Selective disruption of one Cartesian axis of cortical maps and receptive fields by deficiency in ephrin-As and structured activity

The topographic representation of visual space is preserved from retina to thalamus to cortex. We have previously shown that precise mapping of thalamocortical projections requires both molecular cues and structured retinal activity. To probe the interaction between these two mechanisms, we studied mice deficient in both ephrin-As and retinal waves. Functional and anatomical cortical maps in these mice were nearly abolished along the nasotemporal (azimuth) axis of the visual space. Both the structure of single-cell receptive fields and large-scale topography were severely distorted. These results demonstrate that ephrin-As and structured neuronal activity are two distinct pathways that mediate map formation in the visual cortex and together account almost completely for the formation of the azimuth map. Despite the dramatic disruption of azimuthal topography, the dorsoventral (elevation) map was relatively normal, indicating that the two axes of the cortical map are organized by separate mechanisms.     

Modeling Magnification and Anisotropy in the Primate Foveal Confluence

A basic organizational principle of the primate visual system is that it maps the visual environment repeatedly and retinotopically onto cortex. Simple algebraic models can be used to describe the projection from visual space to cortical space not only for V1, but also for the complex of areas V1, V2 and V3. Typically a conformal (angle-preserving) projection ensuring local isotropy is regarded as ideal and primate visual cortex is often regarded as an approximation of this ideal. However, empirical data show systematic deviations from this ideal that are especially relevant in the foveal projection. The aims of this study were to map the nature of anisotropy predicted by existing models, to investigate the optimization targets faced by different types of retino-cortical maps, and finally to propose a novel map that better models empirical data than other candidates. The retino-cortical map can be optimized towards a space-conserving homogenous representation or a quasi-conformal mapping. The latter would require a significantly enlarged representation of specific parts of the cortical maps. In particular it would require significant enlargement of parafoveal V2 and V3 which is not supported by empirical data. Further, the recently published principal layout of the foveal singularity cannot be explained by existing models. We suggest a new model that accurately describes foveal data, minimizing cortical surface area in the periphery but suggesting that local isotropy dominates the most foveal part at the expense of additional cortical surface. The foveal confluence is an important example of the detailed trade-offs between the compromises required for the mapping of environmental space to a complex of neighboring cortical areas. Our models demonstrate that the organization follows clear morphogenetic principles that are essential for our understanding of foveal vision in daily life.     

Coordinated Optimization of Visual Cortical Maps (I) Symmetry-based Analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of orientation columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about a hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference. From basic symmetry assumptions we obtain a comprehensive phenomenological classification of possible inter-map coupling energies and examine representative examples. We show that each individual coupling energy leads to a different class of OP solutions with different correlations among the maps such that inferences about the optimization principle from map layout appear viable. We systematically assess whether quantitative laws resembling experimental observations can result from the coordinated optimization of orientation columns with other feature maps.     

Representation of three-dimensional visual space in the cerebral cortex

This article reviews two issues relevant to the topic of how three-dimensional space is represented in the cerebral cortex. The first is the question of how individual neurons encode information that might contribute to stereoscopic estimation of visual depth. Particular attention is given to the current understanding of the neural representation of motion through three-dimensional space and to the complexities that arise in interpreting neuronal responses to this complex stimulus parameter. The second issue considered is the disorderlines that exists in the retinotopic mapping of the visual field in some cortical visual areas. Several extrastriate areas have been found to contain maps of the contralateral visual hemifield that are disorderly in the sense that the representation of various parts of the visual field are often misplaced or grossly over-or under-represented. It is suggested that this disorderlines may in some cases represent adaptations to facilitate certain types of visual functions.     

Auditory cortex mapmaking: principles, projections, and plasticity

Maps of sensory receptor epithelia and computed features of the sensory environment are common elements of auditory, visual, and somatic sensory representations from the periphery to the cerebral cortex. Maps enhance the understanding of normal neural organization and its modification by pathology and experience. They underlie the derivation of the computational principles that govern sensory processing and the generation of perception. Despite their intuitive explanatory power, the functions of and rules for organizing maps and their plasticity are not well understood. Some puzzles of auditory cortical map organization are that few complete receptor maps are available and that even fewer computational maps are known beyond primary cortical areas. Neuroanatomical evidence suggests equally organized connectional patterns throughout the cortical hierarchy that might underlie map stability. Here, we consider the implications of auditory cortical map organization and its plasticity and evaluate the complementary role of maps in representation and computation from an auditory perspective.     

Stability of cortical responses and the statistics of natural scenes.

The primary visual cortex (V1) of higher mammals contains maps of stimulus features; how these maps influence vision remains unknown. We have examined the functional significance of an asymmetry in the orientation map in cat V1, i.e., the fact that a larger area of V1 is preferentially activated by vertical and horizontal contours than by contours at oblique orientations. Despite the fact that neurons tuned to cardinal and oblique orientations have indistinguishable tuning characteristics, cardinal neurons remain more stable in their response properties after selective perturbation induced by adaptation. Similarly, human observers report different adaptation-induced changes in orientation tuning between cardinal and oblique axes. We suggest that the larger cortical area devoted to cardinal orientations imposes stability on the processing of cardinal contours during visual perception, by retaining invariant cortical responses along cardinal axes.     

Retinotopic organization of striate and extrastriate visual cortex in the golden hamster (Mesocricetus auratus).

The visual topography within striate and lateral extrastriate visual cortices was studied in adult hamsters. The cortical areas 17 and 18a in the left hemisphere were electrophysiologically mapped upon stimulation of the right eye, correlating receptive field positions in the visual field with cortical recording sites. Reference lesions were placed at selected cortical sites. Like in rats and other mammals, the lateral extrastriate cortex contained multiple representations of the visual field. Rostral area 18a contained the rostrolateral maps, with medial and lateral divisions. More caudally and sharing a common border with V1, maps in lateromedial, posterolateral and posterior areas were found. More laterally and forming a "third tier" of visual maps, anterolateral, laterolateral-anterior, laterolateral and laterolateral-posterior areas were found. There was also an indication of a possible pararhinal map. The plan so defined is virtually identical to that of rats. The results may be useful to understand a basic mammalian plan in the organization of the visual cortex.     

Remapping for visual stability

Visual perception is based on both incoming sensory signals and information about ongoing actions. Recordings from single neurons have shown that corollary discharge signals can influence visual representations in parietal, frontal and extrastriate visual cortex, as well as the superior colliculus (SC). In each of these areas, visual representations are remapped in conjunction with eye movements. Remapping provides a mechanism for creating a stable, eye-centred map of salient locations. Temporal and spatial aspects of remapping are highly variable from cell to cell and area to area. Most neurons in the lateral intraparietal area remap stimulus traces, as do many neurons in closely allied areas such as the frontal eye fields the SC and extrastriate area V3A. Remapping is not purely a cortical phenomenon. Stimulus traces are remapped from one hemifield to the other even when direct cortico-cortical connections are removed. The neural circuitry that produces remapping is distinguished by significant plasticity, suggesting that updating of salient stimuli is fundamental for spatial stability and visuospatial behaviour. These findings provide new evidence that a unified and stable representation of visual space is constructed by redundant circuitry, comprising cortical and subcortical pathways, with a remarkable capacity for reorganization.     

A computational framework for topographies of cortical areas

Self-organizing feature maps (SOFMs) represent a dimensionality-reduction algorithm that has been used to replicate feature topographies observed experimentally in primary visual cortex (V1). We used the SOFM algorithm to model possible topographies of generic sensory cortical areas containing up to five arbitrary physiological features. This study explored the conditions under which these multi-feature SOFMs contained two features that were mapped monotonically and aligned orthogonally with one another (i.e., “globally orthogonal”), as well as the conditions under which the map of one feature aligned with the longest anatomical dimension of the modeled cortical area (i.e., “dominant”). In a single SOFM with more than two features, we never observed more than one dominant feature, nor did we observe two globally orthogonal features in the same map in which a dominant feature occurred. Whether dominance or global orthogonality occurred depended upon how heavily weighted the features were relative to one another. The most heavily weighted features are likely to correspond to those physical stimulus properties transduced directly by the sensory epithelium of a particular sensory modality. Our results imply, therefore, that in the primary cortical area of sensory modalities with a two-dimensional sensory epithelium, these two features are likely to be organized globally orthogonally to one another, and neither feature is likely to be dominant. In the primary cortical area of sensory modalities with a one-dimensional sensory epithelium, however, this feature is likely to be dominant, and no two features are likely to be organized globally orthogonally to one another. Because the auditory system transduces a single stimulus feature (i.e., frequency) along the entire length of the cochlea, these findings may have particular relevance for topographic maps of primary auditory cortex. This research was supported by The McDonnell Center for Higher Brain Function, The Wallace H. Coulter Foundation and NIH grant DC008880.     

Self-organizing maps for visual feature representation based on natural binocular stimuli

We model the stimulus-induced development of the topography of the primary visual cortex. The analysis uses a self-organizing Kohonen model based on high-dimensional coding. It allows us to obtain an arbitrary number of feature maps by defining different operators. Using natural binocular stimuli, we concentrate on discussing the orientation, ocular dominance, and disparity maps. We obtain orientation and ocular dominance maps that agree with essential aspects of biological findings. In contrast to orientation and ocular dominance, not much is known about the cortical representation of disparity. As a result of numerical simulations, we predict substructures of orientation and ocular dominance maps that correspond to disparity maps. In regions of constant orientation, we find a wide range of horizontal disparities to be represented. This points to geometrical relations between orientation, ocular dominance, and disparity maps that might be tested in experiments. Received: 9 July 1998 / Accepted in revised form: 2 June 1999     

A Proto-Architecture for Innate Directionally Selective Visual Maps

Self-organizing artificial neural networks are a popular tool for studying visual system development, in particular the cortical feature maps present in real systems that represent properties such as ocular dominance (OD), orientation-selectivity (OR) and direction selectivity (DS). They are also potentially useful in artificial systems, for example robotics, where the ability to extract and learn features from the environment in an unsupervised way is important. In this computational study we explore a DS map that is already latent in a simple artificial network. This latent selectivity arises purely from the cortical architecture without any explicit coding for DS and prior to any self-organising process facilitated by spontaneous activity or training. We find DS maps with local patchy regions that exhibit features similar to maps derived experimentally and from previous modeling studies. We explore the consequences of changes to the afferent and lateral connectivity to establish the key features of this proto-architecture that support DS.     

Cooperative self-organization of afferent and lateral connections in cortical maps

A self-organizing neural network model called LISSOM for the synergetic development of afferent and lateral connections in cortical feature maps is presented. The weight adaptation process is purely activity-dependent, unsupervised, and local. The afferent input weights self-organize into a topological map of the input space. At the same time, the lateral interconnection weights adapt, and a unique lateral interaction profile develops for each neuron. Weak lateral connections die off, leaving a pattern of connections that represents the significant long-term correlations of activity on the feature map. LISSOM demonstrates how self-organization can bootstrap based on input information only, without global supervision or predetermined lateral interaction. The model gives rise to a nontopographically organized lateral connectivity similar to that observed in the mammalian neocortex as illustrated by a LISSOM model of ocular dominance column formation in the primary visual cortex. In addition, LISSOM can potentially account for the development of multiple maps of different modalities on the same undifferentiated cortical architecture. Received: 12 May 1993/Accepted in revised form: 22 September 1993     

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.     

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     

The influence of cortical feature maps on the encoding of the orientation of a short line

The inhomogeneous distribution of the receptive fields of cortical neurons influences the cortical representation of the orientation of short lines seen in visual images. We construct a model of the response of populations of neurons in the human primary visual cortex by combining realistic response properties of individual neurons and cortical maps of orientation and location preferences. The encoding error, which characterizes the difference between the parameters of a visual stimulus and their cortical representation, is calculated using Fisher information as the square root of the variance of a statistically efficient estimator. The error of encoding orientation varies considerably with the location and orientation of the short line stimulus as modulated by the underlying orientation preference map. The average encoding error depends only weakly on the structure of the orientation preference map and is much smaller than the human error of estimating orientation measured psychophysically. From this comparison we conclude that the actual mechanism of orientation perception does not make efficient use of all the information available in the neuronal responses and that it is the decoding of visual information from neuronal responses that limits psychophysical performance. Action Editor: Terrence Sejnowski     

The role of visual experience in the formation of binocular projections in frogs

Many parts of the visual system contain topographic maps of the visual field. In such structures, the binocular portion of the visual field is generally represented by overlapping, matching projections relayed from the two eyes. One of the developmental factors which helps to bring the maps from the two eyes into register is visual input. The role of visual input is especially dramatic in the frog, Xenopus laevis. In tadpoles of this species, the eyes initially face laterally and have essentially no binocular overlap. At metamorphosis, the eyes begin to move rostrodorsally; eventually, their visual fields have a 170 degree region of binocular overlap. Despite this major change in binocular overlap, the maps from the ipsilateral and contralateral eyes to the optic tectum normally remain in register throughout development. This coordination of the two projections is disrupted by visual deprivation. In dark-reared Xenopus, the contralateral projection is nearly normal but the ipsilateral map is highly disorganized. The impact of visual input on the ipsilateral map also is shown by the effect of early rotation of one eye. Examination of the tectal lobe contralateral to the rotated eye reveals that both the contralateral and the ipsilateral maps to that tectum are rotated, even though the ipsilateral map originates from the normal eye. Thus, the ipsilateral map has changed orientation to remain in register with the contralateral map. Similarly, the two maps on the other tectal lobe are in register; in this case, both projections are normally oriented even though the ipsilateral map is from the rotated eye. The discovery that the ipsilateral eye's map reaches the tectum indirectly, via a relay in the nucleus isthmi, has made it possible to study the anatomical changes underlying visually dependent plasticity. Retrograde and anterograde tracing with horseradish peroxidase have shown that eye rotation causes isthmotectal axons to follow abnormal trajectories. An axon's route first goes toward the tectal site where it normally would arborize but then changes direction to reach a new tectal site. Such rearrangements bring the isthmotectal axons into proximity with retinotectal axons which have the same receptive fields. Anterograde horseradish peroxidase filling has also been used to study the trajectories and arborizations of developing isthmotectal axons. The results show that the axons enter the tectum before the onset of eye migration but do not begin to branch profusely until eye movement begins to create a zone of binocular space.(ABSTRACT TRUNCATED AT 400 WORDS)     

Columnar architecture and computational anatomy in primate visual cortex: segmentation and feature extraction via spatial frequency coded difference mapping

Columnar architecture is a well established organizational principle for a variety of cortical systems. If two topographically mapped receptor systems, which receive slightly different views of the same physical stimulus, are interlaced as columns, then the difference map of the afferent inputs is coded within a spatial frequency channel of the resultant map. The difference map of the left and right retinal views of a three dimensensional scene contains cues for the binocular disparity of the objects in the scene. Physical objects which are located at a common distance from the observer will be represented by area's of difference mapping which possesss common cortical textural values. Thus, segmentation of the cortical representation of the visual scene by values of positional disparity may be accomplished by conventional monocular segmentation techniques, applied to the cortical representation.The difference map is carried by a spatial frequency modulation determined by the period of the columnar interlacing. Ocular dominance columns in human striate cortex suggest a spatial frequency carrier which is roughly equal to the inverse of Panum's area. Since the difference mapping is a global attribute of the cortical representation, and is not contingent on the existence of labeled single cell feature extractors, the difference mapping algorithm represents a distinct alternative to conventional single cell approaches to feature extraction.The difference mapping algorithm is briefly discussed in relation to other difference channels, such as color opponent segmentation and binocular orientation disparity. It is suggested that difference mapping may reflect a general synergistic mechanism relating topographic mapping and columnar architecture, which reduces the problem of feature extraction and segmentation for depth and color opponent channels to a single textural mechanism.