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Phase Transitions, Neural Population Models and

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Encyclopedia of Computational Neuroscience

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Definition

A neural population model pictures the cortex as a continuum of excitable tissue comprised of densely interconnected excitatory and inhibitory neurons, with cortical activity encoded as population-average firing rates. For certain ranges of cortical parameters, such models can exhibit multistability, with access to multiple equilibrium (homogeneous and stationary) and nonequilibrium (patterned or dynamic) spatiotemporal states. These distinct states may be identified with particular phases of normal and pathological brain activity such as wakefulness, anesthetic coma, and seizure. Transitions between states can be induced by variations in a control parameter such as neurotransmitter concentration and subcortical stimulation and can be likened to the thermodynamic phase transitions (e.g., melting, freezing) of physical science.

Detailed Description

Equilibrium Phase Transitions

The underlying mechanisms of commonly observed thermodynamic phase transitions – such as water...

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References

  • Bennett MV, Zukin RS (2004) Electrical coupling and neuronal synchronization in the mammalian brain. Neuron 41:495–511

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  Google Scholar 

  • Breakspear M, Roberts JA, Terry JR, Rodrigues S, Mahant N, Robinson PA (2005) A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. Cereb Cortex 16(9):1296–1313. doi:10.1093/cercor/bhj072

    Article  PubMed  Google Scholar 

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

    Article  Google Scholar 

  • Ermentrout GB, Cowan JD (1979a) A mathematical theory of visual hallucination patterns. Biol Cybern 34(3):137–150

    Article  CAS  PubMed  Google Scholar 

  • Ermentrout GB, Cowan JD (1979b) Temporal oscillations in neuronal nets. J Math Biol 7:265–280

    Article  CAS  PubMed  Google Scholar 

  • Kramer MA, Kirsch HE, Szeri AJ (2005) Pathological pattern formation and cortical propagation of epileptic seizures. J R Soc Lond Interface 2:113–207. doi:10.1098/rsif. 2004.0028

    Article  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

    Article  CAS  PubMed  Google Scholar 

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

    CAS  Google Scholar 

  • Nicolis G, Prigogine I (1977) Self-organization in nonequilibrium systems. Wiley, New York

    Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Robinson PA, Rennie CJ, Rowe DL (2002) Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Phy Rev E 65(4):041,924

    Article  CAS  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

    Article  CAS  Google Scholar 

  • Steyn-Ross ML, Steyn-Ross DA, Wilson MT, Sleigh JW (2007) Gap junctions mediate large-scale turing structures in a mean-field cortex driven by subcortical noise. Phys Rev E 76:011,916. doi:10.1103/PhysRevE.76.011916

    Article  Google Scholar 

  • Steyn-Ross ML, Steyn-Ross DA, Sleigh JW (2013) Interacting turing-hopf instabilities drive symmetry-breaking transitions in a mean-field model of the cortex: a mechanism for the slow oscillation. Phys Rev X 3(2):021,005. doi: 10.1103/PhysRevX.3.021005, url: http://link.aps.org/doi/10.1103/PhysRevX.3.021005

  • Turing AM (1952) The chemical basis of morphogenesis. Philos Trans R Soc Lond 237:37–72

    Article  Google Scholar 

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

    Article  CAS  PubMed Central  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Wilson MT, Sleigh JW, Steyn-Ross DA, Steyn-Ross ML (2006) General anesthetic-induced seizures can be explained by a mean-field model of cortical dynamics. Anesthesiology 104:588–593

    Article  PubMed  Google Scholar 

  • Wozny C, Williams SR (2011) Specificity of synaptic connectivity between layer 1 inhibitory interneurons and layer 2/3 pyramidal neurons in the rat neocortex. Cereb Cortex 21(8):1818–1826. doi:10.1093/cercor/bhq257

    Article  PubMed Central  PubMed  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Engineering, University of Waikato, Hamilton, New Zealand

    Prof. D. Alistair Steyn-Ross & Prof. Moira Steyn-Ross

  2. Waikato Clinical School, University of Auckland, Waikato Hospital, Hamilton, New Zealand

    Prof. Jamie Sleigh

Authors
  1. Prof. D. Alistair Steyn-Ross
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  2. Prof. Moira Steyn-Ross
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  3. Prof. Jamie Sleigh
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Corresponding author

Correspondence to D. Alistair Steyn-Ross .

Editor information

Editors and Affiliations

  1. Atlanta, Georgia, USA

    Dieter Jaeger

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

    Ranu Jung

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Steyn-Ross, D.A., Steyn-Ross, M., Sleigh, J. (2014). Phase Transitions, Neural Population Models and. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_73-2

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  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_73-2

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  • Online ISBN: 978-1-4614-7320-6

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Chapter history

  1. Latest

    Phase Transitions, Neural Population Models and
    Published:
    01 August 2014

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_73-2

  2. Original

    Phase Transitions in Neural Population Models
    Published:
    11 April 2014

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_73-1

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