Rating data from the supplemental experiment.

<p>Average ratings across the three observers. L*+M*, penumbral L and M cone modulation; Melanopsin A, melanopsin-directed modulation that did not silence penumbral cones; Melanopsin B, melanopsin-directed modulation with penumbral cones silenced; L+M+L*+M*, modulation visible to both open-field and penumbral L and M cones. Individual observer ratings are shown to the right.</p

Raw fundus photographs.

<p>Unedited fundus photographs (OS = left eye, OD = right eye) obtained for our naïve observer.</p

Contrast splatter.

<p>A: Contrast splatter calculations for the penumbral L and M cone (L*+M*) modulation (27 year old observer). Separate splatter maps for open-field and penumbral L and M cones are provided. Each point in a splatter map indicates in pseudocolor the contrast that will be seen by a variant of the nominal cone spectral sensitivity, as indicated by its position on the age and <i>λ</i>_max axes. The color scale is provided at the bottom of the figure, with negative contrast splatter indicating contrast splatter that is 180° out-of-phase with the nominal stimulus modulation. The open square indicates age and <i>λ</i>_max of the nominal cone spectral sensitivity, while the solid and dashed ellipses indicate the 95% and 99% confidence ellipses for variation around the nominal sensitivity. Open and closed circles on each ellipse show the variant with the minimum and maximum contrast splatter on the ellipse. Open and closed circles on the edges of the map represent the variant with minimum and maximum contrast splatter over the whole range of variants computed. The nominal contrast of the modulation for each cone type is provided in the upper right of each map. B: Comparison of contrast seen by the penumbral vs. open-field L cones across the entire range of photoreceptor variants studied in panel A (top plot) and similarly for the M cones (bottom plot). C: Contrast splatter maps for the modulation that stimulated both penumbral and open-field L and M cones together (27 year old observer). Same format as panel A. D: Same type of comparison as shown in panel B, obtained from the splatter maps shown in panel C.</p

Psychophysical rating results.

<p>A: Time course of a single trial of the rating experiment and summary of the perceptual rating scale (see main text for more detailed description). B: Average ratings across the three observers for the L and M cone directed modulations. L*+M*, penumbral L and M cone modulation; L+M, open-field L and M cone modulation; L+M+L*+M*, modulation visible to both open-field and penumbral L and M cones. Individual observer ratings are shown to the right. C: Average ratings across the three observers for the S cone directed modulations. S*, penumbral S cone modulation; S, open-field S cone modulation; S+S*, modulation visible to both open-field and penumbral S cones. Individual observer ratings are shown to the right.</p

Spectral sensitivities and apparatus.

<p>A: Schematic diagram of the retina showing the shadows cast by the retinal blood vessels lying in front of the photoreceptive layer of the retina. B: The spectral sensitivities of the open-field cones (<i>upper panel</i>) are filtered by the hemoglobin transmittance spectrum (<i>middle panel</i>), resulting in wavelength-specific changes of the cone spectral sensitivities (<i>lower panel</i>). C: All modulations are carried out around a rod-saturating background whose spectrum is shown at the left. On the right are plotted the spectral modulations that target each of the indicated cone class(es), with the targeted class(es) indicated at the upper right of each individual plot. The amplitudes of these modulations are varied sinusoidally in time between the plotted positive (red) and negative (black) modulations and are then added to the background spectrum to produce the stimuli seen by the observer.</p

Errors by visual area for dataset D_10°.

a<p>Errors are calculated in a typical leave-one-out fashion in which each subject is compared to the prediction found using all other subjects; all significant vertices between 1.25° and 8.75° of eccentricity are included, and the reported errors represent the median of all vertices from all subjects.</p>b<p>Median absolute leave-one-out error between expected and observed values of all vertices.</p>c<p>Median signed leave-one-out error, expected value minus observed value, of all vertices.</p>d<p>Median absolute leave-one-out error, as calculated by predicting the polar angle and eccentricity of the left-out subject from the confidence-weighted mean of all other subjects.</p>e<p>Median absolute error between observed values and those predicted by the algebraic model of retinotopy prior to any registration.</p>f<p>Median absolute error between observed values from two identical 20 minute scans.</p><p>Vertices for which the <i>F</i>-statistic of the polar angle and eccentricity assignments were below 5 were discarded.</p

Correction of Distortion in Flattened Representations of the Cortical Surface Allows Prediction of V1-V3 Functional Organization from Anatomy

<div><p>Several domains of neuroscience offer map-like models that link location on the cortical surface to properties of sensory representation. Within cortical visual areas V1, V2, and V3, algebraic transformations can relate position in the visual field to the retinotopic representation on the flattened cortical sheet. A limit to the practical application of this structure-function model is that the cortex, while topologically a two-dimensional surface, is curved. Flattening of the curved surface to a plane unavoidably introduces local geometric distortions that are not accounted for in idealized models. Here, we show that this limitation is overcome by correcting the geometric distortion induced by cortical flattening. We use a mass-spring-damper simulation to create a registration between functional MRI retinotopic mapping data of visual areas V1, V2, and V3 and an algebraic model of retinotopy. This registration is then applied to the flattened cortical surface anatomy to create an anatomical template that is linked to the algebraic retinotopic model. This registered cortical template can be used to accurately predict the location and retinotopic organization of these early visual areas from cortical anatomy alone. Moreover, we show that prediction accuracy remains when extrapolating beyond the range of data used to inform the model, indicating that the registration reflects the retinotopic organization of visual cortex. We provide code for the mass-spring-damper technique, which has general utility for the registration of cortical structure and function beyond the visual cortex.</p></div

The retinotopic organization of visual cortex as measured and modeled.

<p>(<b>A</b>) The polar angle map, of a subject from our 10° dataset, shown on an inflated left hemisphere. (<b>B</b>) The eccentricity map of the subject shown in part A, shown on an inflated right hemisphere. (<b>C</b>) The algebraic model of retinotopic organization. V1, V2, and V3 are colored white, light gray, and dark gray, respectively. (<b>D</b>) The cortical surface atlas space (<i>fsaverage_sym</i>) from the occipital pole after flattening to the 2D surface. The Hinds V1 border <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003538#pcbi.1003538-Hinds1" target="_blank">[7]</a> is indicated by the dashed black line, and the algebraic model of retinotopic organization used in registration is plotted with all 0°, 90°, and 180° polar angle lines colored according to the legend and the 10° and 90° eccentricity lines dashed and colored white. Shown are the Calcarine Sulcus (CaS), the Parietal-occipital Sulcus (PoS), the Lingual sulcus (LiS), the Inferior Occipital Sulcus (IOS), the Collateral Sulcus (CoS), the posterior Collateral Sulcus (ptCoS), the Inferior Temporal Sulcus (ITS), and the Occipital Pole (OP).</p

Polar angle organization.

<p>(<b>A</b>) The mean weighted aggregate polar angle map of all subjects in dataset D_10° shown in the cortical surface atlas space. (<b>B</b>) The mean weighted aggregate polar angle map from panel A shown in the corrected topology following MSD warping. A line plot of the algebraic model to which the MSD simulation registered the functional data is shown over the functional data. (<b>C</b>) The polar angle template plotted on the <i>fsaverage_sym</i> pial surface. This template was calculated by converting the prediction of polar angle from the idealized model, as applied to vertices in the corrected topology, back to the <i>fsaverage_sym</i> atlas. (<b>D</b>) Median absolute leave-one-out polar angle error for all vertices with predicted eccentricties between 1.25° and 8.75° shown in the <i>fsaverage_sym</i> atlas space. This error was calculated by comparing the predicted polar angle generated from each subset of 18 of the 19 subjects in the 10° dataset to the observed polar angle of the remaining subject. The median absolute overall leave-one-out error is 10.93° (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003538#pcbi-1003538-t001" target="_blank">Tab. 1</a>). The highest errors occur near the foveal confluence and at the dorsal border of V3. (<b>E</b>) Absolute leave-one-out error of the polar angle prediction across all regions (V1, V2, and V3), plotted according to the predicted polar angle value. The thin gray line represents the median error while the thick black line shows a best-fit 5th order polynomial to the median error. The dashed lines demarcate similar fits to the upper and lower error quartiles. Error plots for individual regions are given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003538#pcbi.1003538.s001" target="_blank">Fig. S1</a>.</p

Eccentricity organization.

<p>(<b>A</b>) The mean weighted aggregate eccentricity map of all subjects in dataset D_10° shown in the <i>fsaverage_sym</i> cortical atlas space. (<b>B</b>) The mean weighted aggregate eccentricity map from panel A shown in the corrected topology following MSD warping. A line plot of the algebraic model to which the MSD simulation registered the functional data is shown. (<b>C</b>) The eccentricity template plotted on the <i>fsaverage_sym</i> pial surface. This template was calculated by converting the prediction of eccentricity from the algebraic model, as applied to vertices in the corrected topology, back to the <i>fsaverage_sym</i> topology. (<b>D</b>) Median absolute leave-one-out eccentricity error for all vertices with predicted eccentricties between 1.25° and 8.75° shown in the <i>fsaverage_sym</i> atlas space. This error was calculated by comparing the predicted eccentricity generated from each subset of 18 of the 19 subjects in the 10° dataset to the observed eccentricity of the remaining subject. The median absolute overall leave-one-out error is 0.41° (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003538#pcbi-1003538-t001" target="_blank">Tab. 1</a>). The highest errors occur near the outer eccentricity border of of our stimulus. (<b>E</b>) Absolute leave-one-out error of the eccentricity prediction across all regions (V1, V2, and V3), plotted according to the predicted polar angle value. Error plots for individual regions are given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003538#pcbi.1003538.s002" target="_blank">Fig. S2</a>. (<b>F</b>) The mean weighted aggregate eccentricity map of all subjects in dataset D_20° shown in the cortical patch corrected by MSD warping to the D_10° dataset. Although this dataset includes eccentricities beyond those used to discover the corrected topology, the 20° aggregate data is in good (although not perfect) agreement with the prediction.</p