Concepts and models of sleep regulation: an overview
Corresponding Author
ALEXANDER A. BORBÉLY
Institute of Pharmacology, University of Zürich, CH-8006 Zürich, Switzerland
Institute of Pharmacology, University of Zurich, Gloriastrasse 32, CH-8006 Zurich, SwitzerlandSearch for more papers by this authorPETER ACHERMANN
Institute of Pharmacology, University of Zürich, CH-8006 Zürich, Switzerland
Search for more papers by this authorCorresponding Author
ALEXANDER A. BORBÉLY
Institute of Pharmacology, University of Zürich, CH-8006 Zürich, Switzerland
Institute of Pharmacology, University of Zurich, Gloriastrasse 32, CH-8006 Zurich, SwitzerlandSearch for more papers by this authorPETER ACHERMANN
Institute of Pharmacology, University of Zürich, CH-8006 Zürich, Switzerland
Search for more papers by this authorAbstract
SUMMARY Various mathematical models have been proposed to account for circadian, ultradian and homeostatic aspects of sleep regulation. Most circadian models assume that multiple oscillators underlie the differences in period and entrainment properties of the sleep/wake cycle and other rhythms (e.g. body temperature). Interactions of the oscillators have been postulated to account for multimodal sleep/wake patterns. The ultradian models simulate the cyclic alternation of nonREM sleep and REM sleep by assuming a reciprocal interaction of two cell groups. The homeostatic models propose that a sleep/wake dependent process (Process S) underlies the rise in sleep pressure during waking and its decay during sleep. The time course of this process has been derived from EEG slow-wave activity, an indicator of nonREM sleep intensity. The predictions of homeostatic models have been most extensively tested in experiments. The interaction of Process S with a single circadian process can account for multimodal sleep/wake patterns, internal desynchronization and the time course of daytime sleepiness. Close links have emerged between the processes postulated by the various models and specific brain mechanisms. Due to its recent quantitative elaboration and experimental validation, the modelling approach has become one of the potent research strategies in sleep science.
REFERENCES
- Achermann, P. Schlafregulation des Menschen: Modelle und Computersimulationen. PhD Thesis, ETH Zürich , 1988.
- Achermann, P. and Borbély, A. A. Simulation of human sleep: ultradian dynamics of EEG slow-wave activity. J. Biol. Rhythms, 1990, 5: 141–157.
- Achermann, P. and Borbély, A. A. Combining various models of sleep regulation. J. Sleep Res., 1992, 1: 138–141.
- Achermann, P., Beersma, D. G. M. and Borbély, A. A. The two-process model: ultradian dynamics of sleep. In: J. A. Home (Ed.) Sleep ′90. Pontenagel Press, Bochum , 1990: 296–300.
- Akerstedt, T. and Folkard, S. A model of human sleepiness. In: J. A. Home (Ed.) Sleep ′90. Pontenagel Press, Bochum , 1990: 310–313.
- Åkerstedt, T. and Gillberg, M. Sleep duration and the power spectral density of the EEG. Electroenceph. Clin. Neurophysiol., 1986, 64: 119–122.
- Alföldi, P., Tobler, I. and Borbély, A. A. Sleep regulation in rats during early development. Am. J. Physiol., 1990, 258: R634–R644.
- Beersma, D. G. M. and Daan, S. Generation of activity-rest patterns by dual circadian pacemaker systems: a model. J. Sleep Res., 1992, 1: 84–87.
- Beersma, D. G. M., Daan, S. and Dijk, D. J. Sleep intensity and timing—a model for their circadian control. Lect. Math. Life Sci., 1987, 19: 39–62.
- Beersma, D. G. M., Daan, S. and van den Hoofdakker, R. H. Distribution of REM latencies and other sleep phenomena in depression as explained by a single ultradian rhythm disturbance. Sleep, 1984, 7: 126–136.
- Beersma, D. G. M., Dijk, D. J. and Blok, C. G. REM sleep deprivation during 5 hours leads to an immediate REM sleep rebound and to suppression of non-REM sleep intensity. Electroenceph. Clin. Neurophysiol., 1990, 76: 114–122.
-
Blake, H. and
Gerard, R. W.
Brain potentials during sleep.
Am. J. Physiol., 1937, 119: 692–703.
10.1152/ajplegacy.1937.119.4.692 Google Scholar
- Borbély, A. A. Sleep: circadian rhythm versus recovery process. In: M. Koukkou, D. Lehmann and J. Angst (Eds) Functional States of the Brain: their determinants. Elsevier, Amsterdam , 1980: 151–161.
- Borbély, A. A. Sleep regulation: circadian rhythm and homeostasis. In: D. Ganten, and D. Pfaff (Eds) Current Topics in Neuroendocrinology, Vol. 1: Sleep. Clinical and experimental aspects. Springer Verlag, Berlin , 1982a: 83–103.
- Borbély, A. A. A two-process model of sleep regulation. Hum. Neurobiol., 1982b, 1: 195–204.
- Borbély, A. A. The S-deficiency hypothesis of depression and the two-process model of sleep regulation. Pharmacopsychiatry, 1987, 20: 23–29.
- Borbély, A. A. and Neuhaus, H. U. Sleep-deprivation: effect on sleep and EEG in the rat. J. comp. Physiol., 1979, 133: 71–87.
- Borbély, A. A. and Wirz-Justice, A. Sleep, sleep deprivation and depression. A hypothesis derived from a model of sleep regulation. Hum. Neurobiol., 1982, 1: 205–210.
- Borbély, A. A., Achermann, P., Trachsel, L. and Tobler I. Sleep initiation and sleep intensity: interaction of homeostatic and circadian mechanisms. J. Biol. Rhythms, 1989, 4: 149–160.
- Born, J., Muth, S. and Fehm, H.L. The significance of sleep onset and slow wave sleep for nocturnal release of growth hormone (GH) and cortisol. Psychoneuroendocrinology, 1988, 13: 233–243.
- Brandenberger, G., Follenius, M., Simon, C. Ehrhart, J. and Libert, J.P. Nocturnal oscillations in plasma renin activity and REM-NREM sleep cycles in humans: a common regulatory mechanism? Sleep, 1988, 11: 242–250.
- Broughton, R. J. Biorhythmic variations in consciousness and psychological functions. Can. Psychol. Rev., 1975, 16: 217–239.
- Broughton, R. J. and Mullington, J. Circasemidian sleep propensity and the phase-amplitude maintenance model of human sleep-wake regulation. J. Sleep Res., 1992, 1: 93–98.
- Broughton, R. J. de Koninck, J., Gagnon, P., Dunham, W. and Stampi, C. Sleep-wake biorhythms and extended sleep in man. In: J. Montplaisir and R. Godbout (Eds) Sleep and Biological Rhythms. Basic mechanisms and applications to psychiatry. Oxford University Press, New York , 1990: 25–41.
- Brunner, D. P., Dijk, D. J. and Borbély, A. A. A quantitative analysis of phasic and tonic submental EMG activity in human sleep. Physiol. Behav., 1990a, 48: 741–748.
- Brunner, D. P., Dijk, D. J., Tobler, I. and Borbély, A. A. Effect of partial sleep deprivation on sleep stages and EEG power spectra: evidence for nonREM and REM sleep homeostasis. Electroenceph. clin. Neurophysiol., 1990b, 75: 492–499.
- Caekebeke, J. F. V., Dijk, J. G., Rosa, A. C. and Kemp, B. A model relating K-complexes to spontaneous slow-wave activity during sleep. In: M. G. Terzano, P. L. Halász, and A. C. Declerck (Eds) Phasic Events and Dynamic Organization of Sleep. Raven Press, New York , 1991: 41–51.
- Campbell, S. S. and Zulley, J. Ultradian components of human sleep/wake patterns during disentrainment. In: H. Schulz and P. Lavie (Eds) Ultradian Rhythms in Physiology and Behavior. Exp. Brain Res. 1985, suppl. 12: 234–255.
- Campbell, S. S. and Zulley, J. Evidence for circadian influence on human slow wave sleep during daytime sleep episodes. Psychophysiol., 1989, 26: 580–585.
- Carpenter, G. A. and Grossberg, S. A neural theory of circadian rhythms: Aschoff's rule in diurnal and nocturnal mammals. Am. J. Physiol., 1984, 247: R1067–R1082.
- Carpenter, G. A. and Grossberg, S. Mammalian circadian rhythms: a neural network model. Lect. Math. Life Sci., 1987, 19: 151–203.
- Carskadon, M. A. Ontogeny of human sleepiness as measured by sleep latency. In: D.F. Dinges and R.J. Broughton (Eds) Sleep and Alertness: Chronobiological, behavioral, and medical aspects of napping. Raven Press, New York , 1989: 53–69.
- Carskadon, M. A. and Dement, W. C. Midafternoon decline in MSLT scores on a constant routine. Sleep Res., 1985, 14: 292.
- Cauter, Van E. Diurnal and ultradian rhythms in human endocrine function: a minireview. Hormone Res., 1990, 34: 45–53.
- Daan, S. and Beersma, D. G. M. Circadian gating of human sleep-wake cycles. In: M. C. Moore-Ede and C. A. Czeisler (Eds) Mathematical Models of the Circadian Sleep-Wake Cycle. Raven Press, New York , 1984: 129–158.
- Daan, S. and Beersma, D. G. M. A single pacemaker can produce different rates of reentrainment in different overt rhythms. J. Sleep Res., 1992, 1: 80–83.
- Daan, S. and Berde, C. Two coupled oscillators: Simulations of the circadian pacemaker in mammalian activity rhythms. J. Theor. Biol., 1978, 70: 297–313.
- Daan, S. Beersma, D. G. M. and Borbély, A. A. The timing of human sleep: recovery process gated by a circadian pacemaker. Am. J. Physiol., 1984, 246: R161–R178.
- Daan, S., Beersma, D. G. M., Dijk, D. J. Åkerstedt, T. and Gillberg, M. Kinetics of an hourglass component involved in the regulation of human sleep and wakefulness. In: W. T. J. M. Hekkens, G. A. Kerkhof and W. J. Rietveld (Eds) Advances in the Bio-Sciences, Trends in Chronobiology. Pergamon Press, Oxford , 1988, 73: 183–193.
- Da Rosa, A. C., Kemp, B., Paiva, T., Lopes da Silva, F. H. and Kamphuisen, H. A. C. A model-based detector of vertex waves and K complexes in sleep electroencephalogram. Electroenceph. Clin. Neurophysiol, 1991, 78: 71–79.
- Dijk, D. J. and Beersma, D. G. M. Effects of SWS deprivation on subsequent EEG power density and spontaneous sleep duration. Electroenceph. Clin. Neurophysiol., 1989, 72: 312–320.
- Dijk, D. J., Beersma, D. G. M. and Daan, S. EEG power density during nap sleep: Reflection of an hourglass measuring the duration of prior wakefulness. J. Biol. Rhythms, 1987a, 2: 207–219.
- Dijk, D. J., Beersma, D. G. M. and Daan, S. Bright morning light advances the human circadian system without affecting NREM sleep homeostasis. Am. J. Physiol., 1989, 156: R106–R111.
- Dijk, D. J., Brunner, D. P. and Borbély, A. A. Time course of EEG power density during long sleep in humans. Am. J. Physiol., 1990a, 258: R650–R661.
- Dijk, D. J. Brunner, D. P. and Borbély, A. A. EEG power density during recovery sleep in the morning. Electroenceph. Clin. Neurophysiol., 1991a, 78: 203–214.
- Dijk, D. J., Duffy, J. F. and Czeisler, C. A. Circadian and sleep-wake dependent aspects of subjective alertness and cognitive performance. J. Sleep Res., 1992, 1: 112–117.
- Dijk, D. J., Brunner, D. P., Beersma, D. G. M. and Borbély, A. A. Slow wave sleep and electroencephalogram power density as a function of prior waking and circadian phase. Sleep, 1990b, 13: 430–440.
- Dijk, D. J., Cajochen, C., Tobler, I. and Borbély, A. A. Sleep extension in humans: sleep stages, EEG power spectra, and body temperature. Sleep, 1991b, 14: 294–306.
- Dijk, D. J., Beersma, D. G. M., Daan, S., Bloem, G. M. and van den Hoofdakker, R. H. Quantitative analysis of the effects of slow-wave sleep deprivation during the first 3 h of sleep on subsequent EEG power density. Eur. Arch. Psychiatr. Neurol. Sci., 1987b, 236: 323–328.
- Dijk, D. J., Visscher, C. A., Bloem, G. M., Beersma, D. G. M. and Daan, S. Reduction of human sleep duration after bright light exposure in the morning. Neurosci. Lett., 1987c, 73: 181–186.
- Dirlich, G. Looking at human circadian phenomena from a framework of simple stochastic models. In: M. C. Moore-Ede and C. A. Czeisler (Eds) Mathematical Models of the Circadian Sleep-Wake Cycle. Raven Press, New York , 1984: 159–185.
- Eastman, C. Are separate temperature and activity oscillators necessary to explain the phenomena of human circadian rhythms. In: M. C. Moore-Ede and C. A. Czeisler (Eds) Mathematical Models of the Circadian Sleep-Wake Cycle. Raven Press, New York , 1984: 81–103.
-
Enright, J. T.
The Timing of Sleep and Wakefulness. Springer-Verlag,
Berlin
, 1980.
10.1007/978-3-642-81387-0 Google Scholar
- Feinberg, I. Changes in sleep cycle patterns with age. J. Psychiat. Res., 1974, 10: 283–306.
- Feinberg, I., March, J. D., Floyd, T. C., Jimison, R., Bossom-Demitrack, L. and Katz, P. H. Homeostatic changes during post-nap sleep maintain baseline levels of delta EEG. Electroenceph. Clin. Neurophysioi., 1985, 61: 134–137.
- Folkard, S. and Åkerstedt, T. Towards a model for the prediction of alertness and/or fatigue on different sleep/wake schedules. In: A. Oginski, J. Polorski and J. Rutenfranz (Eds) Contemporary Advances in Shiftwork Research: Theoretical and practical aspects in the late eighties. Medical Academy, Krakow , Poland , 1987: 231–240.
- Folkard, S. and Åkerstedt, T. Towards the prediction of alertness on abnormal sleep/wake schedules. In: A. Coblentz (Ed) Vigilance and Performance in Automatized Systems. Kluwer, Dordrecht , 1989: 287–296.
- Folkard, S. and Åkerstedt, T. A three-process model of the regulation of alertness-sleepiness. In: R. J. Broughton and R. D. Ogilvie (Eds) Sleep, Arousal, and Performance. Birkhäuser, Boston 1992: 11–26.
- Foret, J., Touron, N., Clodoré, M., Benoit, O. and Bouard, G. Modification of sleep structure by brief forced awakenings at different times of the night. Electroenceph. Clin. Neurophysiol., 1990, 15: 141–147.
- Gagnon, P. and de Koninck, J. Reappearence of EEG slow waves in extended sleep. Electroenceph. Clin. Neurophysiol., 1984, 58: 155–157.
- Gander, P. H., Kronauer, R. E., Czeisler, C. A. and Moore-Ede, M. C. Simulating the action of zeitgebers on a coupled two-oscillator model of the human circadian system. Am. J. Physiol., 1984a, 247: R418–R426.
- Gander, P. H., Kronauer, R. E., Czeisler, C. A. and Moore-Ede. M. C. Modelling the action of zeitgebers on the human circadian system: comparisons of simulations and data. Am. J. Physiol., 1984b, 247: R427–R444.
- Gander, P. H., Kronauer, R. E. and Graeber, R. C. Phase shifting two coupled circadian pacemakers: implications for jet lag. Am. J. Physiol., 1985, 249: R704–R719.
- Gillberg, M. and Åkerstedt, T. The dynamics of the first sleep cycle. Sleep, 1991, 14: 147–154.
- Gillberg, M., Anderzén, I. and Åkerstedt, T. Recovery within day-time sleep after slow wave sleep suppression. Electroenceph. Clin. Neurophysiol., 1991, 78: 267–273.
- Hobson, J. A., Lydic, R. and Baghdoyan, H. A. Evolving concepts of sleep cycle generation: From brain centers to neuronal populations. Behav. Brain. Sci., 1986, 9: 371–448.
- Home, J. A. Why We Sleep: the functions of sleep in humans and other mammals. Oxford University Press, Oxford , 1988.
- Home, J. A. Dimensions to sleepiness. In: T. H. Monk (Ed.) Sleep, Sleepiness and Performance. John Wiley, Chichester , 1991: 169–196.
- Home, J. A. Human slow wave sleep and the cerebral cortex. J. Sleep Res., 1992, 1: 116–118.
- Illnerová, H. Vaněček, J. and Hoffmann, K. Different mechanisms of phase delays and phase advances of the circadian rhythm in rat pineal N-acetyltransferase activity. J. Biol Rhythms, 1989, 4: 187–200.
- Jewett, M. E. Kronauer, R. E. and Czeisler, C. A. Light-induced suppression of endogenous circadian amplitude in humans. Nature, 1991, 350: 59–62.
- Kawato, M., Fujita, K., Suzuki, R. and Winfree, A. T. A three-oscillator model of the human circadian system controlling the core temperature rhythm and the sleep-wake cycle. J. Theor. Biol., 1982, 98: 369–392.
- Kemp, B. and Kamphuisen, H. A. C. Simulation of human hypnograms using a Markov chain model. Sleep, 1986, 9: 405–414.
- Kleitman, N. and Engelmann, T. G. Sleep characteristics of infants. J. Appl Physiol., 1953, 6: 269–282.
- Knowles, J. B., Coulter, M., Wahnon, S., Reitz, W. and MacLean, A. W. Variation in Process S: effects on sleep continuity and architecture. Sleep, 1990a, 13: 97–107.
- Knowles, J. B., MacLean, A. W., Brunet, D. and Coulter, M. Nap-induced changes in the time course of Process S. Effects on nocturnal slow wave activity. In: J. A. Home (Ed.) Sleep ′90. Pontenagel Press, Bochum , 1990: 68–70.
- Kronauer, R. E. Modeling principles for human circadian rhythms. In: M. C. Moore-Ede and C. A. Czeisler (Eds) Mathematical Models of the Circadian Sleep-Wake Cycle. Raven Press, New York , 1984: 105–128.
- Kronauer, R. E. Temporal subdivision of the circadian cycle. Lect. Math. Life Sci., 1987a, 19: 63–120.
- Kronauer, R. E. A model for the effect of light on the human “deep” circadian rhythm. Sleep Res., 1987b, 16: 620.
- Kronauer, R. E. A quantitative model for the effects of light on the amplitude and phase of the deep circadian pacemaker, based on human data. In: J. A. Home (Ed) Sleep ′90. Pontenagel Press, Bochum , 1990: 306–309.
- Kronauer, R. E. and Frangioni, J. V. Modeling laboratory bright-light protocols. Sleep Res., 1987, 16: 622.
- Kronauer, R. E. and Jewett, M. E. The relation between circadian and hemicircadian components of human endogenous temperature rhythms. J. Sleep Res., 1992, 1: 88–92.
- Kronauer, R. E., Czeisler, C. A., Pilato, S. F., Moore-Ede, M. C. and Weitzmann, E. D. Mathematical model of the human circadian system with two interacting oscillators. Am. J. Physiol., 1982, 242: R3–R17.
- Lancel, M. and Kerkhof, G. A. Sleep structure and EEG power density in morning types and evening types during a simulated day and night shift. Physiol. Behav., 1991, 49: 1195–1201.
- Lavie, P. To nap, perchance to sleep—ultradian aspects of napping. In: D. F. Dinges and R. J. Broughton (Eds) Sleep and Alertness: Chronobiological, behavioral, and medical aspects of napping. Raven Press, New York , 1989: 99–120.
- Lavie, P. The 24-hour sleep propensity function (SPF): practical and theoretical implications. In: T. H. Monk (Ed) Sleep, Sleepiness and Performance. Wiley, Chichester , 1991: 65–93.
- Lawder, R. E. A proposed mathematical model for sleep patterning. J. Biomed. Eng., 1984, 6: 63–69.
- Massaquoi, S. and McCarley, R. W. Resetting the REM sleep oscillator. In: J. A. Home (Ed.) Sleep ′90. Pontenagel Press, Bochum , 1990: 301–305.
-
Massaquoi, S. and
McCarley, R. W.
Extension of the limit cycle reciprocal interaction model of REM cycle control: an integrated sleep control model.
J. Sleep Res.
1992, 1: 32–137.
10.1111/j.1365-2869.1992.tb00027.x Google Scholar
- McCarley, R. W. and Hobson, J. A. Neuronal excitability modulation over the sleep cycle: a structural and mathematical model. Science, 1975, 189: 58–60.
- McCarley, R. W. and Massaquoi, S. A limit cycle mathematical model of the REM sleep oscillator system. Am. J. Physiol. 1986, 251: R1011–R1029.
-
McCarley, R. W. and
Massaquoi, S.
Neurobiological substrates of the revised limit cycle reciprocal interaction model of REM sleep control.
J. Sleep Res., 1992, 1: 126–131.
10.1111/j.1365-2869.1992.tb00026.x Google Scholar
- Meijer, J. H., Daan, S., Overkamp, G. J. F. and Hermann, P. The two-oscillator circadian system of tree shrews (Tupaija belangeri) and its response to light pulses. J. Biol. Rhythms, 1990, 5: 1–16.
- Mendelson, W. B., James, S. P., Martin, J. V., Wagner, R., Sack, D. A., Garnett, D., Milton, J. and Wehr, T. A. Frequency analysis of the sleep EEG in depression. Psychiat. Res., 1987, 21: 89–94.
- Mistlberger, R. E., Bergmann, B. M., Waldenar, W. and Rechtschaffen, A. Recovery sleep following sleep deprivation in intact and suprachiasmatic nuclei lesioned rats. Sleep, 1983, 6: 217–233.
- Mrosovsky, N. and Salmon, P. A. A behavioral method for accelerating re-entrainment of rhythms to new light-dark cycles. Nature, 1987, 330: 372–373.
- Nakao, M., McGinty, D., Szymusiak, R. and Yamamoto, M. Human circadian system model based on thermoregulatory mechanism of slow wave sleep. Proc. 5th Symp. Biol. Physiol. Eng. (Japan), 1990a: 217–220.
- Nakao, M., Takahashi, T., Mizutani, Y. and Yamamoto, M. Simulation study on dynamics transition in neuronal activity during sleep cycle by using asynchronous and symmetry neural network model. Biol. Cybern., 1990b, 63: 243–250.
- Nakao, M., McGinty, D., Szymusiak, R., Ichikawa, T. and Yamamoto, M. A thermoregulatory model of the ultradian rhythm of human sleep. Sleep Res., 1991, 20A: 554.
- Pittendrigh, C. S. and Daan, S. A functional analysis of circadian pacemakers in nocturnal rodents. I. The stability and lability of spontaneous frequency. J. comp. Physiol., 1976, 106: 223–252.
- Remé, C. E., Wirz-Justice, A. and Terman, M. The visual input stage of the mammalian circadian pacemaking system: I. Is there a clock in the mammalian eye? J. Biol. Rhythms, 1991, 6: 5–29.
- Steriade, M., Curró, Dossi R. and Nun̄ez, A. Network modulation of a slow intrinsic oscillation of cat thalamocortical neurons implicated in sleep delta waves: Cortically induced synchronization and brainstem cholinergic suppression. J. Neurosci., 1991, 11: 3200–3217.
-
Strogatz, S. H.
The Mathematical Structure of the Human Sleep-Wake Cycle. Springer-Verlag,
Berlin
, 1986.
10.1007/978-3-642-46589-5 Google Scholar
- Strogatz, S. H. and Kronauer, R. E. Circadian wake-maintenance zones and insomnia in man. Sleep Res., 1985, 14: 219.
- Tobler, I. Effect of forced locomotion on the rest-activity cycle of the cockroach. Behav. Brain Res., 1983, 8: 351–360.
- Tobler, I. and Borbély, A. A. Effect of rest deprivation on motor activity in fish. J. Comp. Physiol., 1985, 157: 817–822.
- Tobler, I. and Borbély, A. A. Sleep and EEG spectra in the pigeon (Columbia Livia) under baseline conditions and after sleep deprivation. J. Comp. Physiol. A, 1988, 163: 729–738.
- Tobler, I. and Stalder, J. Rest in the scorpion—a sleep-like state? J. Comp. Physiol. A, 1988, 163: 227–235.
- Tobler, I. Borbély, A. A. and Groos, G. The effect of sleep deprivation on sleep in rats with suprachiasmatic lesions. Neurosci. Lett., 1983, 42: 49–54.
-
Tobler, I.,
Franken, P.,
Trachsel, L. and
Borbély, A. A.
Models of sleep regulation in mammals.
J. Sleep Res., 1992, 1: 119–121.
10.1111/j.1365-2869.1992.tb00024.x Google Scholar
- Trachsel, L., Tobler, I. and Borbély, A. A. Sleep regulation in rats: effects of sleep deprivation, light and circadian phase. Am. J. Physiol., 1986, 251: R1037–R1044.
- Trachsel, L., Dijk, D. J., Brunner, D. P., Klene, C. and Borbély, A. A. Effect of zopiclone and midazolam on sleep and EEG spectra in a phase-advanced sleep schedule. Neuropsycho-pharmacology, 1990, 3: 11–18.
- Webb, W. B. and Agnew Jr., H. W. Stage 4 sleep: influence of time course variables. Science, 1971, 174: 1354–1356.
- Wehr, T. A. The duration of human melatonin secretion and sleep response to changes in daylength (photoperiod). J. Clin. Endocrinol. Metab., 1991, 73: 1276–1280.
- Wehr, T. A. In short photoperiods, human sleep is biphasic. J. Sleep Res., 1992, 1.
- Wehr, T. A. and Wirz-Justice, A. Internal coincidence model for sleep deprivation and depression. In: W. P. Koella (Ed.) Sleep 1980. Karger, Basel , 1981: 26–33.
- Wever, R. A. Toward a mathematical model of circadian rhythmicity. In: M. C. Moore-Ede and C. A. Czeisler (Eds) Mathematical Models of the Circadian Sleep-Wake Cycle. Raven Press, New York , 1984: 17–79.
-
Wever, R. A.
Modes of interaction between ultradian and circadian rhythms: Toward a mathematical model of sleep. In: H. Schulz and
P. Lavie (Eds) Ultradian Rhythms in Physiology and Behavior. Exp. Brain Res. suppl. 12, 1985: 309–317.
10.1007/978-3-642-70483-3_20 Google Scholar
- Wever, R. A. Mathematical models of circadian one- and multi-oscillator systems. Lect. Math. Life Sci., 1987, 19: 205–265.
- Winfree, A. T. Impact of a circadian clock on the timing of human sleep. Am. J. Physiol., 1983, 245: R497–R504.
- Wollmann, M. and Lavie, P. A hypernycthemeral sleep-wake cycle: some hidden regularities. Sleep, 1986, 9: 324–334.
- Wu, J. C. and Bunney, W. E. The biological basis of an antidepressant response to sleep deprivation and relapse: a review and hypothesis. Am. J. Psychiatry, 1990, 147: 14–21.
- Zulley, J. The four-hour sleep wake cycle. Sleep Res., 1988, 17: 403.
- Zulley, J. and Carr, D. Forced splitting of human sleep in free-running rhythms. J. Sleep Res., 1992, 1: 108–111.