Abstract
BackgroundThe 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.ResultsWe 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 the 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.ConclusionsOur 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.
Highlights
By evaluating the energy assigned to the rhombic pinwheel crystals (rPWCs) and nECPs, we investigated the structure of the two-dimensional phase space of the elastic net (EN) model with an arbitrary orientation stimulus distribution
Together with recent progress on the quantitative characterization of cortical functional architecture [38,69,93], this study lays the foundation for a mathematically rigorous and biologically informative search for optimization principles that successfully explain the architecture of columnar contour representations in the primary visual cortex
A mathematically controlled and quantitatively precise determination of the predictions of candidate optimization principles is demanded by accumulating evidence indicating that geometrical features of visual cortical representations are biologically laid down with a precision in the range of a few percent [38,127,128]
Summary
The pattern of orientation columns in the primary visual cortex (V1) of carnivores, primates, and their close relatives are among the most intensely studied structures in the cerebral cortex and a large body of experimental (e. g., [1,2,3,4,5,6,7,8,9,10,11,12,13]) and theoretical work (e.g., [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]) has been dedicated to uncovering its organization principles and the circuit level mechanisms that underlie its development and operation. Orientation preference maps (OPMs) exhibit a roughly repetitive arrangement of preferred orientations in which adjacent columns preferring the same orientation are separated by a typical distance in the millimeter range [2,3,4,5,10] This range seems to be set by cortical mechanisms both intrinsic to a particular area [40] but potentially involving interactions visual cortex [43,44]. Kaschube et al [38] quantitatively compared pinwheel arrangements in a large dataset from three species widely separated in the evolution of eutherian mammals These authors found that the spatial statistics of pinwheels are surprisingly invariant. 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
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