Skip to main content
SpringerLink
Log in

Neural Population Model

  • Living reference work entry
  • First Online:
Encyclopedia of Computational Neuroscience

Definition

Neuronal population models refer to a class of models that describe the temporal evolution of one or more statistical moments that characterize the dynamical state of interconnected populations of neurons. Existing neuronal population models, for mathematical tractability and direct connection with experiment, are generally restricted to the temporal evolution of mean quantities such as the mean firing rate or mean (soma) membrane potential over an appropriately defined neural ensemble. Such an ensemble is typically defined in terms of the physical domain over which the activity of functionally identical neurons can be, statistically speaking, assumed spatially homogeneous.

Detailed Description

History

By postulating that, in analogy to the collective phenomena of atomic interaction underpinning ferromagnetism, neurons acted cooperatively, Cragg and Temperley (1954) provided the first clear rationale for modeling the collective behavior of populations of neurons. They...

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

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

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Ashby W (1950) The stability of a randomly assembled nerve-network. Electroencephalogr Clin Neuro-Physiol 2:471–482

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  • Bojak I, Liley D (2005) Modeling the effects of anesthesia on the electroencephalogram. Phys Rev E 71:041,902

    Article  CAS  Google Scholar 

  • Bressloff P (2012) Spatiotemporal dynamics of continuum neural fields. J Phys A Math Theor 45:033001

    Google Scholar 

  • Cragg B, Temperley H (1954) The organization of neurones: a co-operative analogy. Electroencephalogr 6:85–92

    Google Scholar 

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

    Article  Google Scholar 

  • De-Miguel FF, Fuxe K (2012) Extrasynaptic neurotransmission as a way of modulating neuronal functions. Front Physiol 3:16

    Article  PubMed Central  PubMed  Google Scholar 

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

    Google Scholar 

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

    Article  PubMed Central  PubMed  Google Scholar 

  • Freeman W (1964) A linear distributed feedback model for prepyriform cortex. Exp Neurol 10:525–547

    Article  CAS  PubMed  Google Scholar 

  • Freeman W (1967) Analysis of function of cerebral cortex by use of control systems theory. Logistics Rev 3:5–40

    Google Scholar 

  • Freeman W (1975) Mass action in the nervous system: examination of the neurophysiological basis of adaptive behavior through the EEG, 1st edn. Academic, New York, also electronic edition. http://sulcus.berkeley.edu/MANSWWW/MANSWWW.html, 2004

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

    Article  CAS  PubMed  Google Scholar 

  • Giaume C, Koulako A, Roux L, Holcman D, Rouach N (2010) Astroglial networks: a step further in neuroglial and gliovascular interactions. Nat Rev Neurosci 11:87–99

    Article  CAS  PubMed  Google Scholar 

  • Grossberg S (1967) Nonlinear difference-differential equations in prediction and learning theory. Proc Natl Acad Sci U S A 58:1329–1334

    Article  CAS  PubMed Central  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Liley D, Cadusch P, Da lis M (2002) A spatially continuous mean field theory of electrocortical activity. Netw Comput Neural Syst 13:67–113

    Article  Google Scholar 

  • Liley D, Cadusch P, Gray M, Nathan P (2003) Drug-induced modification of the system properties associated with spontaneous human electroencephalographic activity. Phys Rev E 68:051,906

    Article  Google Scholar 

  • Liley D, Bojak I, Foster B (2012) Co-operative populations of neurons: mean field models of mesoscopic brain activity. In: Le Novere N (ed) Computational systems neurobiology. Springer, New York, pp 317–364

    Chapter  Google Scholar 

  • Longtin A (2013) Neuronal noise. Scholapedia 8(9):1618

    Article  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Lytton WW (2008) Computer modelling of epilepsy. Nat Rev Neurosci 9(8):626–637

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • McCulloch W, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5:155–133

    Article  Google Scholar 

  • Moran R, Stephan K, Seidenbecher T, Pape H, Dolan R, Friston K (2009) Dynamic causal models of steady-state responses. Neuroimage 44:796–811

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Mozzachiodi R, Byrne JH (2010) More than synaptic plasticity: role of nonsynaptic plasticity in learning and memory. Trends Neurosci 33(1):17–26

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Rall W (1967) Distinguishing theoretical synaptic potentials computed for different soma-dendritic distributions of synaptic input. J Neurophysiol 30:1138–1168

    CAS  PubMed  Google Scholar 

  • Rapoport A (1950) Contribution to the probabilistic theory of neural nets: I. randomization of refractory periods and of stimulus intervals. Bull Math Biophys 12:109–121

    Article  Google Scholar 

  • Robinson P, Rennie C, Rowe D (2002) Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Phys Rev E 65:041,924

    Article  CAS  Google Scholar 

  • Sleigh J, Voss L, Steyn-Ross M, Steyn-Ross D, Wilson M (2011) Modelling sleep and general anaesthesia. In: Hutt A (ed) Sleep and anaesthesia: Neural correlates in theory and experiment. Springer, New York, pp 21–41

    Chapter  Google Scholar 

  • Softky WR, Koch C (1993) The highly irregular ring of cortical cells is inconsistent with temporal integration of random EPSPs. J Neurosci 13:334–350

    CAS  PubMed  Google Scholar 

  • Sohl G, Maxeiner S, Willecke K (2005) Expression and functions of neuronal gap junctions. Nat Rev Neurosci 6(3):191–200

    Article  PubMed  Google Scholar 

  • Steyn-Ross M, Steyn-Ross D, Sleigh J, Liley D (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

    Article  CAS  Google Scholar 

  • Stys PK (2011) The axo-myelinic synapse. Trends Neurosci 34(8):393–400

    Article  CAS  PubMed  Google Scholar 

  • Terzuolo CA, Bullock TH (1956) Measurement of imposed voltage gradient adequate to modulate neuronal ring. Proc Natl Acad Sci U S A 42(9):687–694

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • van Veen L, Liley D (2006) Chaos via Shilnikov’s saddle-node bifurcation in a theory of the electroencephalogram. Phys Rev Lett 97:208,101

    Article  Google Scholar 

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

    Article  CAS  PubMed Central  PubMed  Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Brain and Psychological Sciences Research Centre, Swinburne University of Technology, Hawthorn, VIC, Australia

    Prof. D. T. J. Liley

Authors
  1. Prof. D. T. J. Liley
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. T. J. Liley .

Editor information

Editors and Affiliations

  1. Atlanta, Georgia, USA

    Dieter Jaeger

  2. Department of Biomedical Engineering, Florida International University, Miami, Florida, USA

    Ranu Jung

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this entry

Cite this entry

Liley, D.T.J. (2013). Neural Population Model. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_69-1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_69-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4614-7320-6

  • eBook Packages: Springer Reference Biomedicine and Life SciencesReference Module Biomedical and Life Sciences

Publish with us

Policies and ethics

Search

Navigation