Title : A Master Equation Formalism forMacroscopicModeling of Asynchronous Irregular Activity States
Authors : Sami El Boustani and Alain Destexhe
Year : 2008
Journal : neural computation
Volume : 21
Pages : 46-100
Many efforts have been devoted tomodeling asynchronous irregular (AI) activity states, which resemble the complex activity states seen in the cerebral cortex of awake animals. Most of models have considered bal- anced 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 descrip- tion of such AI states. Using master equation formalism, we derive a second-order mean-?eld set of ordinary differential equations describ- ing the temporal evolution of randomly connected balanced networks. This formalism takes into account ?nite 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 con?gurations 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.