Simulations of X and Y retinal ganglion cell behavior with a nonlinear push-pull model of spatiotemporal retinal processing

A single retinal circuit model for multiple computations

Vision is dependent on extracting intricate features of the visual information from the outside world, and complex visual computations begin to take place as soon as at the retinal level. In multiple studies on salamander retinas, the responses of a subtype of retinal ganglion cells, i.e., fast/biphasic-OFF ganglion cells, have been shown to be able to realize multiple functions, such as the segregation of a moving object from its background, motion anticipation, and rapid encoding of the spatial features of a new visual scene. For each of these visual functions, modeling approaches using extended linear-nonlinear cascade models suggest specific preceding retinal circuitries merging onto fast/biphasic-OFF ganglion cells. However, whether multiple visual functions can be accommodated together in a certain retinal circuitry and how specific mechanisms for each visual function interact with each other have not been investigated. Here, we propose a physiologically consistent, detailed computational model of the retinal circuit based on the spatiotemporal dynamics and connections of each class of retinal neurons to implement object motion sensitivity, motion anticipation, and rapid coding in the same circuit. Simulations suggest that multiple computations can be accommodated together, thereby implying that the fast/biphasic-OFF ganglion cell has potential to output a train of spikes carrying multiple pieces of information on distinct features of the visual stimuli.

Six different roles for crossover inhibition in the retina: correcting the nonlinearities of synaptic transmission

Early retinal studies categorized ganglion cell behavior as either linear or nonlinear and rectifying as represented by the familiar X- and Y-type ganglion cells in cat. Nonlinear behavior is in large part a consequence of the rectifying nonlinearities inherent in synaptic transmission. These nonlinear signals underlie many special functions in retinal processing, including motion detection, motion in motion, and local edge detection. But linear behavior is also required for some visual processing tasks. For these tasks, the inherently nonlinear signals are "linearized" by "crossover inhibition." Linearization utilizes a circuitry whereby nonlinear ON inhibition adds with nonlinear OFF excitation or ON excitation adds with OFF inhibition to generate a more linear postsynaptic voltage response. Crossover inhibition has now been measured in most bipolar, amacrine, and ganglion cells. Functionally crossover inhibition enhances edge detection, allows ganglion cells to recognize luminance-neutral patterns with their receptive fields, permits ganglion cells to distinguish contrast from luminance, and maintains a more constant conductance during the light response. In some cases, crossover extends the operating range of cone-driven OFF ganglion cells into the scotopic levels. Crossover inhibition is also found in neurons of the lateral geniculate nucleus and V1.

A retinal circuit model accounting for wide-field amacrine cells

In previous experimental studies on the visual processing in vertebrates, higher-order visual functions such as the object segregation from background were found even in the retinal stage. Previously, the "linear-nonlinear" (LN) cascade models have been applied to the retinal circuit, and succeeded to describe the input-output dynamics for certain parts of the circuit, e.g., the receptive field of the outer retinal neurons. And recently, some abstract models composed of LN cascades as the circuit elements could explain the higher-order retinal functions. However, in such a model, each class of retinal neurons is mostly omitted and thus, how those neurons play roles in the visual computations cannot be explored. Here, we present a spatio-temporal computational model of the vertebrate retina, based on the response function for each class of retinal neurons and on the anatomical inter-cellular connections. This model was capable of not only reproducing the spatio-temporal filtering properties of the outer retinal neurons, but also realizing the object segregation mechanism in the inner retinal circuit involving the "wide-field" amacrine cells. Moreover, the first-order Wiener kernels calculated for the neurons in our model showed a reasonable fit to the kernels previously measured in the real retinal neuron in situ.

Functional mechanisms shaping lateral geniculate responses to artificial and natural stimuli

Functional models of the early visual system should predict responses not only to simple artificial stimuli but also to sequences of complex natural scenes. An ideal testbed for such models is the lateral geniculate nucleus (LGN). Mechanisms shaping LGN responses include the linear receptive field and two fast adaptation processes, sensitive to luminance and contrast. We propose a compact functional model for these mechanisms that operates on sequences of arbitrary images. With the same parameters that fit the firing rate responses to simple stimuli, it predicts the bulk of the firing rate responses to complex stimuli, including natural scenes. Further improvements could result by adding a spiking mechanism, possibly one capable of bursts, but not by adding mechanisms of slow adaptation. We conclude that up to the LGN the responses to natural scenes can be largely explained through insights gained with simple artificial stimuli.

Basic difference between brain and computer: integration of asynchronous processes implemented as hardware model of the retina

There exists a common view that the brain acts like a Turing machine: The machine reads information from an infinite tape (sensory data) and, on the basis of the machine's state and information from the tape, an action (decision) is made. The main problem with this model lies in how to synchronize a large number of tapes in an adaptive way so that the machine is able to accomplish tasks such as object classification. We propose that such mechanisms exist already in the eye. A popular view is that the retina, typically associated with high gain and adaptation for light processing, is actually performing local preprocessing by means of its center-surround receptive field. We would like to show another property of the retina: The ability to integrate many independent processes. We believe that this integration is implemented by synchronization of neuronal oscillations. In this paper, we present a model of the retina consisting of a series of coupled oscillators which can synchronize on several scales. Synchronization is an analog process which is converted into a digital spike train in the output of the retina. We have developed a hardware implementation of this model, which enables us to carry out rapid simulation of multineuron oscillatory dynamics. We show that the properties of the spike trains in our model are similar to those found in vivo in the cat retina.

The temporal structure of transient ON/OFF ganglion cell responses and its relation to intra-retinal processing

A subpopulation of transient ON/OFF ganglion cells in the turtle retina transmits changes in stimulus intensity as series of distinct spike events. The temporal structure of these event sequences depends systematically on the stimulus and thus carries information about the preceding intensity change. To study the spike events' intra-retinal origins, we performed extracellular ganglion cell recordings and simultaneous intracellular recordings from horizontal and amacrine cells. Based on these data, we developed a computational retina model, reproducing spike event patterns with realistic intensity dependence under various experimental conditions. The model's main features are negative feedback from sustained amacrine onto bipolar cells, and a two-step cascade of ganglion cell suppression via a slow and a fast transient amacrine cell. Pharmacologically blocking glycinergic transmission results in disappearance of the spike event sequence, an effect predicted by the model if a single connection, namely suppression of the fast by the slow transient amacrine cell, is weakened. We suggest that the slow transient amacrine cell is glycinergic, whereas the other types release GABA. Thus, the interplay of amacrine cell mediated inhibition is likely to induce distinct temporal structure in ganglion cell responses, forming the basis for a temporal code.

Learning the Gestalt Rule of Collinearity from Object Motion

The Gestalt principle of collinearity (and curvilinearity) is widely regarded as being mediated by the long-range connection structure in primary visual cortex. We review the neurophysiological and psychophysical literature to argue that these connections are developed from visual experience after birth, relying on coherent object motion. We then present a neural network model that learns these connections in an unsupervised Hebbian fashion with input from real camera sequences. The model uses spatiotemporal retinal filtering, which is very sensitive to changes in the visual input. We show that it is crucial for successful learning to use the correlation of the transient responses instead of the sustained ones. As a consequence, learning works best with video sequences of moving objects. The model addresses a special case of the fundamental question of what represents the necessary a priori knowledge the brain is equipped with at birth so that the self-organized process of structuring by experience can be successful.

The influence of different retinal subcircuits on the nonlinearity of ganglion cell behavior

Y-type retinal ganglion cells show a pronounced, nonlinear, frequency-doubling behavior in response to modulated sinewave gratings. This is not observed in X-type cells. The source of this spatial nonlinear summation is still under debate. We have designed a realistic biophysical model of the cat retina to test the influence of different retinal cell classes and subcircuits on the linearity of ganglion cell responses. The intraretinal connectivity consists of the fundamental feedforward pathway via bipolar cells, lateral horizontal cell connectivity, and two amacrine circuits. The wiring diagram of X- and Y-cells is identical apart from two aspects: (1) Y-cells have a wider receptive field and (2) they receive input from a nested amacrine circuit consisting of narrow- and wide-field amacrine cells. The model was tested with contrast-reversed gratings. First and second harmonic response components were determined to estimate the degree of nonlinearity. By means of circuit dissection, we found that a high degree of the Y-cell nonlinear behavior arises from the spatial integration of temporal photoreceptor nonlinearities. Furthermore, we found a weaker and less uniform influence of the nested amacrine circuit. Different sources of nonlinearities interact in a multiplicative manner, and the influence of the amacrine circuit is approximately 25% weaker than that of the photoreceptor. The model predicts that significant nonlinearities occur already at the level of horizontal cell responses. Pharmacological inactivation of the amacrine circuit is expected to exert a milder effect in reducing ganglion cell nonlinearity.

Neural model of first-order and second-order motion perception and magnocellular dynamics

A neural model of motion perception simulates psychophysical data concerning first-order and second-order motion stimuli, including the reversal of perceived motion direction with distance from the stimulus (gamma display), and data about directional judgments as a function of relative spatial phase or spatial and temporal frequency. Many other second-order motion percepts that have ascribed to a second non-Fourier processing stream can also be explained in the model by interactions between ON and OFF cells within a single, neurobiologically interpreted magnocellular processing stream. Yet other percepts may be traced to interactions between form and motion processing streams, rather than to processing within multiple motion processing streams. The model hereby explains why monkeys with lesions of the parvocellular layers, but not of the magnocellular layers, of the lateral geniculate nucleus (LGN) are capable of detecting the correct direction of second-order motion, why most cells in area MT are sensitive to both first-order and second-order motion, and why after 2-amino-4-phosphonobutyrate injection selectively blocks retinal ON bipolar cells, cortical cells are sensitive only to the motion of a moving bright bar's trailing edge. Magnocellular LGN cells show relatively transient responses, whereas parvocellular LGN cells show relatively sustained responses. Correspondingly, the model bases its directional estimates on the outputs of model ON and OFF transient cells that are organized in opponent circuits wherein antagonistic rebounds occur in response to stimulus offset. Center-surround interactions convert these ON and OFF outputs into responses of lightening and darkening cells that are sensitive both to direct inputs and to rebound responses in their receptive field centers and surrounds. The total pattern of activity increments and decrements is used by subsequent processing stages (spatially short-range filters, competitive interactions, spatially long-range filters, and directional grouping cells) to determine the perceived direction of motion.

Lower-level visual processing and models of light adaptation

Before there was a formal discipline of psychology, there were attempts to understand the relationship between visual perception and retinal physiology. Today, there is still uncertainty about the extent to which even very basic behavioral data (called here candidates for lower-level processing) can be predicted based upon retinal processing. Here, a general framework is proposed for developing models of lower-level processing. It is argued that our knowledge of ganglion cell function and retinal mechanisms has advanced to the point where a model of lower-level processing should include a testable model of ganglion cell function. This model of ganglion cell function, combined with minimal assumptions about the role of the visual cortex, forms a model of lower-level processing. Basic behavioral and physiological descriptions of light adaptation are reviewed, and recent attempts to model lower-level processing are discussed.

Self-organization of binocular disparity tuning by reciprocal corticogeniculate interactions

This article develops a neural model of how sharp disparity tuning can arise through experience-dependent development of cortical complex cells. This learning process clarifies how complex cells can binocularly match left and right eye image features with the same contrast polarity, yet also pool signals with opposite contrast polarities. Antagonistic rebounds between LGN ON and OFF cells and cortical simple cells sensitive to opposite contrast polarities enable anticorrelated simple cells to learn to activate a shared set of complex cells. Feedback from binocularly tuned cortical cells to monocular LGN cells is proposed to carry out a matching process that dynamically stabilizes the learning process. This feedback represents a type of matching process that is elaborated at higher visual processing areas into a volitionally controllable type of attention. We show stable learning when both of these properties hold. Learning adjusts the initially coarsely tuned disparity preference to match the disparities present in the environment, and the tuning width decreases to yield high disparity selectivity, which enables the model to quickly detect image disparities. Learning is impaired in the absence of either antagonistic rebounds or corticogeniculate feedback. The model also helps to explain psychophysical and neurobiological data about adult 3-D vision.

On the significance of temporally structured activity in the dorsal lateral geniculate nucleus (LGN)

Higher organisms perceive information about external or internal physical or chemical stimuli with specialized sensors that encode characteristics of that stimulus by a train of action potentials. Usually, the location and modality of the stimulus is represented by the location and specificity of the receptor and the intensity of the stimulus and its temporal modulation is thought to be encoded by the instantaneous firing rate. Recent studies have shown that, primarily in cortical structures, special features of a stimulus also are represented in the temporal pattern of spike activity. Typical attributes of this time structure are oscillatory patterns of activity and synchronous discharges in spatially distributed neurons that respond to inputs evoked by a coherent object. The origin and functional significance of this kind of activity is less clear. Cortical, subcortical and even very peripheral sources seem to be involved. Most of the relevant studies were devoted to the mammalian visual system and cortical findings on temporally structured activity were reviewed recently (Eckhorn, 1994, Progr. Brain Res., Vol. 102, pp. 405-426; Singer and Gray, 1995, Annu. Rev. Neurosci., Vol. 18, pp. 555-586). Therefore, this article is designed to give an overview, especially of those studies concerned with the temporal structure of visual activity in subcortical centers of the primary visual pathway, which are the retina and the dorsal lateral geniculate nucleus (LGN). We discuss the mechanisms that possibly contribute to the generation and modulation of the subcortical activity time structure and we try to relate to each other the subcortical and cortical patterns of sensory activity.

A neural model of foveal light adaptation and afterimage formation

Psychophysical research has documented the existence of three processes in light adaptation: a fast subtractive process, a divisive process that is fast at light onset and slower at light offset, and a very slow subtractive process (Hayhoe et al., 1987). In the neural model developed here, the fast subtractive process is identified with horizontal cell feedback onto cones and the divisive process with amacrine cell feedback onto bipolar cells. The very slow subtractive process is identified with the modulatory feedback circuit from amacrines via interplexiform cells to horizontal cells. A nonlinear dynamical model is developed incorporating these aspects of retinal circuitry along with both ON- and OFF-center M and P pathways. This model is shown to account for many aspects of foveal light adaptation, including negative afterimage formation, and to explain a number of the physiological differences between M and P ganglion cells, including their differing contrast-response functions.

Linear and non-linear components in the centre-surround response of X- and Y-cells in the cat lateral geniculate nucleus

Thalamocortical projection cells of cat dorsal lateral geniculate nucleus (dLGN) have been described to exhibit different types of non-linear integration of spatial contrast in addition to the linear integration inside their classical receptive field (CRF). We analysed whether a single mechanism might generate the two harmonic distortions of a linear response elicited inside the CRF and the shift effect elicited from regions outside the CRF. Therefore, both non-linear response types were investigated with identical stimulus conditions in the same cell. A quantitative analysis revealed that both response types can be elicited in nearly all Y-cells and in at least 50% of the X-cells. With blockade of GABA(A) inhibition by bicuculline methiodide (BICU) the number of X-cells with shift effect (SE) and second harmonics (2H) increased to more than 80%. Both, SE and 2H exhibited significantly correlated variations in their response-amplitude and -latency and in the frequency of their occurrence with changes in stimulus parameters (contrast, spatial frequency, area) and during BICU application. We assume that both non-linear contrast responses, the SE and the 2H might depend on the same (most probably retinal) mechanisms. We further suggest that the principal organisation of X- and Y-cell receptive fields might be very similar and that the differing spatial contrast responses may result from the different spatial resolution of their CRF subunits.

Gain control and hyperpolarization level in cat horizontal cells as a function of light and dark adaptation

First a model is presented that accurately summarizes the dynamic properties of cat horizontal (H-) cells under photopic conditions as measured in our previous work. The model predicts that asymmetries in response to dark as compared to light flashes are flash-duration dependent. This somewhat surprising prediction is tested and confirmed in intracellular recordings from the optically intact in vivo eye of the cat (Experiment 1). The model implies that the gain of H-cells should be related rather directly to the sustained (baseline) membrane potential. We performed three additional experiments to test this idea. Experiment 2 concerns response vs intensity (R-I-) curves for various flash-diameters and background-sizes with background luminance varying over a 4 log unit range. Results support the assumption of a rather strict coupling between flash sensitivity (gain) and the sustained level of hyperpolarization. In Experiment 3 we investigate this relation for both dark and light flashes given on each of four background light levels. The results suggest that there are fixed minimum and maximum hyperpolarization levels, and that the baseline hyperpolarization for a given illumination thus also sets the available range for dark and light flash-responses. The question then arises whether, or how this changes during dark adaptation, when the rod contribution to H-cell responses gradually increases. The fourth experiment therefore studies the relationship between gain and hyperpolarization level during prolonged dark-adaptation. The results show that the rod contribution increases the polarization range of H-cells, but that the gain and polarization level nevertheless remain directly coupled. H-cell models relying on a close coupling between polarization level and gain thus remain attractive options.

Spatiotemporal adaptation model for retinal ganglion cells

An adaptation model for the level of the ganglion cell in the retina is presented. The model assumes separate adaptation mechanisms for each of the receptive field (RF) regions, i.e., before edge detection. According to the model, the decay in the response time course of each RF region reflects its adaptation process. A mathematical description of adaptation that includes its temporal properties is developed through the change in the semisaturation constant theta in the Naka-Rushton equation. The model and its simulations show a good agreement with a wide variety of physiological studies.