Spherical rotation (permutation) of a parcellated cortical map

Code (in Matlab and R) to perform a spherical rotation (permutation) of a parcellated cortical map.

Includes coordinates on the Freesurfer sphere of 360 regions from the Glasser et al. Nature 2016 HCP parcellation.

For details, see the Váša et al. Cerebral Cortex manuscript referenced below; and in particular the supplementary information section "Spatial permutation test". The current implementation is an updated version of the scheme described in the Cerebral Cortex manuscript; see Notes below.

Code

Each version (Matlab and R) contains two functions: rotate_parcellation and perm_sphere_p.

rotate_parcellation generates a desired number of rotated permutations of a parcellation, given the coordinates of left and right hemispheres of this parcellation on the sphere.

perm_sphere_p generates a permutation p-value, given two parcellated cortical maps to be compared, a set of permutations (generated by rotate_parcellation) and the desired type of correlation to compare the cortical maps (eg: Spearman).

Additionally included is centroid_extraction_sphere, a Matlab function to obtain spherical coordinates of regional centroids from Freesurfer .annot files, for any parcellation (written by Rafael Romero-Garcia). The spherical centroids of the multimodal HCP parcellation (Glasser et al. Nature 536, 2016) are included in the file sphere_HCP.txt; the 360 regions are ordered as left hemishpere -> right hemisphere, with the 180 regions within each hemisphere ordered according to Table 1 in SI Appendix of the Glasser et al. (2016) paper: https://media.nature.com/original/nature-assets/nature/journal/v536/n7615/extref/nature18933-s3.pdf (page 81).

For specific instructions for each function, see the code.

Example

The spatial permutation test was applied three times to cortical maps of the x, y and z coordinates of regional centroids in MNI space. The spatial contiguity and hemispheric symmetry is preserved within the permuted maps.

References

This specific implementation of the code was developed specifically for parcellated cortical maps, and was first applied in the following paper:

• Váša F., Seidlitz J., Romero-Garcia R., Whitaker K. J., Rosenthal G., Vértes P. E., Shinn M., Alexander-Bloch A., Fonagy P., Dolan R. J., Goodyer I. M., the NSPN consortium, Sporns O., Bullmore E. T. (2017). Adolescent tuning of association cortex in human structural brain networks. Cerebral Cortex, 28(1):281–294.

However, the idea of a spherical rotation (permutation) was first proposed for vertex-level cortical maps, and first applied (to the best of my knowledge) in the following paper:

• Alexander-Bloch, A., Raznahan, A., Bullmore, E., and Giedd, J. (2013). The convergence of maturational change and structural covariance in human cortical networks. Journal of Neuroscience, 33(7):2889–99.

The same idea was subsequently explored in other papers.

Finally, the idea was more formally discussed in the following paper, where the methods (for vertex-wise analyses) are made publicly available as well:

• Alexander-Bloch, A., Shou H., Liu, S., Satterthwaite, T. D., Glahn, D. C., Shinohara, R. T., Vandekar, S. N. and Raznahan, A. (2018). On testing for spatial correspondence between maps of human brain structure and function. NeuroImage, 178:540-551.

For code to perform spherical permutations at the vertex level, see https://github.com/spin-test/spin-test.

For an excellent Python implementation, see https://github.com/netneurolab/markello_spatialnulls and the associated manuscript Comparing spatial null models for brain maps by Ross Markello and Bratislav Misic.

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Note 4 | 29th June 2023 The R version of "rotate.parcellation" has now been updated to include a different permutation method; options include 'vasa' and 'hungarian' (default).

Note 3 | 16th October 2019 The R version of "rotate.parcellation" has now been updated to uniformly sample the space of permutations on the sphere.

Note 2 | 5th September 2019: The matlab version of "rotate_parcellation" has been updated to uniformly sample the space of permutations on the sphere (see Note 1 below). The R function has not been updated as yet. Please use R versions of the code with caution.

Note 1 | July 2019: I am grateful to Aaron Alexander-Bloch for recently (June 2019) bringing to my attention that the permutation approach implemented here is biased, and does not uniformly sample the space of permutations on the sphere. For details, see description and references within the document "technical_note_18July2018.docx" at https://github.com/spin-test/spin-test.