Researchers with an interest in using tractography for biomedical and clinical applications.While fiber tractography (FT) plays a key role in connectomics [1], i.e., the comprehensive study of brain connectivity, there are many pitfalls in FT [2-4] which, if not adequately addressed, will have an adverse impact on the validity of scientific findings. The purpose of this work is to highlight the effects of these pitfalls on the reliability of probabilistic FT methods used to assess the “strength” or “degree” of brain connectivity. To this end, we extend previous work [5] and demonstrate that the noise level and the number of gradient directions already significantly affect the spatial configuration of tract pathways generated with probabilistic FT.

The analyses are based on (i) in silico data of fiber tracts and (ii) experimental human brain data from a healthy volunteer.

Synthetic data: The diffusion MRI data were simulated using ExploreDTI [6] with multi-shell diffusion-weighted images along 60 gradient directions (b = 1000 and 3000 s/mm2) and with various SNR levels. The reference tract was calculated from the noise-free dataset with a deterministic FT approach [7, 8] with a fixed length and no other constraints. Probabilistic FT [9, 10] was performed on the noisy datasets using bootstrapping technique with the same seed point, b-value, and tract length criteria as the deterministic FT method. For each dataset 100 noise realizations were used for Monte-Carlo simulations.

Experimental data: A multi-shell diffusion-weighted MRI dataset was acquired on a 3T MR scanner with 250 directions and with an isotropic resolution of 2.5 mm (for more details, see [11]). Correction for subject motion and eddy current induced geometric distortions was performed as described previously [12]. The reference tract was calculated from the full 250-direction dataset using a single seed point with the deterministic FT approach [7, 8]. Probabilistic fiber tracts were then computed from subsets of this main dataset with a decreasing number of gradient directions using bootstrap technique with identical FT settings as for the deterministic FT method. For each subset, 100 realizations of the optimal gradient configurations with the lowest condition numbers [13] were used for Monte-Carlo simulations.

Models: Tractography analyses for all the datasets in this work were performed using both DTI [14] and CSD [8] models. For the DTI model, a robust tensor estimation approach with outlier rejection (REKINDLE) [15] is used (from b=1000 s/mm2 shell). For the CSD model, we considered the datasets with more than 60 gradient directions and utilized the recursive calibration technique [16] for calculation of the response functions for each dataset (from b=3000 s/mm2 shell with l-max = 8).

Error metric: The average error ($$$E$$$), i.e., the point-by-point average distance between the probabilistic tracts and the reference tract was calculated by averaging the distances between the corresponding points in the probabilistic fiber tracts and the reference tract as: $$E_j = \frac{1}{N_b} \sum_{i=1}^{N_b} \mid\mathbf{r}_{i,j}-\mathbf{r}'_j\mid,$$ where $$$N_b$$$ is the number of bootstraps, $$$\mathbf{r}_{i,j} = (x_{i,j},y_{i,j},z_{i,j})$$$ are the coordinates of the $$$j$$$-th point on the $$$i$$$-th bootstrap tract and $$$\mathbf{r}'_j=(x'_j,y'_j,z'_j)$$$ are the coordinates of the $$$j$$$-th point on the reference tract. A schematic visualization of the calculation of error metric is depicted in Fig 1.

For the synthetic data, Fig 2(a) and Fig 2(b) indicate that the dispersion in the connectivity maps was larger at lower SNR levels. The results for the experimental data, Fig 2(c) and Fig 2(d), show that the dispersion in the connectivity maps was smaller for a higher number of gradient directions.

The analyses of average error vs. distance from the seed point presented in Fig 3 demonstrate that (i) the error metric and uncertainties increase as the distance from the seed point increases (accumulation of error), and (ii) the average error and uncertainties decrease as the SNR and/or number of gradient directions increase.

Based on Monte-Carlo simulations, we have demonstrated in line with the previous work [5] that the distribution of fiber tracts reconstructed with probabilistic FT is highly sensitive to the noise level and/or the choice of number of gradient directions, which calls into question the reliability of assessing connectivity “strength” in typical image acquisition SNR ranges. Given this effective SNR dependency, the interpretation of such results along the lines of “strength” or “degree” of connectivity should be used with extreme caution, especially if applied in a clinical context where pathology may further complicate data interpretation.