Topographic Shear and the Relation of Ocular Dominance Columns to Orientation Columns in Prime and Cat Visual Cortex

Shear has been known to exist for many years in the topographic structure of prirnary visual cortex, but has received little attention in the modeling literature. Although the topographic map of V1 is largely conformal (i.e. zero shear), several groups have observed topographic shear in the region of the V1/V2 border. Furthennore, shear has also been revealed by anisotropy of cortical magnification factor within a single ocular dominance colunm. In the present paper, we make a functional hypothesis: the major axis of the topographic shear tensor provides cortical neurons with a preferred direction of orientation tuning. We demonstrate that isotropic neuronal summation of a sheared topographic map, in the presence of additional random shear can provide the major features of corlical functional architecture with the ocular dominance column system acting as the principal source of the shear tensor. The major principal axis of the shear tensor determines the direction and its eigenvalues the relative strength of cortical orientation preference. This hypothesis is then shown to be qualitatively consistent with a variety of experimental results on cat and monkey orientation column properties obtained from optical recording and from other anatomical and physiological techniques. In addition, we show that a recent result of (Das and Gilbert, 1997) is consistent with an infinite set of parameterized solutions for the cortical map. We exploit this freedom to choose a particular instance of the Das-Gilbert solution set which is consistent with the full range of local spatial structure in V1. These results suggest that further relationships between ocular dominance columns, orientation columns, and local topography may be revealed by experimental testing

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

Rules for the Cortical Map of Ocular Dominance and Orientation Columns

Three computational rules are sufficient to generate model cortical maps that simulate the interrelated structure of cortical ocular dominance and orientation columns: a noise input, a spatial band pass filter, and competitive normalization across all feature dimensions. The data of Blasdel from optical imaging experiments reveal cortical map fractures, singularities, and linear zones that are fit by the model. In particular, singularities in orientation preference tend to occur in the centers of ocular dominance columns, and orientation contours tend to intersect ocular dominance columns at right angles. The model embodies a universal computational substrate that all models of cortical map development and adult function need to realize in some form.Air Force Office of Scientific Research (F49620-92-J- 0499, F49620-92-J-0334); Office of Naval Research (N00014-92-J-4015, N00014-91-J-4100); National Science Foundation (IRI-90-24877); British Petroleum (BP 89A-1204

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

Functional Organization of Visual Cortex in the Owl Monkey

In this study, we compared the organization of orientation preference in visual areas V1, V2, and V3. Within these visual areas, we also quantified the relationship between orientation preference and cytochrome oxidase (CO) staining patterns. V1 maps of orientation preference contained both pinwheels and linear zones. The location of CO blobs did not relate in a systematic way to maps of orientation; although, as in other primates, there were approximately twice as many pinwheels as CO blobs. V2 contained bands of high and low orientation selectivity. The bands of high orientation selectivity were organized into pinwheels and linear zones, but iso-orientation domains were twice as large as those in V1. Quantitative comparisons between bands containing high or low orientation selectivity and CO dark and light bands suggested that at least four functional compartments exist in V2, CO dense bands with either high or low orientation selectivity, and CO light bands with either high or low selectivity. We also demonstrated that two functional compartments exist in V3, with zones of high orientation selectivity corresponding to CO dense areas and zones of low orientation selectivity corresponding to CO pale areas. Together with previous findings, these results suggest that the modular organization of V1 is similar across primates and indeed across most mammals. V2 organization in owl monkeys also appears similar to that of other simians but different from that of prosimians and other mammals. Finally, V3 of owl monkeys shows a compartmental organization for orientation selectivity that remains to be demonstrated in other primates

Coordinated optimization of visual cortical maps (II) Numerical studies

It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335

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

Geometry and dimensionality reduction of feature spaces in primary visual cortex

Some geometric properties of the wavelet analysis performed by visual neurons are discussed and compared with experimental data. In particular, several relationships between the cortical morphologies and the parametric dependencies of extracted features are formalized and considered from a harmonic analysis point of view

Coordinated optimization of visual cortical maps : 2. Numerical studies

In the juvenile brain, the synaptic architecture of the visual cortex remains in a state of flux for months after the natural onset of vision and the initial emergence of feature selectivity in visual cortical neurons. It is an attractive hypothesis that visual cortical architecture is shaped during this extended period of juvenile plasticity by the coordinated optimization of multiple visual cortical maps such as orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we introduced a class of analytically tractable coordinated optimization models and solved representative examples, in which a spatially complex organization of the OP map is induced by interactions between the maps. We found that these solutions near symmetry breaking threshold predict a highly ordered map layout. Here we examine the time course of the convergence towards attractor states and optima of these models. In particular, we determine the timescales on which map optimization takes place and how these timescales can be compared to those of visual cortical development and plasticity. We also assess whether our models exhibit biologically more realistic, spatially irregular solutions at a finite distance from threshold, when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. We show that, although maps typically undergo substantial rearrangement, no other solutions than pinwheel crystals and stripes dominate in the emerging layouts. Pinwheel crystallization takes place on a rather short timescale and can also occur for detuned wavelengths of different maps. Our numerical results thus support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the architecture of the visual cortex. We discuss several alternative scenarios that may improve the agreement between model solutions and biological observations