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

Predicted contextual modulation varies with distance from pinwheel centers in the orientation preference map

In the primary visual cortex (V1) of some mammals, columns of neurons with the full range of orientation preferences converge at the center of a pinwheel-like arrangement, the ‘pinwheel center' (PWC). Because a neuron receives abundant inputs from nearby neurons, the neuron's position on the cortical map likely has a significant impact on its responses to the layout of orientations inside and outside its classical receptive field (CRF). To understand the positional specificity of responses, we constructed a computational model based on orientation preference maps in monkey V1 and hypothetical neuronal connections. The model simulations showed that neurons near PWCs displayed weaker but detectable orientation selectivity within their CRFs, and strongly reduced contextual modulation from extra-CRF stimuli, than neurons distant from PWCs. We suggest that neurons near PWCs robustly extract local orientation within their CRF embedded in visual scenes, and that contextual information is processed in regions distant from PWCs

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