• Featured in Physics

Theoretical electroencephalogram stationary spectrum for a white-noise-driven cortex: Evidence for a general anesthetic-induced phase transition

Moira L. Steyn-Ross, D. A. Steyn-Ross, J. W. Sleigh, and D. T. J. Liley
Phys. Rev. E 60, 7299 – Published 1 December 1999
Physics logo
PDFExport Citation

Abstract

We present a model for the dynamics of a cerebral cortex in which inputs to neuronal assemblies are treated as random Gaussian fluctuations about a mean value. We incorporate the effect of general anesthetic agents on the cortex as a modulation of the inhibitory neurotransmitter rate constant. Stochastic differential equations are derived for the state variable he, the average excitatory soma potential, coherent fluctuations of which are believed to be the source of scalp-measured electroencephalogram (EEG) signals. Using this stochastic approach we derive a stationary (long-time limit) fluctuation spectrum for he. The model predicts that there will be three distinct stationary (equilibrium) regimes for cortical activity. In region I (“coma”), corresponding to a strong inhibitory anesthetic effect, he is single valued, large, and negative, so that neuronal firing rates are suppressed. In region II for a zero or small anesthetic effect, he can take on three values, two of which are stable; we label the stable solutions as “active” (enhanced firing) and “quiescent” (suppressed firing). For region III, corresponding to negative anesthetic (i.e., analeptic) effect, he again becomes single valued, but is now small and negative, resulting in strongly elevated firing rates (“seizure”). If we identify region II as associated with the conscious state of the cortex, then the model predicts that there will be a rapid transit between the active-conscious and comatose unconscious states at a critical value of anesthetic concentration, suggesting the existence of phase transitions in the cortex. The low-frequency spectral power in the he signal should increase strongly during the initial stage of anesthesia induction, before collapsing to much lower values after the transition into comatose-unconsciousness. These qualitative predictions are consistent with clinical measurements by Bührer et al. [Anaesthesiology 77, 226 (1992)], MacIver et al. [ibid. 84, 1411 (1996)], and Kuizenga et al. [Br. J. Anaesthesia 80, 725 (1998)]. This strong increase in EEG spectral power in the vicinity of the critical point is similar to the divergences observed during thermodynamic phase transitions. We show that the divergence in low-frequency power in our model is a natural consequence of the existence of turning points in the trajectory of stationary states for the cortex.

  • Received 30 April 1999

DOI:https://doi.org/10.1103/PhysRevE.60.7299

©1999 American Physical Society

Authors & Affiliations

Moira L. Steyn-Ross and D. A. Steyn-Ross

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

J. W. Sleigh

  • Department of Anaesthetics, Waikato Hospital, Hamilton, New Zealand

D. T. J. Liley

  • School of Biophysical Sciences and Electrical Engineering, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia

See Also

Freezing into Unconsciousness

Mark Sincell
Phys. Rev. Focus 4, 30 (1999)

References (Subscription Required)

Click to Expand
Issue

Vol. 60, Iss. 6 — December 1999

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×