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

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

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

Relation of clustered anatomical variation to cross-modal response and fractional anisotropy.

<p>A: For each of 52 subjects (blind and sighted), we obtained the BOLD fMRI response in V1 while subjects listened to auditory sentences played forwards and in reverse, as compared to white noise. We modeled the ability of individual variation in the three anatomical clusters to account for variation in cross-modal BOLD fMRI response. For each subject, the x-axis gives the prediction of the model for BOLD fMRI response, and the y-axis the observed response. There was a significant model fit (p = 0.00051). B: Model weights for the fit to the cross-modal response data. Shown are the mean and standard error of weights upon each of the clusters of anatomical variation in their prediction of V1 BOLD fMRI response. Only the first cluster of anatomical variation (V1 cortical <i>thinness</i>) had a fitting weight significantly different from zero. The loading on this weight is negative, indicating that <i>thicker</i> V1 cortex predicts greater cross-modal responses. C: For each of 59 subjects, we measured fractional anisotropy within the optic radiations and splenium of the corpus callosum. We modeled the ability of individual variation in the three anatomical clusters to account for variation in FA. For each subject, the x-axis gives the prediction of the model for FA, and the y-axis the observed measure. The entire model fits the data above chance (p = 0.016). D: Model weights for the fit to the FA data. Shown are the mean and standard error of weights upon each of the clusters of anatomical variation in their prediction of the FA measure. Only the third cluster of anatomical variation (chiasm and LGN volume) had a fitting weight significantly different from zero.</p

Patterns of shared variation in visual pathway anatomy.

<p>A: The eight measures of visual pathway anatomy are illustrated on an axial schematic of the human brain. The groupings of the measures are to assist subsequent interpretation of the data. B: The Euclidean distance matrix and dendrogram for the 8 measures across the sighted population. <i>Left</i>. The square-root, sum-squared difference in values between two measures across subjects provides a measure of Euclidean distance. Darker shades indicate pairings of measures that have similar variation across subjects, and thus lower distance values. <i>Right</i>. The distance matrix was subjected to hierarchical clustering, yielding a dendrogram. The length of each branch reflects the distance between the paired measures. The three primary clusters of anatomical variation are colored green, blue, and red. C: <i>Left</i>. The distance matrix across the 8 measures for the blind population. A similar overall structure is seen as compared to the sighted. <i>Right</i>. The dendrogram derived from measures from the blind subjects. The same overall cluster structure is seen. Note that there is some rearrangement in the measurements assigned to cluster #2 in the blind as compared to the sighted.</p

Mean group differences in the anatomical measures.

<p>Mean group differences in the anatomical measures.</p

Relation of clustered anatomical variation to cross-modal response and fractional anisotropy.

<p>A: For each of 52 subjects (blind and sighted), we obtained the BOLD fMRI response in V1 while subjects listened to auditory sentences played forwards and in reverse, as compared to white noise. We modeled the ability of individual variation in the three anatomical clusters to account for variation in cross-modal BOLD fMRI response. For each subject, the x-axis gives the prediction of the model for BOLD fMRI response, and the y-axis the observed response. There was a significant model fit (p = 0.00051). B: Model weights for the fit to the cross-modal response data. Shown are the mean and standard error of weights upon each of the clusters of anatomical variation in their prediction of V1 BOLD fMRI response. Only the first cluster of anatomical variation (V1 cortical <i>thinness</i>) had a fitting weight significantly different from zero. The loading on this weight is negative, indicating that <i>thicker</i> V1 cortex predicts greater cross-modal responses. C: For each of 59 subjects, we measured fractional anisotropy within the optic radiations and splenium of the corpus callosum. We modeled the ability of individual variation in the three anatomical clusters to account for variation in FA. For each subject, the x-axis gives the prediction of the model for FA, and the y-axis the observed measure. The entire model fits the data above chance (p = 0.016). D: Model weights for the fit to the FA data. Shown are the mean and standard error of weights upon each of the clusters of anatomical variation in their prediction of the FA measure. Only the third cluster of anatomical variation (chiasm and LGN volume) had a fitting weight significantly different from zero.</p

Blind subject group details.

<p>Blind subject group details.</p