Emergent nonlinear dynamics in the primary visual cortex (V1) may influence information processing in the early visual pathway and has been shown to affect visual perception. A major goal of systems neuroscience is to understand how complex brain functions can arise from the collective nonlinear dynamics of the underlying neuronal network. This challenge has been partly met through electrophysiological recordings, optical imaging and neural population models. However, a full account of how the multi-scale population dynamics emerges from the detailed biophysical properties of individual neurons and the network architecture remains elusive. Previously, working on a homogeneously-coupled network, we derived a series of population dynamics models, ranging from Master equations, to Fokker-Planck equations, and culminating in an augmented system of spatially-coupled ODEs. Here we present an application of this reduction method to a heterogeneously coupled neuronal network that models a spatially-extended portion of V1. We found that the temporal dynamics of individual V1 patches can be well captured by a low-dimensional set of voltage moments. At the same time, the spatially-coupled system can recapitulate the cortical wave generation and propagation induced by many visual stimuli, including those that induce motion illusions. Furthermore, this coarse-graining reveals the importance of the temporal differences between on-/off-pathways, that may account for the directional motion perception from darks to brights.
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