This study systematically investigates a fundamental question for tractogram-based connectomics research: for a given resolution of brain parcellation, how many streamlines are required for reproducible connectome construction? We incorporate state-of-the-art tractography techniques with surface parcellation schemes of multiple granularities to investigate the influence of streamline count on the connectome variability. Our results suggest that selecting an appropriate number of streamlines is crucial for global and per-edge variability of the connectome, revealing important implications for subsequent network analysis and inferences. Methods that investigate structural connectivity with different brain parcellation resolutions should benefit from the experimental workflow and outcomes of this study.
To conduct initial explorations, pre-processed T1 and DWI data of one randomly-selected subject were downloaded from ConnectomeDB10. Data processing procedures were as follows (see also Figure 2):
(a) Tissue surfaces: An in-house script was used to integrate surface representations of brain tissues7 reconstructed using FreeSurfer11 and FSL12.
(b) Tractogram reconstruction: Fibre orientation distributions were computed using multi-shell multi-tissue CSD13. MACT was used to generate tractograms of 0.01-5 million streamlines through the iFOD214 algorithm with dynamic seeding15. Tractography was repeated 10 times for each track count. Each tractogram was post-processed using SIFT215 for quantitative tractogram reconstructions.
(c) Brain parcellation: To enable the generation of multi-granularity parcellations, FreeSurfer11 was used to subdivide the Desikan-Killiany cortical atlas9 into finer surface partitions. An in-house script was used to process the vertex-wise labels for every tissue surface and produce 3 parcellation schemes consisting of 85/203/403 nodes (Figure 3).
(d) Connectome construction: Three hundred connectomes were generated from 10 track counts × 10 repetitions × 3 parcellation schemes. Connectome edge was calculated as the sum of track weighting factors15 scaled by the proportionality coefficient15.
(e) Connectome variability: Per-edge coefficient of variation (CoVe=𝜎e/𝜔e) was used to evaluate variability; 𝜔e and 𝜎e are the mean and standard deviation of edge intensities across 10 repetitions. To provide a summary connectome variability, we propose a probability-weighted CoV (CoVP) calculated using:
$$CoV_P=\frac{\displaystyle\sum_{\forall{P_e>0}}CoV_e\cdot{P_e}}{\displaystyle\sum_{\forall{P_e>0}}P_e}$$
Compared to the weighted mean CoV16, the contribution of CoVe is weighted by the relevant frequency of occurrence (i.e. probability, Pe), instead of assuming the connection plausibility based on edge intensities 𝜔e.
Figure 4 shows the distribution of the edge-wise CoVe as a function of 𝜔e. For any streamline count investigated, we observed an overall downward trend of CoVe towards the edges with larger 𝜔e. In addition, when a finer parcellation was used, edges were distributed more densely towards lower 𝜔e and higher CoVe. As expected, increasing streamline count improved the distribution of CoVe toward lower values; however, the results revealed that most of the edges (>50%) still had a CoVe greater than 0.1 even for the case of using the largest streamline count and the lowest node count; this implies that a much greater number of streamlines were required to reduce CoVe, particularly for edges with smaller 𝜔e.
Figure 5 shows the distribution of CoVP as a function of streamline count. Curve fitting was performed heuristically using a range of models; the best fit was provided by a power-law function (adjusted R-squared > 0.99), by which the predicted minimum streamline counts of ~1.95×107, ~5.97×107, and ~4.70×109 were required to reduce CoVP below 10% for 85/203/403 nodes respectively.
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