 26 locations on the scalp. We observed higher efficiency of SWA in dissipation of Process S in frontal EEG derivations, demonstrating once more that SWA regulation has a clear local aspect. The results further suggest that the Process S involved in SWA regulation is not identical to the Process S involved (together with Process C) in the determination of sleep timing. We therefore propose to distinguish these two representations and identify the former, purely SWA-related process, as 'Process Z'.

12:00 PM
12:30 PM
Sean Hill - Modeling Wakefulness and Sleep in the Thalamocortical System

When the brain goes from wakefulness to sleep, cortical neurons begin to undergo slow oscillations in their membrane potential that are synchronized by thalamocortical circuits and reflected in EEG slow waves. In order to provide a self-consistent account of the transition from wakefulness to sleep and of the generation of sleep slow waves, we have constructed a large-scale computer model that encompasses portions of two visual areas and associated thalamic and reticular thalamic nuclei. Thousands of model neurons, incorporating several intrinsic currents, are interconnected with millions of thalamocortical, corticothalamic, intra- and inter-areal corticocortical connections. In the waking mode, the model exhibits irregular spontaneous firing and selective responses to visual stimuli. In the sleep mode, neuromodulatory changes lead to slow oscillations that closely resemble those observed in vivo and in vitro. A systematic exploration of the effects of intrinsic currents and network parameters on the initiation, maintenance and termination of slow oscillations shows the following: 1. An increase in potassium leak conductances is sufficient to trigger the transition from wakefulness to sleep. 2. The activation of persistent sodium currents is sufficient to initiate the up-state of the slow oscillation. 3. A combination of intrinsic and synaptic currents is sufficient to maintain the up-state. 4. Depolarization-activated potassium currents and synaptic depression terminate the up-state. 5. Corticocortical connections synchronize the slow oscillation. The model is the first to integrate intrinsic neuronal properties with detailed thalamocortical anatomy and reproduce neural activity patterns in both wakefulness and sleep, thereby providing a powerful tool to investigate the role of synaptic strength in slow wave sleep and synaptic homeostasis.

02:00 PM
03:00 PM
David Dinges - Modeling the Link Between Sleep/Wake Dynamics and Human Performance

Human performance capabilities - especially cognitive and neurobehavioral functions - are temporally dynamic reflecting endogenous neurobiological forces for sleep and waking that are genetically programmed into all brains. Mathematical modeling of performance as an output of time awake, circadian dynamics and their interaction has shown considerable promise, but remains incomplete. After reviewing the evidence that sleep-wake dynamics markedly influence cognitive performance functions, the most important scientific issues will be described that require answers to ensure the continued development and operational transition of mathematical models of human performance. These include the following issues that must be resolved: (1) determination of the number of different aspects of cognitive performance that must be accommodated by modeling; (2) establishment of dose-response curves for recovery of performance as a function of prior sleep homeostatic load and the number of days of recovery; (3) determination of the longer-term time constants for fatigue buildup and dissipation (i.e., recycle rates); (4) determination of the extent to which feedback of performance can improve modeled predictions; (5) identification of ways to scale and interpret metrics of performance that optimize model predictions within and between individuals; (6) establishment of the minimum necessary information to input into a model to ensure an accurate prediction of performance; (7) establishment of the extent to which environmental inputs improve modeling predictions of performance; and (8) identification of factors that create risk and modify the relationship between model predictions of performance and risk outcomes.

03:30 PM
04:00 PM
Glenn Gunzelmann - Modeling Fatigue in a Cognitive Architecture: What Is the Value Added?

Biomathematical models of fatigue provide estimates of alertness based upon a representation of circadian rhythm and sleep homeostat components of the human arousal system, allowing for additional complications like sleep inertia, light exposure, or circadian shifts. A key question remains however, concerning precisely what this output represents from a cognitive perspective. It is true that the output of biomathematical models may be scaled to fit various human performance measures, like lapse probability in a sustained attention task or subjective sleepiness as estimated by participants in a sleep deprivation or sleep restriction protocol. What remains at issue is what cognitive and neural mechanisms give rise to human performance and are impacted by fatigue to produce the decrements that are observed on behavioral tasks. Our research is aimed at addressing this question. To do that, we use a cognitive architecture, which instantiates a unified computational theory of human cognition. Within such a theory, it is possible to explore and identify the particular information processing mechanisms that are impacted by fatigue to produce performance decrements like those observed in humans. By refining our understanding of how these mechanisms are affected using existing data, we can extrapolate to generate detailed, quantitative predictions about how performance will be impacted on other tasks and measures that rely on those same cognitive mechanisms.

04:00 PM
04:30 PM
Giulio Tononi - Sleep, Synaptic Homeostasis, and Cortical Synchronization: Models and tests

Sleep slow wave activity (SWA) is homeostatically regulated, increasing with wakefulness and declining with sleep. Sleep SWA is thought to reflect sleep need, but the mechanisms of its homeostatic regulation remain unknown. We have recently suggested that the level of SWA may reflect the strength of corticocortical synapses (Tononi and Cirelli, 2003 2006). Specifically, stronger cortical connections would produce increased network synchronization and thus a higher level of SWA, while weaker connections would reduce network synchronization and thereby SWA. Supporting the hypothesis, procedures associated with synaptic potentiation and depression in local cortical areas lead to corresponding changes in sleep SWA. For example, sleep SWA increased over right parietal cortex after a visuomotor learning task (Huber et al. 2004), and decreased over right sensorimotor cortex after immobilization of the left arm (Huber et al., 2006). To better understand the relationship between synaptic strength and sleep SWA, we took advantage of a large-scale computer model of the cat thalamocortical system (Hill and Tononi, 2005) and examined the dynamics of single cell oscillations, cortical synchronization and LFP slow waves under conditions of high and low strength of excitatory corticocortical connections. The simulations showed that a reduction in the strength of excitatory corticocortical connections was sufficient to produce a marked decrease in sleep SWA. Moreover, the decrease in SWA was associated with characteristic changes in several slow wave parameters, including a decreased incidence of high amplitude waves, a reduced slope of the waves, and an increased occurrence of multiple wave peaks. The simulations also showed that the effects of synaptic strength on slow wave parameters were mediated by changes in the amplitude of single cell oscillations, in the dynamics of network synchronization, and in the rate of neuronal recruitment and decruitment. To test the predictions of the model, we then examined rat LFP recordings and human hd-EEG recordings under conditions of high and low sleep pressure. We found changes in wave morphology that closely mirrored those observed in the model. Thus, the reduction of cortical synaptic strength may be a key factor underlying the decrease in SWA between high and low sleep pressure conditions.

04:30 PM
05:00 PM
Jen-Kuang Huang - An Engineer's View of the Two-process Model of Sleep/wake Regulation

Many biomathematical models of fatigue and performance are developed based on the two-process model of sleep/wake regulation (Borbely, 1982; Achermann, 2004). The two-process model represents the existence of two primary regulatory mechanisms: a sleep/wake-related mechanism that builds up exponentially across time of wakefulness and declines exponentially during sleep, called the homeostatic process; and an oscillatory mechanism with a period of (nearly) 24 hours, called the circadian process. Each process has its own parameters and is modeled by a nonlinear function in the time domain.


It is interesting to see how both the homeostatic and circadian processes can be described by the response of a mechanical system. The analogy indicates that the fatigue and performance can be predicted from a linear dynamic system model. A discrete state-space representation of the system shows that the current circadian state depends only on two former circadian states. This approach opens the possibility to estimate the system parameters by using linear system identification algorithms. Finally, the derived linear state-space model of sleep/wake regulation is validated by a numerical simulation.

Friday, October 27, 2006
Time Session
09:00 AM
10:00 AM
Derk-Jan Dijk - Circadian and Homeostatic Regulation of Sleep and Performance: Implications for the Development of Mathematical Models

Circadian and Homeostatic Regulation of Sleep and Performance: Implications for the Development of Mathematical Models

10:30 AM
11:15 AM
Erik Olofsen - Nonlinear Mixed-Effects Modeling: Individualization and Prediction

Human neurobehavioral data frequently show large interindividual variability. One way to deal with this variability is the two-stage approach of population data analysis, which involves fitting a mathematical model to each individual separately and averaging the parameter estimates across the individuals to obtain population parameters estimates. These estimates are likely to be biased if the number of observations within the individuals is small, and the standard errors are also likely to be biased because intraindividual and interindividual variabilities are not separately quantified. Mixed-effects modeling provides a more proper framework for the analysis of population data, in which the population parameters are given by probability distributions. When these distributions are characterized, they can be used in a Bayesian setting as prior information, and by incorporating observations from a subject under study the posterior distributions can be used for prediction - for example, for one-day-ahead predictions of performance after sleep deprivation.

11:15 AM
11:45 AM
Christopher Mott - Incorporating Parameter Uncertainty and Individual Differences into Cognitive Performance Prediction

While the need to incorporate inter-individual differences into cognitive performance models is recognized, there are currently no techniques for real-time model adaptation when individual differences are unknown a priori. Additionally, current prediction techniques require known initial conditions; and furthermore do not generate statistically valid estimates of prediction accuracy. These limitations diminish their usefulness for predicting the performance of individuals in operational environments. To overcome all of these limitations a modeling and prediction approach was developed based on a statistical technique called Bayesian forecasting. The two-process model of sleep regulation was selected as a model framework. To enable individualization three trait parameters (homeostatic build-up rate, circadian amplitude and basal performance level) and two state parameters (initial homeostatic state and circadian phase) were introduced to the model. The Bayesian forecasting algorithm generated predictions of future performance based on probability distributions of the states and traits for a given individual. The algorithm initially considered the states unknown and used trait distributions representative of the population, then it iteratively adapted the trait and state estimates with each new performance measurement from a given individual. Results from testing of the algorithm on a total sleep deprivation data set revealed that as more data became available for the individuals at hand the performance predictions became progressively more accurate as the model parameters converged efficiently to those that best characterized each individual. These results revealed that the Bayesian forecasting procedure successfully overcame some of the important outstanding challenges for biomathematical prediction of cognitive performance in operational settings. Continuing work involves extending the Bayesian forecasting to accommodate the model discontinuities of sleep/wake transitions, optimizing parameterization of the model, and incorporating the effects of prophylactic napping and caffeine countermeasures.


This work was done in collaboration with Hans P.A. Van Dongen, Sleep and Performance Research Center, Washington State University; Jen-Kuang Huang, Old Dominion University, Norfolk, VA; Daniel J. Mollicone, Pulsar Informatics Inc., Norfolk, VA; Frederic D. McKenzie,Old Dominion University, Norfolk, VA; and David F. Dinges, Unit for Experimental Psychiatry, Department of Psychiatry, University of Pennsylvania School of Medicine, Philadelphia, PA.

Name Affiliation
Achermann, Peter acherman@pharma.unizh.ch Institute of Pharmacology and Toxicology, University of Zurich
Aguda, Baltazar bdaguda@gmail.com MBI - Long Term Visitor, Bioinformatics Institute, Singapore
Balkin, Thomas thomas.balkin@na.amedd.army.mil Department of Behavioral Biology, Walter Reed Army Institute of Research
Beersma, Domien d.g.m.beersma@biol.rug.nl Chronobiology, Rijksuniversiteit te Groningen
Best, Janet jbest@mbi.osu.edu
Blumberg, Mark mark-blumberg@uiowa.edu Psychology, University of Iowa
Booth, Victoria vbooth@umich.edu Mathematics , University of Michigan
Czeisler, Charles caczeisler@hms.harvard.edu Division of Sleep Medicine, Dept. of Medicine, Harvard Medical School
Dembele, Bassidy bdembele@mbi.osu.edu MBI - Long Term Visitor, The Ohio State University
Dijk, Derk-Jan d.j.dijk@surrey.ac.uk Biomedical and Molecular Sciences, University of Surrey
Dinges, David Psychiatry, University of Pennsylvania
Diniz Behn, Cecilia cbehn@bidmc.harvard.edu Neurology, Harvard/Beth Israel Deaconess Medical Center
Djordjevic, Marko mdjordjevic@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Dumont, Guy guyd@ece.ubc.ca Electrical and Computer Engineering, University of British Columbia
Enciso, German German_Enciso@hms.harvard.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Esser, Steve skesser@wisc.edu Neuroscience Training Program , University of Wisconsin
Forger, Daniel forger@umich.edu Mathematics, University of Michigan
Gluck, Kevin kevin.gluck@mesa.afmc.af.mil Senior Research Psychologist, Air Force Research Laboratory
Grajdeanu, Paula pgrajdeanu@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Gunzelmann, Glenn glenn.gunzelmann@mesa.afmc.af.mil Air Force Research Laboratory
Hill, Sean sean.hill@epfl.ch Blue Brain Project, Brain Mind Institute, Lausanne Switzerland
Huang, Jen-Kuang jhuang@odu.edu Mechanical Engineering, Old Dominion University
Hursh, Steven srhursh@ibrinc.org Institutes for Behavioral Research
Johnson, Michael mlj8e@virginia.edu Department of Pharmacology, University of Virginia School of Medicine
Kandelaars, Katie Department of Behavioral Biology, Walter Reed Army Institute of Research
Klerman, Elizabeth elizabeth_klerman@hms.harvard.edu Division of Sleep Medicine, Harvard Medical School
Ko, Taewook Mathematics , University of Pittsburgh
Kronauer, Richard kronauer@deas.harvard.edu Department of Engineering and Applied Science, Harvard University
Larkin, Willard willard.larkin@afosr.af.mil Program Manager, Life Sciences, Air Force Office of Scientific Research
Leite, Fabio leite.11@osu.edu Psychology, The Ohio State University
Lou, Yuan lou@math.ohio-state.edu MBI - Long Term Visitor, The Ohio State University
Mollicone, Daniel danielm2@mail.med.upenn.edu Unit for Experimental Psychology, University of Pennsylvania
Mott, Christopher cmott@pulsarinformatics.com V.P. Engineering, Pulsar Informatics Inc
Nevai, Andrew anevai@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Ng, Bart bng@math.iupui.edu MBI - Long Term Visitor, Indiana University--Purdue University
O'Malley, Thomas omalletj@muc.edu Department of Mathematics, Mount Union College
Olofsen, Erik e.olofsen@lumc.nl Department of Anesthesiology P5Q , Rijksuniversiteit te Leiden
Oster, Andrew aoester@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Park, Choongseok park@math.iupui.edu Mathematics, The Ohio State University
Poe, Gina ginapoe@umich.edu Molecular and Integrative Physiology, University of Michigan
Rajaraman, Srini US Army Medical Command, Fort Dietrich, Biotechnology HPC Institute
Ratcliff, Roger roger@eccles.psy.ohio-state.edu Psychology Department, The Ohio State University
Reifman, Jaques reifman@bioanalysis.org US Army Medical Command, For Dietrich, Biotechnology HPC Institute
Rempe, Michael mrempe@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Rubin, Jonathan rubin@euler.math.pitt.edu Mathematics, University of Pittsburgh
Saper, Clifford Neurology, Harvard Medical School
Schugart, Richard richard.schugart@wku.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Smith, Amber ambersmith@wsu.edu Sleep and Performance Research Center, University of Washington
Srinivasan, Partha p.srinivasan35@csuohio.edu Mathematical Biosciences Institute (MBI), The Ohio State University
St. Hilaire, Melissa msthilaire@rics.bwh.harvard.edu Brigham and Women's Hospital
Stigler, Brandy bstigler@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Szomolay, Barbara b.szomolay@imperial.ac.uk Mathematical Biosciences Institute (MBI), The Ohio State University
Terman, David terman@math.ohio-state.edu MBI, The Ohio State University
Teymuroglu, Zeynep teymurz@email.uc.edu Department of Mathematical Sciences, University of Cincinnati
Thomas, Evelyn ethomas@mbi.osu.edu MBI - Long Term Visitor, The Ohio State University
Tian, Paul tianjj@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Tononi, Giulio gtononi@wisc.edu Psychiatry, School of Medicine, University of Wisconsin
Van Dongen, Hans hvd@wsu.edu Sleep and Performance Research Center, Washington State University
White, Corey white.1198@osu.edu Psychology, The Ohio State University
Zhang, Linghai liz5@lehigh.edu MBI - Long Term Visitor, Lehigh University
The Two-process Model of Sleep Regulation: Background and future directions

The two-process model of sleep regulation posits that the timing of sleep and waking is generated by the interaction of its two constituent processes, the sleep-wake dependent homeostatic Process S and the circadian Process C. In addition to the timing of sleep, the interaction of the two processes accounts for changes in daytime vigilance. The attractiveness of the model derives from its physiological basis and its mathematical simplicity. The time course of Process S was derived from a physiological variable, EEG slow-wave activity (SWA). The two-process model offers a conceptual framework for the analysis of existing and new data and stimulated the establishment of various models of neurobehavioral functions. The major of these models have already inspired a considerable number of experiments.


The background of the two-process model will be reviewed and discussed in the light of new findings. The following topics will be addressed: determination of the parameters of Process S; inter-individual differences; relationship between SWA and Process S in case of disturbed sleep; markers of sleep homeostasis in the waking and sleep EEG; regional and use-dependent aspects of sleep homeostasis; topographical differences in the dynamics of Process S and its consequences for modeling sleep regulation; synaptic plasticity and how slow oscillations (< 1 Hz) contribute to sleep homeostasis ; which additional processes are needed for modeling neurobehavioral functions; and whether the interaction of homeostatic and circadian processes is linear or non-linear.

Mapping NREM Sleep Regulation across the Brain: Process S revisited

The regulation of the timing of sleep is thought to be linked to the temporal dynamics of slow-wave activity (SWA, EEG spectral power in ~0.75-4.5 Hz range) in the cortical NREM sleep EEG. In the two process model of sleep regulation, SWA was used as a direct indication of sleep debt. Originally, this was done in a gross way, by quantifying average SWA across NREM-REM sleep cycles. Later studies demonstrated that SWA could hardly be a direct reflection of S, but that SWA was proportional to the instantaneous decay rate of S. Following up on this, an extended model of SWA dynamics was developed, in which consequences of intrusions of REM sleep and wakefulness were incorporated. For each subject, a 'gain constant' value could be estimated quantifying the efficacy of SWA in dissipating S. Since the course of SWA is variable across cortical locations, local differences are likely to exist in the speed of discharge of Process S, eventually leading to different levels of S in different cortical regions. This disparity is in obvious contradiction with the concept of S in the two process model, because this would induce unambiguity in the regulation of sleep onset and termination. In this study we quantified the extent of local differences of SWA regulation on the basis of the extended model of SWA dynamics, for 26 locations on the scalp. We observed higher efficiency of SWA in dissipation of Process S in frontal EEG derivations, demonstrating once more that SWA regulation has a clear local aspect. The results further suggest that the Process S involved in SWA regulation is not identical to the Process S involved (together with Process C) in the determination of sleep timing. We therefore propose to distinguish these two representations and identify the former, purely SWA-related process, as 'Process Z'.

Tracking the Developmental Dynamics of Sleep and Wakefulness

Difficulties inherent in the measurement of sleep in early infancy have given rise to significant disagreements concerning the nature of infant sleep, its neural control, and its continuity with sleep in adults. By combining measures of nuchal and extraocular EMG during early development in rats, as well as neocortical EEG when possible, we have shown that infant sleep is neither undifferentiated nor primitive, as has been argued in the past. Moreover, the development of techniques for recording neurophysiological activity in infants has demonstrated that neural structures in the medulla, midbrain, and forebrain are involved in the regulation and modulation of behavioral states at ages before state-dependent EEG activity is detectable. Indeed, measurement of muscle tone alone provides surprisingly valuable information for defining infant sleep and for describing pronounced quantitative and qualitative changes in the statistical structure of sleep and wake bouts across development. These insights, gleaned from experiments in normal infant rats, have been extended to orexin knockout mice to suggest a surprising and counterintuitive interpretation of the relationship between fragmented states in adult narcoleptics and normal infants. Finally, our methods are allowing us to detect circadian rhythms of sleep and wakefulness near the time of birth and to track the relationship between circadian and ultradian rhythms across development. All together, these approaches and findings provide a rich foundation for the development of computational models that can account for the dynamics of sleep and wakefulness across the lifespan.

Circadian and Homeostatic Regulation of Sleep and Performance: Implications for the Development of Mathematical Models

Circadian and Homeostatic Regulation of Sleep and Performance: Implications for the Development of Mathematical Models

Modeling the Link Between Sleep/Wake Dynamics and Human Performance

Human performance capabilities - especially cognitive and neurobehavioral functions - are temporally dynamic reflecting endogenous neurobiological forces for sleep and waking that are genetically programmed into all brains. Mathematical modeling of performance as an output of time awake, circadian dynamics and their interaction has shown considerable promise, but remains incomplete. After reviewing the evidence that sleep-wake dynamics markedly influence cognitive performance functions, the most important scientific issues will be described that require answers to ensure the continued development and operational transition of mathematical models of human performance. These include the following issues that must be resolved: (1) determination of the number of different aspects of cognitive performance that must be accommodated by modeling; (2) establishment of dose-response curves for recovery of performance as a function of prior sleep homeostatic load and the number of days of recovery; (3) determination of the longer-term time constants for fatigue buildup and dissipation (i.e., recycle rates); (4) determination of the extent to which feedback of performance can improve modeled predictions; (5) identification of ways to scale and interpret metrics of performance that optimize model predictions within and between individuals; (6) establishment of the minimum necessary information to input into a model to ensure an accurate prediction of performance; (7) establishment of the extent to which environmental inputs improve modeling predictions of performance; and (8) identification of factors that create risk and modify the relationship between model predictions of performance and risk outcomes.

Modeling Fatigue in a Cognitive Architecture: What Is the Value Added?

Biomathematical models of fatigue provide estimates of alertness based upon a representation of circadian rhythm and sleep homeostat components of the human arousal system, allowing for additional complications like sleep inertia, light exposure, or circadian shifts. A key question remains however, concerning precisely what this output represents from a cognitive perspective. It is true that the output of biomathematical models may be scaled to fit various human performance measures, like lapse probability in a sustained attention task or subjective sleepiness as estimated by participants in a sleep deprivation or sleep restriction protocol. What remains at issue is what cognitive and neural mechanisms give rise to human performance and are impacted by fatigue to produce the decrements that are observed on behavioral tasks. Our research is aimed at addressing this question. To do that, we use a cognitive architecture, which instantiates a unified computational theory of human cognition. Within such a theory, it is possible to explore and identify the particular information processing mechanisms that are impacted by fatigue to produce performance decrements like those observed in humans. By refining our understanding of how these mechanisms are affected using existing data, we can extrapolate to generate detailed, quantitative predictions about how performance will be impacted on other tasks and measures that rely on those same cognitive mechanisms.

Modeling Wakefulness and Sleep in the Thalamocortical System

When the brain goes from wakefulness to sleep, cortical neurons begin to undergo slow oscillations in their membrane potential that are synchronized by thalamocortical circuits and reflected in EEG slow waves. In order to provide a self-consistent account of the transition from wakefulness to sleep and of the generation of sleep slow waves, we have constructed a large-scale computer model that encompasses portions of two visual areas and associated thalamic and reticular thalamic nuclei. Thousands of model neurons, incorporating several intrinsic currents, are interconnected with millions of thalamocortical, corticothalamic, intra- and inter-areal corticocortical connections. In the waking mode, the model exhibits irregular spontaneous firing and selective responses to visual stimuli. In the sleep mode, neuromodulatory changes lead to slow oscillations that closely resemble those observed in vivo and in vitro. A systematic exploration of the effects of intrinsic currents and network parameters on the initiation, maintenance and termination of slow oscillations shows the following: 1. An increase in potassium leak conductances is sufficient to trigger the transition from wakefulness to sleep. 2. The activation of persistent sodium currents is sufficient to initiate the up-state of the slow oscillation. 3. A combination of intrinsic and synaptic currents is sufficient to maintain the up-state. 4. Depolarization-activated potassium currents and synaptic depression terminate the up-state. 5. Corticocortical connections synchronize the slow oscillation. The model is the first to integrate intrinsic neuronal properties with detailed thalamocortical anatomy and reproduce neural activity patterns in both wakefulness and sleep, thereby providing a powerful tool to investigate the role of synaptic strength in slow wave sleep and synaptic homeostasis.

An Engineer's View of the Two-process Model of Sleep/wake Regulation

Many biomathematical models of fatigue and performance are developed based on the two-process model of sleep/wake regulation (Borbely, 1982; Achermann, 2004). The two-process model represents the existence of two primary regulatory mechanisms: a sleep/wake-related mechanism that builds up exponentially across time of wakefulness and declines exponentially during sleep, called the homeostatic process; and an oscillatory mechanism with a period of (nearly) 24 hours, called the circadian process. Each process has its own parameters and is modeled by a nonlinear function in the time domain.


It is interesting to see how both the homeostatic and circadian processes can be described by the response of a mechanical system. The analogy indicates that the fatigue and performance can be predicted from a linear dynamic system model. A discrete state-space representation of the system shows that the current circadian state depends only on two former circadian states. This approach opens the possibility to estimate the system parameters by using linear system identification algorithms. Finally, the derived linear state-space model of sleep/wake regulation is validated by a numerical simulation.

Incorporating Parameter Uncertainty and Individual Differences into Cognitive Performance Prediction

While the need to incorporate inter-individual differences into cognitive performance models is recognized, there are currently no techniques for real-time model adaptation when individual differences are unknown a priori. Additionally, current prediction techniques require known initial conditions; and furthermore do not generate statistically valid estimates of prediction accuracy. These limitations diminish their usefulness for predicting the performance of individuals in operational environments. To overcome all of these limitations a modeling and prediction approach was developed based on a statistical technique called Bayesian forecasting. The two-process model of sleep regulation was selected as a model framework. To enable individualization three trait parameters (homeostatic build-up rate, circadian amplitude and basal performance level) and two state parameters (initial homeostatic state and circadian phase) were introduced to the model. The Bayesian forecasting algorithm generated predictions of future performance based on probability distributions of the states and traits for a given individual. The algorithm initially considered the states unknown and used trait distributions representative of the population, then it iteratively adapted the trait and state estimates with each new performance measurement from a given individual. Results from testing of the algorithm on a total sleep deprivation data set revealed that as more data became available for the individuals at hand the performance predictions became progressively more accurate as the model parameters converged efficiently to those that best characterized each individual. These results revealed that the Bayesian forecasting procedure successfully overcame some of the important outstanding challenges for biomathematical prediction of cognitive performance in operational settings. Continuing work involves extending the Bayesian forecasting to accommodate the model discontinuities of sleep/wake transitions, optimizing parameterization of the model, and incorporating the effects of prophylactic napping and caffeine countermeasures.


This work was done in collaboration with Hans P.A. Van Dongen, Sleep and Performance Research Center, Washington State University; Jen-Kuang Huang, Old Dominion University, Norfolk, VA; Daniel J. Mollicone, Pulsar Informatics Inc., Norfolk, VA; Frederic D. McKenzie,Old Dominion University, Norfolk, VA; and David F. Dinges, Unit for Experimental Psychiatry, Department of Psychiatry, University of Pennsylvania School of Medicine, Philadelphia, PA.

Nonlinear Mixed-Effects Modeling: Individualization and Prediction

Human neurobehavioral data frequently show large interindividual variability. One way to deal with this variability is the two-stage approach of population data analysis, which involves fitting a mathematical model to each individual separately and averaging the parameter estimates across the individuals to obtain population parameters estimates. These estimates are likely to be biased if the number of observations within the individuals is small, and the standard errors are also likely to be biased because intraindividual and interindividual variabilities are not separately quantified. Mixed-effects modeling provides a more proper framework for the analysis of population data, in which the population parameters are given by probability distributions. When these distributions are characterized, they can be used in a Bayesian setting as prior information, and by incorporating observations from a subject under study the posterior distributions can be used for prediction - for example, for one-day-ahead predictions of performance after sleep deprivation.

Modeling Sleep and Wakefulness: The flip-flop model

Transitions between sleep and wakefulness are controlled by precise synaptic circuitry in the brain, and much of this has been mapped out in the past decade. Current models are based upon mutually inhibitory interactions between a master sleep switch, the ventrolateral preoptic nucleus, on the one hand, and a series of wake-promoting cell groups in the brainstem and hypothalamus, on the other hand. These interactions produce a flip-flop switch, and may account for the rapid and complete transitions between behavioral states that are seen in all animals.


The transitions between Rapid Eye Movement (REM) and non-REM sleep appear to be due to a second flip-flop switch in the brainstem. This switch is composed of mutually inhibitory neurons in distinct REM-off and REM-on areas of the pons. The REM switch appears under normal circumstances to be subsidiary to the wake-sleep switch, as transitions into REM states from wakefulness do not occur except under specific pathological conditions. One of those conditions is the loss of the orexin/hypocretin neurons in the lateral hypothalamus. These neurons appear to stabilize both the wake-sleep and the REM-nonREM switches.


The transitions between sleep and wake states also oscillate and appear to be under both homeostatic and circadian controls. The homeostatic input is thought to be regulated by buildup of substances in the brain during wakefulness, such as excess adenosine, that inhibit arousal systems, and activate sleep systems. Lesions of the ventrolateral preoptic nucleus prevent the homeostatic system from increasing sleep after sleep deprivation, suggesting that the action of the homeostatic system on this component of the sleep switch are critical.


Circadian drive for sleep and wakefulness appears to be mediated by the dorsomedial nucleus of the hypothalamus. This cell group normally comes under the influence of the brain's master biological clock, the suprachiasmatic nucleus. However, under some circumstances, e.g., when food is available only during the normal sleep period, it can take over (even in the absence of a suprachiasmatic nucleus) and remodel circadian influences to cause wakefulness to co-ordinate with the food availability. The outputs from the dorsomedial nucleus to the ventrolateral preoptic nucleus and to the orexin neurons may explain much of this influence.


These synaptic connections, most of which have been discovered only in the last few years, provide a solid basis for structuring mathematical models of the regulation of sleep and wakefulness.

Sleep, Synaptic Homeostasis, and Cortical Synchronization: Models and tests

Sleep slow wave activity (SWA) is homeostatically regulated, increasing with wakefulness and declining with sleep. Sleep SWA is thought to reflect sleep need, but the mechanisms of its homeostatic regulation remain unknown. We have recently suggested that the level of SWA may reflect the strength of corticocortical synapses (Tononi and Cirelli, 2003 2006). Specifically, stronger cortical connections would produce increased network synchronization and thus a higher level of SWA, while weaker connections would reduce network synchronization and thereby SWA. Supporting the hypothesis, procedures associated with synaptic potentiation and depression in local cortical areas lead to corresponding changes in sleep SWA. For example, sleep SWA increased over right parietal cortex after a visuomotor learning task (Huber et al. 2004), and decreased over right sensorimotor cortex after immobilization of the left arm (Huber et al., 2006). To better understand the relationship between synaptic strength and sleep SWA, we took advantage of a large-scale computer model of the cat thalamocortical system (Hill and Tononi, 2005) and examined the dynamics of single cell oscillations, cortical synchronization and LFP slow waves under conditions of high and low strength of excitatory corticocortical connections. The simulations showed that a reduction in the strength of excitatory corticocortical connections was sufficient to produce a marked decrease in sleep SWA. Moreover, the decrease in SWA was associated with characteristic changes in several slow wave parameters, including a decreased incidence of high amplitude waves, a reduced slope of the waves, and an increased occurrence of multiple wave peaks. The simulations also showed that the effects of synaptic strength on slow wave parameters were mediated by changes in the amplitude of single cell oscillations, in the dynamics of network synchronization, and in the rate of neuronal recruitment and decruitment. To test the predictions of the model, we then examined rat LFP recordings and human hd-EEG recordings under conditions of high and low sleep pressure. We found changes in wave morphology that closely mirrored those observed in the model. Thus, the reduction of cortical synaptic strength may be a key factor underlying the decrease in SWA between high and low sleep pressure conditions.