Computational Modeling of Orientation Tuning Dynamics in Monkey Primary Visual Cortex

In the primate visual pathway, orientation tuning of neurons is first observed in the primary visual cortex. The LGN cells that comprise the thalamic input to V1 are not orientation tuned, but some V1 neurons are quite selective. Two main classes of theoretical models have been offered to explain orientation selectivity: feedforward models, in which inputs from spatially aligned LGN cells are summed together by one cortical neuron; and feedback models, in which an initial weak orientation bias due to convergent LGN input is sharpened and amplified by intracortical feedback. Recent data on the dynamics of orientation tuning, obtained by a cross-correlation technique, may help to distinguish between these classes of models. To test this possibility, we simulated the measurement of orientation tuning dynamics on various receptive field models, including a simple Hubel-Wiesel type feedforward model: a linear spatiotemporal filter followed by an integrate-and-fire spike generator. The computational study reveals that simple feedforward models may account for some aspects of the experimental data but fail to explain many salient features of orientation tuning dynamics in V1 cells. A simple feedback model of interacting cells is also considered. This model is successful in explaining the appearance of Mexican-hat orientation profiles, but other features of the data continue to be unexplained.     

Development of spatial coarse-to-fine processing in the visual pathway

The sequential analysis of information in a coarse-to-fine manner is a fundamental mode of processing in the visual pathway. Spatial frequency (SF) tuning, arguably the most fundamental feature of spatial vision, provides particular intuition within the coarse-to-fine framework: low spatial frequencies convey global information about an image (e.g., general orientation), while high spatial frequencies carry more detailed information (e.g., edges). In this paper, we study the development of cortical spatial frequency tuning. As feedforward input from the lateral geniculate nucleus (LGN) has been shown to have significant influence on cortical coarse-to-fine processing, we present a firing-rate based thalamocortical model which includes both feedforward and feedback components. We analyze the relationship between various model parameters (including cortical feedback strength) and responses. We confirm the importance of the antagonistic relationship between the center and surround responses in thalamic relay cell receptive fields (RFs), and further characterize how specific structural LGN RF parameters affect cortical coarse-to-fine processing. Our results also indicate that the effect of cortical feedback on spatial frequency tuning is age-dependent: in particular, cortical feedback more strongly affects coarse-to-fine processing in kittens than in adults. We use our results to propose an experimentally testable hypothesis for the function of the extensive feedback in the corticothalamic circuit.     

A CORF computational model of a simple cell that relies on LGN input outperforms the Gabor function model

Simple cells in primary visual cortex are believed to extract local contour information from a visual scene. The 2D Gabor function (GF) model has gained particular popularity as a computational model of a simple cell. However, it short-cuts the LGN, it cannot reproduce a number of properties of real simple cells, and its effectiveness in contour detection tasks has never been compared with the effectiveness of alternative models. We propose a computational model that uses as afferent inputs the responses of model LGN cells with center–surround receptive fields (RFs) and we refer to it as a Combination of Receptive Fields (CORF) model. We use shifted gratings as test stimuli and simulated reverse correlation to explore the nature of the proposed model. We study its behavior regarding the effect of contrast on its response and orientation bandwidth as well as the effect of an orthogonal mask on the response to an optimally oriented stimulus. We also evaluate and compare the performances of the CORF and GF models regarding contour detection, using two public data sets of images of natural scenes with associated contour ground truths. The RF map of the proposed CORF model, determined with simulated reverse correlation, can be divided in elongated excitatory and inhibitory regions typical of simple cells. The modulated response to shifted gratings that this model shows is also characteristic of a simple cell. Furthermore, the CORF model exhibits cross orientation suppression, contrast invariant orientation tuning and response saturation. These properties are observed in real simple cells, but are not possessed by the GF model. The proposed CORF model outperforms the GF model in contour detection with high statistical confidence (RuG data set: p < 10⁻⁴, and Berkeley data set: p < 10⁻⁴). The proposed CORF model is more realistic than the GF model and is more effective in contour detection, which is assumed to be the primary biological role of simple cells.     

Feedforward origins of response variability underlying contrast invariant orientation tuning in cat visual cortex

Contrast invariant orientation tuning in simple cells of the visual cortex depends critically on contrast dependent trial-to-trial variability in their membrane potential responses. This observation raises the question of whether this variability originates from within the cortical circuit or the feedforward inputs from the lateral geniculate nucleus (LGN). To distinguish between these two sources of variability, we first measured membrane potential responses while inactivating the surrounding cortex, and found that response variability was nearly unaffected. We then studied variability in the LGN, including contrast dependence, and the trial-to-trial correlation in responses between nearby neurons. Variability decreased significantly with contrast, whereas correlation changed little. When these experimentally measured parameters of variability were applied to a feedforward model of simple cells that included realistic mechanisms of synaptic integration, contrast-dependent, orientation independent variability emerged in the membrane potential responses. Analogous mechanisms might contribute to the stimulus dependence and propagation of variability throughout the neocortex.     

A spherical model for orientation and spatial-frequency tuning in a cortical hypercolumn

A theory is presented of the way in which the hypercolumns in primary visual cortex (V1) are organized to detect important features of visual images, namely local orientation and spatial-frequency. Given the existence in V1 of dual maps for these features, both organized around orientation pinwheels, we constructed a model of a hypercolumn in which orientation and spatial-frequency preferences are represented by the two angular coordinates of a sphere. The two poles of this sphere are taken to correspond, respectively, to high and low spatial-frequency preferences. In Part I of the paper, we use mean-field methods to derive exact solutions for localized activity states on the sphere. We show how cortical amplification through recurrent interactions generates a sharply tuned, contrast-invariant population response to both local orientation and local spatial frequency, even in the case of a weakly biased input from the lateral geniculate nucleus (LGN). A major prediction of our model is that this response is non-separable with respect to the local orientation and spatial frequency of a stimulus. That is, orientation tuning is weaker around the pinwheels, and there is a shift in spatial-frequency tuning towards that of the closest pinwheel at non-optimal orientations. In Part II of the paper, we demonstrate that a simple feed-forward model of spatial-frequency preference, unlike that for orientation preference, does not generate a faithful representation when amplified by recurrent interactions in V1. We then introduce the idea that cortico-geniculate feedback modulates LGN activity to generate a faithful representation, thus providing a new functional interpretation of the role of this feedback pathway. Using linear filter theory, we show that if the feedback from a cortical cell is taken to be approximately equal to the reciprocal of the corresponding feed-forward receptive field (in the two-dimensional Fourier domain), then the mismatch between the feed-forward and cortical frequency representations is eliminated. We therefore predict that cortico-geniculate feedback connections innervate the LGN in a pattern determined by the orientation and spatial-frequency biases of feed-forward receptive fields. Finally, we show how recurrent cortical interactions can generate cross-orientation suppression.     

Visual Receptive Field Properties of Neurons in the Mouse Lateral Geniculate Nucleus

The lateral geniculate nucleus (LGN) is increasingly regarded as a “smart-gating” operator for processing visual information. Therefore, characterizing the response properties of LGN neurons will enable us to better understand how neurons encode and transfer visual signals. Efforts have been devoted to study its anatomical and functional features, and recent advances have highlighted the existence in rodents of complex features such as direction/orientation selectivity. However, unlike well-researched higher-order mammals such as primates, the full array of response characteristics vis-à-vis its morphological features have remained relatively unexplored in the mouse LGN. To address the issue, we recorded from mouse LGN neurons using multisite-electrode-arrays (MEAs) and analysed their discharge patterns in relation to their location under a series of visual stimulation paradigms. Several response properties paralleled results from earlier studies in the field and these include centre-surround organization, size of receptive field, spontaneous firing rate and linearity of spatial summation. However, our results also revealed “high-pass” and “low-pass” features in the temporal frequency tuning of some cells, and greater average contrast gain than reported by earlier studies. In addition, a small proportion of cells had direction/orientation selectivity. Both “high-pass” and “low-pass” cells, as well as direction and orientation selective cells, were found only in small numbers, supporting the notion that these properties emerge in the cortex. ON- and OFF-cells showed distinct contrast sensitivity and temporal frequency tuning properties, suggesting parallel projections from the retina. Incorporating a novel histological technique, we created a 3-D LGN volume model explicitly capturing the morphological features of mouse LGN and localising individual cells into anterior/middle/posterior LGN. Based on this categorization, we show that the ON/OFF, DS/OS and linear response properties are not regionally restricted. Our study confirms earlier findings of spatial pattern selectivity in the LGN, and builds on it to demonstrate that relatively elaborate features are computed early in the visual pathway.     

Receptive field properties of near neighbor orientation selective neurons in the visual cortex: a modeling study

The primary visual cortex is organized into clusters of cells having similar receptive fields (RFs). A purely feedforward model has been shown to produce realistic simple cell receptive fields. The modeled cells capture a wide range of receptive field properties of orientation selective cortical cells. We have analyzed the responses of 78 nearby cell pairs to study which RF properties are clustered. Orientation preference shows strongest clustering. Orientation tuning width (hwhh) and tuning height (spikes/sec) at the preferred orientation are not as tightly clustered. Spatial frequency is also not as tightly clustered and RF phase has the least clustering. Clustering property of orientation preference, orientation tuning height and width depend on the location of cells in the orientation map. No such location dependence is observed for spatial frequency and RF phase. Our results agree well with experimental data.     

Double orientation tuning of neurons in the primary cortex of cat at different levels of alertness

Orientation tuning (OT) of 225 cat neurons of the primary visual cortex (field 17) to the flashing of a light bar in the discharge centers of their receptive field (RFs) were investigated. It was found that 43% of the cells investigated were monomodally tuned, i.e., were primarily detecting horizontal and vertical orientations. The remaining 57% of the neurons exhibited double OT, i.e, exhibited, in addition to a main preferred orientation (PO), an additional preferred orientation (aPO) at a right or acute angle to the main orientation (the mean angle between the two OT maxima equalled 71.4±2.4°). In bimodal cells, the additional maximum of OT was comparable in magnitude to the main maximum (averaging 0.7±0.03 of the PO) in half the cases. The orientational properties of the main and additional maxima were almost indistinguishable. Under light or moderate anesthesia, approximately half the neurons with double OT became monomodal; at the same time, a small fraction of monomodal cells (12%) manifested double OT. Under anesthesia, the angle between two the preferred orientations decreased, while the ratio of amplitude characteristics remained unchanged. Monomodal neurons frequently exhibited simple RFs and OTs unaffected by anesthesia. Neurons with double OT, on the other hand, exhibited simple and complex types of RFs just as often and their OT changed under the influence of anesthesia. It is suggested that neurons with double OT can function as detectors of angles and angles of intersecting lines; such angles, together with line orientation, are important attributes of images. In contrast, monomodal neurons may provide a benchmark for a stable reference system of orientation coordinates. The interaction of the two neuronal systems mentioned may allow effective analysis of image attributes at the level of the primary visual cortex.Institute of Higher Nervous Activity and Neurophysiology, Russian Academy of Sciences Moscow. Translated from Neirofiziologiya, Vol. 24, No. 3, pp. 260–269, May–June, 1992.     

Corticofugal feedback can reduce the visual latency of responses to antagonistic stimuli

 A biophysically realistical model of the primary visual pathway is designed, including feedback connections from the visual cortex to the lateral geniculate nucleus (LGN) – the so-called corticofugal pathway. The model comprises up to 10 000 retina and LGN cells divided into the ON and the OFF pathway according to their contrast response characteristics. An additional 6000 cortical simple cells are modeled. Apart from the direct excitatory afferent pathway we include strong mutual inhibition between the ON and the OFF subsystems. In addition, we propose a novel type of paradoxical corticofugal connection pattern which links ON dominated cortical simple cells to OFF-center LGN cells and vice versa. In accordance with physiological findings these connections are weakly excitatory and do not interfere with the steady-state responses to constant illumination, because during the steady-state inhibition arising from the active pathway effectively silences the nonstimulated pathway. At the moment of a contrast reversal the effect of the paradoxical connection pattern comes into play and the depolarization of the previously silent channel is accelerated, leading to a latency reduction of up to 4 ms using moderate synaptic weights. With increased weights reductions of more than 10 ms can be achieved. We introduce different synaptic characteristics for the feedback (AMPA, NMDA, AMPA+NMDA) and show that the strongest latency reduction is obtained for a combination of the membrane channels (i.e., AMPA+NMDA). The effect of the proposed paradoxical connection pattern is self-regulating; because the levels of inhibition and paradoxical excitation are always driven by the same inputs (strong inhibition is counterbalanced by a stronger paradoxical excitation and vice versa). In addition, the latency reduction for a contrast inversion which ends at a small absolute contrast level (small contrast step) is stronger than the reduction for an inversion with large final contrast (large contrast step). This leads to a more pronounced reduction in the reaction times for weak stimuli. Thus, reaction time differences for different contrast steps are smoothed out. Received: 22 January 1996/Accepted in revised form: 20 May 1996     

Retinal and cortical nonlinearities combine to produce masking in V1 responses to plaids

The visual response of a cell in the primary visual cortex (V1) to a drifting grating stimulus at the cell’s preferred orientation decreases when a second, perpendicular, grating is superimposed. This effect is called masking. To understand the nonlinear masking effect, we model the response of Macaque V1 simple cells in layer 4Cα to input from magnocellular Lateral Geniculate Nucleus (LGN) cells. The cortical model network is a coarse-grained reduction of an integrate-and-fire network with excitation from LGN input and inhibition from other cortical neurons. The input is modeled as a sum of LGN cell responses. Each LGN cell is modeled as the convolution of a spatio-temporal filter with the visual stimulus, normalized by a retinal contrast gain control, and followed by rectification representing the LGN spike threshold. In our model, the experimentally observed masking arises at the level of LGN input to the cortex. The cortical network effectively induces a dynamic threshold that forces the test grating to have high contrast before it can overcome the masking provided by the perpendicular grating. The subcortical nonlinearities and the cortical network together account for the masking effect. Melinda Koelling is formerly from Center for Neural Science and Courant Institute, New York University.     

Combined Hebbian development of geniculocortical and lateral connectivity in a model of primary visual cortex

We present a network model of visual map development in layer 4 of primary visual cortex. Our model comprises excitatory and inhibitory spiking neurons. The input to the network consists of correlated spike trains to mimick the activity of neurons in the lateral geniculate nucleus (LGN). An activity-driven Hebbian learning mechanism governs the development of both the network's lateral connectivity and feedforward projections from LGN to cortex. Plasticity of inhibitory synapses has been included into the model so as to control overall cortical activity. Even without feedforward input, Hebbian modification of the excitatory lateral connections can lead to the development of an intracortical orientation map. We have found that such an intracortical map can guide the development of feedforward connections from LGN to cortical simple cells so that the structure of the final feedforward orientation map is predetermined by the intracortical map. In a scenario in which left- and right-eye geniculocortical inputs develop sequentially one after the other, the resulting maps are therefore very similar, provided the intracortical connectivity remains unaltered. This may explain the outcome of so-called reverse lid-suture experiments, where animals are reared so that both eyes never receive input at the same time, but the orientation maps measured separately for the two eyes are nevertheless nearly identical. Received: 20 December 1999 / Accepted in revised form: 9 June 2000     

Development of feedforward receptive field structure of a simple cell and its contribution to the orientation selectivity: a modeling study

Recent experimental studies of hetero-synaptic interactions in various systems have shown the role of signaling in the plasticity, challenging the conventional understanding of Hebb's rule. It has also been found that activity plays a major role in plasticity, with neurotrophins acting as molecular signals translating activity into structural changes. Furthermore, role of synaptic efficacy in biasing the outcome of competition has also been revealed recently. Motivated by these experimental findings we present a model for the development of simple cell receptive field structure based on the competitive hetero-synaptic interactions for neurotrophins combined with cooperative hetero-synaptic interactions in the spatial domain. We find that with proper balance in competition and cooperation, the inputs from two populations (ON/OFF) of LGN cells segregate starting from the homogeneous state. We obtain segregated ON and OFF regions in simple cell receptive field. Our modeling study supports the experimental findings, suggesting the role of synaptic efficacy and the role of spatial signaling. We find that using this model we obtain simple cell RF, even for positively correlated activity of ON/OFF cells. We also compare different mechanism of finding the response of cortical cell and study their possible role in the sharpening of orientation selectivity. We find that degree of selectivity improvement in individual cells varies from case to case depending upon the structure of RF field and type of sharpening mechanism.     

Spatial structure of complex cell receptive fields measured with natural images

Neuronal receptive fields (RFs) play crucial roles in visual processing. While the linear RFs of early neurons have been well studied, RFs of cortical complex cells are nonlinear and therefore difficult to characterize, especially in the context of natural stimuli. In this study, we used a nonlinear technique to compute the RFs of complex cells from their responses to natural images. We found that each RF is well described by a small number of subunits, which are oriented, localized, and bandpass. These subunits contribute to neuronal responses in a contrast-dependent, polarity-invariant manner, and they can largely predict the orientation and spatial frequency tuning of the cell. Although the RF structures measured with natural images were similar to those measured with random stimuli, natural images were more effective for driving complex cells, thus facilitating rapid identification of the subunits. The subunit RF model provides a useful basis for understanding cortical processing of natural stimuli.     

A reaction-diffusion model to capture disparity selectivity in primary visual cortex

Decades of experimental studies are available on disparity selective cells in visual cortex of macaque and cat. Recently, local disparity map for iso-orientation sites for near-vertical edge preference is reported in area 18 of cat visual cortex. No experiment is yet reported on complete disparity map in V1. Disparity map for layer IV in V1 can provide insight into how disparity selective complex cell receptive field is organized from simple cell subunits. Though substantial amounts of experimental data on disparity selective cells is available, no model on receptive field development of such cells or disparity map development exists in literature. We model disparity selectivity in layer IV of cat V1 using a reaction-diffusion two-eye paradigm. In this model, the wiring between LGN and cortical layer IV is determined by resource an LGN cell has for supporting connections to cortical cells and competition for target space in layer IV. While competing for target space, the same type of LGN cells, irrespective of whether it belongs to left-eye-specific or right-eye-specific LGN layer, cooperate with each other while trying to push off the other type. Our model captures realistic 2D disparity selective simple cell receptive fields, their response properties and disparity map along with orientation and ocular dominance maps. There is lack of correlation between ocular dominance and disparity selectivity at the cell population level. At the map level, disparity selectivity topography is not random but weakly clustered for similar preferred disparities. This is similar to the experimental result reported for macaque. The details of weakly clustered disparity selectivity map in V1 indicate two types of complex cell receptive field organization.     

The Y cell visual pathway implements a demodulating nonlinearity

Neural encoding of sensory signals involves both linear and nonlinear processes. Determining which nonlinear operations are implemented by neural systems is crucial to understanding sensory processing. Here, we ask if demodulation, the process used to decode AM radio signals, describes how Y cells in the cat LGN nonlinearly encode the visual scene. In response to visual AM signals across?a wide range of carrier frequencies, Y cells were found to transmit a demodulated signal, with the firing rate of single-units fluctuating at the envelope frequency but not the carrier frequency. A comparison of temporal frequency tuning properties between LGN Y cells and neurons in two primary cortical areas suggests that Y cells initiate a distinct pathway that carries a demodulated representation of the visual scene to cortex. The nonlinear signal processing carried out by the Y cell pathway simplifies the neural representation of complex visual features and allows high spatiotemporal frequencies to drive cortical responses.     

Integrate-and-fire vs Poisson models of LGN input to V1 cortex: noisier inputs reduce orientation selectivity

One of the reasons the visual cortex has attracted the interest of computational neuroscience is that it has well-defined inputs. The lateral geniculate nucleus (LGN) of the thalamus is the source of visual signals to the primary visual cortex (V1). Most large-scale cortical network models approximate the spike trains of LGN neurons as simple Poisson point processes. However, many studies have shown that neurons in the early visual pathway are capable of spiking with high temporal precision and their discharges are not Poisson-like. To gain an understanding of how response variability in the LGN influences the behavior of V1, we study response properties of model V1 neurons that receive purely feedforward inputs from LGN cells modeled either as noisy leaky integrate-and-fire (NLIF) neurons or as inhomogeneous Poisson processes. We first demonstrate that the NLIF model is capable of reproducing many experimentally observed statistical properties of LGN neurons. Then we show that a V1 model in which the LGN input to a V1 neuron is modeled as a group of NLIF neurons produces higher orientation selectivity than the one with Poisson LGN input. The second result implies that statistical characteristics of LGN spike trains are important for V1’s function. We conclude that physiologically motivated models of V1 need to include more realistic LGN spike trains that are less noisy than inhomogeneous Poisson processes.     

Recording and manipulating the in vivo correlational structure of neuronal activity during visual cortical development.

Many aspects of visual cortical functional architecture, such as orientation and ocular dominance columns, are present before animals have had any visual experience, indicating that the initial formation of cortical circuitry takes place without the influence of environmental cues. For this reason, it has been proposed that spontaneous activity within the developing visual pathway carries instructive information to guide the early establishment of cortical circuits. Recently developed recording and stimulation techniques are revealing new information about the in vivo organization of this spontaneous activity and its contribution to cortical development. Multielectrode recordings in the developing lateral geniculate nucleus (LGN) of ferrets demonstrate that retinal spontaneous activity is not simply relayed to the visual cortex, but is reshaped and transformed by a variety of mechanisms including cortical feedback and endogenous oscillatory activity. The resulting patterns are consistent with many of the predictions of correlation-based models of cortical development. In addition, the introduction of artificially correlated activity into the visual pathway disrupts some but not all aspects of orientation tuning development. Thus, while these results support an instructive role of spontaneous activity in shaping cortical development, there still appears to be a number of aspects of this process that cannot be accounted for by activity alone.     

The emergence of contrast-invariant orientation tuning in simple cells of cat visual cortex

Simple cells in primary visual cortex exhibit contrast-invariant orientation tuning, in seeming contradiction to feed-forward models that rely on lateral geniculate nucleus (LGN) input alone. Contrast invariance has therefore been thought to depend on the presence of intracortical lateral inhibition. In vivo intracellular recordings instead suggest that contrast invariance can be explained by three properties of the excitatory pathway. (1) Depolarizations evoked by orthogonal stimuli are determined by the amount of excitation a cell receives from the LGN, relative to the excitation it receives from other cortical cells. (2) Depolarizations evoked by preferred stimuli saturate at lower contrasts than the spike output of LGN relay cells. (3) Visual stimuli evoke contrast-dependent changes in trial-to-trial variability, which lead to contrast-dependent changes in the relationship between membrane potential and spike rate. Thus, high-contrast, orthogonally oriented stimuli that evoke significant depolarizations evoke few spikes. Together these mechanisms, without lateral inhibition, can account for contrast-invariant stimulus selectivity.     

A computational neural model of orientation detection based on multiple guesses: comparison of geometrical and algebraic models

The implementation of Hubel-Wiesel hypothesis that orientation selectivity of a simple cell is based on ordered arrangement of its afferent cells has some difficulties. It requires the receptive fields (RFs) of those ganglion cells (GCs) and LGN cells to be similar in size and sub-structure and highly arranged in a perfect order. It also requires an adequate number of regularly distributed simple cells to match ubiquitous edges. However, the anatomical and electrophysiological evidence is not strong enough to support this geometry-based model. These strict regularities also make the model very uneconomical in both evolution and neural computation. We propose a new neural model based on an algebraic method to estimate orientations. This approach synthesizes the guesses made by multiple GCs or LGN cells and calculates local orientation information subject to a group of constraints. This algebraic model need not obey the constraints of Hubel-Wiesel hypothesis, and is easily implemented with a neural network. By using the idea of a satisfiability problem with constraints, we also prove that the precision and efficiency of this model are mathematically practicable. The proposed model makes clear several major questions which Hubel-Wiesel model does not account for. Image-rebuilding experiments are conducted to check whether this model misses any important boundary in the visual field because of the estimation strategy. This study is significant in terms of explaining the neural mechanism of orientation detection, and finding the circuit structure and computational route in neural networks. For engineering applications, our model can be used in orientation detection and as a simulation platform for cell-to-cell communications to develop bio-inspired eye chips.