Student Theses and Dissertations

Date of Award

1972

Document Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Thesis Advisor

Israel Abramov

Keywords

retinal ganglion cells, spatial summation, receptive field, non-linear processing, visual response modeling, goldfish retina

Abstract

The axons of retinal ganglion cells convey the signals from which the brain constructs its visual percept of the world. The considerable processing done in the retina is implicit in these signals; it is therefore desirable to understand this processing in some detail. Only one aspect of retinal processing is considered--the spatial interactions within either the center or the surround of the receptive field of the ganglion cell. A generalized model for this restricted processing is proposed: the independent signals in each of two separately stimulated areas may undergo non-linear transformation; the two areas may interact at one or several levels, ultimately converging on a final common pathway (the ganglion cell); a further non-linear transformation may be performed on the combined signal in the final common pathway. To examine the features of such a model, two separate areas within the center of a receptive field are stimulated, both individually and simultaneously. A wide range of intensities is used. Two methods of analysis are applied to these data; each is intended to elucidate particular features of the model. The first method of analysis, the method of response-summation, compares responses when each spot is illuminated separately with responses when both spots are presented together. A graph is presented of the responses to simultaneous stimulation (physiological sum) as a function of the arithmetically summed responses to each spot alone at the same intensity; the independent parameter is intensity. The plot (response-summation) is not affected by non-linearities which occur before the first interaction of the two areas; if there are no nonlinearities at or after the first interaction this plot must be a straight line of unity slope. If there are non-linearities at or after the first interaction of the areas, some other function will be obtained; an analysis is given of the expected forms of this curve for a number of possible non-linearities which might reasonably be postulated. The second form of analysis, the method of sensitivity-summation, considers the intensities required to elicit a particular response in each area stimulated alone as compared with the intensity required for the same response when both are stimulated simultaneously. A graph is presented (sensitivity-summation plot) showing the logarithm of the summed individual sensitivities as a function of the logarithm of the sensitivity to both spots; the criterion response level is the independent parameter. This plot is not affected by any non-linearities after the signals are combined; if there are no non-linearities before the final combination of responses from the two areas, the resultant plot must be a straight line of unity slope passing through the origin. If there are non-linearities at or before the final combination some other function will be obtained; an analysis is presented of the expected forms of this plot for a number of plausible non-linearities. The response-summation plot is affected only by non-linearities at or after the first interaction of the two areas, while the sensitivity-summation plot is affected only by non-linearities at all levels up to that at which the signals are finally combined; thus the concurrent application of both methods to the same data effectively divides the processing into a three stage model. Non-linearities before the areas interact affect only the sensitivity-summation plot, non-linearities in the final common pathway after the final combination affect only the response-summation plot, while non-linearities in the region from the first to the final interaction must affect both plots. The methods of response- and sensitivity-summation are applied to data from single ganglion cells in the excised retinae of goldfish. Chromatic interactions are eliminated by the use of near-infrared lights which stimulate only the long-wavelength receptive cones. Spatial interactions within either center or surround of the receptive fields of ganglion cells are examined. The following minimal model is derived. The receptors in each area perform a non-linear transformation; this may best be described by a square root function, but one which fails at the highest and the lowest intensities. There is also a threshold in each pathway which must be exceeded before the signal from that area will be included in the ganglion cell response. The signals from separate areas combine at a single level by simple linear summation. The final common pathway includes a non-linearity which may best be described as "compressive"--linear for low levels of response, but gradually reaching a limiting value at high levels. No lateral interactions need be postulated; various attempts to demonstrate a level of lateral interactions other than simple spatial summation all fail. The time courses of the responses are also examined by applying the same summation methods to short time segments of the responses. A supplementary method (relative timing) is also applied; in this method the responses to a brief test flash are measured when the test flash is presented at various times relative to a longer conditioning stimulus in another area. These analyses lead to the hypothesis that the decay in firing rate as a function of time after the onset of a stimulus is a part of the same process which gives the compressive function after summation.

Comments

A thesis presented to the faculty of The Rockefeller University in partial fulfillment of the requirements for the degree of Doctor of Philosophy

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Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License
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