Robustness of connectome harmonics to local gray matter and long-range white matter connectivity changes

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Article

Reference

Robustness of connectome harmonics to local gray matter and long-range white matter connectivity changes

NAZE, Sébastien, et al.

NAZE, Sébastien, et al . Robustness of connectome harmonics to local gray matter and long-range white matter connectivity changes. NeuroImage , 2020, vol. 224, p. 117364

DOI : 10.1016/j.neuroimage.2020.117364 PMID : 32947015

Available at:

http://archive-ouverte.unige.ch/unige:144757

Disclaimer: layout of this document may differ from the published version.

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Supplementary Materials (Naze et al. 2020)

This document present supplementary materials for the article:

Naze S., Proix T., Atasoy S., Kozloksi J. R. (2020) Robustness of connectome harmonics to local gray matter and long-range white matter connectivity changes. NeuroImage. DOI: 10.1016/j.neuroimage.2020.117364.

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0 2 4 6 8

nbr of intersections per bound 0

0.1 0.2 0.3 0.4 0.5 0.6

Probability

0 1 2 3 4 5

Step size (mm) 0

0.05 0.1 0.15 0.2 0.25 0.3 0.35

Probability

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0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Probability

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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 edge length (mm)

cvs_avg35_inMNI152 fsaverage5 fsaverage4

C

Supplementary Figure 1: Tracks and cortical surface mesh statistics

A) Alignment of template cortical surface mesh from Freesurfer to tractography streamlines from the Gibbs connectome.

B) Tracks step size (left), track length (middle), and number of intersection between track bound and cortical surface mesh for 10000 randomly selected tracks of the Gibbs dataset. C) Cortical surface mesh edge length distribution for the 3 template meshes shown as box plots. Circled dot shows the mean, boxes span from the 25th to the 75th percentiles and whiskers extend to all values not considered outliers. Outliers are shown by dots away from whiskers.

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Supplementary Text 1

Diffusion MRI acquisition summary from Horn and Blankenburg (2016) [1]

High angular diffusion images (HARDI) were used for global tracking that had been acquired with a diffusion-sensitive multiband sequence (TR = 2400 ms, TE = 85 ms, voxel-size of 2 x 2 x 2 mm³, 64 slices).

An effective mean b-value of 1500 s/mm²was used for 137 diffusion encoding directions. In addition, 9 10

volumes with very low diffusion weighting (b-value = 5 s/mm²) equally distributed throughout the scan were acquired (b0-images). Acquisition time of DTI images lasted 5.58 min. Details of the MR protocol are available online (http://fcon_1000.projects.nitrc.org/indi/enhanced/mri_protocol.html).

For anatomical segmentation and estimation of a group template, high-resolution anatomical images were used that had been acquired using a standard magnetization-prepared rapid gradient-echo (MPRAGE) 15

sequence (TR = 1900 ms, TE = 2.52 ms, isotropic voxel-size of 1 x 1 x 1 mm³, 176 slices with a distance factor of 50% resulting in a slice gap of 0.5 mm).

Tractography summary from Horn and Blakenburg (2016) [1]

To estimate structural connectivity, the Gibbs’ tracking-approach [2] as implemented in the DTI and 20

Fiber Tools for SPM [3] was used to reconstruct the global fiber-dataset directly from the DTI volumes.

In this approach, based on the raw HARDI data, a piecewise approximation of neuronal pathways is achieved by annealing small cylinders to chains that finally form fiber tracts. These cylinders are simulated as particles moving in a Brownian motion fashion, and their polymerization to chains is attained by slowly reducing a simulated temperature. In a Bayesian framework, a signal ˆS^∗ is simulated by a 25

spatially distributed sum of all cylinders and optimized iteratively during cylinder annealing to best explain the empirical MR-signal ˆS. The following parameters were chosen: Starting temperature: 0.1, stop temperature: 0.001, numbers of steps: 50, numbers of iterations: 5 x 108, particle width: 1 mm, particle length: 1 mm, weight (unitless): 0.058, and density penalty: 0.2. Global tracking was performed on a tracking mask that was based on the white matter volume of the anatomical volumes (which was 30

co-registered to the b0-images). These parameters represent the default dense parameter set [3] and were kept identical for fiber tracking in all subjects. On average 1.23 x 105 fibers were obtained for each subject.

References

[1] A. Horn and F. Blankenburg. Toward a standardized structuralfunctional group connectome in MNI 35

space. NeuroImage, 124:310–322, Jan. 2016.

[2] B. W. Kreher, I. Mader, and V. G. Kiselev. Gibbs tracking: a novel approach for the reconstruction of neuronal pathways. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, 60(4):953–963, 2008. Publisher: Wiley Online Library.

[3] M. Reisert, I. Mader, C. Anastasopoulos, M. Weigel, S. Schnell, and V. Kiselev. Global fiber recon- 40

struction becomes practical. NeuroImage, 54(2):955–962, Jan. 2011.

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white matter surface (wm) gray matter surface (pial)

Supplementary Figure 2: Illustration of track-mesh intersection routine to compute high- resolution connectomes. Schematic of the white matter and gray matter cortical meshes (black), and six tracks (blue) from the Gibbs connectome. Inset: magnified area illustrating track mesh intersection routine (see Methods). Red segment: linear extension of track. Pink crosses: coordinates of intersections with meshes.

Green symbols: closest vertex to the intersection with the white matter mesh .

Table 1: Mapping of Resting State Networks onto the Desikan-Killiany atlas.

Resting State Network Region name code

Default Mode Network (DMN) inferiorparietal, isthmuscingulate, middletemporal, parahippocampal, parsorbitalis, posteriorcingulate, precuneus, rostralanteriorcingulate, superiorfrontal, superiortemporal Sensory-Motor (SM) precentral, postcentral, paracentral, transversetemporal, insular

Fronto-Parietal (FP) caudalanteriorcingulate, fusiform, inferiortemporal, rostralmiddlefrontal, parstriangularis Visual (Vis) lateraloccipital, pericalcarine, cuneus, lingual

Limbic (L) entorhinal, lateralorbitofrontal, medialorbitofrontal, frontalpole, temporalpole Ventral Attention (VA) bankssts, parsopercularis, supramarginal

Dorsal Attention (DA) caudalmiddlefrontal, superiorparietal

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0.10.625 zC

0 10 20 30 40 50 60 70 80 90 100

harmonic # 0

0.1 0.2 0.3

MI

0.10.625 zC

0 10 20 30 40 50 60 70 80 90 100

harmonic # 0

0.1 0.2 0.3

MI

Sensory-Motor

Fronto-Parietal

0.10.625 zC

0 10 20 30 40 50 60 70 80 90 100

harmonic # 0

0.1 0.2 0.3

MI

Visual

Limbic

Ventral Attention

0.10.625 zC

0 10 20 30 40 50 60 70 80 90 100

harmonic # 0

0.1 0.2 0.3

MI

0.10.625 zC

0 10 20 30 40 50 60 70 80 90 100

harmonic # 0

0.1 0.2 0.3

MI

0.10.625 zC

0 10 20 30 40 50 60 70 80 90 100

harmonic # 0

0.1 0.2 0.3

MI

Dorsal Attention

0 MI 0.3

0 MI 0.3 ₀ MI _0.3

0 MI 0.3

0 0.1 0.3 0.6

2 3 zC 1

Supplementary Figure 3: Mutual Information between connectome harmonics ψk∈K={1,...,100} and other resting state networks.

Mutual information (MI) is computed between the first 100 harmonics and several resting state networks (RSN) for different values of matrix weight thresholdzC as in main text Figure 2. RSN are mapped on the Desikian- Killiany atlas: Sensory-motor network: pre-central, post-central, paracentral and transverse temporal regions;

Fronto-parietal network: caudal anterior cingulate, rostral middle frontal, inferior temporal, fusiform regions; Vi- sual: lateral occipital, cuneus, pericalcarine and lingual regions; Limbic: entorhinal, lateral orbito-frontal, medial orbito-frontal; Ventral attention: pars opercularis, insular regions; Dorsal attention: superior parietal, caudal middle frontal regions.

SM FP Vis L VA DA

DMN

Supplementary Figure 4: Masks of resting state networks (RSN) mapped onto the Desikan- Killiany atlas.

DMN: Default Mode; SM: Sensory-Motor; FP: Fronto-Parietal; Vis: Visual; L: Limbic; VA: Ventral Attention;

DA: Dorsal Attention.

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10 20 30 40 50 60 70 80 90 100 0.6024

z_C

0 10 20 30 40 50 60 70 80 90 100

harmonic # 0

0.05 0.1

MI

0 0.6 1 2 3 4

z_C 0

0.2 0.4 0.6 0.8 1

Proportion r of local connections probability

number of streamlines

0 20 40 60 80 100

harmonics #

-1 0 1

Correlation

A B

C

D

E F

0 20 40 60 80 100 0

20 40 60 80 100

harmonics #

-1 0 1

Correlation Λ_s = 2 Λ_s = 1

0 20 0

20 40 60 80 100

0 20

10 10

0 20

10 10

0 MI 0.1

00.6 1 34 2 z_C

Supplementary Figure 5: Reproduction of main findings in HCP subject 100307.

(A) Ratio r of local gray matter connections in the adjacency matrixA of the graph Laplacian, for different threshold valuezC applied to the long-range white matter connectivity.

(B)Distribution of connectome weights (number of white matter streamlines between vertices) in log-log scale, described as probability given that the weight is positive (P(W|W >0)). Vertical lines correspond toz_C values with same color code as A).

(C-D) Mutual information (MI) between the first 100 connectome harmonics and the DMN for a range ofzC

resulting in a range of proportions of local to long-range connections. Color code is consistent across panels.

(E) Pearson correlation between 100 first connectome harmonics in coarse-resolution atlas space, of the un- smoothed (fi= 0) vs. smoothed (fi= 21) WMGM cortical surface meshes.

(F)Pearson correlation between 100 first connectome harmonics in high-resolution vertex space, of local connectivity kernel widths Λs= 1 vs. Λs= 2 nearest neighbors. In both(E)and(F),zC is set to 1.

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Supplementary Figure 6: Projection of connectome harmonics ψk∈K={1,...,10} onto cortical surface mesh

Original: First 10 connectome harmonicsψk∈K={1,...,10}based on unaltered local and long-range connectivity, with white matter weight thresholdzC= 1 and other default parameters presented in main text Table 1.

Supplementary Figure 7: Projection of connectome harmonics ψk∈K={1,...,10} onto cortical surface mesh for different types of randomizations

Randomization is performed on subgraphs corresponding to inter-hemispheric connections, intra-hemispheric connections, inter-hemispheric and intra-hemispheric connections randomized separately, and then assembled, or randomized together (global). Framework parameters set to default from main text Table 1. nb: Eigenmodes are fundamentally identical under sign reversal, i.e. spatial pattern is relevant over color code.

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0.1 0.3 0.6 1 2 3 5 z_C

-0.02 0 0.02 0.04 0.06 0.08 0.1

MI

-0.02 0 0.02 0.04 0.06 0.08 0.1

0.1 0.3 0.6 1 2 3 5

z_C 0.1 0.3 0.6 1 2 3 5

z_C

Original Inter-hemi Intra-hemi Inter + intra Global

-0.020.020.040.060.080.120.140.160.180.10 MI

-0.020.020.040.060.080.120.140.160.180.10 0.1 0.3 0.6 1 2 3 5

z_C 0.1 0.3 0.6 1 2 3 5

z_C -0.020.020.040.060.080.120.140.160.180.10

-0.020.020.040.060.080.120.140.160.180.10

A

B

Original Inter-hemi Intra-hemi Inter + intra Global

Supplementary Figure 8: Mutual information with DMN of single and ranges of harmonics are affected by randomizations of long-range connectomes.

A) Mutual information (MI) between the DMN and the 3^rdharmonic for the different randomization schemes and values of zC. B) MI between the DMN and a larger set of harmonics (ψk∈K={2,...,20}) for the different randomization schemes and values ofzC. When no randomization is performed (Original), each dot is the MI of an harmonic and the DMN. When randomization is performed, MI are shown as mean (dot) and standard deviation (whiskers) over 100 samples.

0 0.05

0.1 0.15 0.2 MI

0.1 0.3 0.6 1 2 3 z_C

0 0.05

0.1 0.15 0.2 MI

0.1 0.3 0.6 1 2 3 z_C

0 0.05

0.1 0.15 0.2 MI

0.1 0.3 0.6 1 2 3 zC

0 0.05

0.1 0.15 0.2 MI

0.1 0.3 0.6 1 2 3 zC

0.1 0.3 0.6 1 2 3 z_C

0 0.05

0.1 0.15 0.2 MI

Original Interhemispheric

randomization Intrahemispheric

randomization Inter- and intra-hemispheric

randomization Global

randomization

SMFP Vis DAVAL

Supplementary Figure 9: Mutual Information (MI) between connectome harmonics and the other resting state networks (RSN) for several randomized versions of long-range connectivity.

Mean and standard deviation of connectome harmonics’ ψk∈K={7,8,9,10,11} MIs for different proportion of local:long-range connections (parameterized by the adjacency weight thresholdz_C), and randomizations of the long-range connectivity as in main textFigure 3. Other framework parameters set to default from maon text Table 1. SM: Sensory-Motor; FP: Fronto-Parietal; Vis: Visual; L: Limbic; VA: Ventral Attention; DA: Dorsal Attention.

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Anisotropy ρ (%) Callosectomy κ (%)

0% 4% 8% 12% 16% 20%

0% 20% 40% 60% 80%

Supplementary Figure 10: Illustrations of graph structures for altered combined connectomes.

Graph representations of combined (i.e. local and long-range connectivity for gradual removal of inter-hemispheric connections (top, referred ascallosectomy) and cortical surface mesh edges (bottom, referred asanisotropy)

Supplementary Figure 11: Projection of connectome harmonics ψk∈K={1,...,10} onto cortical surface mesh for gradual fractions of inter-hemispheric connections trimming.

Callosectomy: proportion κ of long-range inter-hemispheric white matter connections trimmed by descending order of track lengths. Other framework parameters set to default from main text Table 1. nb: Eigenmodes are fundamentally identical under sign reversal, i.e. spatial pattern is relevant over color code.

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x (-1) x 1 separated hemisphere

(callosectomy κ = 100%) combined hemispheres

by eigenvalue-eigenvector pairs original

0.1 0.3 0.6 1 2 3

-0.02 0 0.02 0.04 0.06 0.08 0.1

MI

z_C

C

Separated hemisphere (callosectomy κ = 100%), combined eigenvectors paired by eigenvalues

0 10 20

0 0.2 0.4

0.1 0.3

5 15

rank

value

B

eigenvalues

A

78 109 11 Harmonic #

ψ₁

ψ₃ ψ₄ ψ₅ ψ₆ ψ₂

Supplementary Figure 12: Reconstruction of harmonics from separated hemispheres.

A) Illustration of the reconstruction of harmonics from separated hemispheres. Harmonics are assembled by pairs of eigenvectors, computed on each hemisphere separately and assembled by corresponding eigenvalues. Since the sign of the eigenvector is attributed randomly, harmonics are assembled using same (×1) and reverse (×(−1)) signs, therefore for each pair of eigenvectors, two whole brain harmonics are generated. B) 20 first eigenvalues forming the spectrum of the combined connectome in the case of separated hemispheres. Note how eigenvalues a grouped 2-by-2 , one for each hemisphere in each pair. C) MI between DMN and harmonicsψk∈K={7,8,9,10,11}for different values of zC, in the case of 100% callosectomy (κ= 1) whereby harmonics are computed on each hemisphere separately and combined by eigenvalue-eigenvector pairs.

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None (Original)

Inter-hemispheric only

Intra-hemispheric only

Intra + inter-hemispheric

(separate) Intra + inter-hemispheric (global)

0% 20% 40% 60% 80%

Callosectomy 20

40 60 80

00 20 40 60 80 0 20 40 60 80 0 20 40 60 80 0 20 40 60 80 0 20 40 60 80 100

20 40 60 80

00 20 40 60 80 0 20 40 60 80 0 20 40 60 80 0 20 40 60 80 0 20 40 60 80

Randomization

Supplementary Figure 13: Correlations between connectome harmonics ψk∈K={1,...,10} for connectome randomizations and callosal trimming κ.

top: Correlation matrices of connectome harmonics ψk∈K={1,...,100} between Original (None) and different randomization types. bottom: Correlation matrices of connectome harmonicsψk∈K={1,...,100}between Original(0%)and increasing degrees of callosal trimmingκ(i.e. callosectomy).

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Supplementary Figure 14: Projection of connectome harmonics ψk∈K={1,...,10} onto cortical surface mesh for gradual fraction of local trimming ρ.

Anisotropy: proportionρof local mesh connections are trimmed randomly. Other framework parameters are set to default from Table 1. nb: Eigenmodes are fundamentally identical under sign reversal, i.e. spatial pattern is relevant over color code.