Generation of Direction Selectivity by Isotropic Intracortical Connections

To what extent do the mechanisms generating different receptive field properties of neurons depend on each other? We investigated this question theoretically within the context of orientation and direction tuning of simple cells in the mammalian visual cortex. In our model a cortical cell of the "simple" type receives its orientation tuning by afferent convergence of aligned receptive fields of the lateral geniculate nucleus (Hubel and Wiesel 1962). We sharpen this orientation bias by postulating a special type of radially symmetric long-range lateral inhibition called circular inhibition. Surprisingly, this isotropic mechanism leads to the emergence of a strong bias for the direction of motion of a bar. We show that this directional anisotropy is neither caused by the probabilistic nature of the connections nor is it a consequence of the specific columnar structure chosen but that it is an inherent feature of the architecture of visual cortex

A detailed model of the primary visual pathway in the cat: comparison of afferent excitatory and intracortical inhibitory connection schemes for orientation selectivity

In order to arrive at a quantitative understanding of the dynamics of cortical neuronal networks, we simulated a detailed model of the primary visual pathway of the adult cat. This computer model comprises a 5 degrees x 5 degrees patch of the visual field at a retinal eccentricity of 4.5 degrees and includes 2048 ON- and OFF-center retinal beta-ganglion cells, 8192 geniculate X-cells, and 4096 simple cells in layer IV in area 17. The neurons are implemented as improved integrate-and-fire units. Cortical receptive fields are determined by the pattern of afferent convergence and by inhibitory intracortical connections. Orientation columns are implemented continuously with a realistic receptive field scatter and jitter in the preferred orientations. We first show that realistic ON-OFF-responses, orientation selectivity, velocity low-pass behaviour, null response, and responses to spot stimuli can be obtained with an appropriate alignment of geniculate neurons converging onto the cortical simple cell (Hubel and Wiesel, 1962) and in the absence of intracortical connections. However, the average receptive field elongation (length to width) required to obtain realistic orientation tuning is 4.0, much higher than the average observed elongation. This strongly argues for additional intracortical mechanisms sharpening orientation selectivity. In the second stage, we simulated five different inhibitory intracortical connection patterns (random, local, sparse-local, circular, and cross-orientation) in order to investigate the connection specificity necessary to achieve orientation tuning. Inhibitory connection schemes were superimposed onto Hubel and Wiesel-type receptive fields with an elongation of 1.78. Cross-orientation inhibition gave rise to different horizontal and vertical orientation tuning curves, something not observed experimentally. A combination of two inhibitory schemes, local and circular inhibition (a weak form of cross-orientation inhibition), is in good agreement with observed receptive field properties. The specificity required to establish these connections during development is low. We propose that orientation selectivity is caused by at least three different mechanisms (“eclectic” model): a weak afferent geniculate bias, broadly tuned cross-orientation inhibition, and some iso-orientation inhibition. The most surprising finding is that an isotropic connection scheme, circular inhibition, in which a cell inhibits all of its postsynaptic target cells at a distance of approximately 500 microns, enhances orientation tuning and leads to a significant directional bias. This is caused by the embedding of cortical cells within a columnar structure and does not depend on our specific assumptions

Invariant computations in local cortical networks with balanced excitation and inhibition

[Abstract] Cortical computations critically involve local neuronal circuits. The computations are often invariant across a cortical area yet are carried out by networks that can vary widely within an area according to its functional architecture. Here we demonstrate a mechanism by which orientation selectivity is computed invariantly in cat primary visual cortex across an orientation preference map that provides a wide diversity of local circuits. Visually evoked excitatory and inhibitory synaptic conductances are balanced exquisitely in cortical neurons and thus keep the spike response sharply tuned at all map locations. This functional balance derives from spatially isotropic local connectivity of both excitatory and inhibitory cells. Modeling results demonstrate that such covariation is a signature of recurrent rather than purely feed-forward processing and that the observed isotropic local circuit is sufficient to generate invariant spike tuning

Local networks in visual cortex and their influence on neuronal responses and dynamics

[Abstract] Networks of neurons in the cerebral cortex generate complex outputs that are not simply predicted by their inputs. These emergent responses underlie the function of the cortex. Understanding how cortical networks carry out such transformations requires a description of the responses of individual neurons and of their networks at multiple levels of analysis. We focus on orientation selectivity in primary visual cortex as a model system to understand cortical network computations. Recent experiments in our laboratory and others provide significant insight into how cortical networks generate and maintain orientation selectivity. We first review evidence for the diversity of orientation tuning characteristics in visual cortex. We then describe experiments that combine optical imaging of orientation maps with intracellular and extracellular recordings from individual neurons at known locations in the orientation map. The data indicate that excitatory and inhibitory synaptic inputs are summed across the cortex in a manner that is consistent with simple rules of integration of local inputs. These rules arise from known anatomical projection patterns in visual cortex. We propose that the generation and plasticity of orientation tuning is strongly influenced by local cortical networks—the diversity of these properties arises in part from the diversity of neighbourhood features that derive from the orientation map

Cortical column design: a link between the maps of preferred orientation and orientation tuning strength?

We demonstrate that the map of the preferred orientations and the corresponding map of the orientation tuning strengths as measured with optical imaging are not independent, but that band-pass filtering of the preferred orientation map at each location yields a good approximation of the orientation tuning strength. Band-pass filtering is performed by convolving the map of orientation preference with its own autocorrelation function. We suggest an interpretation of the autocorrelation function of the preferred orientations as synaptic coupling function, i.e., synaptic strength as a function of intracortical distance between cortical cells. In developmental models it has been shown previously that a “Mexican hat”-shaped synaptic coupling function (with a shape similar to that of the autocorrelation function) can produce a realistical-looking pattern of preferred orientations. Since optical imaging performs surface averaging, we discuss the possibility that the connection between the two maps is a measurement artifact of optical imaging. Whether this is the case can only be decided by combining electrode penetrations with optical imaging techniques for which we suggest experiments. We present a model for the generation of both maps from a single computational concept. The model is based on inverse Fourier transform of rather simple two-dimensional annulus-shaped spectra which will produce a column structure very similar to real data. Thus, our approach shows that the complex appearance of cortical orientation columns has a rather simple description in the Fourier domain. Our theoretical analysis explains why singularities in the cortex do not have vorticities other than ±1/2, a result which corresponds to recent experimental findings. This study combines the results from several modeling approaches with recently available optical imaging data to construct a model of both aspects (angle and strength) of the cortical orientation column system. This could alter ideas about cortical development if the link between the two maps can be established as a physiological result

Neural network model of the primary visual cortex: From functional architecture to lateral connectivity and back

The role of intrinsic cortical dynamics is a debatable issue. A recent optical imaging study (Kenet et al., 2003) found that activity patterns similar to orientation maps (OMs), emerge in the primary visual cortex (V1) even in the absence of sensory input, suggesting an intrinsic mechanism of OM activation. To better understand these results and shed light on the intrinsic V1 processing, we suggest a neural network model in which OMs are encoded by the intrinsic lateral connections. The proposed connectivity pattern depends on the preferred orientation and, unlike previous models, on the degree of orientation selectivity of the interconnected neurons. We prove that the network has a ring attractor composed of an approximated version of the OMs. Consequently, OMs emerge spontaneously when the network is presented with an unstructured noisy input. Simulations show that the model can be applied to experimental data and generate realistic OMs. We study a variation of the model with spatially restricted connections, and show that it gives rise to states composed of several OMs. We hypothesize that these states can represent local properties of the visual scene

Design principles of columnar organization in visual cortex

Visual space is represented by cortical cells in an orderly manner. Only little variation in the cell behavior is found with changing depth below the cortical surface, that is, all cells in a column with axis perpendicular to the cortical plane have approximately the same properties (Hubel and Wiesel 1962, 1963, 1968). Therefore, the multiple features of the visual space (e.g., position in visual space, preferred orientation, and orientation tuning strength) are mapped on a two-dimensional space, the cortical plane. Such a dimension reduction leads to complex maps (Durbin and Mitchison 1990) that so far have evaded an intuitive understanding. Analyzing optical imaging data (Blasdel 1992a, b; Blasdel and Salama 1986; Grinvald et al. 1986) using a theoretical approach we will show that the most salient features of these maps can be understood from a few basic design principles: local correlation, modularity, isotropy, and homogeneity. These principles can be defined in a mathematically exact sense in the Fourier domain by a rather simple annulus-like spectral structure. Many of the models that have been developed to explain the mapping of the preferred orientations (Cooper et al. 1979; Legendy 1978; Linsker 1986a, b; Miller 1992; Nass and Cooper 1975; Obermayer et al. 1990, 1992; Soodak 1987; Swindale 1982, 1985, 1992; von der Malsburg 1973; von der Malsburg and Cowan 1982) are quite successful in generating maps that are close to experimental maps. We suggest that this success is due to these principles, which are common properties of the models and of biological maps

Coverage, Continuity and Visual Cortical Architecture

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far. We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise. Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure

Can retinal ganglion cell dipoles seed iso-orientation domains in the visual cortex?

It has been argued that the emergence of roughly periodic orientation preference maps (OPMs) in the primary visual cortex (V1) of carnivores and primates can be explained by a so-called statistical connectivity model. This model assumes that input to V1 neurons is dominated by feed-forward projections originating from a small set of retinal ganglion cells (RGCs). The typical spacing between adjacent cortical orientation columns preferring the same orientation then arises via Moir\'{e}-Interference between hexagonal ON/OFF RGC mosaics. While this Moir\'{e}-Interference critically depends on long-range hexagonal order within the RGC mosaics, a recent statistical analysis of RGC receptive field positions found no evidence for such long-range positional order. Hexagonal order may be only one of several ways to obtain spatially repetitive OPMs in the statistical connectivity model. Here, we investigate a more general requirement on the spatial structure of RGC mosaics that can seed the emergence of spatially repetitive cortical OPMs, namely that angular correlations between so-called RGC dipoles exhibit a spatial structure similar to that of OPM autocorrelation functions. Both in cat beta cell mosaics as well as primate parasol receptive field mosaics we find that RGC dipole angles are spatially uncorrelated. To help assess the level of these correlations, we introduce a novel point process that generates mosaics with realistic nearest neighbor statistics and a tunable degree of spatial correlations of dipole angles. Using this process, we show that given the size of available data sets, the presence of even weak angular correlations in the data is very unlikely. We conclude that the layout of ON/OFF ganglion cell mosaics lacks the spatial structure necessary to seed iso-orientation domains in the primary visual cortex.Comment: 9 figures + 1 Supplementary figure and 1 Supplementary tabl