Simple cells in the visual cortex have been subdivided into nondirection-selective (NDS), direction asymmetric (DA), and direction-selective (DS) cells. DA cells reverse their preferred direction with reversal of the stimulus contrast; DS2 cells respond with the same preferred direction for light and dark stimuli, whereas DS1 cells respond only to one (light or dark) contrast. Also, four velocity response groups have been distinguished: velocity broadband, low-pass, high-pass, and -tuned cells. This study describes an analytic model of feed-forward spatiotemporal interactions within a receptive field that reproduces these basic features of cortical simple cell behavior in the cat. The spatial structure of the receptive fields is simulated with Gabor functions. Two neurobiologically plausible mechanisms, temporal low-pass filtering and intracortical spatial distribution of activity, are modeled. The central feature of the study is the implementation of both mechanisms in a spatially continuous way. The model is analytic, but an equivalent neural network diagram was drawn and is used to explain the features of the model. First-order temporal low-pass filtering is performed both after convolving the stimulus light-intensity function with the Gabor type receptive field and also at the final output step of the model. In the circuit diagram this would correspond to low-pass filtering in lateral geniculate nucleus (LGN) and cortical cells. Filtering was adjusted to have a -3-dB drop-off frequency of 2-3 Hz, corresponding to the drop-off frequencies observed in response to temporal modulation of sine-wave gratings. The mechanism that we call intracortical distribution of activity is implemented along the axis of stimulus motion. A response elicited from the part of the receptive field that is stimulated at a given time will spread out in the receptive field, influencing regions that have not been stimulated. It is equivalent to spreading of activity on the cortical surface. This mechanism extends the existing ideas of discrete interactions between subfields to a continuous scheme throughout the whole receptive field. It is based on findings that intracortical interactions exist even within single subfields. The impact of distributing the activity is assumed to decrease exponentially with the Euclidian distance between the stimulated region and the region under consideration. Thresholds are implemented only at the level of the cortex. Both the activity distributing mechanism and the output of the cell being studied are thresholded. For odd Gabor functions, mere low-pass filtering without activity distribution and thresholding results in DA cells with velocity low-pass or velocity broadband behavior. Widening the receptive field makes the cells more sensitive to higher velocities. Velocity-tuned DS (DS1) cells can be modeled by including the activity distribution mechanism. These cells require phase-shifted odd symmetrical receptive fields, which are common among cortical cells. In real cells the response to a moving dot is, in most cases, stronger if the dot moves along the receptive field's long axis than if it moves across. This result is directly reflected in the model with or without activity distribution. The preferred axis of motion for a dot is 90° apart from those for a bar. Reports of shifts in the preferred axis of motion <90° are explained in the model by assuming that the center of rotation of the stimulus was not exactly centered on the excitatory zone of the receptive field. The model predicts that the optimal velocity for a moving dot should always be higher than those for a bar. Also the sharpness of the tuning for a moving dot should increase with increasing velocity, whereas the sharpness of tuning for a bar should decrease. In the present study simple cells are described in an analytic form. The model reproduces the basic spatiotemporal behavior of real cells and makes two predictions that can easily be tested experimentally. In a possible extension of this approach, the computationally simple model cells could be treated as direction- and velocity-selective modules in an artificial neural network architecture.
