Abstract
AbstractThe goal of this paper is twofold. We propose and explore a model to study the synchronization among populations in the canonical model of the neocortex proposed previously by (R.J. Douglas, K.A.C. Martin, A functional microcircuit for cat visual cortex. J.Physiol. 440(1991) 735–769). For this, a model describing N synapses of each m-population (m = 1, 2,3) is proposed. Each synapse is described by a system of 2 stochastic differential equations (SDEs). Then, by using the dynamical mean field approximation (DMA) (H. Hasegawa, Dynamical mean-field theory of spiking neuron ensembles: Response to a single spike with independent noises, Phys. Rev. E. (2003)1-19.) the system of several SDEs is reduced to 12 ordinary differential equations for the means and the second-order moments of global variables. The connectivity among populations is obtained by summarizing in the canonical model the detailed information from a quantitative description of the circuits formed in cat area 17 given in (T.Binzegger, R.J. Douglas, K.A. Martin, A Quantitative Map of the Circuit of Cat Primary Visual Cortex, J. Neurosci. 24 (2004) 8441- 8453). In the framework of the used DMA we propose a measure for inter-population synchronization. Simulations are carried out for exploring how inter-population synchrony is related to the variation of firing frequency of each population. Our results suggest that superficial pyramidal clusters appear to have a predominant influence on the synchronization process among pyramidal populations as well as put forward the active role of inhibition in the rest of the synchronizations between populations.
Highlights
The neural processes responsible for the generation of the electroencephalogram (EEG) and functional magnetic resonance imaging data, can be investigated using models suited for mesoscopic and macroscopic scales, known as neural mass models (NMMs) [1,2,3,4,5,6,7] despite progress in this direction, as well as numerous neurophysiological and neuroimaging experiments we still lack understanding of what are the neural mechanisms that select and synchronize the distributed brain activity that gives rise to EEG and fMRI data
In this paper we propose a mean field approximation for the canonical cortical model proposed by Douglas and Martin [10], based on the dynamical mean field approximation (DMA) theory
Here we first explore using model (41)-(54), how the inter-population synchronization is affected by the parameters (b1,b2,b3 ) responsible for each population firing frequency in the FN framework
Summary
The neural processes responsible for the generation of the electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI) data, can be investigated using models suited for mesoscopic and macroscopic scales, known as neural mass models (NMMs) [1,2,3,4,5,6,7] despite progress in this direction, as well as numerous neurophysiological and neuroimaging experiments we still lack understanding of what are the neural mechanisms that select and synchronize the distributed brain activity that gives rise to EEG and fMRI data. Spatially averaged magnitudes are assumed to characterize the collective behavior of populations of neurons of a given type In this approach, brain rhythms can be generated as a result of coupling excitatory and inhibitory populations [3]. Hasegawa [8,9] proposed a dynamical mean field approximation (DMA) for a neuronal population that allows to obtain a measure of the intra-population synchronization. He extended this approach to multiple coupled populations but didn’t propose a measure for inter-population synchronization. Simulations are carried out for exploring how inter-population synchronization is related to the rhythms exhibited by the model
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