A Likelihood Method for Estimating Visual Motion Parameters From Retinal Ganglion Cell Responses

Abstract

Purpose: : This work is related to the efforts of the Boston Retinal Implant Project to develop a sub-retinal prosthesis to restore vision to the blind. The specific purpose of this work is to develop receptive field models for ganglion cells via a maximum likelihood approach and to use these to accurately determine global motion parameters.

Methods: : We recorded from the flat-mount New Zealand white rabbit retina using a 60 channel electrode array with 200um spacing between electrodes. In the "training phase" we examined ganglion cell outputs elicited by moving edges with different speeds and directions. The model parameters (cell location, receptive field dimensions, firing strength, delay and spontaneous firing rate) were chosen to maximize the likelihood of the experimentally observed spike train from the cell. In the "testing phase" we examined ganglion cell outputs elicited by moving edges with speeds and directions unknown to the analyst. The edges’ speed and direction were determined by maximizing the joint likelihood for the models of the cells’ observed responses to the stimuli. Each model represented one cell’s spike train as an inhomogeneous Poisson process with a rate that was determined by the moving edge in combination with that model’s parameters.

Results: : Accurate indications of speed and angle were obtained when using a modest number of OFF ganglion cells; the accuracy somewhat degraded when fewer cells were used. The fidelity of the speed and direction determinations did not depend significantly on whether the cells used were tightly clustered or spread apart. Specifically, data from 9 OFF cells yielded an error in speed with a median absolute value of around 4% for an edge moving at 714um/sec and an error in angle with a median absolute value of 2°. The worst estimates were obtained when using data from only 3 OFF cells: the median absolute speed error rose to 8% for an edge moving at 714um/sec and the median absolute angle error rose to 8°.

Conclusions: : These initial measurements show that modest numbers of OFF ganglion cells send quite accurate information on global motion to the brain. The likelihood method can be extended to solve the visual "inverse problem" (determining the moving scene from examination of ganglion cell spike trains) to more detailed ganglion cell models and more complex moving scenes.

Keywords: retina • motion-2D • ganglion cells