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EEG Modeling in Anesthesia: A New Insight into Mean-Field Approach for Delta Activity Generation

  • Chapter
Sleep and Anesthesia

Part of the book series: Springer Series in Computational Neuroscience ((NEUROSCI,volume 15))

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Abstract

In the last two decades, progress in neuroscience has contributed to refining mesoscopic modeling by including new mechanisms. Computational modeling is now developing in many areas both for normal and abnormal representation of neural populations. In this chapter, an enhanced local mean-field (MF) model that is suitable for simulating the electroencephalogram (EEG) in different depths of anesthesia (DOA) is presented. The main building elements of the model (e.g. excitatory and inhibitory populations) are taken from two MF models designed by Steyn-Ross et al. and Bojak and Liley group, and then a new slow ionic mechanism is included in the main model. Generally, in MF models, some sigmoid-shape functions determine firing rates of neural populations according to their mean membrane potentials. In the enhanced model, the sigmoid function corresponding to excitatory population is redefined to be also a function of the slow ionic mechanism. This modification adapts the firing rate of neural populations to slow ionic activities in the brain. When an anesthetic drug is administered, the slow mechanism leads neural cells to alternate between two levels of activity referred to as up and down states. Basically, the frequency of up-down switching is in the delta band and this is the main reason behind high-amplitude, low-frequency fluctuations of EEG signals in anesthesia. The enhanced model has different working states driven by anesthetic drug concentration. It is settled in the up state in waking period, it may switch to up and down states in moderate anesthesia, whilst in deep anesthesia it remains in the down state.

The new introduced mechanism according to which slow oscillations are generated may open new routs in the field of mesoscopic modeling of brain activities. For instance, it has been pointed out by Steriade and colleagues that slow EEG rhythms related to the up and down states have a key role for generating higher frequency EEG bands. This is corroborated by examples of the modulating effect of delta activity on alpha activity in different depths of desflurane anesthesia. Therefore, more comprehensive models can be built based on the concepts which are introduced in the enhanced model regarding slow EEG rhythms and the up and down states.

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References

  • Amzica F, Steriade M (2002) The functional significance of k-complexes. Sleep Med Rev 6(2):139–149

    Article  PubMed  Google Scholar 

  • Antkowiak B (1999) Different actions of general anesthetics on the firing patterns of neocortical neurons mediated by the GABAA receptor. Anesthesiology 91(2):500–511

    Article  PubMed  CAS  Google Scholar 

  • Antkowiak B (2001) How do general anaesthetics work? Naturwissenschaften 88(5):201–213

    Article  PubMed  CAS  Google Scholar 

  • Antkowiak B, Heck D (1997) Effects of the volatile anesthetic enflurane on spontaneous discharge rate and GABA(a)-mediated inhibition of Purkinje cells in rat cerebellar slices. J Neurophysiol 77(5):2525–2538

    PubMed  CAS  Google Scholar 

  • Antkowiak B, Helfrich-Forster C (1998) Effects of small concentrations of volatile anesthetics on action potential firing of neocortical neurons in vitro. Anesthesiology 88(6):1592–1605

    Article  PubMed  CAS  Google Scholar 

  • Antkowiak B, Hentschke H, Kirschfeld K (1997) Effects of volatile anaesthetics on spontaneous action potential firing of cerebellar Purkinje cells in vitro do not follow the Meyer-Overton rule. Br J Anaesth 79(5):617–624

    PubMed  CAS  Google Scholar 

  • Bal T, von Krosigk M, McCormick DA (1995) Synaptic and membrane mechanisms underlying synchronized oscillations in the ferret lateral geniculate nucleus in vitro. J Physiol 483:641–663

    PubMed  CAS  Google Scholar 

  • Barash PG, Cullen BF, Stoetting RK (2005) Cellular and molecular mechanisms of anesthesia, 5th edn. Lippincott, Philadelphia, pp 111–131

    Google Scholar 

  • Bazhenov M, Timofeev I, Steriade M, Sejnowski TJ (2002) Model of thalamocortical slow-wave sleep oscillations and transitions to activated states. J Neurosci 22(19):8691–8704

    PubMed  CAS  Google Scholar 

  • Benoit O, Daurat A, Prado J (2000) Slow (0.7–2 Hz) and fast (2–4 Hz) delta components are differently correlated to theta, alpha and beta frequency bands during nrem sleep. Clin Neurophysiol 111(12):2103–2106

    Article  PubMed  CAS  Google Scholar 

  • Bleakman D, Jones MV, Harrison NL (1995) The effects of four general anesthetics on intracellular [Ca2+] in cultured rat hippocampal neurons. Neuropharmacology 34(5):541–551

    Article  PubMed  CAS  Google Scholar 

  • Blumenfeld H, McCormick DA (2000) Corticothalamic inputs control the pattern of activity generated in thalamocortical networks. J Neurosci 20(13):5153–5162

    PubMed  CAS  Google Scholar 

  • Bojak I, Liley DT (2005) Modeling the effects of anesthesia on the electroencephalogram. Phys Rev E 71:041902

    Article  CAS  Google Scholar 

  • 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(5):2707–2725

    Article  PubMed  Google Scholar 

  • Constant I, Seeman R, Murat I (2005) Sevoflurane and epileptiform EEG changes. Paediatr Anaesth 15(4):266–274

    Article  PubMed  Google Scholar 

  • Contreras D, Steriade M (1995) Cellular basis of EEG slow rhythms: a study of dynamic corticothalamic relationships. J Neurosci 15:604–622

    PubMed  CAS  Google Scholar 

  • Contreras D, Steriade M (1996) Spindle oscillation in cats: the role of corticothalamic feedback in a thalamically generated rhythm. J Physiol 490:159–179

    PubMed  CAS  Google Scholar 

  • Contreras D, Destexhe A, Sejnowski TJ, Steriade M (1996) Control of spatiotemporal coherence of a thalamic oscillation by corticothalamic feedback. Science 274(5288):771–774

    Article  PubMed  CAS  Google Scholar 

  • Deco G, Jirsa VK, Robinson PA, Breakspear M, Friston K (2008) The dynamic brain: from spiking neurons to neural masses and cortical fields. PLoS Comput Biol 4(8):e1000,092

    Article  Google Scholar 

  • Destexhe A, Contreras D, Steriade M (1998) Mechanisms underlying the synchronizing action of corticothalamic feedback through inhibition of thalamic relay cells. J Neurophysiol 79(2):999–1016

    PubMed  CAS  Google Scholar 

  • Destexhe A, Contreras D, Steriade M (1999) Cortically-induced coherence of a thalamic-generated oscillation. Neuroscience 92(2):427–443

    Article  PubMed  CAS  Google Scholar 

  • Destexhe A, Rudolph M, Fellous JM, Sejnowski TJ (2001) Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons. Neuroscience 107(1):13–24

    Article  PubMed  CAS  Google Scholar 

  • Eger NEI (1987) Partition coefficients of i-653 in human blood, saline, and olive oil. Anesth Analg 66(10):971–973

    PubMed  CAS  Google Scholar 

  • Fell J, Elfadil H, Roschke J, Burr W, Klaver P, Elger CE, Fernandez G (2002) Human scalp recorded sigma activity is modulated by slow EEG oscillations during deep sleep. Int J Neurosci 112(7):893–900

    Article  PubMed  Google Scholar 

  • Fell J, Widman G, Rehberg B, Elger CE, Fernandez G (2005) Human mediotemporal EEG characteristics during propofol anesthesia. Biol Cybern 92(2):92–100

    Article  PubMed  CAS  Google Scholar 

  • Franks NP, Lieb WR (1993) Selective actions of volatile general anaesthetics at molecular and cellular levels. Br J Anaesth 71(1):65–76

    Article  PubMed  CAS  Google Scholar 

  • Franks NP, Lieb WR (1996) Temperature dependence of the potency of volatile general anesthetics: implications for in vitro experiments. Anesthesiology 84(3):716–720

    Article  PubMed  CAS  Google Scholar 

  • Fujisawa S, Matsuki N, Ikegaya Y (2006) Single neurons can induce phase transitions of cortical recurrent networks with multiple internal states. Cereb Cortex 16(5):639–654

    Article  PubMed  Google Scholar 

  • Hutt A, Longtin A (2009) Effects of the anesthetic agent propofol on neural populations. Cogn Neurodyn 4(1):37–59

    Article  Google Scholar 

  • Jansen B, Rit V (1995) Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biol Cybern 73(4):357–366

    Article  PubMed  CAS  Google Scholar 

  • Jansen B, Zouridakis G, Brandt M (1993) A neurophysiologically-based mathematical model of flash visual evoked potentials. Biol Cybern 68(3):275–283

    Article  PubMed  CAS  Google Scholar 

  • Kasanetz F, Riquelme LA, Murer MG (2002) Disruption of the two-state membrane potential of striatal neurones during cortical desynchronisation in anaesthetised rats. J Physiol 543:577–589

    Article  PubMed  CAS  Google Scholar 

  • 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(6):725–732

    PubMed  CAS  Google Scholar 

  • Kuizenga K, Proost JH, Wierda JM, 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(3):607–615

    Article  PubMed  CAS  Google Scholar 

  • Kuizenga K, Wierda JM, 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(3):354–360

    Article  PubMed  CAS  Google Scholar 

  • Liley DT, Bojak I (2005) Understanding the transition to seizure by modeling the epileptiform activity of general anesthetic agents. J Clin Neurophysiol 22(5):300–313

    PubMed  CAS  Google Scholar 

  • Liley DT, Cadusch PJ, Dafilis MP (2002) A spatially continuous mean field theory of electrocortical activity. Network 13(1):67–113

    PubMed  Google Scholar 

  • Mahon S, Deniau JM, Charpier S (2001) Relationship between EEG potentials and intracellular activity of striatal and cortico-striatal neurons: an in vivo study under different anesthetics. Cereb Cortex 11(4):360–373

    Article  PubMed  CAS  Google Scholar 

  • Mapleson WW (1996) Effect of age on mac in humans: a meta-analysis. Br J Anaesth 76(2):179–185

    PubMed  CAS  Google Scholar 

  • Massimini M, Amzica F (2001) Extracellular calcium fluctuations and intracellular potentials in the cortex during the slow sleep oscillation. J Neurophysiol 85(3):1346–1350

    PubMed  CAS  Google Scholar 

  • McCormick DA, Bal T (1997) Sleep and arousal: thalamocortical mechanisms. Annu Rev Neurosci 20:185–215

    Article  PubMed  CAS  Google Scholar 

  • Molaee-Ardekani B (2008) Modelling electrical activities of the brain and analysis of the EEG in general anesthesia. Joint PhD thesis, University of Rennes 1 and Sharif University of technology, Rennes-France and Tehran-Iran

    Google Scholar 

  • Molaee-Ardekani B, Shamsollahi MB, Senhadji L, Wodey E, Vosoughi-Vahdat B (2006) An investigation on different EEG patterns from awake to deep anesthesia: application to improve methods of determining depth of anesthesia. IFMBE proceedings, vol 14/1. Springer, Berlin, pp 909–912

    Google Scholar 

  • 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 76:041911

    Article  CAS  Google Scholar 

  • Molaee-Ardekani B, Benquet P, Bartolomei F, Wendling F (2010a) Computational modeling of high-frequency oscillations at the onset of neocortical partial seizures: from ‘altered structure’ to ‘dysfunction’. Neuroimage 52(3):1109–1122

    Article  PubMed  Google Scholar 

  • Molaee-Ardekani B, Shamsollahi MB, Tirel O, Vosoughi Vahdat B, Wodey E, Senhadji L (2010b) Investigation of the modulation between EEG alpha waves and slow/fast delta waves in children in different depths of desflurane anesthesia. IRBM 31(1):55–66

    Article  Google Scholar 

  • Nishikawa K, MacIver MB (2001) Agent-selective effects of volatile anesthetics on GABAA receptor-mediated synaptic inhibition in hippocampal interneurons. Anesthesiology 94(2):340–347

    Article  PubMed  CAS  Google Scholar 

  • Pare D, Shink E, Gaudreau H, Destexhe A, Lang EJ (1998) Impact of spontaneous synaptic activity on the resting properties of cat neocortical pyramidal neurons in vivo. J Neurophysiol 79(3):1450–1460

    PubMed  CAS  Google Scholar 

  • Rennie CJ, Wright JJ, Robinson PA (2000) Mechanisms of cortical electrical activity and emergence of gamma rhythm. J Theor Biol 205(1):17–35

    Article  PubMed  CAS  Google Scholar 

  • Ries CR, Puil E (1999a) Ionic mechanism of isoflurane’s actions on thalamocortical neurons. J Neurophysiol 81(4):1802–1809

    PubMed  CAS  Google Scholar 

  • Ries CR, Puil E (1999b) Mechanism of anesthesia revealed by shunting actions of isoflurane on thalamocortical neurons. J Neurophysiol 81(4):1795–1801

    PubMed  CAS  Google Scholar 

  • Robinson PA, Rennie CJ, Rowe DL (2002) Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Phys Rev E 65:041924

    Article  CAS  Google Scholar 

  • Robinson PA, Rennie CJ, Rowe DL, O’Connor SC, Wright JJ, Gordon E, Whitehouse RW (2003) Neurophysical modeling of brain dynamics. Neuropsychopharmacology 28(Suppl 1):S74–S79

    Article  PubMed  Google Scholar 

  • Robinson PA, Wu H, Kim JW (2008) Neural rate equations for bursting dynamics derived from conductance-based equations. J Theor Biol 250(4):663–672

    Article  PubMed  CAS  Google Scholar 

  • Rudolph M, Pelletier JG, Pare D, Destexhe A (2005) Characterization of synaptic conductances and integrative properties during electrically induced EEG-activated states in neocortical neurons in vivo. J Neurophysiol 94(4):2805–2821

    Article  PubMed  Google Scholar 

  • Schultz A, Grouven U, Zander I, Beger FA, Siedenberg M, Schultz B (2004) Age-related effects in the EEG during propofol anaesthesia. Acta Anaesthesiol Scand 48(1):27–34

    Article  PubMed  CAS  Google Scholar 

  • Schurmann M, Demiralp T, Basar E, Basar Eroglu C (2000) Electroencephalogram alpha (8–15 Hz) responses to visual stimuli in cat cortex, thalamus, and hippocampus: a distributed alpha network? Neurosci Lett 292(3):175–178

    Article  PubMed  CAS  Google Scholar 

  • Schwender D, Daunderer M, Klasing S, Finsterer U, Peter K (1998) Power spectral analysis of the electroencephalogram during increasing end-expiratory concentrations of isoflurane, desflurane and sevoflurane. Anaesthesia 53(4):335–342

    Article  PubMed  CAS  Google Scholar 

  • Sirota A, Csicsvari J, Buhl D, Buzsaki G (2003) Communication between neocortex and hippocampus during sleep in rodents. Proc Natl Acad Sci USA 100(4):2065–2069

    Article  PubMed  CAS  Google Scholar 

  • Steriade M (2006) Grouping of brain rhythms in corticothalamic systems. Neuroscience 137(4):1087–1106

    Article  PubMed  CAS  Google Scholar 

  • Steriade M, Contreras D (1995) Relations between cortical and thalamic cellular events during transition from sleep patterns to paroxysmal activity. J Neurosci 15:623–642

    PubMed  CAS  Google Scholar 

  • Steriade M, Domich L, Oakson G, Deschenes M (1987) The deafferented reticular thalamic nucleus generates spindle rhythmicity. J Neurophysiol 57(1):260–273

    PubMed  CAS  Google Scholar 

  • Steriade M, Nunez A, Amzica F (1993) Intracellular analysis of relations between the slow (<1 Hz) neocortical oscillation and other sleep rhythms of the electroencephalogram. J Neurosci 13(8):3266–3283

    PubMed  CAS  Google Scholar 

  • Steriade M, Timofeev I, Grenier F (2001) Natural waking and sleep states: a view from inside neocortical neurons. J Neurophysiol 85(5):1969–1985

    PubMed  CAS  Google Scholar 

  • Steyn-Ross DA (2002) Modelling the anaestheto-dynamic phase transition of the cerebral cortex. PhD thesis

    Google Scholar 

  • 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. numerical simulations, spectral entropy, and correlation times. Phys Rev E 64:011918

    Article  CAS  Google Scholar 

  • 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 thermodynamics analogy. Phys Rev E 64:011917

    Article  CAS  Google Scholar 

  • 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(2–3):369–385

    Article  PubMed  CAS  Google Scholar 

  • Suffczynski P, Kalitzin S, Lopes Da Silva FH (2004) Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network. Neuroscience 126(2):467–484

    Article  PubMed  CAS  Google Scholar 

  • Timofeev I, Steriade M (1996) Low-frequency rhythms in the thalamus of intact-cortex and decorticated cats. J Neurophysiol 76(6):4152–4168

    PubMed  CAS  Google Scholar 

  • Timofeev I, Grenier F, Bazhenov M, Sejnowski T, Steriade M (2000) Origin of slow cortical oscillations in deafferented cortical slabs. Cereb Cortex 10(12):1185–1199

    Article  PubMed  CAS  Google Scholar 

  • Tirel O, Wodey E, Harris R, Bansard JY, Ecoffey C, Senhadji L (2006) The impact of age on bispectral index values and EEG bispectrum during anaesthesia with desflurane and halothane in children. Br J Anaesth 96(4):480–485

    Article  PubMed  CAS  Google Scholar 

  • Wendling F, Bartolomei F, Bellanger JJ, Chauvel P (2002) Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition. Eur J Neurosci 15(9):1499–1508

    Article  PubMed  CAS  Google Scholar 

  • Wendling F, Hernandez A, Bellanger JJ, Chauvel P, Bartolomei F (2005) Interictal to ictal transition in human temporal lobe epilepsy: insights from a computational model of intracerebral EEG. J Clin Neurophysiol 22(5):343–356

    PubMed  Google Scholar 

  • Weyand TG, Boudreaux M, Guido W (2001) Burst and tonic response modes in thalamic neurons during sleep and wakefulness. J Neurophysiol 85(3):1107–1118

    PubMed  CAS  Google Scholar 

  • Wilson HR, Cowan J (1973) A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13:55–80

    Article  PubMed  CAS  Google Scholar 

  • Wilson HR, Cowan JD (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J 12(1):1–24

    Article  PubMed  CAS  Google Scholar 

  • Wilson MT, Steyn-Ross DA, Sleigh JW, Steyn-Ross ML, Wilcocks LC, Gillies IP (2006) The k-complex and slow oscillation in terms of a mean-field cortical model. J Comput Neurosci 21(3):243–257

    Article  PubMed  CAS  Google Scholar 

  • Wilson MT, Barry M, Reynolds JN, Crump WP, Steyn-Ross DA, Steyn-Ross ML, Sleigh JW (2009) An analysis of the transitions between down and up states of the cortical slow oscillation under urethane anaesthesia. J Biol Phys

    Google Scholar 

  • Wodey E, Tirel O, Bansard JY, Terrier A, Chanavaz C, Harris R, Ecoffey C, Senhadji L (2005) Impact of age on both bis values and EEG bispectrum during anaesthesia with sevoflurane in children. Br J Anaesth 94(6):810–820

    Article  PubMed  CAS  Google Scholar 

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Authors and Affiliations

  1. LTSI, University of Rennes 1, Inserm U642, Rennes, 35000, France

    B. Molaee-Ardekani & L. Senhadji

  2. BiSIPL, Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran

    M. B. Shamsollahi

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  1. B. Molaee-Ardekani
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  2. M. B. Shamsollahi
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  3. L. Senhadji
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Correspondence to B. Molaee-Ardekani .

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  1. Equipe Cortex, INRIA CR Nancy, rue du Jardin Botanique 615, Villers-lès-Nancy CX, 54602, France

    Axel Hutt

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Molaee-Ardekani, B., Shamsollahi, M.B., Senhadji, L. (2011). EEG Modeling in Anesthesia: A New Insight into Mean-Field Approach for Delta Activity Generation. 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_9

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