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

The influence of restricted orientation rearing on map structure in primary visual cortex

Visual experience is critical to the development of the structure of the primary visual cortex and, in turn, normal functional vision. The primary visual cortex contains maps of multiple features of the visual input, and these maps are characterised by specific types of geometric relationships. Manipulations of the visual environment during development in animals such as ferrets, cats and monkeys provide an opportunity to probe the rules governing map formation via their effect on these relationships. Here we use a computational model of map formation based on dimension-reduction principles to predict the effect on map relationships of presenting only a single orientation to one eye and the orthogonal orientation to the other eye. Since orientation preference and ocular dominance are now tightly coupled one might expect orientation and ocular dominance contours to lose their normally orthogonal relationship and instead run parallel to each other. However, surprisingly, the model predicts that orthogonal intersection can sometimes be preserved in this case. The model also predicts that orientation pinwheels can migrate from the centre to the borders of ocular dominance columns, and that the wavelengths of the ocular dominance and orientation maps can become coupled. These predictions provide a way to further test the adequacy of dimension reduction principles for explaining map structure under perturbed as well as normal rearing conditions, and thus allow us to deepen our understanding of the effect of the visual environment on visual cortical development. Copyright © 2009 Elsevier Inc. All rights reserved

Using theoretical models to analyse neural development

The development of the nervous system is an extremely complex and dynamic process. Through the continuous interplay of genetic information and changing intra- and extracellular environments, the nervous system constructs itself from precursor cells that divide and form neurons, which migrate, differentiate and establish synaptic connections. Our understanding of neural development can be greatly assisted by mathematical and computational modelling, because it allows us to bridge the gap between system-level dynamics and the lower level cellular and molecular processes. This Review shows the potential of theoretical models to examine many aspects of neural development. © 2011 Macmillan Publishers Limited. All rights reserved