Impulse: The Premier Journal for Undergraduate Publications in the Neurosciences. June 2004, 1 (1): 1-58 A Mathematical Model of Retinal Receptive Fields Capable of Form & Color Analysis Sarah N. Blythe1, John H. Krantz2 1Northwestern University, Evanston, Illinois 60201; 2Hanover College, Hanover, Indiana 47243 In an effort to understand the workings of the sensitive model, the model was exposed to retinal receptive fields, Enroth-Cugell and pure color fields that ranged in hue from Robson developed a mathematical model that 400nm to 700nm. The results obtained from utilized the difference-of-Gaussian (DOG) this full-field stimulation were highly function, an equation in which the inhibitory correlated to the findings of past portion of a receptive field is subtracted from physiological experiments. To further the excitatory portion. Additions to the validate the model, two participants original Enroth-Cugell and Robson equation performed a series of psychophysical have been successful in modeling a two- matching tasks involving simultaneous color dimensional array of different-sized receptive contrast stimuli. The model was presented cells. However, this model could be greatly with an identical set of stimuli. The results enhanced if it were able to respond to the obtained by the behavioral testing were highly chromatic characteristics of a stimulus. In correlated with those produced by the model this study, the existing model was extended to indicating that the color-opponent processing include chromatic analysis. Using responsible for simultaneous color contrast Mathematica, the spectrally opponent nature begin at the level of the ganglionic receptive of the receptive field and the trichromatic fields. features of the cone pigment systems were added to the model via a filter placed before Key Words: Vision; Retina; Receptive Fields; the existing equation. To validate this color Computer Modeling; Simultaneous Contrast Background Color is an integral feature of how human beings yellowish tint while the gray box in the yellow perceive the surrounding world. We describe field appears blue-gray. The original gray hue has objects as if color were an integral feature of that not changed, but our perception of the color has object. However, color perception depends been effected. The hue shift caused by the greatly upon the structure and function of the interaction between two colors is known as visual system. The way in which the visual simultaneous color contrast. Several researchers system operates can cause the same object to have postulated about the possible physiological appear to have more than one color in different mechanisms that cause simultaneous color circumstances and surroundings. For an example contrast. Jameson and Hurvich (1964) suggested of the mutable nature of color look at Figure 1. In simultaneous color contrast occurs because of the this illustration, there are two complimentary inhibitory effects between adjacent neurons. To color fields with an identical gray square in the continue with the previous simultaneous color center of each. By examining the figure, one can contrast example, Jameson and Hurvich proposed see that the gray box in the blue field takes on a that retinal neurons which are part of a blue Pages 38 to 50 Impulse: The Premier Journal for Undergraduate Publications in the Neurosciences. June 2004, 1 (1): 1-58 receptive field research was conducted in cats and frogs, center-surround receptive fields have since been found in the primate visual system (Hubel & Wiesel, 1960; DeValois et al, 1958). Receptive fields act as funneling system within the retina. There are over 125 million receptor cells and only 1 million ganglion cells in the retina. Thus, receptive fields must funnel the information from many receptor cells into a single ganglion cell. Yet, it is important to note that a single receptor is Figure 1: Simultaneous color contrast example. able to send outputs to multiple ganglion cells due to an intervening layers of intermediate cells . This overlapping arrangement in ganglionic response system are highly activated by the large receptive fields causes inhibitory effects known as blue field surrounding the gray box. lateral inhibition. Lateral inhibition was first Consequently, these activated neurons will inhibit described by Hartline and Ratliff (1957) using the the blue response in the adjacent retinal neurons compound eye of the Limulus as a model. Lateral which react to the gray square. The inhibition of a inhibition is defined as the process of adjacent color offsets the typical balance that exists sensory units inhibiting one another. The process between that hue and its compliment. The of lateral inhibition compiles information from compliment of blue is yellow, and the adjoining cells and thereby heightens any existing aforementioned blue inhibition causes the yellow differences within the stimulus pattern. Just like compliment to be integrated into the gray the ommatidia of the Limulus, center-surround response. Jameson and Hurvich used the term receptive fields are sites of lateral inhibition in the “neuron” when describing the location of the primate visual system. The oppositional inhibitory actions responsible for simultaneous organization of the center and surround portions color contrast. Neuron is broad, especially when of the receptive field generates the lateral referring to highly specialized structures like the inhibition. The complete stimulation of the center eye and the retina. Consequently, an cancels out total stimulation of surround. understanding of more accurate and descriptive However, different stimulation patterns across the terminology is required before the discussion of receptive field will yield different ganglionic simultaneous color contrast and color opponency firing rates. Lateral inhibition within receptive can proceed. In 1953, Kuffler and Barlow independently described the structure of what came to be known as a receptive field. By inserting microelectrodes into individual ganglion + cells, they found that the firing rate of some neurons increased when exposed to a concentrated + + light stimulus while the firing rates of other neurons decreased. Furthermore, these excitatory _ _ and inhibitory inputs are arranged in a very + + particular way, a center-surround organization _ _ (Figure 2). The example shows an off-center, on- surround arrangement; this basically means that if light falls on the surround the firing rate of the + + neuron would increase and if light hits only the center region the firing rate would decrease. The + opponency created by the center-surround arrangement became a key feature in many later experiments and discoveries. Though the initial Figure 2: An off-center, on-surround receptive field. Pages 38 to 50 Model of Retina for Form and Color; Blythe & Krantz fields accounts for a number of perceptual phenomena like simultaneous brightness contrast B+ (Figure 3). Simultaneous brightness contrast B+ B+ occurs because of inhibitory interactions between adjacent receptive fields. The gray square surrounded by black will appear lighter than the Y- Y- identical gray square on the white background. B+ B+ The strong excitation caused by the white Y- Y- surround will yield greater levels of lateral inhibition in the gray box, and as a result the gray area appears darker than it truly is. Kuffler and B+ B+ Barlow’s work with receptive fields only utilized achromatic stimuli, but their discoveries did B+ stimulate other researchers to experiment with diverse types of stimuli and single-cell recording techniques. Three years after Kuffler and Figure 4: Color-opponent receptive field organization. Barlow’s landmark discovery, Svaetichin (1956) published findings from an experiment in which paired, red-green and blue-yellow. Within a given different wavelengths of light were found to cause pair, it was hypothesized that the primaries would varied response patterns in the retinal bipolar cells act in opposition to one another. For example if of goldfish. Svaetichin found response patterns the red primary was fully stimulated, green which were very similar to the center-surround primary would be totally inhibited. The color- distribution noted by Kuffler and Barlow (Figure opponent theory is also supported by perceptual 4). Color-opponent receptive fields, as they came phenomenon like the color aftereffects. If a man to be known, operate through the paired- stares at a red wall for a few minutes and then opposition of a color and its compliment. looks at a bare wall, he will perceive a green tint Spectrally-opponent receptive fields can have a on the bare wall. This green coloring appears myriad of color combinations: red on-green off, because staring at the red wall fatigued the red red off-green on, blue on-yellow off, and blue off- channels in the man’s eye. When the man looked yellow on. Receptive fields with color away from the red wall, his red channels ceased to capabilities have also been found in the visual fire, and the opponent green channels were systems of primates (DeValois, Smith, Kitai & inversely stimulated. This color opponency Karoly, 1958; DeValois, 1960). The discovery of processing is a salient factor in the simultaneous the color-opponent receptive field gave color contrast phenomenon, and it seems logical physiological support to the color-opponent to conclude that the color-opponent receptive theory of vision. Proponents of color-opponent fields of the retinal ganglia may be the sites where theory