VisionRes. Vol. 29, No. 3, pp. 271-291, 1989 Printed in Great Britain. All rights reserved 0042-6989/89 83.00 + 0.00 Copyright 0 1989 Pcrgamon Press plc A MODEL FOR SPATIOTEMPORAL FREQUENCY RESPONSES IN THE X CELL PATHWAY OF THE CAT’S RETINA EMILEP.CHEN and ALAN W. FREEMAN* Biomedical Engineering Department and Neurobiology and Physiology Department, Northwestern University, Evanston, IL 60201, U.S.A. zyxwvutsrqponmlkjihgfedcbaZYXWVUT (Received 24 August 1987; in revisedjhn 1 August 1988) Abstract-A linear model is described for the cat eye’s signal-processing pathway, from the visual stimulus at the cornea, to cones, to X-type ganglion cells. The model contains elements representing the eye’s optics, phototransduction, gain control, spatiotemporal processing by cell layers, and pure delay. Centre- surround antagonism in the model arises through the presence of a centre element producing a small spatial spread of signals, and an antagonistic element producing a larger spread. Two arrangements were tried, feedforward and feedback, in which the antagonistic element’s output was subtracted from the centre element’s outptB, and input, respectively. The model was fitted to empirical spatial and temporal frequency responses collected by Frishman et al. (1987), and accounted qualitatively for these data in the feedback, but not the feedforward, arrangement. The model’s centre pathway comprises a cascade of low-pass spatial filters, as does the surround pathway. As a consequence, the spatial frequency responses for these two pathways closely approximate Gaussian functions of spatial frequency, and the spatial frequency response of the complete model at low temporal frequency closely matches that of the difference of Gaussians model. Cat Retina Ganglion cell Spatial frequency Temporal frequency INTRODUCTION Most ganglion cells in the cat retina have centre- surround receptive fields: illumination of a small area away from the receptive field middle pro- duces a response with opposite sign to that produced by illumination at the middle. The zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJ Difference of Gaussians model, introduced by Rodieck in 1965, has dominated the interpre- tation of this receptive field spatial structure. Rodieck postulated that the ganglion cell’s re- sponse is equal to the difference between the signals from two circularly symmetric response mechanisms, the centre and surround. Sensi- tivity is assumed to be a Gaussian function of distance from the receptive field middle in both mechanisms, but since the Gaussian represent- ing the centre mechanism is taller and narrower than that representing the surround, the centre mechanism dominates the surround at the middle of the receptive field and the surround signal is the major one at outer locations. In this paper we explore an alternative model with two major differences from Rodieck’s. *Send correspondence to A.W.F., whose address is: Physi- ology Department F13, University of Sydney, N.S.W. 2006, Australia. First, our cable model (named for the model element used to represent a cell layer) comprises a number of elements, each of which stands for a known physiological property of the eye. There is, for instance, an element representing the eye’s optical system, and other elements representing the spatial spread of signals within a cell layer. The difference of Gaussians model makes no explicit reference to such properties, while they are part of the basic formulation of the cable model. Secondly, our model predicts not only the spatial structure of the receptive field, but also its temporal properties. There has been increasing interest recently in the temporal properties of ganglion cell receptive fields. The difference of Gaussians model has been modified to address these temporal properties (Enroth-Cugell et al., 1983) but the modification must be regarded as ad hoc: while the modified model is capable of explaining the relationship between the centre and surround components, it says nothing about the form of the temporal frequency response for the individual com- ponents. The cable model, on the other hand, can be given various configurations, each of which predicts a specific form for the temporal frequency response. 271