Spatial asymmetries in cat retinal ganglion cell responses

. Enroth-Cugell and Robson (1966) first proposed a classification of retinal ganglion cells into X cells, which exhibit approximate linear spatial summation and largely sustained responses, and Y cells, which exhibit nonlinearities and transient responses. Gaudiano (1992a, 1992b, 1994) has suggested that the dominant characteristics of both X and Y cells can be simulated with a single model simply by changing receptive field profiles to match those of the anatomical counterparts of X and Y cells. He also proposed that a significant component of the spatial nonlinearities observed in Y (and sometimes X) cells can result from photoreceptor nonlinearities coupled with push-pull bipolar connections. Specifically, an asymmetry was predicted in the ganglion cell response to rectangular gratings presented at different locations in the receptive field under two conditions: introduction/withdrawal (on-off) or contrast reversal. When measuring the response to these patterns as a function of spatial phase, the standard difference-of-Gaussians model predicts symmetrical responses about the receptive field center, while the push-pull model predicts slight but significant asymmetry in the on-off case only. To test this hypothesis, we have recorded ganglion cell responses from the optic tract fibers of anesthetized cat. The mean and standard deviations of responses to on-off and contrast-reversed patterns were compared. We found that all but one of the cells that yielded statistically significant data confirmed the hypothesis. These results largely support the theoretical prediction. Received: 21 March 1997 / Accepted in revised form: 6 May 1998     

视网膜神经节细胞感受野的一种新模型 I.含大周边的感受野模型

感受野是视觉系统信息处理的基本结构和功能单元。Ｘ、Ｙ细胞是两类主要的视网膜神经节细胞。生理实验发现,在经典感受野之外还存在一个大范围的在周边去抑制区。文中采用周边去抑制区对经典外周的去抑制非线性使用方式,建立一个二维的与实验结果联系紧密的Ｘ、Ｙ细胞统一的复合感受野模型。该模型不仅能模拟Ｘ细胞的ｎｕｌｌ－ｔｅｓｔ反应和Ｙ细胞的ｏｎ－ｏｆｆ反应,还模拟了Ｙ细胞在低空频刺激时的信频反应、圆面积空间的倍频     

A linear model for symmetric receptive fields: implications for classification tests with flashed and moving images

The purpose of this study was to explore the effects of spatial and temporal properties on the expected responses of visual neurons that have linear receptive fields (RFs), particularly those having a mirror symmetric distribution of spatial subregions. Receptive fields that are symmetric in at least one spatial dimension occur in neurons of the retina, the lateral geniculate nucleus (LGN), and the visual cortex of mammals. Responses to flashing bars, moving bars, and moving edges were studied for different configurations of an analog RF model in which spatial and temporal aspects were varied independently. Responses of the model at intermediate stimulus speeds were found to agree with responses in the literature for X and Y units of the LGN and often for simple units of the visual cortex. In particular, having separated regions of response to light and dark edges, an identifying property of simple cells, was found to be a linear consequence of RF regions responding inversely to stimuli of opposite polarity. Model differences from responses of cortical complex units show that a linear model cannot mimic their responses, and imply that complex units employ major nonlinearities in coding image polarity (light vs dark), which signifies a nonlinearity in coding intensity. Because sudden flux changes inherent in flashing bars test mainly temporal RF properties, and slowly moving edges test mainly spatial properties, these two tests form a useful minimal set with which to describe and classify RFs. The usefulness of this set derives both from its sensitivity to spatial and temporal variables, and from the correlation between the linearity of a cell's processing of stimulus intensity and its RF classification.     

Receptive field mechanisms of cat X and Y retinal ganglion cells

We investigated receptive field properties of cat retinal ganglion cells with visual stimuli which were sinusoidal spatial gratings amplitude modulated in time by a sum of sinusoids. Neural responses were analyzed into the Fourier components at the input frequencies and the components at sum and difference frequencies. The first-order frequency response of X cells had a marked spatial phase and spatial frequency dependence which could be explained in terms of linear interactions between center and surround mechanisms in the receptive field. The second-order frequency response of X cells was much smaller than the first-order frequency response at all spatial frequencies. The spatial phase and spatial frequency dependence of the first-order frequency response in Y cells in some ways resembled that of X cells. However, the Y first-order response declined to zero at a much lower spatial frequency than in X cells. Furthermore, the second-order frequency response was larger in Y cells; the second-order frequency components became the dominant part of the response for patterns of high spatial frequency. This implies that the receptive field center and surround mechanisms are physiologically quite different in Y cells from those in X cells, and that the Y cells also receive excitatory drive from an additional nonlinear receptive field mechanism.     

Spatial properties of goldfish ganglion cells

We systematically classified goldfish ganglion cells according to their spatial summation properties using the same techniques and criteria used in cat and monkey research. Results show that goldfish ganglion cells can be classified as X-, Y-, or W-like based on their responses to contrast-reversal gratings. Like cat X cells, goldfish X-like cells display linear spatial summation. Goldfish Y-like cells, like cat Y cells, respond with frequency doubling at all spatial positions when the contrast-reversal grating consists of high spatial frequencies. There is also a third class of neurons, which is neither X- nor Y-like; many of these cells' properties are similar to those of the "not-X" cells found in the eel retina. Spatial filtering characteristics were obtained for each cell by drifting sinusoidal gratings of various spatial frequencies and contrasts across the receptive field of the cell at a constant temporal rate. The spatial tuning curves of the cell depend on the temporal parameters of the stimulus; at high drift rates, the tuning curves lose their low spatial frequency attenuation. To explore this phenomenon, temporal contrast response functions were derived from the cells' responses to a spatially uniform field whose luminance varied sinusoidally in time. These functions were obtained for the center, the surround, and the entire receptive field. The results suggest that differences in the cells' spatial filtering across stimulus drift rate are due to changes in the interaction of the center and surround mechanisms; at low temporal frequencies, the center and surround responses are out-of-phase and mutually antagonistic, but at higher temporal rates their responses are in-phase and their interaction actually enhances the cell's responsiveness.     

Mathematical principles in afferent visual neurons: Differentiation,integration and transient proportionality related to receptive fields and shift-effect

The dual reciprocal and antagonistic organization of B- and D-neurons of the afferent visual system is obtained using differentiation and integration as mathematical equivalents of visual information processing by an impulse frequency code. The spatial and temporal derivatives lead to the transient responses. A constant and a time-dependent term proportional to the luminance distribution describe the sustained response components and the shift-effect of retinal on- and off-center ganglion cells. Receptive field properties of lateral geniculate cells and their antagonistic shift-effect are obtained by passing the retinal output, i.e. the difference between B- and D-neurons' activity, once again through the same operations. However, the factor of proportionality is applied to the retina alone. The surprisingly small difference between retinal and geniculate receptive field properties on the one hand and the dramatic change from a synergistic to an antagonistic shift-effect on the other hand are thereby explained. The theory offers an understanding of a a possible functional significance of the shift-effect as a mechanism of transientrestoration of visual information, which prevents the system from total fading by means of shifts of the retinal image, normally produced by eye movements.     

Extended difference-of-Gaussians model incorporating cortical feedback for relay cells in the lateral geniculate nucleus of cat

A striking feature of the organization of the early visual pathway is the significant feedback from primary visual cortex to cells in the dorsal lateral geniculate nucleus (LGN). Despite numerous experimental and modeling studies, the functional role for this feedback remains elusive. We present a new firing-rate-based model for LGN relay cells in cat, explicitly accounting for thalamocortical loop effects. The established DOG model, here assumed to account for the spatial aspects of the feedforward processing of visual stimuli, is extended to incorporate the influence of thalamocortical loops including a full set of orientation-selective cortical cell populations. Assuming a phase-reversed push-pull arrangement of ON and OFF cortical feedback as seen experimentally, this extended DOG (eDOG) model exhibits linear firing properties despite non-linear firing characteristics of the corticothalamic cells. The spatiotemporal receptive field of the eDOG model has a simple algebraic structure in Fourier space, while the real-space receptive field, as well as responses to visual stimuli, are found by evaluation of an integral. As an example application we use the eDOG model to study effects of cortical feedback on responses to flashing circular spots and patch-grating stimuli and find that the eDOG model can qualitatively account for experimental findings.     

Temporal pattern discrimination within the receptive field of cat retinal ganglion cells

ON-center and OFF-center receptive fields of cat retinal ganglion cells can be divided into two categories: sensitive (type N) and insensitive (type L) to three statistical temporal visual stimuli with different second order statistics but identical first order statistics (Tsukada et al. 1982). The temporal pattern sensitivity of type N response is closely related to the nonlinear stage of Y cells depending on the interaction between center and surround mechanism. The temporal pattern sensitivity of type N responses has a spatial profile within the receptive field; it is highly sensitive in the center region of the receptive field and less sensitive toward the field periphery. The temporal pattern sensitivity in the center region of the receptive field to statistical properties (irregular or regular) of a surrounding flash annulus shows modulation like a switching element: when the surrounding area is stimulated by a more regular flash stimulus with normal distribution of inter-stimulus intervals the system is sensitive (switching on) to the temporal pattern, while a change to an irregular one with an exponential distribution makes it insensitive (switching off) to the temporal pattern.     

The role of cortical feedback in the generation of the temporal receptive field responses of lateral geniculate nucleus neurons: a computational modelling study

The influence of cortical feedback on thalamic visual responses has been a source of much discussion in recent years. In this study we examine the possible role of cortical feedback in shaping the spatiotemporal receptive field (STRF) responses of thalamocortical (TC) cells in the lateral geniculate nucleus (LGN) of the thalamus. A population-based computational model of the thalamocortical network is used to generate a representation of the STRF response of LGN TC cells within the corticothalamic feedback circuit. The cortical feedback is shown to have little influence on the spatial response properties of the STRF organization. However, the model suggests that cortical feedback may play a key role in modifying the experimentally observed biphasic temporal response property of the STRF, that is, the reversal over time of the polarity of ON and OFF responses of the centre and surround of the receptive field, in particular accounting for the experimentally observed mismatch between retinal cells and TC cells in respect of the magnitude of the second (rebound) phase of the temporal response. The model results also show that this mismatch may result from an anti-phase corticothalamic feedback mechanism.     

The peri-saccadic perception of objects and space

Eye movements affect object localization and object recognition. Around saccade onset, briefly flashed stimuli appear compressed towards the saccade target, receptive fields dynamically change position, and the recognition of objects near the saccade target is improved. These effects have been attributed to different mechanisms. We provide a unifying account of peri-saccadic perception explaining all three phenomena by a quantitative computational approach simulating cortical cell responses on the population level. Contrary to the common view of spatial attention as a spotlight, our model suggests that oculomotor feedback alters the receptive field structure in multiple visual areas at an intermediate level of the cortical hierarchy to dynamically recruit cells for processing a relevant part of the visual field. The compression of visual space occurs at the expense of this locally enhanced processing capacity.     

Emergence of spatiotemporal receptive fields and its application to motion detection

A model of motion sensitivity as observed in some cells of area V1 of the visual cortex is proposed. Motion sensitivity is achieved by a combination of different spatiotemporal receptive fields, in particular, spatial and temporal differentiators. The receptive fields emerge if a Hebbian learning rule is applied to the network. Similar to a Linsker model the network has a spatially convergent, linear feedforward structure. Additionally, however, delays omnipresent in the brain are incorporated in the model. The emerging spatiotemporal receptive fields are derived explicitly by extending the approach of MacKay and Miller. The response characteristic of the network is calculated in frequency space and shows that the network can be considered as a spacetime filter for motion in one direction. The emergence of different types of receptive field requires certain structural constraints regarding the spatial and temporal arborisation. These requirements can be derived from the theoretical analysis and might be compared with neuroanatomical data. In this way an explicit link between structure and function of the network is established.     

An information integration model of the primary visual cortex under grating stimulations

During the course of information processing, a visual system extracts characteristic information of the visual image and integrates the spatial and temporal visual information simultaneously. In this study, we investigate the integration effect of neurons in the primary visual cortex (V1 area) under the grating stimulation. First, an information integration model was established based on the receptive field properties of the extracted features of the visual images features, the interaction between neurons and the nonlinear integration of those neurons. Then the neuropsychological experiments were designed both to provide parameters for the model and to verify its effect. The experimental results with factual visual image were largely consistent with the model’s forecast output. This demonstrates that our model can truly reflect the integration effect of the primary visual system when being subjected to grating stimulations with different orientations. Our results indicate the primary visual system integrates the visual information in the following manner: it first extracts visual information through different types of receptive field, and then its neurons interact with each other in a non-linear manner, finally the neurons fire spikes recorded as responses to the visual stimulus.     

Initial processing of visual information within the retina and the LGN

The initial stage of information processing by the visual system reduces the information contained in the continuous image on the retina into a discrete set of responses which are carried from the lateral geniculate nucleus (LGN) to the visual cortex.-1. The optimal sampling of the light intensity distribution in the visual environment is achieved only if each channel in the visual pathways carries undistorted information corresponding to an image element. The visual system approaches as closely as possible the scheme of optimal spatial sampling, retaining the full information on the low spatial frequency content of the object light intensity. The ideal receptive field of a sustained LGN cell is then of the form J ₁ (Kr)/Kr.-2. The experimentally determined receptive fields of sustained LGN cells (and to some extent retinal ganglion cells as well) in cat closely resemble the functional form J ₁ (Kr)/Kr. The centre-surround organization of the receptive fields is therefore understood as a scheme which leads to a maximal information flow through the visual pathways.-3. The optimal sampling scheme cannot be realized by the retina alone, because of restrictions on the size of neural networks. It is therefore constructed in two stages, ending at the LGN level. A recombination of ganglion cell signals into optimal receptive fields is a major role of the LGN.     

Features and functions of nonlinear spatial integration by retinal ganglion cells

Ganglion cells in the vertebrate retina integrate visual information over their receptive fields. They do so by pooling presynaptic excitatory inputs from typically many bipolar cells, which themselves collect inputs from several photoreceptors. In addition, inhibitory interactions mediated by horizontal cells and amacrine cells modulate the structure of the receptive field. In many models, this spatial integration is assumed to occur in a linear fashion. Yet, it has long been known that spatial integration by retinal ganglion cells also incurs nonlinear phenomena. Moreover, several recent examples have shown that nonlinear spatial integration is tightly connected to specific visual functions performed by different types of retinal ganglion cells. This work discusses these advances in understanding the role of nonlinear spatial integration and reviews recent efforts to quantitatively study the nature and mechanisms underlying spatial nonlinearities. These new insights point towards a critical role of nonlinearities within ganglion cell receptive fields for capturing responses of the cells to natural and behaviorally relevant visual stimuli. In the long run, nonlinear phenomena of spatial integration may also prove important for implementing the actual neural code of retinal neurons when designing visual prostheses for the eye.     

The Gaussian derivative model for spatial-temporal vision: I. Cortical model

How do we see the motion of objects as well as their shapes? The Gaussian Derivative (GD) spatial model is extended to time to help answer this question. The GD spatio-temporal model requires only two numbers to describe the complete three-dimensional space-time shapes of individual receptive fields in primate visual cortex. These two numbers are the derivative numbers along the respective spatial and temporal principal axes of a given receptive field. Nine transformation parameters allow for a standard geometric association of these intrinsic axes with the extrinsic environment. The GD spatio-temporal model describes in one framework the following properties of primate simple cell fields: motion properties, number of lobes in space-time, spatial orientation. location, and size. A discrete difference-of-offset-Gaussians (DOOG) model provides a plausible physiological mechanism to form GD-like model fields in both space and time. The GD model hypothesizes that receptive fields at the first stage of processing in the visual cortex approximate 'derivative analyzers' that estimate local spatial and temporal derivatives of the intensity profile in the visual environment. The receptive fields as modeled provide operators that can allow later stages of processing in either a biological or machine vision system to estimate the motion as well as the shapes of objects in the environment.     

Electrical coupling of photoreceptors in retinal network models

The spatial width of photoreceptor receptive fields affects the processing of signals in neural networks of the retina. This effect has been examined using the simple recurrent and non-recurrent network models, where lateral interaction strength was adjusted to approximate a prescribed receptive field profile. The results indicate that the optimal performance of the networks is obtained with photoreceptor receptive fields wider than the ganglion cell separation. It is thus concluded that while electrical coupling of photoreceptors in the retina reduces the intrinsic noise in the system, it also improves the sampling efficiency of the laterally coupled neural network of the retina.     

Asymmetric temporal properties in the receptive field of retinal transient amacrine cells

The speed of signal conduction is a factor determining the temporal properties of individual neurons and neuronal networks. We observed very different conduction velocities within the receptive field of fast-type On-Off transient amacrine cells in carp retina cells, which are tightly coupled to each other via gap junctions. The fastest speeds were found in the dorsal area of the receptive fields, on average five times faster than those detected within the ventral area. The asymmetry was similar in the On- and Off-part of the responses, thus being independent of the pathway, pointing to the existence of a functional mechanism within the recorded cells themselves. Nonetheless, the spatial decay of the graded-voltage photoresponse within the receptive field was found to be symmetrical, with the amplitude center of the receptive field being displaced to the faster side from the minimum-latency location. A sample of the orientation of varicosity-laden polyaxons in neurobiotin-injected cells supported the model, revealing that approximately 75% of these processes were directed dorsally from the origin cells. Based on these results, we modeled the velocity asymmetry and the displacement of amplitude center by adding a contribution of an asymmetric polyaxonal inhibition to the network. Due to the asymmetry in the conduction velocity, the time delay of a light response is proposed to depend on the origin of the photostimulus movement, a potentially important mechanism underlying direction selectivity within the inner retina.     

Perisaccadic Remapping and Rescaling of Visual Responses in Macaque Superior Colliculus

Visual neurons have spatial receptive fields that encode the positions of objects relative to the fovea. Because foveate animals execute frequent saccadic eye movements, this position information is constantly changing, even though the visual world is generally stationary. Interestingly, visual receptive fields in many brain regions have been found to exhibit changes in strength, size, or position around the time of each saccade, and these changes have often been suggested to be involved in the maintenance of perceptual stability. Crucial to the circuitry underlying perisaccadic changes in visual receptive fields is the superior colliculus (SC), a brainstem structure responsible for integrating visual and oculomotor signals. In this work we have studied the time-course of receptive field changes in the SC. We find that the distribution of the latencies of SC responses to stimuli placed outside the fixation receptive field is bimodal: The first mode is comprised of early responses that are temporally locked to the onset of the visual probe stimulus and stronger for probes placed closer to the classical receptive field. We suggest that such responses are therefore consistent with a perisaccadic rescaling, or enhancement, of weak visual responses within a fixed spatial receptive field. The second mode is more similar to the remapping that has been reported in the cortex, as responses are time-locked to saccade onset and stronger for stimuli placed in the postsaccadic receptive field location. We suggest that these two temporal phases of spatial updating may represent different sources of input to the SC.     

A Push-Pull CORF Model of a Simple Cell with Antiphase Inhibition Improves SNR and Contour Detection

We propose a computational model of a simple cell with push-pull inhibition, a property that is observed in many real simple cells. It is based on an existing model called Combination of Receptive Fields or CORF for brevity. A CORF model uses as afferent inputs the responses of model LGN cells with appropriately aligned center-surround receptive fields, and combines their output with a weighted geometric mean. The output of the proposed model simple cell with push-pull inhibition, which we call push-pull CORF, is computed as the response of a CORF model cell that is selective for a stimulus with preferred orientation and preferred contrast minus a fraction of the response of a CORF model cell that responds to the same stimulus but of opposite contrast. We demonstrate that the proposed push-pull CORF model improves signal-to-noise ratio (SNR) and achieves further properties that are observed in real simple cells, namely separability of spatial frequency and orientation as well as contrast-dependent changes in spatial frequency tuning. We also demonstrate the effectiveness of the proposed push-pull CORF model in contour detection, which is believed to be the primary biological role of simple cells. We use the RuG (40 images) and Berkeley (500 images) benchmark data sets of images with natural scenes and show that the proposed model outperforms, with very high statistical significance, the basic CORF model without inhibition, Gabor-based models with isotropic surround inhibition, and the Canny edge detector. The push-pull CORF model that we propose is a contribution to a better understanding of how visual information is processed in the brain as it provides the ability to reproduce a wider range of properties exhibited by real simple cells. As a result of push-pull inhibition a CORF model exhibits an improved SNR, which is the reason for a more effective contour detection.