Mathematica is used to study retinal processing as part of an effort to build a synthetic retina. We present numerical solutions for one-dimensional coupled syncytia, with 20 nodes each, which are qualitatively similar to measured retinal responses. We also derive analytic expressions for the impulse response and show how it depends on the model parameters. Finally, an analog VLSI pixel circuit for this model is described.
The above figure illustrates the interactions between cells in the outer plexiform layer of the retina. Retinal photoreceptors transduce incident light into current. The receptors are electrically coupled to their neighbors by gap junctions, which occur at the cone terminals. Thus, the receptors form a syncytium within which their current signals diffuse. The horizontal cells make up the next layer of the retina. They also form a syncytium, allowing electrical signals to diffuse freely from cell to cell. These syncytia may be modeled by resistive networks.
A linear model of the outer plexiform is analyzed to obtain an analytic solution of the receptive field of photoreceptors, and produces a response qualitatively similar to that measured in physiological experiments, displaying the well-known center/surround organization. There is an excitatory center and an inhibitory surround. This is shown in the two-dimensional solution above. The three-dimensional case may be extrapolated by revolving this two-dimensional view about the V axis.
