document: Coarse-grained reduction and analysis of a network model of cortical response : I. Drifting grating stimuli We present a reduction of a large-scale network model of visual cortex developed by McLaughlin , Shapley , Shelley , and Wielaard . The reduction is from many integrate-and-fire neurons to a spatially coarse-grained system for firing rates of neuronal subpopulations . It accounts explicitly for spatially varying architecture , ordered cortical maps -LRB- such as orientation preference -RRB- that vary regularly across the cortical layer , and disordered cortical maps -LRB- such as spatial phase preference or stochastic input conductances -RRB- that may vary widely from cortical neuron to cortical neuron . The result of the reduction is a set of nonlinear spatiotemporal integral equations for `` phase-averaged '' firing rates of neuronal subpopulations across the model cortex , derived asymptotically from the full model without the addition of any extra phenomological constants . This reduced system is used to study the response of the model to drifting grating stimuli - where it is shown to be useful for numerical investigations that reproduce , at far less computational cost , the salient features of the point-neuron network and for analytical investigations that unveil cortical mechanisms behind the responses observed in the simulations of the large-scale computational model . For example , the reduced equations clearly show -LRB- 1 -RRB- phase averaging as the source of the time-invariance of cortico-cortical conductances , -LRB- 2 -RRB- the mechanisms in the model for higher firing rates and better orientation selectivity of simple cells which are near pinwheel centers , -LRB- 3 -RRB- the effects of the length-scales of cortico-cortical coupling , and -LRB- 4 -RRB- the role of noise in improving the contrast invariance of orientation selectivity
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extractive_keyphrases: visual cortex nonlinear spatiotemporal integral equations orientation selectivity
abstractive_keyphrases: large-scale network model neuronal networks coarse-graining point-neuron network phase-averaged firing rates dynamics