Modeling of the vertebrate visual system. II. Application to the turtle cone retina

Electronic simulation of cones, horizontal cells and bipolar cells of generalized vertebrate cone retina

Electronic analogue of my theoretical model of generalized vertebrate cone retina [Siminoff: J. Theor. Biol. 86, 763 (1980)] is presented. Cone mosaic is simulated by 25 X 21 grid of phototransistors that have colored filters mounted in front of then to produce red-, green-, and blue-sensitive cones arranged in a "trichromatic" retina. Each retinal element is simulated by Summator-Integrator and unit gain voltage invertes are used to give correct polarities to output voltages. Dynamic properties of retinal elements are developed solely by temporal interplay of antagonistic input voltages with differing time courses, and spatial organization of receptive fields is developed by unit hexagons that precisely define cone input voltages to subsequent elements. Electronic model contains both color- and non-color-coded channels. Negative feedback from L-horizontal cells to cones, electrical coupling of like-cones, and electrical coupling of like-horizontal cells are simulated by feedforward circuits. Stray light is present due to light scattering properties of colored filters used to simulate color selectivety of cones. Stationary and moving spots of white and colored lights of varied sizes and intensities are used to study characteristics of electronic analogue. Results demonstrate practicality of electronic simulation to function analogues to real cone retinas to process visual stimuli and give information to higher centers as to size, shape, color and motion of objects in visual world.

Influence of amacrine cells on receptive field organization of ganglion cells of the generalized vertebrate cone retina: electronic simulation

Two classes of amacrine cells are simulated, small-field and large-field. Small-field amacrine cells are formed by input from a single bipolar cell, while large-field amacrine cell is formed by inputs from same 7 bipolar cells that form the ganglion cell. Only tonic amacrine cells are studied with both chromatic and luminosity types as well as double- and single-opponent receptive fields. Amacrine cells are used in both feedforward to ganglion cells and feedback to bipolar and horizontal cells. Feedback to bipolar cells or feedforward to ganglion cells affected steady state levels in a predictable fashion. Negative feedback to bipolar cells and positive feedforward to ganglion cells does not introduce transients to ganglion cells while negative feedback to horizontal cells and negative feedforward does. Feedback to horizontal cells produces complex effects on bipolar, amacrine and ganglion cells dependent on such factors as center-surround field balance and negative feedback from luminosity type of horizontal cell to cones.

Electronic simulation of ganglion cells of generalized vertebrate cone retina

Electronic simulation of generalized vertebrate cone retina consists of 43 X 41 grid of red-, green-, and blue-sensitive cones. Each retinal element is simulated by a linear summator in series with a leaky integrator and spatial-temporal properties are developed by spatial organization of cone mosaic into unit hexagons and interplay of antagonistic inputs of differing time courses. Model has full compliments of horizontal and bipolar cells including color- and non-color coding as well as single- and double-opponent receptive fields for bipolar cells. Electronic simulation also has negative feedback from L-horizontal cells to cones. Ganglion cells are formed by convergence of 7 bipolar cells, either all same and thus homogeneous, or else with a central-DPBC (or HPBC) and 6 surround-HPBCs (or DPBCs) and thus non-homogeneous. Responses of color- and non-color-coded ganglion cells as well as single- and double-opponents are investigated with stationary and moving light spots using white and colored lights. While responses to stationary light spots are predictable from digital models, responses to moving spots are complicated by differing time lags of components involved in total response. Therefore, responses to moving stimuli are more readily simulated by analogue models.

An analogue model of the luminosity-channel in the vertebrate cone retina. 3. Physiological correlates

A model of the vertebrate cone retina was tested with physiological stimuli. Results confirm previous findings that, except for photoreceptors, the spatial and temporal properties of simulated retinal elements conform to a linear system. The model is consistent with known physiological correlates. Tonic units detect intensity when the light spot is within the center field, while phasic units detect movement across borders of contrast. There is a dynamic balance between the tonic and phasic channels: the tonic channel is favored by a center field input voltage, while the phasic channel is favored by a surround field input voltage to bipolar cells. The ON discharge of the phasic ganglion cell is developed by the excitatory center field input to the depolarizing-center bipolar cell, which has the shortest delay, while the OFF discharge is the result of the excitatory surround field input voltage to the hyperpolarizing-center bipolar cell, which has the longest delay.

An analogue model of the luminosity-channel in the vertebrate cone retina. 1. Hardware and responses to square wave voltages

An analogue simulation was built of the vertebrate cone retina based on the model of Siminoff [J. Theor. Biol. 86, 673 (1980)]. Linear operational amplifiers were used for a few simple processes such as summation, integration (for synaptic delay), inversion and gain. Spatial and temporal properties of retinal elements were developed by interaction of simulated retinal neurons. Tonic and phasic ganglion cells were formed from the center-surround antagonistic receptive fields of bipolar cells. Center field input voltages favored the static levels of tonic units, while surround field input voltages favored the phasic units. Properties of receptive fields of retinal neurons could be simulated by the model using 2 antagonistic input voltages, one of which had a longer synaptic delay. Negative feedback from horizontal cells to cones and its potentiation by electrical coupling of horizontal cells reinforced overshoot produced by surround field input voltages with its extra synaptic delay as compared to the center field input voltage. In spite of simplifications, the model was a good representation of some properties of the retina.

Recursive features of circular receptive fields

The distribution of excitability in retinal receptive fields may be well approximated by functions with recursive features. Physiological data do not exclude an implementation of recursive structures in the visual system. It is the most remarkable advantage of a recursive visual system, that cortical receptive fields tuned to different spatial frequencies will have an identical neuronal circuitry. Structural consequences for retina, LGN and visual cortex are discussed.