This page describes a template of the human brain that can be used to predict with known accuracy and precision the retinotopic organization of primary visual cortex based upon cortical surface anatomy. The work is described in this paper:
The template is comprised of cortical surface representations in MGH/MGZ format suitable for use in FreeSurfer. This page provides links to download these files, access to the raw data used to construct the template, and additional information about the template not reported in the paper.
The template is free to use (with appropriate attribution) for academic or commercial purposes. The atlas may not be distributed for commercial gain. Please refer any questions regarding the template to firstname.lastname@example.org.
The relationship between the folding structure of the brain and cortical visual representation was first described in schematic form by Gordon Holmes in 1918.1) This mapping of structure-to-function was further refined based upon lesion analysis 2), but remained a general scheme and not a system for individual prediction. An important advance in 2008 was provided by Oliver Hinds, Bruce Fischl, and their colleagues 3) when they demonstrated that the location of the stria of Gennari (an anatomical marker of primary visual cortex) may be accurately predicted with reference to cortical surface topology. This provided a means of aligning the edges of primary visual cortex across individuals using a surface based atlas (FreeSurfer). We have now shown that the retinotopic organization of different people is well aligned within primary visual cortex once transformed to the surface atlas space (and following some basic surface transformations). Moreover, we can use a simple algebraic form to fit these functional data on the cortical surface and successfully extend the prediction beyond the mapping data.
Practically, we find that cortical surface anatomy predicts the retinotopic organization of area V1 at least as accurately as a 10-25 minute, retinotopic mapping fMRI scan at 3 Tesla conducted in a young, cooperative subject4). Additionally, as the retinotopic organization of left and right area V1 within the template space is highly similar and statistically independent, the measures from the two hemispheres may be treated as separate subjects.
The file formats used to distribute the template include:
.datfile consists of 6 columns and 163,842 rows. Columns are separated by tabs (
\tin C/C++) while rows are separated by newlines (
\nin C/C++). Each row represents a single vertex in
fsaverage_symspace. The first three columns of a given row provide the x, y, and z coordinates of the vertex; the last three columns provide the observed polar angle, the observed eccentricity, and the F-statistic associated with that retinotopic assignment.
V1 Polar Angle template - fsaverage_sym MGH overlay.
V1 Eccentricity template - fsaverage_sym MGH overlay.
V1 Polar Angle template (Axis Normalized distance)- fsaverage_sym MGH overlay.
V1 Eccentricity template (Axis Normalized distance)- fsaverage_sym MGH overlay.
Raw data - VTK format - direct download.
Raw data - VTK format - gzipped tarball (.tar.gz).
A Mathematica notebook containing the complete template fitting routine used in the paper is available for download. This notebook, if unmodified, will automatically read our raw data from our website. Alternately, you may download our raw data as a gzipped tarball (
.tar.gz; see links above), unpack it, and change the
$TemplateDirectory variable at the top of the Mathematica notebook if you desire faster load-times.
Mathematica notebook – CODE
Mathematica notebook – PDF format
The polar angle and eccentricity templates are stored as a FreeSurfer overlay (MGH) file sampled for the hemisphere-symmetric
fsaverage_sym surface space. The hemisphere-symmetric atlas was created by Douglas Greve and colleagues and is described in this conference abstract:
Below we describe the steps required to convert data from the standard FreeSurfer atlas to the hemisphere-symmetric template.
To run the data through the combining hemispheres pipeline,
recon-all -s subjid -autorecon-all)
surfreg) and atlas (
fsaverage_sym), which are not part of the standard FreeSurfer 5.1 distribution, should be installed
surfregshould be installed in
fsaverage_symshould be copied to the FreeSufer subject data directory
These two steps first mirror reverses the right hemisphere of the subject, and then registers the surface to the left hemisphere. The data are therefore cast within a pseudo-left hemisphere space.
surfreg --s $subject --t fsaverage_sym --lh surfreg --s $Subject --t fsaverage_sym --lh --xhemi
Steps for resampling a subject overlay data to the symmetric hemisphere:
mri_surf2surf --srcsubject <subject> --srcsurfreg fsaverage_sym.sphere.reg --trgsubject fsaverage_sym --trgsurfreg sphere.reg --hemi lh --sval <lh.data.mgh> --tval <lh.data.sym.mgh>
mri_surf2surf --srcsubject <subject>/xhemi --srcsurfreg fsaverage_sym.sphere.reg --trgsubject fsaverage_sym --trgsurfreg sphere.reg --hemi lh --sval <rh.data.mgh> --tval <rh.data.sym.mgh>
Note that the above code accomplishes the transformation of a subject's specific surface topology to the fsaverage_sym topology. If you wish to, for example, compare the polar angle predictions in V1 with the BOLD activation pattern from an fMRI experiment, you will need to either inverse this transform, such that the polar angle data is resampled to the subject's specific space, or transform your subject's BOLD activation data to the fsaverage_sym sphere as well.
To transform the fsaverage_sym template files to match your subject's specific topology, the following code should be used:
mri_surf2surf --srcsubject fsaverage_sym --srcsurfreg sphere.reg --trgsubject <subject> --trgsurfreg fsaverage_sym.sphere.reg --hemi lh --sval <lh.data.sym.mgh> --tval <lh.data.mgh>
mri_surf2surf --srcsubject fsaverage_sym --srcsurfreg sphere.reg --trgsubject <subject>/xhemi --trgsurfreg fsaverage_sym.sphere.reg --hemi lh --sval <rh.data.sym.mgh> --tval <rh.data.mgh>
The ability of the template to predict retinotopic organization is limited by several sources of variability and error. One source is structure-structure variability, in which residual differences in anatomical organization are not resolved by the cortical registration technique.
The figure shows the average and standard deviation of sulcal/gyral curvature across subjects after registration to the FSAverage template within our studied V1 cortical patch. The mean curvature appropriately matches the curvature of the template (compare with Figure 1B). The standard deviation of curvature across subjects is nearly uniform across the template space. This accords with the generally uniform performance of the template in predicting retinotopic values across the template space.
We asked if variability across subjects in the quality of anatomical normalization could explain variability in the quality of template prediction. We obtained the mean Jacobian value (average warp parameter) across subjects and related this to the median error in template prediction for that subject from the leave-one-out analysis. No significant correlation was seen between these measures, even after accounting for differences in the first-order surface area of the V1 patch, which contributes to the Jacobian measure.
Therefore, it seems that residual variation in structure-structure alignment across subjects does not account for a substantial portion of the error in retinotopic map predictions.
The algebraic form we developed for fitting retinotopy on the cortical surface is influenced by the work of Schira and colleagues 5). A distinctive property of the Schira model is that it exhibits constant areal magnification along polar angle. Our model implementation is capable of fitting data that has this property, although it does not enforce this constraint. In our data, we observe a violation of constant areal magnification. This is seen as the “flattening” of the model fit presented in Fig. 2E, where measured polar angle changes more slowly per unit change in cortical position close to the horizontal meridian; and in Fig. S1B where there is a magnification of representation near the horizontal meridian.
While this apparent distortion does not impact the predictive properties of the template, it does differ from empirical surface measurements of retinotopic organization in primates. What is the source of this distortion? At least some of the variation in areal magnification across polar angle is a consequence of the cortical inflation process and projection to a two-dimensional surface. The inflation and flattening process necessarily violates either equal areas of the triangular mesh or equal angles, or both. FreeSurfer adopts a balance between these two types of distortion. We confirmed the presence of areal distortion by comparing the surface areas of equivalent regions of projected visual space in the flattened surface representation and on the folded pial surface. This distortion may also be appreciated in the following figure, which shows the mean Jacobian6) across the V1 cortical patch. There is areal compression at the gyral ridge, resulting in a relative expansion of the sulcal plane, and thus the apparent violation of the constant areal magnification along polar angle observed in our retinotopic template representations.