Model of the cone-horizontal cell circuit in the catfish retina

A model of the cone-L-type horizontal cell circuit of the catfish contains 3 stages. The outer segment consists of a compression factor producing the Naka-Rushton relationship between amplitude of response and intensity and 7 low-pass filters in tandem that produces an absolute delay of about 15 ms. The cone pedicle consists of an internal negative feedback circuit in series with a low-pass filter. The L-type horizontal cell acts as a linear low-pass filter and forms the external negative feedback circuit with the cone pedicle. The system shows peicewise linearity with the feedback gain of the external negative feedback circuit directly proportional to the dc level of the horizontal cell. Thus, at any given mean illuminance the impulse response of the cone and L-HC adequately defines the dynamics of the responses. The conversion of a slow monophasic to a faster biphasic impulse response due to either an increase in mean illuminace or use of a steady annulus results from the change in the characteristic equation as the effective value of the feedback gain changes. By proper adjustement of gains and time constants, the cone-L-HC circuit of the catfish retina simulates the experimental data.     

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 25x21 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-colorcoded channels. Negative feedback from L-horizontal cells to cones, electrical coupling of like-cones, and electrical coupling of like-horizontal cells are simulated by feedfoward 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 analogous 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.     

Modelling of the vertebrate visual system 3. topological analysis of the cone mosaic

Spatial organization of the cone mosaic of the generalized vertebrate retina consists of rows of red and green cones alternating with rows of blue and blank cones. Cone inputs to retinal elements are defined spatially by red and green unit hexagons. Topological analysis entails determining for each cone in the mosaic the number of each cone type present in the unit hexagon which the activated cone can influence via electrical coupling between cones and/or stray light. Only weighted inputs in one-half of a sextant of the unit hexagon need be designated, since all other weighted inputs can be determined by rules giving systematic transformations of all cone types from one sextant to another: these rules arise from symmetries of the cone mosaic. Four retinal types are possible depending on replacement of blank cones by specific cone types; three cone-dominant retinas, where all blank cones are replaced by a specific cone type, and two forms of a trichromatic retina, where blank cones are replaced by equal numbers of red and green cones. The weighted input is the sum of individual cone type contributions and depends on the number of each cone type in the unit hexagon which can influence the cone in question. Weighted inputs for cone-dominant retinas are readily found by replacing blank cones with the proper cone type, while weighted inputs for trichromatic retinas require use of a specified cone mosaic to determine extra red and green cones. Receptive field size of post-cone elements as well as overlap of the center and surround fields of annular organized receptive fields of retinal elements increased with increasing values for attenuation factors.     

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

The model of the vertebrate cone retina was adapted to the turtle retina with its red cone- and L-channel-dominances. The model consists of an ordering of four spatial organizations of unit hexagons, weighted inputs for all cones in the receptive fields, and linear polarization factors based on data from literature on turtle retina. Data generated by the model for spatial and chromatic patterns of receptive fields, intensity-response curves, dynamic ranges for cones, horizontal and bipolar cells proved remarkably consistent with literature. The model also generates observed phenomena such as near-field enhancement of cones due to stray light effects and electrical coupling of like-cones and far-field decrease in responses due to negative feedback from L-type horizontal cells to cones. Annular stimuli were shown to be more effective than spot stimuli for horizontal cells. The formal approach of the model demonstrates factors which play roles in various observed phenomena and all aspects of model can be displayed and tested both qualitatively and quantitatively.     

Dynamics of chromaticity horizontal cells in the freshwater turtle retina

A model of the cone-horizontal cell circuit is presented based on morphological evidence recently found in the Reeves' turtle: a luminosity horizontal cell (LHC) that receives inputs from red-, green-, and blue-sensitive cones in the ratio of 15:3:1, a triphasic horizontal cell (THC) that receives inputs from one class of red-sensitive and from blue-sensitive cones in the ratio of 2:1; and a biphasic chromaticity horizontal cell (BHC) that receives inputs from green-sensitive cones as well as from a special class of red-sensitive (i.e. the broad spectrum) and from blue-sensitive cones in the ratio of 3:2:1. A study of the simulated impulse responses strongly suggests that the basic response patterns of the BHC and THC can be readily explained by a simple wiring diagram consisting of direct hyper-polarizing inputs from the appropriate cones and a depolarizing input from the LHC which acts as a voltage inverter. A negative feedback circuit from the LHC to the cone pedicles is included and its negative feedback gain increases as the mean illuminance level (Io) increases. The negative feedback circuit, which promotes adaptation in the cones to changing Io's, is not necessary for opponent polarization in the BHC or THC, but does explain variabilities of impulse responses.     

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 feedfoward to ganglion cells affected steady state levels in a predictable fashion. Negative feedback to bipolar cells and positive feedfoward to ganglion cells does not introduce transients to ganglion cells while negative feedback to horizontal cells and negative feedfoward 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.     

Simulated fovea of the human retina: psychophysical data confirming the model's ability to accurately predict resolution

A series of psychophysical tests were designed to determine whether a computer simulation of the human retina could accurately predict the geometry of various stimuli that were optimally resolved for human foveal vision. Stimuli were used that were of the order of the grain of the cone mosaic, i.e., of the order of 2 × 2. In the first set of experiments, resolution was tested using a two-bar stimulus. In one experimental series the gap between the two bars was varied, and in a second series the gap was kept constant and the width of the bars varied. In a second set of experiments, various block letters and a number of series for each letter were used; in each experimental series a single parameter was systematically varied. The same stimuli were also used as inputs for the computer simulation. When proper controls were used, the psychophysical data and computer simulation gave remarkably comparable results. Care was taken to differentiate between simple detection of a pattern, and resolution, which involved proper identification of the image.     

Dynamics of L-type bipolar and phasic amacrine cells in the vertebrate cone retina

The model of the cone-L-HC circuit of the catfish retina (Siminoff 1985a) is extended to Luminosity bipolar cells (BC) and non-linear phasic amacrine cells (AC), but now applicable to the generalized vertebrate cone retina that involves only one cone type. Two types of BC's are simulated by linear transformation of 2 antagonistic inputs of differing time courses; the faster center field hyperpolarization from the cone and the slower surround field depolarization from the L-HC. The phasic AC was made non-linear by various methods: full- or half-wave rectification using either both or only one of the BC's as the inputs with rectification first and then summation or summation first and then rectification. A method is described using Laplace transforms in conjunction with the convolution theorem to obtain the impulse responses of BC's and AC's, in spite of the non-linearities of the AC even when used as feedback to the BC's. Since the input to the BC consists of 2 antagonistic inputs, feedback from the AC reeinforces one input and attenuates the other.     

Dynamics of chromatic adaptation in cones of freshwater turtle

The closer the wavelength of a steady background of monochromatic light is to the peak sensitivity of a cone that is being illuminated, the stronger is the desensitization of that cone; this is chromatic adaptation. A model of the freshwater turtle retina with the neural components of chromatic adaptation via negative feedback circuits is used to simulate and study various aspects of chromatic adaptation. An internal negative feedback circuit resides solely within the cone pedicle and thereby, its adaptive effects are relatively specific, so that univariance is maintained. The cone-L-horizontal cell circuit is an external negative feedback circuit and its adaptive effects are less specific since all 3 chromatic cone types are involved, so that univariance is violated. Chromatic adaptation is the result of the decrease in the cone gain due to the dependency of the gains of the negative feedback circuits on the mean illuminance level. The results of the model are consistent with von Kries law, but the changes in gains of the cones due to chromatic adaptation are dependent on wavelength, intensity of the adapting light and size.