Traveling waves and the processing of weakly tuned inputs in a cortical network module

Recent studies have shown that local cortical feedback can have an important effect on the response of neurons in primary visual cortex to the orientation of visual stimuli. In this work, we study the role of the cortical feedback in shaping the spatiotemporal patterns of activity in cortex. Two questions are addressed: one, what are the limitations on the ability of cortical neurons to lock their activity to rotating oriented stimuli within a single receptive field? Two, can the local architecture of visual cortex lead to the generation of spontaneous traveling pulses of activity? We study these issues analytically by a population-dynamic model of a hypercolumn in visual cortex. The order parameter that describes the macroscopic behavior of the network is the time-dependent population vector of the network. We first study the network dynamics under the influence of a weakly tuned input that slowly rotates within the receptive field. We show that if the cortical interactions have strong spatial modulation, the network generates a sharply tuned activity profile that propagates across the hypercolumn in a path that is completely locked to the stimulus rotation. The resultant rotating population vector maintains a constant angular lag relative to the stimulus, the magnitude of which grows with the stimulus rotation frequency. Beyond a critical frequency the population Vector does not lock to the stimulus but executes a quasi-periodic motion with an average frequency that is smaller than that of the stimulus. In the second part we consider the stable intrinsic state of the cortex under the influence of isotropic stimulation. We show that if the local inhibitory feedback is sufficiently strong, the network does not settle into a stationary state but develops spontaneous traveling pulses of activity. Unlike recent models of wave propagation in cortical networks, the connectivity pattern in our model is spatially symmetric, hence the direction of propagation of these waves is arbitrary. The interaction of these waves with an external-oriented stimulus is studied. It is shown that the system can lock to a weakly tuned rotating stimulus if the stimulus frequency is close to the frequency of the intrinsic wave.