Abstract
We present a mean-field model of the cortex that attempts to describe the gross changes in brain electrical activity for the cycles of natural sleep. We incorporate within the model two major sleep modulatory effects: slow changes in both synaptic efficiency and in neuron resting voltage caused by the ∼90-min cycling in acetylcholine, together with even slower changes in resting voltage caused by gradual elimination during sleep of somnogens (fatigue agents) such as adenosine. We argue that the change from slow-wave sleep (SWS) to rapid-eye-movement (REM) sleep can be understood as a first-order phase transition from a low-firing, coherent state to a high-firing, desychronized cortical state. We show that the model predictions for changes in EEG power, spectral distribution, and correlation time at the SWS-to-REM transition are consistent not only with those observed in clinical recordings of a sleeping human subject, but also with the on-cortex EEG patterns recently reported by Destexhe et al. [J. Neurosci. 19(11), (1999) 4595–4608] for the sleeping cat.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- 2-D:
-
two-dimensional
- ACh:
-
acetylcholine
- EEG:
-
electroencephalogram
- EMG:
-
electromyogram
- EOG:
-
electro-oculogram
- LFP:
-
local field potential
- OU:
-
Ornstein–Uhlenbeck
- PSP:
-
postsynaptic potential
- REM sleep:
-
rapid-eye-movement sleep
- SWS:
-
slow-wave sleep
References
Courant, R. and John, F.: Introduction to Calculus and Analysis, Vol. 2, Wiley-Interscience, New York, 1974.
Destexhe, A., Contreras, D. and Steriade, M.: Spatiotemporal Analysis of Local Field Potentials and Unit Discharges in Cat Cerebral Cortex During Natural Wake and Sleep States, J. Neurosci. 19(11) (1999), 4595–4608.
España, R.A. and Scammell, T.E.: Sleep Neurobiology for the Clinician, Sleep 27(4) (2004), 811–820.
Freeman, W.J.: Mass Action in the Nervous System, Academic Press, New York, 1975.
Gardiner, C.W.: Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences, Vol. 13: Springer Series in Synergetics, 3rd edn., Springer-Verlag, Berlin/Heidelberg/ New York, 2004.
Hasselmo, M.E.: Neuromodulation and Cortical Function: Modeling the Physiological Basis of Behavior., Behav Brain Res. 67 (1995), 1–27.
Kayama, K. and Koyama, Y.: Control of Sleep and Wakefulness by Brainstem Monoaminergic and Cholinergic Neurons, Acta Neurochirurgica Suppl. 87 (2003), 3–6.
Kelly, D.D.: Disorders of Sleep and Consciousness, in E.R. Kandel, J.H. Schwartz and T.M. Jessell (eds.), Principles of Neural Science, 3rd edn., Prentice-Hall, Toronto, 1991, Chapter 52, pp. 805–819.
Kloeden, P.E. and Platen, E.: Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1992.
Liley, D.T.J., Cadusch, P.J. and Wright, J.J.: A Continuum Theory of Electro-Cortical Activity, Neurocomputing 26–27 (1999), 795–800.
Nunez, P.L.: Neocortical Dynamics and Human EEG Rhythms, Oxford University Press, Oxford, 1995.
Rechtschaffen, A. and Kale, A.: A Manual of Standardized Terminology, Techniques, and Scoring System for Sleep Stages of Human Subjects, U.S. Govt Printing Office, Washington, DC, 1968.
Rennie, C.J., Wright, J.J. and Robinson, P.A.: Mechanisms for Cortical Electrical Activity and Emergence of Gamma Rhythm, J. Theor. Biol. 205 (2000), 17–35.
Robinson, P.A., Rennie, C.J. and Wright, J.J.: Propagation and Stability of Waves of Electrical Activity in the Cerebral Cortex, Phys. Rev. E 56 (1997), 826–840.
Steyn-Ross, M.L., Steyn-Ross, D.A., Sleigh, J.W. and Liley, D.T.J.: Theoretical Electroencephalogram Stationary Spectrum for a White-Noise-Driven Cortex: Evidence for a General Anesthetic-Induced Phase Transition, Phys. Rev. E 60 (1999), 7299–7311.
Steyn-Ross, M.L., Steyn-Ross, D.A., Sleigh, J.W. and Wilcocks, L.C.: Toward a Theory of the General Anesthetic-Induced Phase Transition of the Cerebral Cortex: I. A Statistical Mechanics Analogy, Phys. Rev. E 64 (2001), 011917.
Steyn-Ross, D.A., Steyn-Ross, M.L., Wilcocks, L.C. and Sleigh, J.W.: Toward a Theory of the General Anesthetic-Induced Phase Transition of the Cerebral Cortex: II. Stochastic Numerical Simulations, Spectral Entropy, and Correlations, Phys. Rev. E 64 (2001), 011918.
Steyn-Ross, M.L., Steyn-Ross, D.A., Sleigh, J.W. and Whiting, D.R.: Theoretical Predictions for Spatial Covariance of the EEG Signal During the Anesthetic-Induced Phase Transition: Increased Correlation Length and Emergence of Self-Organization, Phys. Rev. E 68 (2003), 021902.
Steyn-Ross, M.L., Steyn-Ross, D.A. and Sleigh, J.W.: Modelling General Anaesthesia as a First-Order Phase Transition in the Cortex, Prog. Biophys. Mol. Biol. 85 (2004), 369–385.
Tuckwell, H.C.: Introduction to Theoretical Neurobiology: Nonlinear and Stochastic Theories, Vol. 2, Cambridge University Press, Cambridge, 1988.
Wiberg, D.M.: State Space and Linear Systems, Schaum's Outline Series, McGraw-Hill, New York, 1971.
Wilson, M.T., Steyn-Ross, M.L., Steyn-Ross, D.A. and Sleigh, J.W.: Predictions and Simulations of Cortical Dynamics During Natural Sleep Using a Continuum Approach, in review, 2004.
Wright, J.J. and Liley, D.T.J.: Dynamics of the Brain at Global and Microscopic Scales: Neural Networks and the EEG, Behav. Brain Sci. 19 (1996), 285–316.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Steyn-Ross, D.A., Steyn-Ross, M.L., Sleigh, J.W. et al. The Sleep Cycle Modelled as a Cortical Phase Transition. J Biol Phys 31, 547–569 (2005). https://doi.org/10.1007/s10867-005-1285-2
Issue Date:
DOI: https://doi.org/10.1007/s10867-005-1285-2