Mathematical models of regulatory mechanisms of sleep-wake rhythms

Abstract.Studies of regulatory mechanisms of sleep-wake rhythms have benefited greatly from mathematical modeling. There are two major frameworks of modeling: one integrates homeostatic and circadian regulations and the other consists of multiple interacting oscillators. In this article, model constructions based on these respective frameworks and their characteristics are reviewed. The two-process model and the multioscillator model are explained in detail. An appropriate mathematical abstraction is also shown to provide a viewpoint unifying the model structures, which might seem to be distinct. Recently acquired knowledge of neural regulatory mechanisms of sleep-wake rhythm has prompted modeling at the neural network level. Such a detailed model is also reviewed, and could be used to explore a possible neural mechanism underlying a pathological state of sleep-wake rhythm.

[1]  R. Szymusiak,et al.  A thermoregulatory model of sleep control. , 1995, The Japanese journal of physiology.

[2]  A A Borbély,et al.  Simulation of Human Sleep: Ultradian Dynamics of Electroencephalographic Slow-Wave Activity , 1990, Journal of biological rhythms.

[3]  M. Moore-Ede,et al.  Mathematical Models of the Circadian Sleep-Wake Cycle. , 1984 .

[4]  J. Aschoff.  Problems of Re-entrainment of Circadian Rhythms: Asymmetry Effect, Dissociation and Partition , 1978 .

[5]  Jürgen Zulley,et al.  The dependence of onset and duration of sleep on the circadian rhythm of rectal temperature , 1981, Pflügers Archiv.

[6]  Emmanuel Mignot,et al.  The Sleep Disorder Canine Narcolepsy Is Caused by a Mutation in the Hypocretin (Orexin) Receptor 2 Gene , 1999, Cell.

[7]  R Suzuki,et al.  A three-oscillator model of the human circadian system controlling the core temperature rhythm and the sleep-wake cycle. , 1982, Journal of theoretical biology.

[8]  S H Strogatz,et al.  Human sleep and circadian rhythms: a simple model based on two coupled oscillators , 1987, Journal of mathematical biology.

[9]  Jon T. Willie,et al.  Distinct Narcolepsy Syndromes in Orexin Receptor-2 and Orexin Null Mice Molecular Genetic Dissection of Non-REM and REM Sleep Regulatory Processes , 2003, Neuron.

[10]  M. Nakao,et al.  An Interpretation of the Internal Desynchronizations Based on Dynamics of the Two-process Model , 1997, Methods of Information in Medicine.

[11]  J A Hobson,et al.  Neuronal excitability modulation over the sleep cycle: a structural and mathematical model. , 1975, Science.

[12]  S. Honma,et al.  A Phase Dynamics Model of Human Circadian Rhythms , 2002, Journal of biological rhythms.

[13]  P. Achermann,et al.  Sleep Homeostasis and Models of Sleep Regulation , 1999 .

[14]  P. Achermann,et al.  Combining different models of sleep regulation , 1992, Journal of sleep research.

[15]  Derk-Jan Dijk,et al.  Functional Genomics of Sleep and Circadian Rhythm Invited Review : Integration of human sleep-wake regulation and circadian rhythmicity , 2001 .

[16]  Mitsuyuki Nakao,et al.  A quartet neural system model orchestrating sleep and wakefulness mechanisms. , 2006, Journal of neurophysiology.

[17]  Sebastiaan Overeem,et al.  Hypocretin (orexin) deficiency in human narcolepsy , 2000, The Lancet.

[18]  C A Czeisler,et al.  Mathematical model of the human circadian system with two interacting oscillators. , 1982, The American journal of physiology.

[19]  Daniel J Buysse,et al.  Amplitude reduction of the circadian temperature and sleep rhythms in the elderly. , 1996, Chronobiology international.

[20]  Dennis McGinty,et al.  Keeping cool: a hypothesis about the mechanisms and functions of slow-wave sleep , 1990, Trends in Neurosciences.

[21]  Peter Achermann,et al.  Simulation of daytime vigilance by the additive interaction of a homeostatic and a circadian process , 1994, Biological Cybernetics.

[22]  J. Proll.  R. A. Wever: The Circadian System of Man, Results of Experiments under Temporal Isolation. XII und 276 Seiten, 181 Abb. Springer Verlag, New York, Heidelberg, Berlin (West) 1979. Preis: 98,— DM , 1981 .

[23]  D.G.M. Dijk,et al.  Contribution of the circadian pacemaker and the sleep homeostat to sleep propensity, sleep structure, electroencephalographic slow waves, and sleep spindle activity in humans , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[24]  R. P. Pascual,et al.  Coupled relaxation oscillators and circle maps , 1988 .

[25]  A. Borbély.  A two process model of sleep regulation. , 1982, Human neurobiology.

[26]  Mitsuaki Yamamoto,et al.  A model-based interpretation of the biphasic daily pattern of sleepiness , 1999, Biological Cybernetics.

[27]  M. Candito,et al.  Circadian rhythms in depression and recovery: Evidence for blunted amplitude as the main chronobiological abnormality , 1989, Psychiatry Research.

[28]  T. Åkerstedt,et al.  The three-process model of alertness and its extension to performance, sleep latency, and sleep length. , 1997, Chronobiology international.

[29]  R. Kronauer,et al.  Reply to Technical Note: Nonlinear Interactions between Circadian and Homeostatic Processes: Models or Metrics? , 1999, Journal of biological rhythms.

[30]  Keisuke Yamamoto,et al.  Modeling interactions between photic and nonphotic entrainment mechanisms in transmeridian flights , 2004, Biological Cybernetics.

[31]  R. Kronauer,et al.  Interactive Mathematical Models of Subjective Alertness and Cognitive Throughput in Humans , 1999, Journal of biological rhythms.

[32]  S G Massaquoi,et al.  A limit cycle mathematical model of the REM sleep oscillator system. , 1986, The American journal of physiology.

[33]  Thomas E. Scammell,et al.  The sleep switch: hypothalamic control of sleep and wakefulness , 2001, Trends in Neurosciences.

[34]  D. Dijk,et al.  Circadian and sleep/wake dependent aspects of subjective alertness and cognitive performance , 1992, Journal of sleep research.

[35]  R. Pérez,et al.  Fine Structure of Phase Locking , 1982 .

[36]  Jon T. Willie,et al.  Genetic Ablation of Orexin Neurons in Mice Results in Narcolepsy, Hypophagia, and Obesity , 2001, Neuron.

[37]  Dennis McGinty,et al.  The sleep–wake switch: A neuronal alarm clock , 2000, Nature Medicine.

[38]  Non-photic entrainment of human rest-activity cycle independent of circadian pacemaker , 2004 .

[39]  A. Goldbeter,et al.  Toward a detailed computational model for the mammalian circadian clock , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[40]  T. Åkerstedt,et al.  Validation of the S and C components of the three-process model of alertness regulation. , 1995, Sleep.

[41]  M. Nakao,et al.  Bifurcation properties of the two process model , 1998, Psychiatry and clinical neurosciences.

[42]  R. McCarley,et al.  Extension of the Limit Cycle Reciprocal Interaction Model of REM cycle control. An integrated sleep control model , 1992, Journal of sleep research.

[43]  M. Nakao,et al.  Thermoregulatory Model of Sleep Control: Losing the Heat Memory , 1999, Journal of biological rhythms.

[44]  J. Hobson,et al.  The Neurobiology of Sleep: Genetics, cellular physiology and subcortical networks , 2002, Nature Reviews Neuroscience.

[45]  S. Daan,et al.  Timing of human sleep: recovery process gated by a circadian pacemaker. , 1984, The American journal of physiology.

[46]  S. Honma,et al.  A sighted man with non‐24‐hour sleep‐wake syndrome shows damped plasma melatonin rhythm , 1997, Psychiatry and clinical neurosciences.

[47]  P. Achermann.  The two-process model of sleep regulation revisited. , 2004, Aviation, space, and environmental medicine.