Advertisement

Co-operative Populations of Neurons: Mean Field Models of Mesoscopic Brain Activity

  • David T. J. Liley
  • Brett L. Foster
  • Ingo Bojak
Chapter

Abstract

While the basic units of computation in the brain are the neuronal cells, their sheer number, complexity of structural organisation and widespread connectivity make it difficult, if not impossible, to perform realistic simulations of activity at millimetre range or beyond. Furthermore, it is becoming increasingly clear that a range of non-neuronal and stochastic factors influence neuronal excitability, and must be taken into account when developing models and theories of brain function. One answer to the these persistent difficulties is to model cortical tissue not as a network of spike-based enumerable neurons, but to take inspiration from statistical physics and model directly the bulk properties of the populations constituting the cortical tissue. Such an approach proves compatible with many experimental recording techniques and has led to a successful class of so-called “mean field theories” that, when constrained by meaningful physiological and anatomical parameterisations, reveal a rich repertoire of biologically plausible and predictive dynamics. The aim of this chapter is to outline the historical genesis of this important modelling framework, and to detail its many successes in accounting for the experimentally observed neuronal population activity in cortex.

Keywords

Firing Rate Pyramidal Neuron Apical Dendrite Alpha Rhythm fMRI Bold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Aboitiz F, Scheibel AB, Fisher RS, Zaidel E (1992a) Fiber composition of the human corpus callosum. Brain Res 598:143–153PubMedGoogle Scholar
  2. Aboitiz F, Scheibel AB, Fisher RS, Zaidel E (1992b) Individual differences in brain asymmetries and fiber composition in the human corpus callosum. Brain Res 598:154–161PubMedGoogle Scholar
  3. Adrian ED, Matthews BHC (1934) The Berger rhythm, potential changes from the occipital lobe in man. Brain 57:355–385Google Scholar
  4. Amari SI (1975) Homogeneous nets of neuron-like elements. Biol Cybern 17:211–220PubMedGoogle Scholar
  5. Amari SI (1977) Dynamics of pattern formation in lateral-inhibition type neural fields. Biol Cybern 27:77–87PubMedGoogle Scholar
  6. Araque A, Navarrete M (2010) Glial cells in neuronal network function. Philos Trans R Soc B 365:2375–2381Google Scholar
  7. Azevedo FAC, Carvalho LRB, Grinberg LT, Farfel JM, Ferretti REL, Leite REP, Jacob Filho W, Lent R, Herculano-Houzel S (2009) Equal numbers of neuronal and nonneuronal cells make the human brain an isometrically scaled-up primate brain. J Comp Neurol 513:532–541PubMedGoogle Scholar
  8. Babajani A, Soltaninan-Zadeh H (2006) Integrated MEG/EEG and fMRI model based on neural masses. IEEE Trans Biomed Eng 53:1794–1801PubMedGoogle Scholar
  9. Babajani A, Nekooei MH, Soltaninan-Zadeh H (2005) Integrated MEG and fMRI model: synthesis and analysis. Brain Topogr 18:101–113PubMedGoogle Scholar
  10. Babajani-Feremi A, Soltaninan-Zadeh H (2010) Multi-area neural mass modeling of EEG and MEG signals. NeuroImage 52:793–811PubMedGoogle Scholar
  11. Babajani-Feremi A, Soltaninan-Zadeh H, Moran JE (2008) Integrated MEG/fMRI model validated using real auditory data. Brain Topogr 21:61–74PubMedGoogle Scholar
  12. Ben Achour S, Pascual O (2010) Glia: the many ways to modulate synaptic plasticity. Neurochem Int 57:440–445PubMedGoogle Scholar
  13. Berger H (1929) Über das Elektrenkephalogramm des Menschen. Arch Psychiatr Nervenkr 87:527–570Google Scholar
  14. Berger H (1930) Über das Elektrenkephalogramm des Menschen. Zweite Mitteilung. J Psychol Neurol 40:160–179Google Scholar
  15. Beurle RL (1956) Properties of a mass of cells capable of regenerating pulses. Philos Trans R Soc B 240:55–94Google Scholar
  16. Biswal BB, Mennes M, Zuo XN, Gohel S, Kelly C, Smith SM, Beckmann CF, Adelstein JS, Buckner RL, Colcombe S, Dogonowski AM, Ernst M, Fair D, Hampson M, Hoptman MJ, Hyde JS, Kiviniemi VJ, Kötter R, Li SJ, Lin CP, Lowe MJ, Mackay C, Madden DJ, Madsen KH, Margulies DS, Mayberg HS, McMahon K, Monk CS, Mostofsky SH, Nagel BJ, Pekar JJ, Peltier SJ, Petersen SE, Riedl V, Rombouts SARB, Rypma B, Schlaggar BL, Schmidt S, Seidler RD, Siegle GJ, Sorg C, Teng GJ, Veijola J, Villringer A, Walter M, Wang L, Weng XC, Whitfield-Gabrieli S, Williamson P, Windischberger C, Zang YF, Zhang HY, Castellanos FX, Milham MP (2010) Toward discovery science of human brain function. Proc Natl Acad Sci USA 107:4734–4739PubMedGoogle Scholar
  17. Blinowska K, Müller-Putz G, Kaiser V, Astolfi L, Vanderperren K, Van Huffel S, Lemieux L (2009) Multimodal imaging of human brain activity: rational, biophysical aspects and modes of integration. Comput Intell Neurosci 2009:813607Google Scholar
  18. Bojak I, Liley DTJ (2005) Modeling the effects of anesthesia on the electroencephalogram. Phys Rev E 71:041902Google Scholar
  19. Bojak I, Liley DTJ (2007) Self-organized 40 hz synchronization in a physiological theory of EEG. Neurocomputing 70:2085–2090Google Scholar
  20. Bojak I, Liley DTJ (2010) Axonal velocity distributions in neural field equations. PLoS Comput Biol 6:e1000653PubMedGoogle Scholar
  21. Bojak I, Oostendorp TF, Reid AT, Kötter R (2010) Connecting mean field models of neural activity to EEG and fMRI data. Brain Topogr 23:139–149PubMedGoogle Scholar
  22. Bojak I, Oostendorp TF, Reid AT, Kötter R (2011) Towards a model-based integration of co-registered EEG/fMRI data with realistic neural population meshes. Philos Trans R Soc A 369:3785–3801 to be publishedGoogle Scholar
  23. Braitenberg V, Schüz A (1998) Cortex: statistics and geometry of neuronal connectivity, 2nd edn. Springer, BerlinGoogle Scholar
  24. Branco TP, Staras K (2009) The probability of neurotransmitter release: variability and feedback control at single synapses. Nat Rev Neurosci 10:373–383PubMedGoogle Scholar
  25. Breakspear M, Roberts JAG, Terry JR, Rodrigues S, Mahant N, Robinson PA (2006) A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. Cereb Cortex 16:1296–1313PubMedGoogle Scholar
  26. Bressler SL, Kelso JAS (2001) Cortical coordination dynamics and cognition. Trends Cogn Sci 5:26–36PubMedGoogle Scholar
  27. Britz J, Van De Ville D, Michel CM (2010) BOLD correlates of EEG topography reveal rapid resting-state network dynamics. NeuroImage 52:1162–1170PubMedGoogle Scholar
  28. Brodmann K, Garey LJ (2006) Brodmann’s localisation in the cerebral cortex: the principles of comparative localisation in the cerebral cortex based on cytoarchitectonics – translated with editorial notes and an introduction, 3rd edn. Springer, New YorkGoogle Scholar
  29. Brunel N, Wang XJ (2001) Effects of neuromodulation in a cortical network model of object working memory dominated by recurrent inhibition. J Comput Neurosci 11:63–85PubMedGoogle Scholar
  30. Buice MA, Cowan JD, Chow CC (2010) Systematic fluctuation expansion for neural network activity equations. Neural Comput 22:377–426PubMedGoogle Scholar
  31. Bullock TH, McClune MC, Achimowicz JZ, Iragui-Madoz VJ, Duckrow RB, Spencer SS (1995) EEG coherence has structure in the millimeter domain: subdural and hippocampal recordings from epileptic patients. Electroencephalogr Clin Neurophysiol 95:161–177PubMedGoogle Scholar
  32. Buxhoeveden DP, Casanova MF (2002) The minicolumn and evolution of the brain. Brain Behav Evol 60:125–151PubMedGoogle Scholar
  33. Buxton RB, Frank LR (1997) A model for the coupling between cerebral blood flow and oxygen metabolism during neural stimulation. J Cereb Blood Flow Metab 17:64–72PubMedGoogle Scholar
  34. Buxton RB, Wong ECC, Frank LR (1998) Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn Reson Med 39:855–864PubMedGoogle Scholar
  35. Ciulla C, Takeda T, Endo H (1999) MEG characterization of spontaneous alpha rhythm in the human brain. Brain Topogr 11:211–222PubMedGoogle Scholar
  36. Contreras D (2004) Electrophysiological classes of neocortical neurons. Neural Netw 17:633–646PubMedGoogle Scholar
  37. Coombes S (2005) Waves, bumps, and patterns in neural field theories. Biol Cybern 93:91–108PubMedGoogle Scholar
  38. Coombes S (2010) Large-scale neural dynamics: simple and complex. NeuroImage 52:731–739PubMedGoogle Scholar
  39. Coombes S, Venkov NA, Shiau LJ, Bojak I, Liley DTJ, Laing CR (2007) Modeling electrocortical activity through improved local approximations of integral neural field equations. Phys Rev E 76:051901Google Scholar
  40. Daunizeau J, Kiebel SJ, Friston KJ (2009) Dynamic causal modelling of distributed electromagnetic responses. NeuroImage 47:590–601PubMedGoogle Scholar
  41. David O, Friston KJ (2003) A neural mass model for MEG/EEG: coupling and neuronal dynamics. NeuroImage 20:1743–1755PubMedGoogle Scholar
  42. David O, Harrison LM, Friston KJ (2005) Modelling event-related responses in the brain. NeuroImage 25:756–770PubMedGoogle Scholar
  43. David O, Kiebel SJ, Harrison LM, Mattout J, Kilner JM, Friston KJ (2006) Dynamic causal modeling of evoked responses in EEG and MEG. NeuroImage 30:1255–1272PubMedGoogle Scholar
  44. Deco GR, Rolls ET (2005) Neurodynamics of biased competition and cooperation for attention: a model with spiking neurons. J Neurophysiol 94:295–313PubMedGoogle Scholar
  45. Deco GR, Jirsa VK, Robinson PA, Breakspear M, Friston KJ (2008) The dynamic brain: from spiking neurons to neural masses and cortical fields. PLoS Comput Biol 4:e1000092PubMedGoogle Scholar
  46. Deco GR, Jirsa VK, McIntosh AR, Sporns O, Kötter R (2009) Key role of coupling, delay, and noise in resting brain fluctuations. Proc Natl Acad Sci USA 106:10302–10307PubMedGoogle Scholar
  47. Deco GR, Jirsa VK, McIntosh AR (2011) Emerging concepts for the dynamical organization of resting-state activity in the brain. Nat Rev Neurosci 12:43–56PubMedGoogle Scholar
  48. Deneux T, Faugeras O (2010) EEG-fMRI fusion of paradigm-free activity using Kalman filtering. Neural Comput 22:906–948PubMedGoogle Scholar
  49. Dienel GA, Cruz NF (2003) Neighborly interactions of metabolically-activated astrocytes in vivo. Neurochem Int 43:339–354PubMedGoogle Scholar
  50. Dutta S, Matsumoto Y, Gothgen NU, Ebling WF (1997) Concentration-EEG effect relationship of propofol in rats. J Pharm Sci 86:37–43PubMedGoogle Scholar
  51. Eccles JC (1992) Evolution of consciousness. Proc Natl Acad Sci USA 89:7320–7324PubMedGoogle Scholar
  52. Ermentrout BG (1998) Neural networks as spatio-temporal pattern-forming systems. Rep Prog Phys 61:353–430Google Scholar
  53. Faugeras O, Touboul J, Cessac B (2009) A constructive mean-field analysis of multi-population neural networks with random synaptic weights and stochastic inputs. Front Comput Neurosci 3:1PubMedGoogle Scholar
  54. Feshchenko VA, Veselis RA, Reinsel RA (2004) Propofol-induced alpha rhythm. Neuropsychobiology 50:257–266PubMedGoogle Scholar
  55. Fleischhauer K, Petsche H, Wittkowski W (1972) Vertical bundles of dendrites in the neocortex. Z Anat Entwicklungsgesch 136:213–223PubMedGoogle Scholar
  56. Foster BL, Bojak I, Liley DTJ (2008) Population based models of cortical drug response: insights form anaesthesia. Cogn Neurodyn 2:283–296PubMedGoogle Scholar
  57. Frascoli F, van Veen L, Bojak I, Liley DTJ (2011) Metabifurcation analysis of a mean field model of the cortex. Physica D (in press). doi:10.1016/j.physd.2011.02.002Google Scholar
  58. Freeman WJ (1975) Mass action in the nervous system: examination of the neurophysiological basis of adaptive behavior through the EEG, 1st edn. Academic Press, New York, also electronic edn.: http://sulcus.berkeley.edu/MANSWWW/MANSWWW.html,2004
  59. Freeman WJ (1979) Nonlinear gain mediating cortical stimulus-response relations. Biol Cybern 33:237–247PubMedGoogle Scholar
  60. Freeman WJ, Holmes MD (2005) Metastability, instability, and state transition in neocortex. Neural Netw 18:497–504PubMedGoogle Scholar
  61. Freeman WJ, Ahlfors SP, Menon V (2009) Combining fMRI with EEG and MEG in order to relate patterns of brain activity to cognition. Int J Psychophysiol 73:43–52PubMedGoogle Scholar
  62. Friston KJ (1997) Transients, metastability, and neuronal dynamics. NeuroImage 5:164–171PubMedGoogle Scholar
  63. Friston KJ (2000) The labile brain. I. Neuronal transients and nonlinear coupling. Philos Trans R Soc B 355:215–236Google Scholar
  64. Friston KJ (2002) Bayesian estimation of dynamical systems: an application to fMRI. NeuroImage 16:513–530PubMedGoogle Scholar
  65. Friston KJ, Mechelli A, Turner R, Price CJ (2000) Nonlinear responses in fMRI: The Balloon model, Volterra kernels, and other hemodynamics. NeuroImage 12:466–477PubMedGoogle Scholar
  66. Friston KJ, Penny WD, Phillips C, Kiebel SJ, Hinton GE, Ashburner J (2002) Classical and Bayesian inference in neuroimaging: theory. NeuroImage 16:465–483PubMedGoogle Scholar
  67. Friston KJ, Harrison LM, Penny WD (2003) Dynamic causal modelling. NeuroImage 19: 1273–1302PubMedGoogle Scholar
  68. Friston KJ, Mattout J, Trujillo-Barreto NJ, Ashburner J, Penny WD (2007) Variational free energy and the Laplace approximation. NeuroImage 34:220–234PubMedGoogle Scholar
  69. Ghosh A, Rho YA, McIntosh AR, Kötter R, Jirsa VK (2008) Noise during rest enables the exploration of the brain’s dynamic repertoire. PLoS Comput Biol 4:e1000196PubMedGoogle Scholar
  70. Gloor P (1969) Hans Berger on the electroencephalogram of man. Electroencephalogr Clin Neurophysiol S28:350Google Scholar
  71. Goldman PS, Nauta WJH (1977) Columnar distribution of cortico-cortical fibers in the frontal association, limbic, and motor cortex of the developing rhesus monkey. Brain Res 122:393–413PubMedGoogle Scholar
  72. Griffith JS (1963) A field theory of neural nets: I: derivation of field equations. Bull Math Biol 25:111–120Google Scholar
  73. Griffith JS (1965) A field theory of neural nets: II: properties of the field equations. Bull Math Biol 27:187–195Google Scholar
  74. Hagmann P, Cammoun L, Gigandet X, Meuli RA, Wedeen VJ, Sporns O (2008) Mapping the structural core of human cerebral cortex. PLoS Biol 6:e159PubMedGoogle Scholar
  75. Haken H (1983) Synergetics: an introduction. Nonequilibrium phase transitions and self-organization in physics, chemistry, and biology, 3rd edn. Springer, BerlinGoogle Scholar
  76. Hellwig B (2000) A quantitative analysis of the local connectivity between pyramidal neurons in layers 2/3 of the rat visual cortex. Biol Cybern 82:111–121PubMedGoogle Scholar
  77. Herculano-Houzel S (2009) The human brain in numbers: a linearly scaled-up primate brain. Front Hum Neurosci 3:31PubMedGoogle Scholar
  78. Honey CJ, Kötter R, Breakspear M, Sporns O (2007) Network structure of cerebral cortex shapes functional connectivity on multiple time scales. Proc Natl Acad Sci USA 104:10240–10245PubMedGoogle Scholar
  79. Honey CJ, Sporns O, Cammoun L, Gigandet X, Thiran JP, Meuli RA, Hagmann P (2009) Predicting human resting-state functional connectivity from structural connectivity. Proc Natl Acad Sci USA 106:2035–2040PubMedGoogle Scholar
  80. Hughes SW, Crunelli V (2005) Thalamic mechanisms of EEG alpha rhythms and their pathological implications. Neuroscientist 11:357–372PubMedGoogle Scholar
  81. Hughes SW, Crunelli V (2007) Just a phase they’re going through: the complex interaction of intrinsic high-threshold bursting and gap junctions in the generation of thalamic alpha and theta rhythms. Int J Psychophysiol 64:3–17PubMedGoogle Scholar
  82. Hutt A, Longtin A (2010) Effects of the anesthetic agent propofol on neural populations. Cogn Neurodyn 4:37–59PubMedGoogle Scholar
  83. Jansen BH, Rit VG (1995) Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biol Cybern 73:357–366PubMedGoogle Scholar
  84. Jirsa VK, Haken H (1996) Field theory of electromagnetic brain activity. Phys Rev Lett 77:960–963PubMedGoogle Scholar
  85. Jirsa VK, Jantzen KJ, Fuchs A, Kelso JAS (2002) Spatiotemporal forward solution of the EEG and MEG using network modeling. IEEE Trans Med Imaging 21:493–504PubMedGoogle Scholar
  86. Johansen-Berg H, Rushworth MFS (2009) Using diffusion imaging to study human connectional anatomy. Annu Rev Neurosci 32:75–94PubMedGoogle Scholar
  87. Jones EG (2000) Microcolumns in the cerebral cortex. Proc Natl Acad Sci USA 97:5019–5021PubMedGoogle Scholar
  88. Jones EG, Burton H, Porter R (1975) Commissural and cortico-cortical “columns” in the somatic sensory cortex of primates. Science 190:572–574PubMedGoogle Scholar
  89. Kaiser M, Hilgetag CC, van Ooyen A (2009) A simple rule for axon outgrowth and synaptic competition generates realistic connection lengths and filling fractions. Cereb Cortex 19:3001–3010PubMedGoogle Scholar
  90. Kandel ER, Schwartz JH, Jessell TM (2000) Principles of neural science, 4th edn. McGraw-Hill, New YorkGoogle Scholar
  91. Kelso JAS (1995) Dynamic patterns: the self-organization of brain and behavior. The MIT Press, CambridgeGoogle Scholar
  92. Kiebel SJ, David O, Friston KJ (2006) Dynamic causal modelling of evoked responses in EEG/MEG with lead field parameterization. NeuroImage 30:1273–1284PubMedGoogle Scholar
  93. Kim JS, Singh V, Lee JK, Lerch J, Ad-Dab’bagh Y, MacDonald DJ, Lee JM, Kim SI, Evans AC (2005) Automated 3-D extraction and evaluation of the inner and outer cortical surfaces using a Laplacian map and partial volume effect classification. NeuroImage 27:210–221PubMedGoogle Scholar
  94. Kötter R, Wanke E (2005) Mapping brains without coordinates. Philos Trans R Soc B 360:751–766Google Scholar
  95. Kramer MA, Kirsch HE, Szeri AJ (2005) Pathological pattern formation and cortical propagation of epileptic seizures. J R Soc Interface 2:113–127PubMedGoogle Scholar
  96. 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 80:725–732PubMedGoogle Scholar
  97. Kuizenga K, Wierda JMKH, Kalkman CJ (2001) Biphasic EEG changes in relation to loss of consciousness during induction with thiopental, propofol, etomidate, midazolam or sevoflurane. Br J Anaesth 86:354–360PubMedGoogle Scholar
  98. Laufs H, Daunizeau J, Carmichael DW, Kleinschmidt AK (2008) Recent advances in recording electrophysiological data simultaneously with magnetic resonance imaging. NeuroImage 40:515–528PubMedGoogle Scholar
  99. Liley DTJ, Bojak I (2005) Understanding the transition to seizure by modeling the epileptiform activity of general anesthetic agents. J Clin Neurophysiol 22:300–313PubMedGoogle Scholar
  100. Liley DTJ, Wright JJ (1994) Intracortical connectivity of pyramidal and stellate cells: estimates of synaptic densities and coupling symmetry. Netw Comput Neural Syst 5:175–189Google Scholar
  101. Liley DTJ, Alexander DM, Wright JJ, Aldous MD (1999a) Alpha rhythm emerges from large-scale networks of realistically coupled multicompartmental model cortical neurons. Netw Comput Neural Syst 10:79–92Google Scholar
  102. Liley DTJ, Cadusch PJ, Wright JJ (1999b) A continuum theory of electro-cortical activity. Neurocomputing 26-27:795–800Google Scholar
  103. Liley DTJ, Cadusch PJ, Dafilis MP (2002) A spatially continuous mean field theory of electrocortical activity. Netw Comput Neural Syst 13:67–113Google Scholar
  104. Liley DTJ, Cadusch PJ, Dafilis MP (2003a) Corrigendum. Netw Comput Neural Syst 14:369Google Scholar
  105. Liley DTJ, Cadusch PJ, Gray M, Nathan PJ (2003b) Drug-induced modification of the system properties associated with spontaneous human electroencephalographic activity. Phys Rev E 68:051906Google Scholar
  106. Liley DTJ, Bojak I, Dafilis MP, van Veen L, Frascoli F, Foster BL (2010) Bifurcations and state changes in the human alpha rhythm: theory and experiment. In: Steyn-Ross DA, Steyn-Ross ML (eds) Modeling phase transitions in the brain. Springer series in computational neuroscience, vol 4. Springer, New York, pp 117–145Google Scholar
  107. Liley DTJ, Bojak I, Foster BL (2011) A mesoscopic modelling approach to anaesthetic action on brain electrical activity. In: Hutt A (ed) Sleep and anesthesia: neural correlates in theory and experiment. Springer, New York, to be publishedGoogle Scholar
  108. Llinás RR (1988) The intrinsic electrophysiological properties of mammalian neurons: insights into central nervous system function. Science 242:1654–1664PubMedGoogle Scholar
  109. Logothetis NK (2008) What we can do and what we cannot do with fMRI. Nature 453:869–878PubMedGoogle Scholar
  110. Lopes da Silva FH, Hoeks A, Smits H, Zetterberg LH (1974) Model of brain rhythmic activity: the alpha-rhythm of the thalamus. Kybernetik 15:27–37PubMedGoogle Scholar
  111. Lopes da Silva FH, Blanes W, Kalitzin SN, Parra J, Suffczyński P, Velis DN (2003) Dynamical diseases of brain systems: different routes to epileptic seizures. IEEE Trans Biomed Eng 50:540–548PubMedGoogle Scholar
  112. López-Muñoz F, Boya J, Alamo C (2006) Neuron theory, the cornerstone of neuroscience, on the centenary of the Nobel Prize award to Santiago Ramón y Cajal. Brain Res Bull 70:391–405PubMedGoogle Scholar
  113. Lübke J, Feldmeyer D (2007) Excitatory signal flow and connectivity in a cortical column: focus on barrel cortex. Brain Struct Funct 212:3–17PubMedGoogle Scholar
  114. Mandeville JB, Marota JJA, Ayata C, Zaharchuk G, Moskowitz MA, Rosen BR, Weisskoff RM (1999) Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J Cereb Blood Flow Metab 19:679–689PubMedGoogle Scholar
  115. Marder E, Taylor AL (2011) Multiple models to capture the variability in biological neurons and networks. Nat Neurosci 14:133–138PubMedGoogle Scholar
  116. Markram H (2006) The blue brain project. Nat Rev Neurosci 7:153–160PubMedGoogle Scholar
  117. Markram H (2008) Fixing the location and dimensions of functional neocortical columns. HFSP J 2:132–135PubMedGoogle Scholar
  118. Markram H, Toledo-Rodriguez M, Wang Y, Gupta A, Silberberg G, Wu C (2004) Interneurons of the neocortical inhibitory system. Nat Rev Neurosci 5:793–807PubMedGoogle Scholar
  119. Marten F, Rodrigues S, Benjamin O, Richardson MP, Terry JR (2009) Onset of polyspike complexes in a mean-field model of human electroencephalography and its application to absence epilepsy. Philos Trans R Soc A 367:1145–1161Google Scholar
  120. Matthews PM, Honey GD, Bullmore ET (2006) Applications of fMRI in translational medicine and clinical practice. Nat Rev Neurosci 7:732–744PubMedGoogle Scholar
  121. Mavritsaki E, Heinke D, Allen H, Deco GR, Humphreys GW (2011) Bridging the gap between physiology and behavior: Evidence from the sSoTS model of human visual attention. Psychol Rev 118:3–41PubMedGoogle Scholar
  122. McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5:115–133, reprinted 1990 in Bull Math Biol 52: 99–115Google Scholar
  123. Miguel-Hidalgo JJ (2005) Lower packing density of glial fibrillary acidic protein-immunoreactive astrocytes in the prelimbic cortex of alcohol-naive and alcohol-drinking alcohol-preferring rats as compared with alcohol-nonpreferring and Wistar rats. Alcohol Clin Exp Res 29:766–772PubMedGoogle Scholar
  124. 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 76:041911Google Scholar
  125. Molaee-Ardekani B, Benquet P, Bartolomei F, Wendling F (2010) Computational modeling of high-frequency oscillations at the onset of neocortical partial seizures: from ‘altered structure’ to ‘dysfunction’. NeuroImage 52:1109–1122PubMedGoogle Scholar
  126. Moran RJ, Kiebel SJ, Stephan KE, Reilly RB, Daunizeau J, Friston KJ (2007) A neural mass model of spectral responses in electrophysiologys. NeuroImage 37:706–720PubMedGoogle Scholar
  127. Moran RJ, Stephan KE, Kiebel SJ, Rombach N, OConnor WT, Murphy KJ, Reilly RB, Friston KJ (2008) Bayesian estimation of synaptic physiology from the spectral responses of neural masses. NeuroImage 42:272–284Google Scholar
  128. Moran RJ, Stephan KE, Seidenbecher T, Pape HC, Dolan RJ, Friston KJ (2009) Dynamic causal models of steady-state responses. NeuroImage 44:796–811PubMedGoogle Scholar
  129. Mori S, Wakana S, van Zijl PCM, Nagae-Poetscher LM (2005) MRI atlas of human white matter. Elsevier, AmsterdamGoogle Scholar
  130. Mountcastle VB (1957) Modality and topographic properties of single neurons of cat’s somatic sensory cortex. J Neurophysiol 20:408–434PubMedGoogle Scholar
  131. Mountcastle VB (1979) An organizing principle for cerebral function: the unit module and the distributed system. In: Schmitt FO, Worden FG (eds) The neurosciences: fourth study program. The MIT Press, Cambridge, pp 21–42Google Scholar
  132. Mountcastle VB (1997) The columnar organization of the neocortex. Brain 120:701–722PubMedGoogle Scholar
  133. Mulert C, Pogarell O, Hegerl U (2008) Simultaneous EEG-fMRI: perspectives in psychiatry. Clin EEG Neurosci 39:61–64PubMedGoogle Scholar
  134. Musso F, Brinkmeyer J, Mobascher A, Warbrick T, Winterer G (2010) Spontaneous brain activity and EEG microstates. A novel EEG/fMRI analysis approach to explore resting-state networks. NeuroImage 52:1149–1161Google Scholar
  135. Niedermeyer E, Lopes da Silva FH (eds) (2005) Electroencephalography: Basic principles, clinical applications, and related fields, 5th edn. Lippincott Williams & Wilkins, PhiladelphiaGoogle Scholar
  136. Nieuwenhuys R, Voogd J, van Huijzen C (2008) The human central nervous system, 4th edn. Springer, Berlin, pp 491–679Google Scholar
  137. Norris DG (2006) Principles of magnetic resonance assessment of brain function. J Magn Reson Imaging 23:794–807PubMedGoogle Scholar
  138. Nunez PL (1974a) The brain wave equation: a model for the EEG. Math Biosci 21:279–297Google Scholar
  139. Nunez PL (1974b) Wave-like properties of the alpha rhythm. IEEE Trans Biomed Eng 21:473–482Google Scholar
  140. Nunez PL (1981) Electric fields of the brain: the neurophysics of EEG, 1st edn. Oxford University Press, New YorkGoogle Scholar
  141. Nunez PL (1995) Neocortical dynamics and human EEG rhythms. Oxford University Press, New YorkGoogle Scholar
  142. Nunez PL, Srinivasan R (2006) A theoretical basis for standing and traveling brain waves measured with human EEG with implications for an integrated consciousness. Clin Neurophysiol 117:2424–2435PubMedGoogle Scholar
  143. Nunez PL, Reid L, Bickford RG (1978) The relationship of head size to alpha frequency with implications to a brain wave model. Electroencephalogr Clin Neurophysiol 44:344–352PubMedGoogle Scholar
  144. Nunez PL, Wingeier BM, Silberstein RB (2001) Spatial-temporal structures of human alpha rhythms: theory, microcurrent sources, multiscale measurements, and global binding of local networks. Hum Brain Mapp 13:125–164PubMedGoogle Scholar
  145. Pakkenberg B, Gundersen HJG (1997) Neocortical neuron number in humans: effect of sex and age. J Comp Neurol 384:312–320PubMedGoogle Scholar
  146. Perea G, Araque A (2010) GLIA modulates synaptic transmission. Brain Res Rev 63:93–102PubMedGoogle Scholar
  147. Perea G, Navarrete M, Araque A (2009) Tripartite synapses: astrocytes process and control synaptic information. Trends Neurosci 32:421–431PubMedGoogle Scholar
  148. Peters A, Sethares C (1997) The organization of double bouquet cells in monkey striate cortex. J Neurocytol 26:779–797PubMedGoogle Scholar
  149. Petersen CCH (2007) The functional organization of the barrel cortex. Neuron 56:339–355PubMedGoogle Scholar
  150. 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 22:167–179PubMedGoogle Scholar
  151. Rabinovich MI, Huerta R, Laurent G (2008a) Neuroscience. Transient dynamics for neural processing. Science 321:48–50Google Scholar
  152. Rabinovich MI, Huerta R, Varona P, Afraimovich VS (2008b) Transient cognitive dynamics, metastability, and decision making. PLoS Comput Biol 4:e1000072PubMedGoogle Scholar
  153. Raichle ME, MacLeod AM, Snyder AZ, Powers WJ, Gusnard DA, Shulman GL (2001) A default mode of brain function. Proc Natl Acad Sci USA 98:676–682PubMedGoogle Scholar
  154. Regan D (1989) Human brain electrophysiology: evoked potentials and evoked magnetic fields in science and medicine. Elsevier, New YorkGoogle Scholar
  155. Rennie CJ, Wright JJ, Robinson PA (2000) Mechanisms of cortical electrical activity and emergence of gamma rhythm. J Theor Biol 205:17–35PubMedGoogle Scholar
  156. Rennie CJ, Robinson PA, Wright JJ (2002) Unified neurophysical model of EEG spectra and evoked potentials. Biol Cybern 86:457–471PubMedGoogle Scholar
  157. Riera JJ, Aubert E, Iwata K, Kawashima R, Wan X, Ozaki T (2005) Fusing EEG and fMRI based on a bottom-up model: inferring activation and effective connectivity in neural masses. Philos Trans R Soc B 360:1025–1041Google Scholar
  158. Riera JJ, Wan X, Jimenez JC, Kawashima R (2006) Nonlinear local electrovascular coupling. I: a theoretical model. Hum Brain Mapp 27:896–914Google Scholar
  159. Riera JJ, Jimenez JC, Wan X, Kawashima R, Ozaki T (2007) Nonlinear local electrovascular coupling. II: from data to neuronal masses. Hum Brain Mapp 28:335–354Google Scholar
  160. Robinson PA (2006) Patchy propagators, brain dynamics, and the generation of spatially structured gamma oscillations. Phys Rev E 73:041904Google Scholar
  161. Robinson PA, Rennie CJ, Wright JJ (1997) Propagation and stability of waves of electrical activity in the cerebral cortex. Phys Rev E 56:826–840Google Scholar
  162. Robinson PA, Rennie CJ, Wright JJ, Bahramali H, Gordon E, Rowe DL (2001) Prediction of electroencephalographic spectra from neurophysiology. Phys Rev E 63:021903Google Scholar
  163. Robinson PA, Rennie CJ, Rowe DL (2002) Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Phys Rev E 65:041924Google Scholar
  164. Rockland KS, Ichinohe N (2004) Some thoughts on cortical minicolumns. Exp Brain Res 158:265–277PubMedGoogle Scholar
  165. Rockland KS, Pandya DN (1979) Laminar origins and terminations of cortical connections of the occipital lobe in the rhesus monkey. Brain Res 179:3–20PubMedGoogle Scholar
  166. Rodrigues S, Terry JR, Breakspear M (2006) On the genesis of spike-wave oscillations in a mean-field model of human thalamic and corticothalamic dynamics. Phys Lett A 355:352–357Google Scholar
  167. Rowe DL, Robinson PA, Gordon E (2005) Stimulant drug action in attention deficit hyperactivity disorder (ADHD): inference of neurophysiological mechanisms via quantitative modelling. Clin Neurophysiol 116:324–335PubMedGoogle Scholar
  168. Scheperjans F, Eickhoff SB, Hömke L, Mohlberg H, Hermann K, Amunts K, Zilles K (2008) Probabilistic maps, morphometry, and variability of cytoarchitectonic areas in the human superior parietal cortex. Cereb Cortex 18:2141–2157PubMedGoogle Scholar
  169. Shibasaki H (2008) Human brain mapping: hemodynamic response and electrophysiology. Clin Neurophysiol 119:731–743PubMedGoogle Scholar
  170. Silva LR, Amitai Y, Connors BW (1991) Intrinsic oscillations of neocortex generated by layer 5 pyramidal neurons. Science 251:432–435PubMedGoogle Scholar
  171. Sotero RC, Trujillo-Barreto NJ (2008) Biophysical model for integrating neuronal activity, EEG, fMRI and metabolism. NeuroImage 39:290–309PubMedGoogle Scholar
  172. Sotero RC, Trujillo-Barreto NJ, Iturria-Medina Y, Carbonell F, Jimenez JC (2007) Realistically coupled neural mass models can generate EEG rhythms. Neural Comput 19:478–512PubMedGoogle Scholar
  173. Spiegler A, Kiebel SJ, Atay FM, Knösche TR (2010) Bifurcation analysis of neural mass models: impact of extrinsic inputs and dendritic time constants. NeuroImage 52:1041–1058PubMedGoogle Scholar
  174. Spruston N (2008) Pyramidal neurons: dendritic structure and synaptic integration. Nat Rev Neurosci 9:206–221PubMedGoogle Scholar
  175. Stam CJ (2005) Nonlinear dynamical analysis of EEG and MEG: review of an emerging field. Clin Neurophysiol 116:2266–2301PubMedGoogle Scholar
  176. Stam CJ, Pijn JPM, Suffczyński P, Lopes da Silva FH (1999) Dynamics of the human alpha rhythm: evidence for non-linearity? Clin Neurophysiol 110:1801–1813PubMedGoogle Scholar
  177. Stephan KE, Kamper L, Bozkurt A, Burns GAPC, Young MP, Kötter R (2001) Advanced database methodology for the collation of connectivity data on the macaque brain (CoCoMac). Philos Trans R Soc B 356:1159–1186Google Scholar
  178. Steriade M (2005) Cellular substrates of brain rhythms. In: Niedermeyer E, Lopes da Silva FH (eds) Electroencephalography: basic principles, clinical applications, and related fields, 5th edn. Lippincott Williams & Wilkins, Philadelphia, pp 31–83Google Scholar
  179. 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 60:7299–7311Google Scholar
  180. 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 85:369–385PubMedGoogle Scholar
  181. Steyn-Ross DA, Steyn-Ross ML, Sleigh JW, Wilson MT, Gillies IP, Wright JJ (2005a) The sleep cycle modelled as a cortical phase transition. J Biol Phys 31:547–569Google Scholar
  182. Steyn-Ross ML, Steyn-Ross DA, Sleigh JW, Wilson MT, Wilcocks LC (2005b) Proposed mechanism for learning and memory erasure in a white-noise-driven sleeping cortex. Phys Rev E 72:061910Google Scholar
  183. Steyn-Ross ML, Steyn-Ross DA, Wilson MT, Sleigh JW (2009) Modeling brain activation patterns for the default and cognitive states. NeuroImage 45:298–311PubMedGoogle Scholar
  184. Steyn-Ross ML, Steyn-Ross DA, Sleigh JW, Wilson MT (2011) A mechanism for ultra-slow oscillations in the cortical default network. Bull Math Biol (in press). doi:10.1007/s11538-010-9565-9Google Scholar
  185. Stufflebeam SM, Rosen BR (2007) Mapping cognitive function. Neuroimaging Clin N Am 17:469–484PubMedGoogle Scholar
  186. Suffczyński P, Lopes da Silva FH, Parra J, Velis DN, Kalitzin SN (2005) Epileptic transitions: model predictions and experimental validation. J Clin Neurophysiol 22:288–299PubMedGoogle Scholar
  187. Szentágothai J (1978) The Ferrier lecture, 1977 – the neuron network of the cerebral cortex: a functional interpretation. Proc R Soc Lond B 201:219–248PubMedGoogle Scholar
  188. Szentágothai J (1983) The modular architectonic principle of neural centers. Rev Physiol Biochem Pharmacol 98:11–61PubMedGoogle Scholar
  189. Tang Y, Nyengaard JR, De Groot DM, Gundersen HJG (2001) Total regional and global number of synapses in the human brain neocortex. Synapse 41:258–273PubMedGoogle Scholar
  190. Thomson AM, Bannister AP (2003) Interlaminar connections in the neocortex. Cereb Cortex 13:5–14PubMedGoogle Scholar
  191. Toga AW, Thompson PM, Mori S, Amunts K, Zilles K (2006) Towards multimodal atlases of the human brain. Nat Rev Neurosci 7:952–966PubMedGoogle Scholar
  192. Tsuda I (2001) Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems. Behav Brain Sci 24:793–810PubMedGoogle Scholar
  193. Valdés-Hernández PA, Ojeda-Gonzeález A, Martínez-Montes E, Lage-Castellanos A, Virués-Alba T, Valdés-Urrutia L, Valdes-Sosa PA (2010) White matter architecture rather than cortical surface area correlates with the EEG alpha rhythm. NeuroImage 49:2328–2339Google Scholar
  194. Valdes-Sosa PA, Sánchez-Bornot JM, Sotero RC, Iturria-Medina Y, Alemán-Gómez Y, Bosch-Bayard J, Carbonell F, Ozaki T (2009) Model driven EEG/fMRI fusion of brain oscillations. Hum Brain Mapp 30:2701–2721PubMedGoogle Scholar
  195. van Albada SJ, Robinson PA (2009) Mean-field modeling of the basal ganglia-thalamocortical system. I. Firing rates in healthy and Parkinsonian states. J Theor Biol 257:642–663Google Scholar
  196. Van Essen DC (2005) A Population-Average, Landmark- and Surface-based (PALS) atlas of human cerebral cortex. NeuroImage 28:635–662PubMedGoogle Scholar
  197. van Rotterdam A, Lopes da Silva FH, van den Ende J, Viergever MA, Hermans AJ (1982) A model of the spatial-temporal characteristics of the alpha rhythm. Bull Math Biol 44:283–305PubMedGoogle Scholar
  198. Waage P, Guldberg CM, Abrash HI (1986) Studies concerning affinity (English translation). J Chem Educ 63:1044–1047Google Scholar
  199. Wendling F, Bellanger JJ, Bartolomei F, Chauvel PY (2000) Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals. Biol Cybern 83:367–378PubMedGoogle Scholar
  200. Wendling F, Hernández AI, Bellanger JJ, Chauvel PY, Bartolomei F (2005) Interictal to ictal transition in human temporal lobe epilepsy: insights from a computational model of intracerebral EEG. J Clin Neurophysiol 22:343–356PubMedGoogle Scholar
  201. White EL (1989) Cortical circuits. Synaptic organization of the cerebral cortex: structure, function and theory. Birkhäuser, BostonGoogle Scholar
  202. Williamson SJ, Kaufman L (1989) Advances in neuromagnetic instrumentation and studies of spontaneous brain activity. Brain Topogr 2:129–139PubMedGoogle Scholar
  203. Wilson HR, Cowan JD (1972) Excitatory and inhibitory interactions in localized populations of model neuron. Biophys J 12:1–24PubMedGoogle Scholar
  204. Wilson HR, Cowan JD (1973) A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13:55–80PubMedGoogle Scholar
  205. 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 21:243–257PubMedGoogle Scholar
  206. Wilson MT, Steyn-Ross ML, Steyn-Ross DA, Sleigh JW (2007) Going beyond a mean-field model for the learning cortex: second-order statistics. J Biol Phys 33:213–246PubMedGoogle Scholar
  207. Wolfe J, Houweling AR, Brecht M (2010) Sparse and powerful cortical spikes. Curr Opin Neurobiol 20:306–312PubMedGoogle Scholar
  208. Wright JJ (1997) EEG simulation: variation of spectral envelope, pulse synchrony and ≈ 40 hz oscillation. Biol Cybern 76:181–194PubMedGoogle Scholar
  209. Wright JJ, Liley DTJ (1995) Simulation of electrocortical waves. Biol Cybern 72:347–356PubMedGoogle Scholar
  210. Wright JJ, Liley DTJ (1996) Dynamics of the brain at global and microscopic scales: neural networks and the EEG. Behav Brain Sci 19:285–320Google Scholar
  211. Wu JY, Huang XY, Zhang C (2008) Propagating waves of activity in the neocortex: what they are, what they do. Neuroscientist 14:487–502PubMedGoogle Scholar
  212. Zilles K, Amunts K (2010) Centenary of Brodmanns map – conception and fate. Nat Rev Neurosci 11:139–145PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • David T. J. Liley
    • 1
  • Brett L. Foster
    • 2
  • Ingo Bojak
    • 3
  1. 1.Brain Sciences InstituteSwinburne University of TechnologyHawthornAustralia
  2. 2.Department of Neurology and Neurological SciencesStanford UniversityStanfordUSA
  3. 3.Donders Institute for Brain, Cognition and Behaviour, Centre for NeuroscienceRadboud University Nijmegen Medical CentreNijmegenThe Netherlands

Personalised recommendations