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.     

The coordinated mapping of visual space and response features in visual cortex

Whether general principles can explain the layouts of cortical maps remains unresolved. In primary visual cortex of ferret, the relationships between the maps of visual space and response features are predicted by a "dimension-reduction" model. The representation of visual space is anisotropic, with the elevation and azimuth axes having different magnification. This anisotropy is reflected in the orientation, ocular dominance, and spatial frequency domains, which are elongated such that their directions of rapid change, or high-gradient axes, are orthogonal to the high-gradient axis of the visual map. The feature maps are also strongly interdependent-their high-gradient regions avoid one another and intersect orthogonally where essential, so that overlap is minimized. Our results demonstrate a clear influence of the visual map on each feature map. In turn, the local representation of visual space is smooth, as predicted when many features are mapped within a cortical area.     

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.     

Standing waves and traveling waves distinguish two circuits in visual cortex

The visual cortex represents stimuli through the activity of neuronal populations. We measured the evolution of this activity in space and time by imaging voltage-sensitive dyes in cat area V1. Contrast-reversing stimuli elicit responses that oscillate at twice the stimulus frequency, indicating that signals originate mostly in complex cells. These responses stand clear of the noise, whose amplitude decreases as 1/frequency, and yield high-resolution maps of orientation preference and retinotopy. We first show how these maps are combined to yield the responses to focal, oriented stimuli. We then study the evolution of the oscillating activity in space and time. In the orientation domain, it is a standing wave. In the spatial domain, it is a traveling wave propagating at 0.2-0.5 m/s. These different dynamics indicate a fundamental distinction in the circuits underlying selectivity for position and orientation, two key stimulus attributes.     

Prediction of orientation selectivity from receptive field architecture in simple cells of cat visual cortex

From the intracellularly recorded responses to small, rapidly flashed spots, we have quantitatively mapped the receptive fields of simple cells in the cat visual cortex. We then applied these maps to a feedforward model of orientation selectivity. Both the preferred orientation and the width of orientation tuning of the responses to oriented stimuli were well predicted by the model. Where tested, the tuning curve was well predicted at different spatial frequencies. The model was also successful in predicting certain features of the spatial frequency selectivity of the cells. It did not successfully predict the amplitude of the responses to drifting gratings. Our results show that the spatial organization of the receptive field can account for a large fraction of the orientation selectivity of simple cells.     

Modulation of activity in human visual area V1 during memory masking

Neurons in the primary visual cortex, V1, are specialized for the processing of elemental features of the visual stimulus, such as orientation and spatial frequency. Recent fMRI evidence suggest that V1 neurons are also recruited in visual perceptual memory; a number of studies using multi-voxel pattern analysis have successfully decoded stimulus-specific information from V1 activity patterns during the delay phase in memory tasks. However, consistent fMRI signal modulations reflecting the memory process have not yet been demonstrated. Here, we report evidence, from three subjects, that the low V1 BOLD activity during retention of low-level visual features is caused by competing interactions between neural populations coding for different values along the spectrum of the dimension remembered. We applied a memory masking paradigm in which the memory representation of a masker stimulus interferes with a delayed spatial frequency discrimination task when its frequency differs from the discriminanda with ±1 octave and found that impaired behavioral performance due to masking is reflected in weaker V1 BOLD signals. This cross-channel inhibition in V1 only occurs with retinotopic overlap between the masker and the sample stimulus of the discrimination task. The results suggest that memory for spatial frequency is a local process in the retinotopically organized visual cortex.     

New paradigm for optical imaging: temporally encoded maps of intrinsic signal

We present a new technique for acquiring and analyzing intrinsic signal optical images of brain activity, using continuous stimulus presentation and data acquisition. The main idea is to present a temporally periodic stimulus and to analyze the component of the response at the stimulus frequency. Advantages of the new technique include the removal of heart, respiration, and vasomotor artifacts, a dramatic increase in spatial resolution, and a 30-fold or greater reduction in acquisition time. We also present a novel approach to localizing instantaneous neuronal responses using time-reversed stimuli that is widely applicable to brain imaging. To demonstrate the power of the technique, we present high-resolution retinotopic maps of five visual areas in mouse cortex and orientation maps in cat visual cortex.     

On the origin of the functional architecture of the cortex

The basic structure of receptive fields and functional maps in primary visual cortex is established without exposure to normal sensory experience and before the onset of the critical period. How the brain wires these circuits in the early stages of development remains unknown. Possible explanations include activity-dependent mechanisms driven by spontaneous activity in the retina and thalamus, and molecular guidance orchestrating thalamo-cortical connections on a fine spatial scale. Here I propose an alternative hypothesis: the blueprint for receptive fields, feature maps, and their inter-relationships may reside in the layout of the retinal ganglion cell mosaics along with a simple statistical connectivity scheme dictating the wiring between thalamus and cortex. The model is shown to account for a number of experimental findings, including the relationship between retinotopy, orientation maps, spatial frequency maps and cytochrome oxidase patches. The theory's simplicity, explanatory and predictive power makes it a serious candidate for the origin of the functional architecture of primary visual cortex.     

Spatial cognition and neuro-mimetic navigation: a model of hippocampal place cell activity

 A computational model of hippocampal activity during spatial cognition and navigation tasks is presented. The spatial representation in our model of the rat hippocampus is built on-line during exploration via two processing streams. An allothetic vision-based representation is built by unsupervised Hebbian learning extracting spatio-temporal properties of the environment from visual input. An idiothetic representation is learned based on internal movement-related information provided by path integration. On the level of the hippocampus, allothetic and idiothetic representations are integrated to yield a stable representation of the environment by a population of localized overlapping CA3-CA1 place fields. The hippocampal spatial representation is used as a basis for goal-oriented spatial behavior. We focus on the neural pathway connecting the hippocampus to the nucleus accumbens. Place cells drive a population of locomotor action neurons in the nucleus accumbens. Reward-based learning is applied to map place cell activity into action cell activity. The ensemble action cell activity provides navigational maps to support spatial behavior. We present experimental results obtained with a mobile Khepera robot. Received: 02 July 1999 / Accepted in revised form: 20 March 2000     

Stereopsis and the random element in the organization of the striate cortex.

Receptive field position and orientation disparities are both properties of binocularly discharged striate neurons. Receptive field position desparities have been used as a key element in the neural theory for binocular depth discrimination. Since most striate cells in the cat are binocular, these position disparities require that cells immediately adjacent to one another in the cortex should show a random scatter in their monocular receptive field positions. Superimposed on the progressive topographical representation of the visual field on the striate cortex there is experimental evidence for a localized monocular receptive field position scatter. The suggestion is examined that the binocular position disparities are built up out of the two monocular position scatters. An examination of receptive field orientation disparities and their relation to the random variation in the monocular preferred orientations of immediately adjacent striate neurons also leads to the conclusion that binocular orientation disparities are a consequence of the two monocular scatters. As for receptive field position, the local scatter in preferred orientation is superimposed on a progressive representation of orientation over larger areas of the cortex. The representation in the striate cortex of visual field position and of stimulus orientation is examined in relation to the correlation between the disparities in receptive field position and preferred orientation. The role of orientation disparities in binocular vision is reviewed.     

Input-Dependent Frequency Modulation of Cortical Gamma Oscillations Shapes Spatial Synchronization and Enables Phase Coding

Fine-scale temporal organization of cortical activity in the gamma range (∼25–80Hz) may play a significant role in information processing, for example by neural grouping (‘binding’) and phase coding. Recent experimental studies have shown that the precise frequency of gamma oscillations varies with input drive (e.g. visual contrast) and that it can differ among nearby cortical locations. This has challenged theories assuming widespread gamma synchronization at a fixed common frequency. In the present study, we investigated which principles govern gamma synchronization in the presence of input-dependent frequency modulations and whether they are detrimental for meaningful input-dependent gamma-mediated temporal organization. To this aim, we constructed a biophysically realistic excitatory-inhibitory network able to express different oscillation frequencies at nearby spatial locations. Similarly to cortical networks, the model was topographically organized with spatially local connectivity and spatially-varying input drive. We analyzed gamma synchronization with respect to phase-locking, phase-relations and frequency differences, and quantified the stimulus-related information represented by gamma phase and frequency. By stepwise simplification of our models, we found that the gamma-mediated temporal organization could be reduced to basic synchronization principles of weakly coupled oscillators, where input drive determines the intrinsic (natural) frequency of oscillators. The gamma phase-locking, the precise phase relation and the emergent (measurable) frequencies were determined by two principal factors: the detuning (intrinsic frequency difference, i.e. local input difference) and the coupling strength. In addition to frequency coding, gamma phase contained complementary stimulus information. Crucially, the phase code reflected input differences, but not the absolute input level. This property of relative input-to-phase conversion, contrasting with latency codes or slower oscillation phase codes, may resolve conflicting experimental observations on gamma phase coding. Our modeling results offer clear testable experimental predictions. We conclude that input-dependency of gamma frequencies could be essential rather than detrimental for meaningful gamma-mediated temporal organization of cortical activity.     

The Caenorhabditis elegans Six/sine oculis class homeobox gene ceh-32 is required for head morphogenesis

Repulsion plays a fundamental role in the establishment of a topographic map of the chick retinotectal projections. This has been highlighted by studies demonstrating the role of opposing gradients of the EphA3 receptor tyrosine kinase on retinal axons and two of its ligands, ephrin-A2 and ephrin-A5, in the tectum. We have analyzed the distribution of these two ephrins in other retinorecipient structures in the chick diencephalon and mesencephalon during the period when visual connections are being established. We have found that both ephrin-A2 and ephrin-A5 and their receptors EphA4 and EphA7 are expressed in gradients whose orientation is consistent with the topography of the nasotemporal axis of the respective retinofugal projections. In addition, their distribution suggests that receptor-ligand interactions may be involved in the organization of connections between the different primary visual centers and, thus, in the topographic organization of secondary visual projections. Interestingly, where projections lack a clear topographic representation, a uniform expression of the Eph-ephrin molecules was observed. Finally, we also show that a similar patterning mechanism may be implicated in the transfer of visual information to the telencephalon. These results suggest a conserved function for EphA receptors and their ligands in the elaboration of topographic maps at multiple levels of the visual pathway.     

Imaging cortical dynamics at high spatial and temporal resolution with novel blue voltage-sensitive dyes

Conventional imaging techniques have provided high-resolution imaging either in the spatial domain or in the temporal domain. Optical imaging utilizing voltage-sensitive dyes has long had the unrealized potential to achieve high resolution in both domains simultaneously, providing subcolumnar spatial detail with millisecond precision. Here, we present a series of developments in voltage-sensitive dyes and instrumentation that make functional imaging of cortical dynamics practical, in both anesthetized and awake behaving preparations, greatly facilitating exploration of the cortex. We illustrate this advance by analyzing the millisecond-by-millisecond emergence of orientation maps in cat visual cortex.     

A mathematical model of the primary visual cortex and hypercolumn

A mathematical model of the primary visual cortex is presented. Basically, the model comprises two features. Firstly, in analogy with the principle of the computerized tomography (CT), it assumes that simple cells in each hypercolumn are not merely detecting line segments in images as features, but rather that they are as a whole representing the local image with a certain representation. Secondly, it assumes that each hypercolumn is performing spatial frequency analyses of local images using that representation, and that the resultant spectra are represented by complex cells. The model is analyzed using numerical simulations and its advantages are discussed from the viewpoint of visual information processing. It is shown that 1) the proposed processing is tolerant to shifts in position of input images, and that 2) spatial frequency filtering operations can be easily performed in the model.     

Application of Kohonen's self-organizing feature map algorithm to cortical maps of orientation and direction preference

Cortical maps of orientation preference in cats, ferrets and monkeys contain numerous half-rotation point singularities. Experimental data have shown that direction preference also has a smooth representation in these maps, with preferences being for the most part orthogonal to the axis of preferred orientation. As a result, the orientation singularities induce an extensive set of linear fractures in the direction map. These fractures run between and connect nearby point orientation singularities. Their existence appears to pose a puzzle for theories that postulate that cortical maps maximize continuity of representation, because the fractures could be avoided if the orientation map contained full-rotation singularities. Here we show that a dimension-reduction model of cortical map formation, which implements principles of continuity and completeness, produces an arrangement of linear direction fractures connecting point orientation singularities which is similar to that observed experimentally. We analyse the behaviour of this model and suggest reasons why the model maps contain half-rotation rather than full-rotation orientation singularities.     

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     

Generalized spin models for coupled cortical feature maps obtained by coarse graining correlation based synaptic learning rules

We derive generalized spin models for the development of feedforward cortical architecture from a Hebbian synaptic learning rule in a two layer neural network with nonlinear weight constraints. Our model takes into account the effects of lateral interactions in visual cortex combining local excitation and long range effective inhibition. Our approach allows the principled derivation of developmental rules for low-dimensional feature maps, starting from high-dimensional synaptic learning rules. We incorporate the effects of smooth nonlinear constraints on net synaptic weight projected from units in the thalamic layer (the fan-out) and on the net synaptic weight received by units in the cortical layer (the fan-in). These constraints naturally couple together multiple feature maps such as orientation preference and retinotopic organization. We give a detailed illustration of the method applied to the development of the orientation preference map as a special case, in addition to deriving a model for joint pattern formation in cortical maps of orientation preference, retinotopic location, and receptive field width. We show that the combination of Hebbian learning and center-surround cortical interaction naturally leads to an orientation map development model that is closely related to the XY magnetic lattice model from statistical physics. The results presented here provide justification for phenomenological models studied in Cowan and Friedman (Advances in neural information processing systems 3, 1991), Thomas and Cowan (Phys Rev Lett 92(18):e188101, 2004) and provide a developmental model realizing the synaptic weight constraints previously assumed in Thomas and Cowan (Math Med Biol 23(2):119–138, 2006).     

Features of the Retinotopic Representation in the Visual Wulst of a Laterally Eyed Bird,the Zebra Finch (Taeniopygia guttata)

The visual wulst of the zebra finch comprises at least two retinotopic maps of the contralateral eye. As yet, it is not known how much of the visual field is represented in the wulst neuronal maps, how the organization of the maps is related to the retinal architecture, and how information from the ipsilateral eye is involved in the activation of the wulst. Here, we have used autofluorescent flavoprotein imaging and classical anatomical methods to investigate such characteristics of the most posterior map of the multiple retinotopic representations. We found that the visual wulst can be activated by visual stimuli from a large part of the visual field of the contralateral eye. Horizontally, the visual field representation extended from -5° beyond the beak tip up to +125° laterally. Vertically, a small strip from -10° below to about +25° above the horizon activated the visual wulst. Although retinal ganglion cells had a much higher density around the fovea and along a strip extending from the fovea towards the beak tip, these areas were not overrepresented in the wulst map. The wulst area activated from the foveal region of the ipsilateral eye, overlapped substantially with the middle of the three contralaterally activated regions in the visual wulst, and partially with the other two. Visual wulst activity evoked by stimulation of the frontal visual field was stronger with contralateral than with binocular stimulation. This confirms earlier electrophysiological studies indicating an inhibitory influence of the activation of the ipsilateral eye on wulst activity elicited by stimulating the contralateral eye. The lack of a foveal overrepresentation suggests that identification of objects may not be the primary task of the zebra finch visual wulst. Instead, this brain area may be involved in the processing of visual information necessary for spatial orientation.