Skip to main content
SpringerLink
Log in

The K-complex and slow oscillation in terms of a mean-field cortical model

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

Abstract

We use a mean-field macrocolumn model of the cerebral cortex to offer an interpretation of the K-complex of the electroencephalogram to complement those of more detailed neuron-by-neuron models. We interpret the K-complex as a momentary excursion of the cortex from a stable low-firing state to an unstable high-firing state, and hypothesize that the related slow oscillation can be considered as the periodic oscillation between two meta-stable solutions of the mean-field model. By incorporating a Hebbian-style learning rule that links the growth in synapse strength to fluctuations in soma potential, we demonstrate a self-organization behaviour that draws the modelled cortex close to the edge of stability of the low-firing state. Furthermore, a very slow oscillation can occur in the excitability of the cortex that has similarities with the infra-slow oscillation of sleep.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Amzica F, Steriade M (2002) The functional significance of Kcomplexes. Sleep Med. Rev. 6: 139–149.

  • Bazhenov M, Timofeev I, Steriade M, Sejnowski TJ (2002) Model of thalamocortical slow-wave sleep oscillations and transitions to activated states. J. Neurosci. 22: 8691–8704.

  • Bienenstock E, Lehmann D (1998) Regulated criticality in the brain? Adv. Comp. Syst. 1: 361–384.

  • Bienenstock EL, Cooper LN, Munro PW (1982) Theory for the development of neuron selectivity: orientation specificity and binocular interation in visual cortex. J. Neurosci. 2: 32–48.

  • Bojak I, Liley DTJ (2005) Modelling the effects of anaesthesia on the electroencephalogram. Phys. Rev. E 71: 41902.

  • Colrain IM (2005) The K-complex: A 7-decade history. Sleep 28(2): 255–273.

  • Compte A, Sanchez-Vives MV, McCormick DA, Wang XJ (2003) Cellular and network mechanisms of slow oscillatory activity (<1 Hz) and wave propagations in a cortical network model. J. Neurophysiol. 89: 2707–2725.

  • Contreras D, Destexhe A, Sejnowski TJ, Steriade M (1997) Spatiotemporal patterns of spindle oscillations in cortex and thalamus. J. Neurosci. 17: 1179–1196.

  • Destexhe A, Contreras D, Steriade M (1999) Spatiotemporal analysis of local field potentials and unit discharges in cat cerebral cortex during natural wake and sleep states. J. Neurosci. 19(11): 4595–4608

  • Freeman WJ (1992) Predictions on neocortical dynamics derived from studies in paleocortex. In: E Basar, TH Bullock, eds., Induced Rhythms of the Brain, Birkhaeuser, Boston, pp. 183–199.

  • Gardiner CW (2003) Handbook of Sochastic Methods for Physics, Chemistry and the Natural Sciences, Springer series in synergetics, Springer-Verlag, Berlin, Heidelberg, New York.

  • Golomb D, Amitai Y (1997) Propagating neuronal discharges in neocortical slices: Computational and experimental study. J. Neurophysiol. 78(3): 1199–1211.

  • Hebb DO (1949) The Organization of Behaviour, Wiley, New York.

  • Hill S, Tononi G (2005) Modeling sleep and wakefulness in the thalamocortical system. J. Neurophysiol. 93: 1671–1698.

  • Kramer MA, Kirsch HE, Szeri AJ (2005) Pathalogical pattern formation and epileptic seizures. J. Royal Soc. Interface 2: 113–127.

  • Liley DTJ, Cadusch PJ, Wright JJ (1999) A continuum theory of electro-cortical activity. Neurocomputing 26–27: 795–800.

  • Marshall L, Mölle M, Born J (2003) Spindle and slow wave rhythms at slow wave sleep transitions are linked to strong shifts in the cortical direct current potential. Neuroscience 121: 1047–1053.

  • Massimini M, Huber R, Ferrarelli F, Hill S, Tononi G (2004) The sleep slow oscillation as a traveling wave. J. Neurosci. 24: 6862–6870.

  • Numminen J, Makela JP, Hari R (1996) Distributions and sources of magnetoencephalographic K-complexes. Electroencephalograpr. Clin. Neurophysil. 99: 544–555.

  • Nunez PL (1974) The brain wave function: A model for the EEG. Math. Biosci. 21: 279–297.

  • Pace-Schott EF, Hobson JA (2002) The neurobiology of sleep: genetics, cellular physiology and subcortical networks. Nature Rev.: Neurosci. 3: 591–605.

  • Patenaude C, Massicotte G, Lacaille J-C (2005) Cell-type specific GABA synaptic transmission and activity-dependent plasticity in rat hippocampal stratum radiatum interneurons. Eur. J. Neurosci. 22: 179–188.

  • Rennie CJ, Wright JJ, Robinson PA (2000) Mechanisms for cortical electrical activity and emergence of gamma rhythm. J. Theor. Biol. 205: 17–35.

  • Robinson PA, Rennie CJ, Wright JJ (1997) Propagation and stability of waves of electrical activity in the cerebral cortex. Phys. Rev. E 56: 826–840.

  • Robinson PA, Wright JJ, Rennie CJ (1998) Synchronous oscillations in the cerebral cortex. Phys. Rev. E 57: 4578–4588.

  • Sanchez-Vives MV, McCormick DA (2000) Cellular and network mechanisms of rhythmic recurrent activity in neocortex. Nat. Neurosci. 3: 1027–1034.

  • Steriade M, Núnez A, Amzica F (1993) A novel slow (<1 Hz) oscillation of neocortical neurons in vivo: Depolarizing and hyperpolarizing components. J. Neurosci. 13: 3252–3265.

  • Steriade M, Timofeev I, Grenier F (2001) Natural waking and sleep states: A view from inside neocortical neurons. J. Neurophysiol. 85: 1969–1985.

  • Steyn-Ross DA, Steyn-Ross ML, Sleigh JW, Wilson MT, Gillies IP, Wright JJ (2005) The sleep cycle modelled as a cortical phase transition. J. Biophys. 31: 543–565.

  • Steyn-Ross ML, Steyn-Ross DA, Sleigh JW (2004) Modelling general anaesthesia as a first-order phase transition in the cortex. Prog. Biophys. Mol. Biol. 85: 369–385.

  • Steyn-Ross ML, Steyn-Ross DA, Sleigh JW, Wilson MT, Wilcocks LC (2005) A mechanism for learning and memory erasure in a white-noisedriven sleeping cortex. Phys. Rev. E 72: 061910

  • Vanhatalo S, Palva JM, Holmes MD, Miller JW, Voipio J, Kaila K (2003) Infraslow oscillations modulate excitability and interictal epileptic activity in the human cortex during sleep. Proc. Natl. Acad. Sci. 101: 5053–5057.

  • Wilson MT, Steyn-Ross ML, Steyn-Ross DA, Sleigh JW (2005) Predictions and simulations of cortical dynamics during natural sleep using a continuum approach. Phys. Rev. E 72: 051910

  • Wright JJ, Liley DTJ (1996) Dynamics of the brain at global and microscopic scales: Neural networks and the EEG. Behav. Brain Sci. 19: 285–316.

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Electronic Engineering, University of Waikato, Private Bag 3105, Hamilton, New Zealand

    M. T. Wilson, D. A. Steyn-Ross, M. L. Steyn-Ross, L. C. Wilcocks & I. P. Gillies

  2. Department of Anaesthetics, Waikato Hospital, Hamilton, New Zealand

    J. W. Sleigh

Authors
  1. M. T. Wilson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. A. Steyn-Ross
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. W. Sleigh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. L. Steyn-Ross
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. L. C. Wilcocks
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. I. P. Gillies
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. T. Wilson.

Additional information

Action Editor: Nicolas Brunel

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wilson, M.T., Steyn-Ross, D.A., Sleigh, J.W. et al. The K-complex and slow oscillation in terms of a mean-field cortical model. J Comput Neurosci 21, 243–257 (2006). https://doi.org/10.1007/s10827-006-7948-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-006-7948-6

Keywords

Search

Navigation