Skip to main content
SpringerLink
Log in

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

  • Chapter
  • First Online:
Computational Systems Neurobiology

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.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Here and in the following we mean by “vertically/radially” through the several millimetres thickness of cortex and by “horizontally/tangentially” parallel to its pial surface.

  2. 2.

    For realistic cortical geometries Euclidean distance is not a good approximation to axonal fibre length. However, one can adjust the \({f}_{jk}\left (v\,\vert \,\vec{x},\vec{x}\prime\right )\) to compensate for geometry.

  3. 3.

    For \({\mathcal{G}}_{jk}\) to be homogeneous, the connected region must be a closed (hyper)surface, e.g., a sphere.

References

  • Aboitiz F, Scheibel AB, Fisher RS, Zaidel E (1992a) Fiber composition of the human corpus callosum. Brain Res 598:143–153

    PubMed  CAS  Google Scholar 

  • Aboitiz F, Scheibel AB, Fisher RS, Zaidel E (1992b) Individual differences in brain asymmetries and fiber composition in the human corpus callosum. Brain Res 598:154–161

    PubMed  CAS  Google Scholar 

  • Adrian ED, Matthews BHC (1934) The Berger rhythm, potential changes from the occipital lobe in man. Brain 57:355–385

    Google Scholar 

  • Amari SI (1975) Homogeneous nets of neuron-like elements. Biol Cybern 17:211–220

    PubMed  CAS  Google Scholar 

  • Amari SI (1977) Dynamics of pattern formation in lateral-inhibition type neural fields. Biol Cybern 27:77–87

    PubMed  CAS  Google Scholar 

  • Araque A, Navarrete M (2010) Glial cells in neuronal network function. Philos Trans R Soc B 365:2375–2381

    Google Scholar 

  • 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 513:532–541

    PubMed  Google Scholar 

  • Babajani A, Soltaninan-Zadeh H (2006) Integrated MEG/EEG and fMRI model based on neural masses. IEEE Trans Biomed Eng 53:1794–1801

    PubMed  Google Scholar 

  • Babajani A, Nekooei MH, Soltaninan-Zadeh H (2005) Integrated MEG and fMRI model: synthesis and analysis. Brain Topogr 18:101–113

    PubMed  Google Scholar 

  • Babajani-Feremi A, Soltaninan-Zadeh H (2010) Multi-area neural mass modeling of EEG and MEG signals. NeuroImage 52:793–811

    PubMed  Google Scholar 

  • Babajani-Feremi A, Soltaninan-Zadeh H, Moran JE (2008) Integrated MEG/fMRI model validated using real auditory data. Brain Topogr 21:61–74

    PubMed  Google Scholar 

  • Ben Achour S, Pascual O (2010) Glia: the many ways to modulate synaptic plasticity. Neurochem Int 57:440–445

    PubMed  CAS  Google Scholar 

  • Berger H (1929) Über das Elektrenkephalogramm des Menschen. Arch Psychiatr Nervenkr 87:527–570

    Google Scholar 

  • Berger H (1930) Über das Elektrenkephalogramm des Menschen. Zweite Mitteilung. J Psychol Neurol 40:160–179

    Google Scholar 

  • Beurle RL (1956) Properties of a mass of cells capable of regenerating pulses. Philos Trans R Soc B 240:55–94

    Google Scholar 

  • 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 107:4734–4739

    PubMed  CAS  Google Scholar 

  • 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 2009:813607

    Google Scholar 

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

    CAS  Google Scholar 

  • Bojak I, Liley DTJ (2007) Self-organized 40 hz synchronization in a physiological theory of EEG. Neurocomputing 70:2085–2090

    Google Scholar 

  • Bojak I, Liley DTJ (2010) Axonal velocity distributions in neural field equations. PLoS Comput Biol 6:e1000653

    PubMed  Google Scholar 

  • Bojak I, Oostendorp TF, Reid AT, Kötter R (2010) Connecting mean field models of neural activity to EEG and fMRI data. Brain Topogr 23:139–149

    PubMed  Google Scholar 

  • 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 published

    Google Scholar 

  • Braitenberg V, Schüz A (1998) Cortex: statistics and geometry of neuronal connectivity, 2nd edn. Springer, Berlin

    Google Scholar 

  • Branco TP, Staras K (2009) The probability of neurotransmitter release: variability and feedback control at single synapses. Nat Rev Neurosci 10:373–383

    PubMed  CAS  Google Scholar 

  • 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 16:1296–1313

    PubMed  CAS  Google Scholar 

  • Bressler SL, Kelso JAS (2001) Cortical coordination dynamics and cognition. Trends Cogn Sci 5:26–36

    PubMed  Google Scholar 

  • Britz J, Van De Ville D, Michel CM (2010) BOLD correlates of EEG topography reveal rapid resting-state network dynamics. NeuroImage 52:1162–1170

    PubMed  Google Scholar 

  • 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 York

    Google Scholar 

  • Brunel N, Wang XJ (2001) Effects of neuromodulation in a cortical network model of object working memory dominated by recurrent inhibition. J Comput Neurosci 11:63–85

    PubMed  CAS  Google Scholar 

  • Buice MA, Cowan JD, Chow CC (2010) Systematic fluctuation expansion for neural network activity equations. Neural Comput 22:377–426

    PubMed  Google Scholar 

  • 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 95:161–177

    PubMed  CAS  Google Scholar 

  • Buxhoeveden DP, Casanova MF (2002) The minicolumn and evolution of the brain. Brain Behav Evol 60:125–151

    PubMed  Google Scholar 

  • 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 17:64–72

    PubMed  CAS  Google Scholar 

  • Buxton RB, Wong ECC, Frank LR (1998) Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn Reson Med 39:855–864

    PubMed  CAS  Google Scholar 

  • Ciulla C, Takeda T, Endo H (1999) MEG characterization of spontaneous alpha rhythm in the human brain. Brain Topogr 11:211–222

    PubMed  CAS  Google Scholar 

  • Contreras D (2004) Electrophysiological classes of neocortical neurons. Neural Netw 17:633–646

    PubMed  Google Scholar 

  • Coombes S (2005) Waves, bumps, and patterns in neural field theories. Biol Cybern 93:91–108

    PubMed  CAS  Google Scholar 

  • Coombes S (2010) Large-scale neural dynamics: simple and complex. NeuroImage 52:731–739

    PubMed  CAS  Google Scholar 

  • 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 76:051901

    CAS  Google Scholar 

  • Daunizeau J, Kiebel SJ, Friston KJ (2009) Dynamic causal modelling of distributed electromagnetic responses. NeuroImage 47:590–601

    PubMed  Google Scholar 

  • David O, Friston KJ (2003) A neural mass model for MEG/EEG: coupling and neuronal dynamics. NeuroImage 20:1743–1755

    PubMed  Google Scholar 

  • David O, Harrison LM, Friston KJ (2005) Modelling event-related responses in the brain. NeuroImage 25:756–770

    PubMed  Google Scholar 

  • David O, Kiebel SJ, Harrison LM, Mattout J, Kilner JM, Friston KJ (2006) Dynamic causal modeling of evoked responses in EEG and MEG. NeuroImage 30:1255–1272

    PubMed  Google Scholar 

  • Deco GR, Rolls ET (2005) Neurodynamics of biased competition and cooperation for attention: a model with spiking neurons. J Neurophysiol 94:295–313

    PubMed  CAS  Google Scholar 

  • 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:e1000092

    PubMed  Google Scholar 

  • 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 106:10302–10307

    PubMed  CAS  Google Scholar 

  • Deco GR, Jirsa VK, McIntosh AR (2011) Emerging concepts for the dynamical organization of resting-state activity in the brain. Nat Rev Neurosci 12:43–56

    PubMed  CAS  Google Scholar 

  • Deneux T, Faugeras O (2010) EEG-fMRI fusion of paradigm-free activity using Kalman filtering. Neural Comput 22:906–948

    PubMed  Google Scholar 

  • Dienel GA, Cruz NF (2003) Neighborly interactions of metabolically-activated astrocytes in vivo. Neurochem Int 43:339–354

    PubMed  CAS  Google Scholar 

  • Dutta S, Matsumoto Y, Gothgen NU, Ebling WF (1997) Concentration-EEG effect relationship of propofol in rats. J Pharm Sci 86:37–43

    PubMed  CAS  Google Scholar 

  • Eccles JC (1992) Evolution of consciousness. Proc Natl Acad Sci USA 89:7320–7324

    PubMed  CAS  Google Scholar 

  • Ermentrout BG (1998) Neural networks as spatio-temporal pattern-forming systems. Rep Prog Phys 61:353–430

    Google Scholar 

  • 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 3:1

    PubMed  Google Scholar 

  • Feshchenko VA, Veselis RA, Reinsel RA (2004) Propofol-induced alpha rhythm. Neuropsychobiology 50:257–266

    PubMed  CAS  Google Scholar 

  • Fleischhauer K, Petsche H, Wittkowski W (1972) Vertical bundles of dendrites in the neocortex. Z Anat Entwicklungsgesch 136:213–223

    PubMed  CAS  Google Scholar 

  • Foster BL, Bojak I, Liley DTJ (2008) Population based models of cortical drug response: insights form anaesthesia. Cogn Neurodyn 2:283–296

    PubMed  Google Scholar 

  • 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.2011.02.002

    Google Scholar 

  • 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

  • Freeman WJ (1979) Nonlinear gain mediating cortical stimulus-response relations. Biol Cybern 33:237–247

    PubMed  CAS  Google Scholar 

  • Freeman WJ, Holmes MD (2005) Metastability, instability, and state transition in neocortex. Neural Netw 18:497–504

    PubMed  Google Scholar 

  • 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 73:43–52

    PubMed  Google Scholar 

  • Friston KJ (1997) Transients, metastability, and neuronal dynamics. NeuroImage 5:164–171

    PubMed  CAS  Google Scholar 

  • Friston KJ (2000) The labile brain. I. Neuronal transients and nonlinear coupling. Philos Trans R Soc B 355:215–236

    CAS  Google Scholar 

  • Friston KJ (2002) Bayesian estimation of dynamical systems: an application to fMRI. NeuroImage 16:513–530

    PubMed  CAS  Google Scholar 

  • Friston KJ, Mechelli A, Turner R, Price CJ (2000) Nonlinear responses in fMRI: The Balloon model, Volterra kernels, and other hemodynamics. NeuroImage 12:466–477

    PubMed  CAS  Google Scholar 

  • Friston KJ, Penny WD, Phillips C, Kiebel SJ, Hinton GE, Ashburner J (2002) Classical and Bayesian inference in neuroimaging: theory. NeuroImage 16:465–483

    PubMed  CAS  Google Scholar 

  • Friston KJ, Harrison LM, Penny WD (2003) Dynamic causal modelling. NeuroImage 19: 1273–1302

    PubMed  CAS  Google Scholar 

  • Friston KJ, Mattout J, Trujillo-Barreto NJ, Ashburner J, Penny WD (2007) Variational free energy and the Laplace approximation. NeuroImage 34:220–234

    PubMed  Google Scholar 

  • 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:e1000196

    PubMed  Google Scholar 

  • Gloor P (1969) Hans Berger on the electroencephalogram of man. Electroencephalogr Clin Neurophysiol S28:350

    Google Scholar 

  • 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 122:393–413

    PubMed  CAS  Google Scholar 

  • Griffith JS (1963) A field theory of neural nets: I: derivation of field equations. Bull Math Biol 25:111–120

    CAS  Google Scholar 

  • Griffith JS (1965) A field theory of neural nets: II: properties of the field equations. Bull Math Biol 27:187–195

    CAS  Google Scholar 

  • Hagmann P, Cammoun L, Gigandet X, Meuli RA, Wedeen VJ, Sporns O (2008) Mapping the structural core of human cerebral cortex. PLoS Biol 6:e159

    PubMed  Google Scholar 

  • Haken H (1983) Synergetics: an introduction. Nonequilibrium phase transitions and self-organization in physics, chemistry, and biology, 3rd edn. Springer, Berlin

    Google Scholar 

  • Hellwig B (2000) A quantitative analysis of the local connectivity between pyramidal neurons in layers 2/3 of the rat visual cortex. Biol Cybern 82:111–121

    PubMed  CAS  Google Scholar 

  • Herculano-Houzel S (2009) The human brain in numbers: a linearly scaled-up primate brain. Front Hum Neurosci 3:31

    PubMed  Google Scholar 

  • 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 104:10240–10245

    PubMed  CAS  Google Scholar 

  • 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 106:2035–2040

    PubMed  CAS  Google Scholar 

  • Hughes SW, Crunelli V (2005) Thalamic mechanisms of EEG alpha rhythms and their pathological implications. Neuroscientist 11:357–372

    PubMed  Google Scholar 

  • 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 64:3–17

    PubMed  Google Scholar 

  • Hutt A, Longtin A (2010) Effects of the anesthetic agent propofol on neural populations. Cogn Neurodyn 4:37–59

    PubMed  Google Scholar 

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

    PubMed  CAS  Google Scholar 

  • Jirsa VK, Haken H (1996) Field theory of electromagnetic brain activity. Phys Rev Lett 77:960–963

    PubMed  CAS  Google Scholar 

  • Jirsa VK, Jantzen KJ, Fuchs A, Kelso JAS (2002) Spatiotemporal forward solution of the EEG and MEG using network modeling. IEEE Trans Med Imaging 21:493–504

    PubMed  Google Scholar 

  • Johansen-Berg H, Rushworth MFS (2009) Using diffusion imaging to study human connectional anatomy. Annu Rev Neurosci 32:75–94

    PubMed  CAS  Google Scholar 

  • Jones EG (2000) Microcolumns in the cerebral cortex. Proc Natl Acad Sci USA 97:5019–5021

    PubMed  CAS  Google Scholar 

  • Jones EG, Burton H, Porter R (1975) Commissural and cortico-cortical “columns” in the somatic sensory cortex of primates. Science 190:572–574

    PubMed  CAS  Google Scholar 

  • 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 19:3001–3010

    PubMed  Google Scholar 

  • Kandel ER, Schwartz JH, Jessell TM (2000) Principles of neural science, 4th edn. McGraw-Hill, New York

    Google Scholar 

  • Kelso JAS (1995) Dynamic patterns: the self-organization of brain and behavior. The MIT Press, Cambridge

    Google Scholar 

  • Kiebel SJ, David O, Friston KJ (2006) Dynamic causal modelling of evoked responses in EEG/MEG with lead field parameterization. NeuroImage 30:1273–1284

    PubMed  Google Scholar 

  • 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 27:210–221

    PubMed  Google Scholar 

  • Kötter R, Wanke E (2005) Mapping brains without coordinates. Philos Trans R Soc B 360:751–766

    Google Scholar 

  • Kramer MA, Kirsch HE, Szeri AJ (2005) Pathological pattern formation and cortical propagation of epileptic seizures. J R Soc Interface 2:113–127

    PubMed  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 80:725–732

    PubMed  CAS  Google Scholar 

  • 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 86:354–360

    PubMed  CAS  Google Scholar 

  • Laufs H, Daunizeau J, Carmichael DW, Kleinschmidt AK (2008) Recent advances in recording electrophysiological data simultaneously with magnetic resonance imaging. NeuroImage 40:515–528

    PubMed  CAS  Google Scholar 

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

    PubMed  CAS  Google Scholar 

  • Liley DTJ, Wright JJ (1994) Intracortical connectivity of pyramidal and stellate cells: estimates of synaptic densities and coupling symmetry. Netw Comput Neural Syst 5:175–189

    Google Scholar 

  • 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 10:79–92

    CAS  Google Scholar 

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

    Google Scholar 

  • Liley DTJ, Cadusch PJ, Dafilis MP (2002) A spatially continuous mean field theory of electrocortical activity. Netw Comput Neural Syst 13:67–113

    Google Scholar 

  • Liley DTJ, Cadusch PJ, Dafilis MP (2003a) Corrigendum. Netw Comput Neural Syst 14:369

    Google Scholar 

  • 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 68:051906

    Google Scholar 

  • 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 117–145

    Google Scholar 

  • 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 published

    Google Scholar 

  • Llinás RR (1988) The intrinsic electrophysiological properties of mammalian neurons: insights into central nervous system function. Science 242:1654–1664

    PubMed  Google Scholar 

  • Logothetis NK (2008) What we can do and what we cannot do with fMRI. Nature 453:869–878

    PubMed  CAS  Google Scholar 

  • Lopes da Silva FH, Hoeks A, Smits H, Zetterberg LH (1974) Model of brain rhythmic activity: the alpha-rhythm of the thalamus. Kybernetik 15:27–37

    PubMed  CAS  Google Scholar 

  • 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 50:540–548

    PubMed  Google Scholar 

  • 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 70:391–405

    PubMed  Google Scholar 

  • Lübke J, Feldmeyer D (2007) Excitatory signal flow and connectivity in a cortical column: focus on barrel cortex. Brain Struct Funct 212:3–17

    PubMed  Google Scholar 

  • 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 19:679–689

    PubMed  CAS  Google Scholar 

  • Marder E, Taylor AL (2011) Multiple models to capture the variability in biological neurons and networks. Nat Neurosci 14:133–138

    PubMed  CAS  Google Scholar 

  • Markram H (2006) The blue brain project. Nat Rev Neurosci 7:153–160

    PubMed  CAS  Google Scholar 

  • Markram H (2008) Fixing the location and dimensions of functional neocortical columns. HFSP J 2:132–135

    PubMed  Google Scholar 

  • Markram H, Toledo-Rodriguez M, Wang Y, Gupta A, Silberberg G, Wu C (2004) Interneurons of the neocortical inhibitory system. Nat Rev Neurosci 5:793–807

    PubMed  CAS  Google Scholar 

  • 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 367:1145–1161

    Google Scholar 

  • Matthews PM, Honey GD, Bullmore ET (2006) Applications of fMRI in translational medicine and clinical practice. Nat Rev Neurosci 7:732–744

    PubMed  CAS  Google Scholar 

  • 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 118:3–41

    PubMed  Google Scholar 

  • 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: 99–115

    Google Scholar 

  • 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 29:766–772

    PubMed  CAS  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

    CAS  Google Scholar 

  • 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 52:1109–1122

    PubMed  Google Scholar 

  • Moran RJ, Kiebel SJ, Stephan KE, Reilly RB, Daunizeau J, Friston KJ (2007) A neural mass model of spectral responses in electrophysiologys. NeuroImage 37:706–720

    PubMed  CAS  Google Scholar 

  • 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 42:272–284

    Google Scholar 

  • Moran RJ, Stephan KE, Seidenbecher T, Pape HC, Dolan RJ, Friston KJ (2009) Dynamic causal models of steady-state responses. NeuroImage 44:796–811

    PubMed  CAS  Google Scholar 

  • Mori S, Wakana S, van Zijl PCM, Nagae-Poetscher LM (2005) MRI atlas of human white matter. Elsevier, Amsterdam

    Google Scholar 

  • Mountcastle VB (1957) Modality and topographic properties of single neurons of cat’s somatic sensory cortex. J Neurophysiol 20:408–434

    PubMed  CAS  Google Scholar 

  • 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 21–42

    Google Scholar 

  • Mountcastle VB (1997) The columnar organization of the neocortex. Brain 120:701–722

    PubMed  Google Scholar 

  • Mulert C, Pogarell O, Hegerl U (2008) Simultaneous EEG-fMRI: perspectives in psychiatry. Clin EEG Neurosci 39:61–64

    PubMed  Google Scholar 

  • 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 52:1149–1161

    CAS  Google Scholar 

  • Niedermeyer E, Lopes da Silva FH (eds) (2005) Electroencephalography: Basic principles, clinical applications, and related fields, 5th edn. Lippincott Williams & Wilkins, Philadelphia

    Google Scholar 

  • Nieuwenhuys R, Voogd J, van Huijzen C (2008) The human central nervous system, 4th edn. Springer, Berlin, pp 491–679

    Google Scholar 

  • Norris DG (2006) Principles of magnetic resonance assessment of brain function. J Magn Reson Imaging 23:794–807

    PubMed  Google Scholar 

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

    Google Scholar 

  • Nunez PL (1974b) Wave-like properties of the alpha rhythm. IEEE Trans Biomed Eng 21:473–482

    Google Scholar 

  • Nunez PL (1981) Electric fields of the brain: the neurophysics of EEG, 1st edn. Oxford University Press, New York

    Google Scholar 

  • Nunez PL (1995) Neocortical dynamics and human EEG rhythms. Oxford University Press, New York

    Google Scholar 

  • 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 117:2424–2435

    PubMed  Google Scholar 

  • 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 44:344–352

    PubMed  CAS  Google Scholar 

  • 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 13:125–164

    PubMed  CAS  Google Scholar 

  • Pakkenberg B, Gundersen HJG (1997) Neocortical neuron number in humans: effect of sex and age. J Comp Neurol 384:312–320

    PubMed  CAS  Google Scholar 

  • Perea G, Araque A (2010) GLIA modulates synaptic transmission. Brain Res Rev 63:93–102

    PubMed  CAS  Google Scholar 

  • Perea G, Navarrete M, Araque A (2009) Tripartite synapses: astrocytes process and control synaptic information. Trends Neurosci 32:421–431

    PubMed  CAS  Google Scholar 

  • Peters A, Sethares C (1997) The organization of double bouquet cells in monkey striate cortex. J Neurocytol 26:779–797

    PubMed  CAS  Google Scholar 

  • Petersen CCH (2007) The functional organization of the barrel cortex. Neuron 56:339–355

    PubMed  CAS  Google Scholar 

  • 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 22:167–179

    PubMed  CAS  Google Scholar 

  • Rabinovich MI, Huerta R, Laurent G (2008a) Neuroscience. Transient dynamics for neural processing. Science 321:48–50

    CAS  Google Scholar 

  • Rabinovich MI, Huerta R, Varona P, Afraimovich VS (2008b) Transient cognitive dynamics, metastability, and decision making. PLoS Comput Biol 4:e1000072

    PubMed  Google Scholar 

  • Raichle ME, MacLeod AM, Snyder AZ, Powers WJ, Gusnard DA, Shulman GL (2001) A default mode of brain function. Proc Natl Acad Sci USA 98:676–682

    PubMed  CAS  Google Scholar 

  • Regan D (1989) Human brain electrophysiology: evoked potentials and evoked magnetic fields in science and medicine. Elsevier, New York

    Google Scholar 

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

    PubMed  CAS  Google Scholar 

  • Rennie CJ, Robinson PA, Wright JJ (2002) Unified neurophysical model of EEG spectra and evoked potentials. Biol Cybern 86:457–471

    PubMed  CAS  Google Scholar 

  • 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 360:1025–1041

    CAS  Google Scholar 

  • Riera JJ, Wan X, Jimenez JC, Kawashima R (2006) Nonlinear local electrovascular coupling. I: a theoretical model. Hum Brain Mapp 27:896–914

    Google Scholar 

  • Riera JJ, Jimenez JC, Wan X, Kawashima R, Ozaki T (2007) Nonlinear local electrovascular coupling. II: from data to neuronal masses. Hum Brain Mapp 28:335–354

    CAS  Google Scholar 

  • Robinson PA (2006) Patchy propagators, brain dynamics, and the generation of spatially structured gamma oscillations. Phys Rev E 73:041904

    CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • Robinson PA, Rennie CJ, Wright JJ, Bahramali H, Gordon E, Rowe DL (2001) Prediction of electroencephalographic spectra from neurophysiology. Phys Rev E 63:021903

    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

    CAS  Google Scholar 

  • Rockland KS, Ichinohe N (2004) Some thoughts on cortical minicolumns. Exp Brain Res 158:265–277

    PubMed  Google Scholar 

  • Rockland KS, Pandya DN (1979) Laminar origins and terminations of cortical connections of the occipital lobe in the rhesus monkey. Brain Res 179:3–20

    PubMed  CAS  Google Scholar 

  • 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 355:352–357

    CAS  Google Scholar 

  • 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 116:324–335

    PubMed  CAS  Google Scholar 

  • 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 18:2141–2157

    PubMed  Google Scholar 

  • Shibasaki H (2008) Human brain mapping: hemodynamic response and electrophysiology. Clin Neurophysiol 119:731–743

    PubMed  Google Scholar 

  • Silva LR, Amitai Y, Connors BW (1991) Intrinsic oscillations of neocortex generated by layer 5 pyramidal neurons. Science 251:432–435

    PubMed  CAS  Google Scholar 

  • Sotero RC, Trujillo-Barreto NJ (2008) Biophysical model for integrating neuronal activity, EEG, fMRI and metabolism. NeuroImage 39:290–309

    PubMed  Google Scholar 

  • Sotero RC, Trujillo-Barreto NJ, Iturria-Medina Y, Carbonell F, Jimenez JC (2007) Realistically coupled neural mass models can generate EEG rhythms. Neural Comput 19:478–512

    PubMed  Google Scholar 

  • Spiegler A, Kiebel SJ, Atay FM, Knösche TR (2010) Bifurcation analysis of neural mass models: impact of extrinsic inputs and dendritic time constants. NeuroImage 52:1041–1058

    PubMed  Google Scholar 

  • Spruston N (2008) Pyramidal neurons: dendritic structure and synaptic integration. Nat Rev Neurosci 9:206–221

    PubMed  CAS  Google Scholar 

  • Stam CJ (2005) Nonlinear dynamical analysis of EEG and MEG: review of an emerging field. Clin Neurophysiol 116:2266–2301

    PubMed  CAS  Google Scholar 

  • Stam CJ, Pijn JPM, Suffczyński P, Lopes da Silva FH (1999) Dynamics of the human alpha rhythm: evidence for non-linearity? Clin Neurophysiol 110:1801–1813

    PubMed  CAS  Google Scholar 

  • 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 356:1159–1186

    CAS  Google Scholar 

  • 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 31–83

    Google Scholar 

  • 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

    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 85:369–385

    PubMed  CAS  Google Scholar 

  • 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 31:547–569

    Google Scholar 

  • 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 72:061910

    Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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/s11538-010-9565-9

    Google Scholar 

  • Stufflebeam SM, Rosen BR (2007) Mapping cognitive function. Neuroimaging Clin N Am 17:469–484

    PubMed  Google Scholar 

  • Suffczyński P, Lopes da Silva FH, Parra J, Velis DN, Kalitzin SN (2005) Epileptic transitions: model predictions and experimental validation. J Clin Neurophysiol 22:288–299

    PubMed  Google Scholar 

  • Szentágothai J (1978) The Ferrier lecture, 1977 – the neuron network of the cerebral cortex: a functional interpretation. Proc R Soc Lond B 201:219–248

    PubMed  Google Scholar 

  • Szentágothai J (1983) The modular architectonic principle of neural centers. Rev Physiol Biochem Pharmacol 98:11–61

    PubMed  Google Scholar 

  • Tang Y, Nyengaard JR, De Groot DM, Gundersen HJG (2001) Total regional and global number of synapses in the human brain neocortex. Synapse 41:258–273

    PubMed  CAS  Google Scholar 

  • Thomson AM, Bannister AP (2003) Interlaminar connections in the neocortex. Cereb Cortex 13:5–14

    PubMed  Google Scholar 

  • Toga AW, Thompson PM, Mori S, Amunts K, Zilles K (2006) Towards multimodal atlases of the human brain. Nat Rev Neurosci 7:952–966

    PubMed  CAS  Google Scholar 

  • Tsuda I (2001) Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems. Behav Brain Sci 24:793–810

    PubMed  CAS  Google Scholar 

  • 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 49:2328–2339

    Google Scholar 

  • 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 30:2701–2721

    PubMed  Google Scholar 

  • 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 257:642–663

    Google Scholar 

  • Van Essen DC (2005) A Population-Average, Landmark- and Surface-based (PALS) atlas of human cerebral cortex. NeuroImage 28:635–662

    PubMed  Google Scholar 

  • 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 44:283–305

    PubMed  Google Scholar 

  • Waage P, Guldberg CM, Abrash HI (1986) Studies concerning affinity (English translation). J Chem Educ 63:1044–1047

    Google Scholar 

  • 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 83:367–378

    PubMed  CAS  Google Scholar 

  • 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 22:343–356

    PubMed  Google Scholar 

  • White EL (1989) Cortical circuits. Synaptic organization of the cerebral cortex: structure, function and theory. Birkhäuser, Boston

    Google Scholar 

  • Williamson SJ, Kaufman L (1989) Advances in neuromagnetic instrumentation and studies of spontaneous brain activity. Brain Topogr 2:129–139

    PubMed  CAS  Google Scholar 

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

    PubMed  CAS  Google Scholar 

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

    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 21:243–257

    PubMed  CAS  Google Scholar 

  • 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 33:213–246

    PubMed  CAS  Google Scholar 

  • Wolfe J, Houweling AR, Brecht M (2010) Sparse and powerful cortical spikes. Curr Opin Neurobiol 20:306–312

    PubMed  CAS  Google Scholar 

  • Wright JJ (1997) EEG simulation: variation of spectral envelope, pulse synchrony and ≈ 40 hz oscillation. Biol Cybern 76:181–194

    PubMed  CAS  Google Scholar 

  • Wright JJ, Liley DTJ (1995) Simulation of electrocortical waves. Biol Cybern 72:347–356

    PubMed  CAS  Google Scholar 

  • Wright JJ, Liley DTJ (1996) Dynamics of the brain at global and microscopic scales: neural networks and the EEG. Behav Brain Sci 19:285–320

    Google Scholar 

  • Wu JY, Huang XY, Zhang C (2008) Propagating waves of activity in the neocortex: what they are, what they do. Neuroscientist 14:487–502

    PubMed  CAS  Google Scholar 

  • Zilles K, Amunts K (2010) Centenary of Brodmanns map – conception and fate. Nat Rev Neurosci 11:139–145

    PubMed  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Brain Sciences Institute, Swinburne University of Technology, 218, Hawthorn, VIC, 3122, Australia

    David T. J. Liley

  2. Department of Neurology and Neurological Sciences, Stanford University, Stanford, CA, 94305, USA

    Brett L. Foster

  3. Donders Institute for Brain, Cognition and Behaviour, Centre for Neuroscience, Radboud University Nijmegen Medical Centre, 9101 // 126, 6500 HB, Nijmegen, The Netherlands

    Ingo Bojak

Authors
  1. David T. J. Liley
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Brett L. Foster
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ingo Bojak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David T. J. Liley .

Editor information

Editors and Affiliations

  1. European Bioinformatics Institute, EMBL-Outstation-Hinxton, Wellcome Trust Genome Campus, Welcome-Trust Genome Campus, Hinxton, Cambridge, CB10 1SD, United Kingdom

    N. Le Novère

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Liley, D.T.J., Foster, B.L., Bojak, I. (2012). Co-operative Populations of Neurons: Mean Field Models of Mesoscopic Brain Activity. In: Le Novère, N. (eds) Computational Systems Neurobiology. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-3858-4_11

Download citation

Publish with us

Policies and ethics

Search

Navigation