Signal sampling and propagation through multiple cell layers in the retina: modeling and analysis with multirate...

The retina is a multilayered structure. Each layer consists of one or more classes of cell, each at its own density and with its own anatomic and physiologic properties. Signals converge from many cells in one layer onto single cells in another layer, and a signal from a single cell diverges to many cells in the next layer. In this methods paper we develop a general approach to retinal analysis and modeling that incorporates multiple cell classes, their densities, and related anatomic properties. The method is based on multirate filtering, a branch of signal processing in which signals of different sampling rates are manipulated. By drawing a correspondence between cell density and signal sampling rate, we define multirate models that incorporate different cell densities, convergence, divergence, variation in dendritic field shape, cell-to-cell variation in synaptic weights, and other anatomic features. We develop the multirate approach and apply it to the cat cone-->cone bipolar CBb1-->on-beta ganglion cell pathway as an example. We calculate the spatial frequency responses of the CBb1 and on-beta cells based on the cone spatial frequency response and find that the attenuation of high frequencies in the cones prevents aliasing that would otherwise occur in CBb1 and on-beta cells. We compare the calculations with cat psychophysics. We show that the optics of the cat eye are insufficient in themselves for the prevention of aliasing in these cells; additional attenuation by the cone-cone gap junctions and the cone aperture is necessary. By including this postreceptoral filtering, we demonstrate that the highest spatial frequency that can be passed by the retina without aliasing is determined not always only by the densities of cones, bipolar cells, and ganglion cells but also by the synaptic and the dendritic weighting between these cells.