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    January 01 2009

    A Master Equation Formalism for Macroscopic Modeling of Asynchronous Irregular Activity States

    In Special Collection:CogNet
    Sami El Boustani,
    Sami El Boustani
    Unité de Neurosciences Intégratives et Computationnelles, CNRS, 91198 Gif-sur-Yvette, France[email protected]
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    Alain Destexhe
    Alain Destexhe
    Unité de Neurosciences Intégratives et Computationnelles, CNRS, 91198 Gif-sur-Yvette, France[email protected]
    Search for other works by this author on:
    Crossmark: Check for Updates
    Sami El Boustani
    Unité de Neurosciences Intégratives et Computationnelles, CNRS, 91198 Gif-sur-Yvette, France[email protected]
    Alain Destexhe
    Unité de Neurosciences Intégratives et Computationnelles, CNRS, 91198 Gif-sur-Yvette, France[email protected]
    Received:February 12 2008
    Accepted:May 16 2008
    Online ISSN: 1530-888X
    Print ISSN: 0899-7667
    © 2008 Massachusetts Institute of Technology
    2008
    Neural Computation (2009) 21 (1): 46–100.
    Article history
    Received:
    February 12 2008
    Accepted:
    May 16 2008
    Citation

    Sami El Boustani,Alain Destexhe; A Master Equation Formalism for Macroscopic Modeling of Asynchronous Irregular Activity States.Neural Comput 2009; 21 (1): 46–100. doi:https://doi.org/10.1162/neco.2009.02-08-710

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      Abstract

      Many efforts have been devoted to modeling asynchronous irregular (AI) activity states, which resemble the complex activity states seen in the cerebral cortex of awake animals. Most of models have considered balanced networks of excitatory and inhibitory spiking neurons in which AI states are sustained through recurrent sparse connectivity, with or without external input. In this letter we propose a mesoscopic description of such AI states. Using master equation formalism, we derive a second-order mean-field set of ordinary differential equations describing the temporal evolution of randomly connected balanced networks. This formalism takes into account finite size effects and is applicable to any neuron model as long as its transfer function can be characterized. We compare the predictions of this approach with numerical simulations for different network configurations and parameter spaces. Considering the randomly connected network as a unit, this approach could be used to build large-scale networks of such connected units, with an aim to model activity states constrained by macroscopic measurements, such as voltage-sensitive dye imaging.

      Issue Section:
      Letters
      © 2008 Massachusetts Institute of Technology
      2008
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