Floyd Ratliff

Spatial and Temporal Aspects of Retinal Inhibitory Interaction

The inhibitory interaction among neural elements in the compound eye of Limulus was investigated by recording impulses from two or more optic nerve fibers simultaneously. The inhibitory influences are exerted mutually and recurrently, with an appreciable time delay, over a network of interconnections among the interacting elements.Under steady conditions of retinal illumination the activity of any group of interacting elements may be described by a set of simultaneous equations, one equation for each element. In each equation the activity of the particular element represented is expressed as the resultant of the excitatory stimulus to it and the opposing inhibitory influences exerted on it by all the others. By also taking account of the time required for an inhibitory effect exerted by one element to act upon another, this quantitative description may be extended to include transient phenomena associated with changes in the pattern of retinal illumination.The influences exerted over the inhibitory network give rise to maxima and minima in the optic nerve responses to spatial patterns of illumination, and to fluctuations in the responses to temporal patterns. The spatial and temporal properties of the responses of the population of interacting elements are analogous to a number of familiar phenomena in human vision and may offer an explanation for them. These properties also lend support to the view that inhibition may play a role in the generation of the transient “on” and “off” responses observed in a wide variety of visual systems.

A two-dimensional computer-controlled visual stimulator

A computer-controlled instrument that creates complex two-dimensional patterns on a CRT monitor is described. These patterns are used to elicit visual evoked responses. Patterns are produced on a raster that is rotatable about its center. It is possible to assign to arbitrary regions in the raster any of four independent one-dimensional spatial-temporal functions. For each spatial-temporal function, the experimenter can select an arbitrary spatial profile, the spatial frequency of the profile, the starting phase of the profile, the temporal function, and the depth of modulation.

Intermodulation components of the visual evoked potential: Responses to lateral and superimposed stimuli

Nonlinear interactions in the human visual system were studied using visual evoked potentials (VEPs). In one experiment (superimposed condition), all segments of a dartboard pattern were contrast reversed in time by a sum of two sinusoidal signals. In a second experiment (lateral condition), segments in some regions of the dartboard pattern were contrast reversed by a single sinusoid of one frequency, while segments in other (contiguous) regions of the pattern were contrast reversed by a single sinusoid of another frequency. An identical set of ten frequency pairs was used in each experiment. The frequency pairs were chosen such that the difference between frequencies in each pair was 2 Hz. Amplitudes and phases of the sum and difference frequency components of the VEP (intermodulation terms) were retrieved by Fourier analysis and served as measures of nonlinear interactions. The use of input pairs with a fixed separation in frequency enabled the estimation of the temporal characteristics of the visual pathways prior to a second linear stage. The use of superimposed and lateral conditions revealed antagonistic contributions to the VEP, possibly reflecting direct-through excitatory and lateral inhibitory pathways, respectively.

Inhibitory Interaction in the Retina of Limulus

The interplay of excitation and inhibition lies at the foundation of nervous integrative function. Modern neurophysiology builds on Sherrington’s analysis of motor function, extending his concepts to all the sensory systems and to the infinite complexity of the higher nervous centers (cf. Granit, 1966). Antagonistic processes in vision recall Hering; the role of inhibition in vision was clearly recognized by Mach. Sherrington (1897) himself ventured into this field, but it was Granit’s work that played an essential role in introducing Sherringtonian concepts in the study of retinal function. “The retina is a nervous center” writes Granit, quoting Cajal, and this he proceeds to confirm, exhibiting the interplay of excitation and inhibition in the retinal action potential and in the unitary discharges of retinal ganglion cells.

Fourier analysis of dynamics of excitation and inhibition in the eye of Limulus: amplitude, phase and distance.

Abstract Three basic processes—excitation, self-inhibition and lateral inhibition govern the dynamics of the neural network in the lateral eye of Limulus . Experiments show that all lateral inhibition may be represented by a single transfer function scaled by the summed lateral inhibitory coefficients. Discharges of impulses from three units were recorded simultaneously. Results: 1. (1) Variation in amplitude of excitation produces proportional variation in amplitude of lateral inhibition on a neighboring unit at a fixed distance but no phase shift. 2. (2) The amplitude of lateral inhibition varies with distance to the units affected, but there is no phase shift.

Why Mach bands are not seen at the edges of a step.

UNLABELLED Mach bands are seen at the two ends of a ramp in luminance from one uniform level to another. Narrow, sharp-edged stimuli centered on the ramp attenuate both Mach bands simultaneously. CONCLUSION Mach bands are not seen at the edges of an abrupt step change in luminance because the sharp edges actively suppress them.

Equivalence classes of visual stimuli

Physically different visual stimuli may be viSI.taily indistinguishable. Well-known examples of such equivalence are the Craik-O’Brien-Comsweet effects and related phenomena (Craik, 1940,1966; O’Brien, 1958; Cornsweet, 19702. in this note we formalize some old ideas on stimulus equivalence (some explicit in the earlier work, some implicit) and express them in terms of equivalence classes. We show that the concept of null stimuli is basic to a linear formulation and we demonstrate the dependence of one equivalence class on the relative strengths of excitation and inhibition in a model neural network.

SOME NEW METHODS FOR THE ANALYSIS OF LATERAL INTERACTIONS THAT INFLUENCE THE VISUAL EVOKED POTENTIAL

The use of patterned stimuli that vary periodically in either space or time, or both, has a very long history in vision research.’ Applications in the study of visual evoked potentials, however, are relatively The rationale behind the use of such stimuli is that analysis of the responses to the periodicity of the pattern can reveal significant information about the form and function of underlying mechanisms-in particular, about the important space constants and time constants of the system. This approach is based on sound physical and physiological principles concerning the transfer of information through complex systems, and well-established mathematical methods of systems analysis can be a ~ p l i e d . ~ Commonly used one-dimensional patterns such as periodic bar gratings or sinusoidal gratings are relatively easy to generate and to display with modern electronic equipment. Waveform generators can be bought “off the shelf” and by using them to control the raster of an oscilloscope one can display a wide variety of simple one-dimensional spatial grating patterns. The technical problems rapidly become more complex, however, as more variables such as contrast reversal, drift, and rotation of the patterns are introduced. The generation and control of two-dimensional patterns, which can be modulated in both space and time, are even more complex and approach the limits of our present affordable technology. Nevertheless, the problem must be faced. Indeed, the development of methods for the generation and control of complex two-dimensional stimulus patterns is essential for the advancement of vision research. The visual system contains a network of heterogeneous parallel channels that interact with one another in complex ways. To reach a full understanding of these interactions requires methods of stimulus control capable of eliciting the interactions and methods of data analysis capable of treating them. This paper describes our recent efforts to develop methods of stimulus control and data analysis that have these capabilities. First we describe new methods of generating and displaying a wide variety of two-dimensional patterns that can be varied in both space and time. We then discuss new applications of some of these patterns in the analysis of the influence of lateral interactions on the visual evoked potential.

INHIBITORY INTERACTION IN THE RETINA: TECHNIQUES OF EXPERIMENTAL AND THEORETICAL ANALYSIS*

This paper describes the use of a small general purpose digital computer (Control Data Corporation 160-A) as an aid to experimental and theoretical studies of nervous interactions in visual systems. The experimental work has been primarily concerned with the inhibitory interaction in the lateral eye of the horseshoe crab, Limulus polyphemus. The theoretical work has been concerned with developing models of the spatial and dynamical properties of the interactions in this eye, and with the application of these models to the study of the vertebrate retina and to the explanation of more complex visual phenomena encountered in human psychophysib. The earlier experimental work on steady state properties of the eye of Limulus was amenable to relatively simple techniques of data collection such as gated counters and photography. For reviews of this work see Hartline, Ratliff, and Miller (1961) and Ratliff (1961). The work is now being extended to the dynamical properties of the eye. For a review of some of the preliminary observations on dynamics see Ratliff, Hartline, and Miller (1963). In the case of dynamics, the continuous, impulse-by-impulse, collection of very large volumes of data is required. I t is also necessary to have immediate information on the course of the experiment so that adjustments can be made in procedures. The computer is therefore employed at all levels of the study; namely, data collection, data storage, data processing, model simulation, and comparison of experimental and theoretical results. Complete descriptions of the experimental procedure and results of previous studies are readily available in the references cited above, and therefore we will limit ourselves to a short summary as a background to the discussion of the computer techniques. The anatomy of the Limulus lateral eye has been extensively studied by Miller (1957, 1958). FIGURE 1 is a composite three-dimensional light micrograph of a portion of the eye. The upper horizontal plane contains the facets (F) of the corneal surface (c). Light enters more or less perpendicularly to this plane. The upper vertical plane is a view of the longitudinal aspect of the functional units or ommatidia. Each unit has a crystalline cone lens (cc) which focuses an image onto the rhabdom ( r ) . The rhabdom is formed from the convergence of the microvillous borders of a dozen or more retinular cells ( R ) . These retinular cells are radially arranged around the distal process (D. P.)

Haldan Keffer Hartline

By the methods of comparative physiology, or of experimental biology, by the choice of a suitable organ, tissue or process, in some animal far removed in evolution, we may often throw light upon some function or process in the higher animals, or in man.