Traveling Waves and the Processing of Weakly Tuned Inputs in a Cortical Network Module

Recent studies have shown that local cortical feedback can havean important effect on the response of neurons in primary visualcortex to the orientation of visual stimuli. In this work, westudy the role of the cortical feedback in shaping thespatiotemporal patterns of activity in cortex. Two questionsare addressed: one, what are the limitations on the ability ofcortical neurons to lock their activity to rotatingoriented stimuli within a single receptive field? Two, can thelocal architecture of visual cortex lead to the generation ofspontaneous traveling pulses of activity? We study theseissues analytically by a population-dynamic model of ahypercolumn in visual cortex. The order parameter thatdescribes the macroscopic behavior of the network is thetime-dependent population vector of the network. We firststudy the network dynamics under the influence of a weakly tunedinput that slowly rotates within the receptive field. We showthat if the cortical interactions have strong spatialmodulation, the network generates a sharply tuned activityprofile that propagates across the hypercolumn in a path thatis completely locked to the stimulus rotation. The resultantrotating population vector maintains a constant angular lagrelative to the stimulus, the magnitude of which grows with thestimulus rotation frequency. Beyond a critical frequency thepopulation vector does not lock to the stimulus but executes aquasi-periodic motion with an average frequency that is smallerthan that of the stimulus. In the second part we consider thestable intrinsic state of the cortex under the influence of isotropic stimulation. We show that if the local inhibitoryfeedback is sufficiently strong, the network does not settleinto a stationary state but develops spontaneous travelingpulses of activity. Unlike recent models of wave propagation incortical networks, the connectivity pattern in our model isspatially symmetric, hence the direction of propagation ofthese waves is arbitrary. The interaction of these waves withan external-oriented stimulus is studied. It is shown that thesystem can lock to a weakly tuned rotating stimulus if thestimulus frequency is close to the frequency of the intrinsic wave.