Abstract
It is a well established clinical observation that, at low concentrations, most anesthetic agents produce a surge in brain activity that occurs around the time of loss of consciousness. At higher concentrations, brain activity slows, and eventually tends towards electrical silence. A second surge in EEG power occurs during the return to consciousness. These induction and recovery biphasic power surges were first explained in terms of a first-order switching transition between distinct active and quiescent neural states, but subsequent modeling by other researchers has demonstrated that biphasic surges can also be generated by a smooth, graduated transition between normal and suppressed levels of cortical activity. In this chapter we examine the contrasting predictions of the switching model versus the continuous model for anesthetic induction. If the continuous non-switching picture is correct, then the return path to recovery will retrace the trajectory for induction, so the biphasic peaks should occur at identical drug concentrations. In contrast, the switching model predicts that there must be a hysteresis separation between the entry and recovery EEG power maxima, and that the patient will awaken at a lower drug concentration than that required to put her to sleep.
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Notes
- 1.
This is analogous to the noise immunity provided by the positive-feedback hysteresis engineered into an electronic Schmitt trigger for clean binary switching in digital circuits.
- 2.
The convolve2 function is written by David Young, and available for download from www.mathworks.com/matlabcentral/fileexchange/22619-fast-2-d-convolution.
- 3.
G. Ludbrook, C. Grant, and R. Upton, from the Department of Anaesthesia and Intensive Care, University of Adelaide, Adelaide, South Australia, Australia. Experimental methods were approved by the Animal Ethics Committee of University of Adelaide.
References
Bojak I, Liley DTJ (2005) Modeling the effects of anesthesia on the electroencephalogram. Phys Rev E 71:041902
Chaturvedi S, Gardiner CW, Matheson IS, Walls DF (1977) Stochastic analysis of a chemical reaction with spatial and temporal structures. J Stat Phys 17:469–489
Eilers PHC (1994) Smoothing and interpolation with finite differences. In: Heckbert PS (ed) Graphic gems IV. Academic Press, San Diego, pp 241–250
Foster BL, Bojak I, Liley DTJ (2008) Population based models of cortical drug response: insights from anaesthesia. Cog Neurodyn 2(4):283–296
Franks NP, Lieb WR (1994) Molecular and cellular mechanisms of general anaesthesia. Nature 367:607–613
Franks NP, Dickenson R, de Sousa SLM, Hall AC, Lieb WR (1998) How does xenon produce anaesthesia? Nature 396:324
Fulcher BD, Phillips AJK, Robinson PA (2008) Modeling the impact of impulsive stimuli on sleep-wake dynamics. Phys Rev E 78(5):051920
Guedel AE (1937) Inhalational anesthesia: a fundamental guide. Macmillan, New York
Hutt A, Longtin A (2010) Effects of the anesthetic agent propofol on neural populations. Cog Neurodyn 4(1):37–59
Hutt A, Schimansky-Geier L (2008) Anesthetic-induced transitions by propofol modeled by nonlocal neural populations involving two neuron types. J Biol Phys 34(3–4):433–440
John ER, Prichep LS, Kox W, Valdés-Sosa P, Bosch-Bayard J, Aubert E, Tom M, diMichele F, Guginoi LD (2001) Invariant reversible QEEG effects of anesthetics. Conscious Cogn 10:165–183
Kelly DD (1991) Sleep and dreaming. In: Kandel ER, Schwartz JH, Jessell TM (eds) Principles of neural science, 3rd edn. Prentice-Hall, Toronto, pp 792–804
Kitamura A, Marszalec W, Yeh JZ, Narahashi T (2002) Effects of halothane and propofol on excitatory and inhibitory synaptic transmission in rat cortical neurons. J Pharmacol 304(1):162–171
Kuizenga K, Kalkman CJ, Hennis PJ (1998) Quantitative electroencephalographic analysis of the biphasic concentration–effect relationship of propofol in surgical patients during extradural analgesia. Br J Anaesth 80:725–732
Kuizenga K, Proost JH, Wierda JMKH, Kalkman CJ (2001a) Predictability of processed electroencephalography effects on the basis of pharmacokinetic–pharmacodynamic modeling during repeated propofol infusions in patients with extradural analgesia. Anesthesiology 95:607–615
Kuizenga K, Wierda JMKH, Kalkman CJ (2001b) Biphasic EEG changes in relation to loss of consciousness during induction with thiopental, propofol, etomidate, midazolam or sevoflurane. Br J Anaesth 86:354–360
Liley DTJ, Bojak I (2005) Understanding the transition to seizure by modeling the epileptiform activity of general anesthetic agents. Clin Neurophysiol 22(5):300–313
Liley DTJ, Cadusch PJ, Wright JJ (1999) A continuum theory of electro-cortical activity. Neurocomputing 26–27:795–800
Ludbrook GL, Upton RN, Grant C, Gray EC (1996) Brain and blood concentrations of propofol after rapid intravenous injection in sheep and their relationships to cerebral effects. Anaesth Intensive Care 24(4):445–452
Ludbrook GL, Upton RN, Grant C, Martinez A (1999) Prolonged dysequilibrium between blood and brain concentrations of propofol during infusions in sheep. Acta Anaesthesiol Scand 43(2):206–211
Molaee-Ardekani B, Senhadji L, Shamsollahi MB, Vosoughi-Vahdat B, Wodey E (2007) Brain activity modeling in general anesthesia: enhancing local mean-field models using a slow adaptive firing rate. Phys Rev E 76(4):041911
Olofsen E, Sleigh JW, Dahan A (2008) Permutation entropy of the electroencephalogram: a measure of anaesthetic drug effect. Br J Anaesth 101(6):810–821
Phillips AJK, Robinson PA (2007) A quantitative model of sleep-wake dynamics based on the physiology of the brainstem ascending arousal system. J Biol Rhythms 22(2):167–179
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, Rennie CJ, Wright JJ, Bourke PD (1998) Steady states and global dynamics of electrical activity in the cerebral cortex. Phys Rev E 58:3557–3571
Robinson P, Rennie C, Phillips A, Kim J, Roberts J (2010) Phase transitions in physiologically-based multiscale mean-field brain models. In: Steyn-Ross DA, Steyn-Ross ML (eds) Modeling phase transitions in the brain. Springer series in computational neuroscience, vol 4. Springer, Berlin, pp 179–201
Steyn-Ross ML, Steyn-Ross DA, Sleigh JW, Liley DTJ (1999) Theoretical electroencephalogram stationary spectrum for a white-noise-driven cortex: evidence for a general anesthetic-induced phase transition. Phys Rev E 60:7299–7311
Steyn-Ross DA, Steyn-Ross ML, Wilcocks LC, Sleigh JW (2001a) 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 64:011918
Steyn-Ross ML, Steyn-Ross DA, Sleigh JW, Wilcocks LC (2001b) Toward a theory of the general anesthetic-induced phase transition of the cerebral cortex: I. A statistical mechanics analogy. Phys Rev E 64:011917
Steyn-Ross ML, Steyn-Ross DA, Sleigh JW, Whiting DR (2003) 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 68:021902
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 DA, Steyn-Ross ML, Sleigh JW, Wilson MT, Gillies IP, Wright JJ (2005) The sleep cycle modelled as a cortical phase transition. J Biol Phys 31:547–569
Steyn-Ross DA, Steyn-Ross ML, Wilson MT, Sleigh JW (2006) White-noise susceptibility and critical slowing in neurons near spiking threshold. Phys Rev E 74:051920
Steyn-Ross ML, Steyn-Ross DA, Wilson MT, Sleigh JW (2007) Gap junctions mediate large-scale Turing structures in a mean-field cortex driven by subcortical noise. Phys Rev E 76:011916
Steyn-Ross ML, Steyn-Ross DA, Wilson MT, Sleigh JW (2009) Modeling brain activation patterns for the default and cognitive states. NeuroImage 45:298–311
Steyn-Ross DA, Steyn-Ross ML, Wilson MT, Sleigh JW (2010a) Phase transitions in single neurons and neural populations: Critical slowing, anesthesia, and sleep cycles. In: Steyn-Ross DA, Steyn-Ross ML (eds) Modeling phase transitions in the brain. Springer series in computational neuroscience, vol 4. Springer, Berlin, pp 1–26
Steyn-Ross ML, Steyn-Ross DA, Wilson MT, Sleigh JW (2010b) Cortical patterns and gamma genesis are modulated by reversal potentials and gap-junction diffusion. In: Steyn-Ross DA, Steyn-Ross ML (eds) Modeling phase transitions in the brain. Springer series in computational neuroscience, vol 4. Springer, Berlin, pp 271–299
Strogatz SH (2000) Nonlinear dynamics and chaos. Westview Press, Cambridge
Upton RN, Mather LE, Runciman WB, Nancarrow C, Carapetis RJ (1988) The use of mass balance principles to describe regional drug distribution and elimination. J Pharmacokinet Biopharm 16(1):13–29
Voss LJ, Ludbrook G, Grant C, Upton R, Sleigh JW (2007) A comparison of pharmacokinetic/pharmacodynamic versus mass-balance measurement of brain concentrations of intravenous anesthetics in sheep. Anesth Analg 104(6):1440–1446
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
Wilson MT, Sleigh JW, Steyn-Ross DA, Steyn-Ross ML (2006) General anesthetic-induced seizures can be explained by a mean-field model of cortical dynamics. Anesthesiology 104:588–593
Wilson MT, Steyn-Ross ML, Steyn-Ross DA, Sleigh JW, Gillies IP, Hailstone DJ (2010) What can a mean-field model tell us about the dynamics of the cortex. In: Steyn-Ross DA, Steyn-Ross ML (eds) Modeling phase transitions in the brain. Springer series in computational neuroscience, vol 4. Springer, Berlin, pp 223–242
Wright JJ, Robinson PA, Rennie CJ, Gordon E, Bourke PD, Chapman CL, Hawthorn N, Lees GJ, Alexander D (2001) Toward an integrated continuum model of cerebral dynamics: the cerebral rhythms, synchronous oscillation and cortical stability. Biosystems 73:71–88
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Steyn-Ross, D.A., Steyn-Ross, M.L., Sleigh, J.W., Wilson, M.T. (2011). Progress in Modeling EEG Effects of General Anesthesia: Biphasic Response and Hysteresis. In: Hutt, A. (eds) Sleep and Anesthesia. Springer Series in Computational Neuroscience, vol 15. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0173-5_8
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