Visuomotor fields of the superior colliculus: A quantitative model

Electrophysiological and electrical stimulation studies in the monkey have disclosed that both the retinal surface and the metrics of saccades are topographically represented in the superior colliculus. This mapping of sensory and motor space onto the colliculus is nonhomogeneous in that the central region is over-represented in both the visual and the motor map. Single unit studies have revealed that visual receptive fields of collicular neurons are typically quite large and are characterized by a skewed (asymmetrical) sensitivity profile. Analyses by McIlwain [ J. Neurophysiol. 38, 219–230 (1975) ] in the cat have suggested that this skewness property reflects mainly the spatial distortion inherent in the afferent mapping. In this paper we describe a quantitative model, based on a logarithmic mapping function combined with a Gaussian connectivity function in the colliculus, which can account for the extent and the shape of collicular receptive fields. Collicular neurons in the deeper layers have movement-related bursts of activity for saccades in a limited amplitude and direction range related to their location in the collicular map. These movement fields, like visual receptive fields, may be quite extensive and typically have a skewed profile. In our model, an efferent-mapping function is defined, which relates the locus of a population of recruited cells to the metrics of the ensuing saccade. The parameters of this function, which was taken to be identical with the afferent mapping function, were estimated from Robinson's [ Vision Res. 12, 1795–1808 (1972) ] electrical stimulation data. Based on the assumption that the population-activity profile resembles a two-dimensional Gaussian function, the shape and the size of movement fields can then be described with just 2 or 3 free parameters. Electrophysiological data recorded from a small sample of collicular visuomotor neurons were used to illustrate the procedure, which we designed to enable application of our model to the experimental data. The best fit was obtained when the mapping function was slightly anisotropic. Suggestions on how the model could be improved and extended are offered in the Discussion.