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

Pinwheel stabilization by ocular dominance segregation

We present an analytical approach for studying the coupled development of ocular dominance and orientation preference columns. Using this approach we demonstrate that ocular dominance segregation can induce the stabilization and even the production of pinwheels by their crystallization in two types of periodic lattices. Pinwheel crystallization depends on the overall dominance of one eye over the other, a condition that is fulfilled during early cortical development. Increasing the strength of inter-map coupling induces a transition from pinwheel-free stripe solutions to intermediate and high pinwheel density states.Comment: 10 pages, 4 figure

Saturation in phosphene size with increasing current levels delivered to human visual cortex

Electrically stimulating early visual cortex results in a visual percept known as a phosphene. Although phosphenes can be evoked by a wide range of electrode sizes and current amplitudes, they are invariably described as small. To better understand this observation, we electrically stimulated 93 electrodes implanted in the visual cortex of 13 human subjects who reported phosphene size while stimulation current was varied. Phosphene size increased as the stimulation current was initially raised above threshold, but then rapidly reached saturation. Phosphene size also depended on the location of the stimulated site, with size increasing with distance from the foveal representation. We developed a model relating phosphene size to the amount of activated cortex and its location within the retinotopic map. First, a sigmoidal curve was used to predict the amount of activated cortex at a given current. Second, the amount of active cortex was converted to degrees of visual angle by multiplying by the inverse cortical magnification factor for that retinotopic location. This simple model accurately predicted phosphene size for a broad range of stimulation currents and cortical locations. The unexpected saturation in phosphene sizes suggests that the functional architecture of cerebral cortex may impose fundamental restrictions on the spread of artificially evoked activity and this may be an important consideration in the design of cortical prosthetic devices

Temporal decorrelation of collective oscillations in neural networks with local inhibition and long-range excitation

We consider two neuronal networks coupled by long-range excitatory interactions. Oscillations in the gamma frequency band are generated within each network by local inhibition. When long-range excitation is weak, these oscillations phase-lock with a phase-shift dependent on the strength of local inhibition. Increasing the strength of long-range excitation induces a transition to chaos via period-doubling or quasi-periodic scenarios. In the chaotic regime oscillatory activity undergoes fast temporal decorrelation. The generality of these dynamical properties is assessed in firing-rate models as well as in large networks of conductance-based neurons.Comment: 4 pages, 5 figures. accepted for publication in Physical Review Letter

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

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

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 OP 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 an 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.Comment: 90 pages, 16 figure

Self-organization and the selection of pinwheel density in visual cortical development

Self-organization of neural circuitry is an appealing framework for understanding cortical development, yet its applicability remains unconfirmed. Models for the self-organization of neural circuits have been proposed, but experimentally testable predictions of these models have been less clear. The visual cortex contains a large number of topological point defects, called pinwheels, which are detectable in experiments and therefore in principle well suited for testing predictions of self-organization empirically. Here, we analytically calculate the density of pinwheels predicted by a pattern formation model of visual cortical development. An important factor controlling the density of pinwheels in this model appears to be the presence of non-local long-range interactions, a property which distinguishes cortical circuits from many nonliving systems in which self-organization has been studied. We show that in the limit where the range of these interactions is infinite, the average pinwheel density converges to $\pi$. Moreover, an average pinwheel density close to this value is robustly selected even for intermediate interaction ranges, a regime arguably covering interaction-ranges in a wide range of different species. In conclusion, our paper provides the first direct theoretical demonstration and analysis of pinwheel density selection in models of cortical self-organization and suggests to quantitatively probe this type of prediction in future high-precision experiments.Comment: 22 pages, 3 figure

Optimality of Human Contour Integration

For processing and segmenting visual scenes, the brain is required to combine a multitude of features and sensory channels. It is neither known if these complex tasks involve optimal integration of information, nor according to which objectives computations might be performed. Here, we investigate if optimal inference can explain contour integration in human subjects. We performed experiments where observers detected contours of curvilinearly aligned edge configurations embedded into randomly oriented distractors. The key feature of our framework is to use a generative process for creating the contours, for which it is possible to derive a class of ideal detection models. This allowed us to compare human detection for contours with different statistical properties to the corresponding ideal detection models for the same stimuli. We then subjected the detection models to realistic constraints and required them to reproduce human decisions for every stimulus as well as possible. By independently varying the four model parameters, we identify a single detection model which quantitatively captures all correlations of human decision behaviour for more than 2000 stimuli from 42 contour ensembles with greatly varying statistical properties. This model reveals specific interactions between edges closely matching independent findings from physiology and psychophysics. These interactions imply a statistics of contours for which edge stimuli are indeed optimally integrated by the visual system, with the objective of inferring the presence of contours in cluttered scenes. The recurrent algorithm of our model makes testable predictions about the temporal dynamics of neuronal populations engaged in contour integration, and it suggests a strong directionality of the underlying functional anatomy