We implemented the systematic construction of connectome harmonics (Fig. 1), that we integrated into an existing processing pipeline (SCRIPTS, (Proix et al., 2016)). Briefly, SCRIPTS is an open-source pipeline that processes MRI and dMRI to build subject-specific surface meshes, parcellations and corresponding connectivity matrices. We extended this pipeline with new features allowing for computing subject-specific and subject-averaged high-resolution surface-based connectivity matrices, and connectome harmonics. The framework combines local and long-range connectivity matrices to form a high-resolution structural connectome, on which the graph Laplacian is applied, and from which the connectome harmonics are computed. Only parameters relevant to the high-resolution connectome and the construction of those harmonics are explored in this work.

Overview of the workflow for the construction of the connectome harmonics. Local connectivity from cortical surface mesh (bottom left) and long-range connections from tractography (top left) are combined in a high-resolution structural connectome (middle), from which a graph Laplacian L is computed based on the adjacency (A) and the degree (D) matrices of the combined connectivities. Connectome harmonics (right) are the eigenvectors of the graph Laplacian.

To alleviate the known shortcomings associated with subject-specific imaging methods (Bürgel et al., 2006; Willats et al., 2014) from our study, we used validated template datasets from open-source studies to generate our results. For the surface mesh, we used subject-averaged FreeSurfer templates cvs_avg35_in_MNI152 (default), of 20,000 vertices, as well as fsaverage5 (20,484 vertices) and fsaverage4 (5,124 vertices). All surfaces were registered in the MNI space so the impact of different mesh resolutions could be assessed without manual intervention. For the white-matter streamlines, we used the Gibbs dataset, which contains 20,712,081 streamlines computed by probabilistic tractography from 169 subjects (Horn and Blankenburg, 2016). All streamlines are registered in MNI coordinates and normalized to minimize inter-subject differences of brain sizes and shapes. The dataset has been cross validated across cortico-cortical and cortico-thalamo-cortical atlases (Behrens et al., 2003; Bürgel et al., 2006; Horn and Blankenburg, 2016). See Supplementary Text 1 for further details about the acquisition and processing of images from the Gibbs connectome database, whereby individual subjects were registered in MNI space and normalized using the DARTEL procedure (Ashburner, 2007) in order to correct for inter-subject differences in brain volume and estimate a group connectome.

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