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 configurations^1-2 have facilitated the investigation of structural connectivity using fiber tractography methods^3-6. 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 general^7-10.

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.

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 tools^12-14. 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 MRtrix3^17-18. 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 Toolbox^11,20. 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.

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.

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 tractography^2,22, 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.