Neural fields refer to integro-differential equations which model the average neural activity of a neural population at a coarse-grained limit. In classical neural fields, which follow Wilson-Cowan-Amari formalism, the neural interactions are modeled based on a distance-based connectivity, without taking into account the modulatory effects of functional properties of neurons on the connectivity. Such effects are observed in particular in the primary visual cortex (V1). In this work, we consider a neural field which takes into account these effects in the connectivity by focusing on the functional architecture of V1. This model was applied to a specific family of visual illusions, to reproduce the cortical activity generating the illusions. We will explain this model, and discuss its potential to an extension towards pathological cortical activity.