Methodological considerations on graph theoretical analysis of structural brain networks
Timo Roine1, Ben Jeurissen1, Daniele Perrone2, Jan Aelterman2, Wilfried Philips2, Jan Sijbers1, and Alexander Leemans3

1iMinds-Vision Lab, Department of Physics, University of Antwerp, Wilrijk (Antwerp), Belgium, 2Ghent University-iMinds/Image Processing and Interpretation, Ghent, Belgium, 3Image Sciences Institute, University Medical Center Utrecht, Utrecht, Netherlands

Synopsis

We studied the reproducibility of whole-brain structural brain connectivity networks reconstructed with constrained spherical deconvolution based probabilistic fiber tractography. Our main finding is that a low spherical harmonics order decreases the reproducibility of graph measures in connectomics. This is most likely caused by the wider peaks in the fiber orientation distributions, which increase the variation in orientations sampled by the tractography algorithm. Based on our observations, we recommend using spherical harmonics decomposition with an order of at least eight whenever the data allows so. In addition, threshold value was important for binary networks, and some network properties were highly intercorrelated.

Purpose

Diffusion-weighted magnetic resonance imaging (DW-MRI) can be used to noninvasively probe brain microstructure and connectivity. Recent advances that can deal with complex fiber configurations1-2 have facilitated the investigation of structural connectivity using fiber tractography methods3-6. However, the reproducibility of these analyses has not yet been sufficiently studied. For example, the effect of spherical harmonics (SH) order on the reproducibility has not been studied earlier, and only limited knowledge exists about the reproducibility of the structural brain network properties in general7-10.

Here, we studied the reproducibility of whole-brain structural brain connectivity networks, i.e. connectomes, reconstructed with constrained spherical deconvolution (CSD)1. Graph theoretical analysis was used to measure both global and local properties of these complex networks11. We investigated the reproducibility by calculating intraclass correlation coefficients (ICC). We selected six network properties: normalized characteristic path length (nCPL), normalized clustering coefficient (nCC), normalized global efficiency (nGE), average local efficiency (LE), betweenness centrality (BC), and small-worldness (SW), and five weights: binary, number of streamlines, percentage of streamlines, streamline density, and fractional anisotropy. In addition, the effect of two reconstruction parameters was studied: spherical harmonics (SH) order was varied from four to ten and reconstruction density, i.e. the number of streamlines, was varied from 10 million to 100 million. Moreover, correlations between the different network properties and weights were computed.

Methods

Material and preprocessing

In addition to T1-weighted data, we acquired DW-MRI data from 19 healthy subjects in 75 gradient orientations with b=2800 s/mm2 and 2.5 mm isotropic voxel size. Non-DW MRI data were acquired in both forward and reverse phase-encoding direction. Subject motion, eddy current and echo-planar imaging induced distortions were corrected using FMRIB Software Library’s (FSL) TOPUP and EDDY tools12-14. Rigid coregistration was performed to align the corrected DW data to T1-weighted data.

Network reconstruction

Cortical parcellation was performed in Freesurfer using the Destrieux atlas15 and combined with subcortical structures parcellated with FSL’s FIRST16. Probabilistic streamlines tractography was performed to reconstruct 10 and 100 million streamlines with CSD using the iFOD2 algorithm as implemented in MRtrix317-18. In the tractography, anatomically constrained tractography was used and streamlines were seeded from the gray matter-white matter interface19. The number of seed points per voxel was constant and selected to produce approximately 10 million streamlines per subject. The maximum spherical harmonics (SH) order was varied from four to ten. The network reconstruction process is illustrated in Fig. 1.

Reproducibility analyses

To investigate reproducibility, nine additional realizations were generated for each subject using residual bootstrapping with 8th order SH decomposition2. Then, ICC was calculated as follows:

$$\frac{{\sigma_\text{inter}}^2}{{\sigma_\text{inter}}^2+{\sigma_\text{intra}}^2}$$

where ${\sigma_\text{inter}}^2$ is the intersubject and ${\sigma_\text{intra}}^2$ the intrasubject variance of the same network metric. We calculated the network properties using the Brain Connectivity Toolbox11,20. Networks were weighted with the number and percentage of streamlines, streamline density21, and fractional anisotropy (FA). In addition, binary networks with varying threshold values were studied.

Results

Reproducibility analyses

The results showed that higher SH orders produced more reproducible results than lower SH orders (Fig. 2). In addition, increasing the reconstruction density from 10M to 100M further improved the reproducibility (Fig. 2). Unthresholded binary networks resulted in very irreproducible results for nGE and nCPL. The reproducibility was greatly improved by thresholding the networks with 1000 streamlines (Fig. 3).

Correlation analyses

The correlation analyses showed that nCC and SW were highly correlated, as were nGE and LE (Fig. 4). In addition, weighting by the number or percentage of streamlines produced highly correlated results (Fig. 5), although efficiency properties were negatively correlated.

Discussion

Our main finding was that SH order plays a significant role in the reproducibility of structural connectomics. This is most likely caused by the wider peaks of the fiber orientation distributions when estimated with lower SH orders. Thus, the variation of the fiber orientations sampled by the tractography algorithm is larger. We recommend to use at least a SH order eight whenever possible. Further tests need to be performed to define the most reproducible way to analyze data acquired with a low b-value or insufficient number of gradient directions. Other approaches, such as residual bootstrapping based tractography2,22, may result in better reproducibility for the low SH orders. For the binary networks, thresholding was important especially for nCPL and nGE. A suitable value, based on Fig. 3, could be 0.01% of the total number of streamlines.

Conclusion

We showed that reproducible reconstruction of structural brain networks can be performed with an SH order eight or more. In addition, adequate reconstruction density and careful selection of network weights and properties are important.

Acknowledgements

This work was supported by the Fund for Scientific Research-Flanders (FWO), Belgium and by the Interuniversity Attraction Poles Program (P7/11) initiated by the Belgian Science Policy Office, Belgium. The research of A.L. is supported by VIDI Grant 639.072.411 from the Netherlands Organization for Scientific Research (NWO). T.R. received support from the Instrumentarium Scientific Foundation, Finland. B.J. is a postdoctoral fellow supported by the Research Foundation Flanders (FWO Vlaanderen).

References

1. Tournier JD, Calamante F, Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: non-negativity constrained super-resolved spherical deconvolution. NeuroImage. 2007;35(4):1459-1472.

2. Jeurissen B, Leemans A, Tournier JD, et al. Investigating the prevalence of complex fiber configurations in white matter tissue with diffusion magnetic resonance imaging. Hum Brain Mapp. 2013;34(11):2747-66.

3. Jeurissen B, Leemans A, Jones DK, et al. Probabilistic fiber tracking using the residual bootstrap with constrained spherical deconvolution. Hum Brain Mapp. 2011;32(3):461-79.

4. Tournier JD, Yeh CH, Calamante F, et al. Resolving crossing fibres using constrained spherical deconvolution: validation using diffusion-weighted imaging phantom data. NeuroImage. 2008;15;42(2):617-25.

5. Farquharson S, Tournier JD, Calamante F, et al. White matter fiber tractography: why we need to move beyond DTI. J Neurosurg. 2013;118(6):1367-77.

6. Kristo G, Leemans A, Raemaekers M, et al. Reliability of two clinically relevant fiber pathways reconstructed with constrained spherical deconvolution. Magn Reson Med. 2013;70(6):1544-56.

7. Bastiani M, Shah NJ, Goebel R, et al. Human cortical connectome reconstruction from diffusion weighted MRI: the effect of tractography algorithm. NeuroImage. 2012;62(3):1732-1749.

8. Owen JP, Ziv E, Bukshpun P, et al. Test–retest reliability of computational network measurements derived from the structural connectome of the human brain. Brain Connect. 2013;3(2):160-176.

9. Buchanan CR, Pernet CR, Gorgolewski KJ, et al. Test–retest reliability of structural brain networks from diffusion MRI. NeuroImage. 2014;86:231-243.

10. Smith RE, Tournier JD, Calamante F, et al. The effects of SIFT on the reproducibility and biological accuracy of the structural connectome. NeuroImage. 2015;104:253-265.

11. Bullmore E, Sporns O. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci. 2009;10(3):186-98.

12. Andersson JL, Skare S, Ashburner J. How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging. NeuroImage. 2003;20(2):870-88.

13. Smith SM, Jenkinson M, Woolrich MW, et al. Advances in functional and structural MR image analysis and implementation as FSL. Neuroimage. 2004;23 Suppl 1:S208-19.

14. Andersson JL, Sotiropoulos SN. An integrated approach to correction for off-resonance effects and subject movement in diffusion MR imaging. NeuroImage. 2015. doi: 10.1016/j.neuroimage.2015.10.019.

15. Fischl B, van der Kouwe A, Destrieux C, et al. Automatically parcellating the human cerebral cortex. Cereb Cortex. 2004;14(1):11-22.

16. Patenaude B, Smith SM, Kennedy D, et al. A Bayesian Model of Shape and Appearance for Subcortical Brain. NeuroImage. 2011;56(3):907-922.

17. Tournier JD, Calamante F, Connelly A. Improved probabilistic streamlines tractography by 2nd order integration over fibre orientation distributions. In Proc Intl Soc Mag Reson Med. 2009;1670.

18. Tournier JD, Calamante F, Connelly A. MRtrix: diffusion tractography in crossing fiber regions. Int J Imaging Syst Technol. 2012;22(1), 53-66.

19. Smith RE, Tournier JD, Calamante F, et al. Anatomically-constrained tractography: improved diffusion MRI streamlines tractography through effective use of anatomical information. NeuroImage. 2012;62(3):1924-38.

20. Rubinov M Sporns O. Complex network measures of brain connectivity: uses and interpretations. NeuroImage. 2010;52(3):1059-69.

21. Hagmann P, Cammoun L, Gigandet X, et al. Mapping the structural core of human cerebral cortex. PLoS Biol. 2008;6(7):e159.

22. Leemans A, Jeurissen B, Sijbers J, et al. ExploreDTI: a graphical toolbox for processing, analyzing, and visualizing diffusion MR data. In Proc Intl Soc Mag Reson Med. 2009;3536.

Figures

Fig. 1. The pipeline for structural brain network reconstruction. First, whole-brain probabilistic fiber tractography is performed (A), then cortical and subcortical gray matter is parcellated (B) and then the network (C) is reconstructed by defining the nodes based on B and the edges based on A.

Fig. 2. Reproducibility of network properties for varying spherical harmonics (SH) orders with reconstruction densities of 10 and 100 million streamlines. Networks were weighted with the number of streamlines. nCC:normalized clustering coefficient, nCPL:normalized characteristic path length, nGE:normalized global efficiency, LE:average local efficiency, BC:betweenness centrality, SW:small-worldness

Fig. 3. Reproducibility of network properties in binary networks reconstructed from the number of streamlines using varying threshold values. Networks were reconstructed with spherical harmonics (SH) order 8 and 10 million streamlines. nCC:normalized clustering coefficient, nCPL:normalized characteristic path length, nGE:normalized global efficiency, LE:average local efficiency, BC:betweenness centrality, SW:small-worldness

Fig. 4. Correlation of various network properties to nCC, nGE and nCPL in networks weighted with the number of streamlines, and reconstructed with 10 million streamlines using a spherical harmonics order 8. nCC:normalized clustering coefficient, nCPL:normalized characteristic path length, nGE:normalized global efficiency, LE:average local efficiency, BC:betweenness centrality, SW:small-worldness

Fig. 5. Correlation of network properties using various network weights compared to number of streamlines weighted networks. Networks were reconstructed with 10 million streamlines and a spherical harmonics order 8. nCC:normalized clustering coefficient, nCPL:normalized characteristic path length, nGE:normalized global efficiency, LE:average local efficiency, BC:betweenness centrality, SW:small-worldness

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
3437