Fingerprinting Orientation Distribution Functions in diffusion MRI detects smaller crossing angles

Abstract

Diffusion tractography is routinely used to study white matter architecture and brain connectivity in vivo. A key step for successful tractography of neuronal tracts is the correct identification of tract directions in each voxel. Here we propose a fingerprinting-based methodology to identify these fiber directions in Orientation Distribution Functions, dubbed ODF-Fingerprinting (ODF-FP). In ODF-FP, fiber configurations are selected based on the similarity between measured ODFs and elements in a pre-computed library. In noisy ODFs, the library matching algorithm penalizes the more complex fiber configurations. ODF simulations and analysis of bootstrapped partial and whole-brain in vivo datasets show that the ODF-FP approach improves the detection of fiber pairs with small crossing angles while maintaining fiber direction precision, which leads to better tractography results. Rather than focusing on the ODF maxima, the ODF-FP approach uses the whole ODF shape to infer fiber directions to improve the detection of fiber bundles with small crossing angle. The resulting fiber directions aid tractography algorithms in accurately displaying neuronal tracts and calculating brain connectivity.

Keywords: Crossing angle; Diffusion MRI; Fiber identification; Fiber tractography; Fingerprinting; Multi-shell Q-ball imaging; Orientation distribution function; Radial diffusion spectrum imaging.

Figure 1:

a-d) Exact ODFs of single (a) and crossing (b-d) fibers (FA = 0.7) acquired with full q-space sampling. e) ODF-Fingerprinting: For each ODF of which the directions are to be determined, the proposed method searches the pre-constructed ODF library for the best match. Once the match is identified, the ODF’s directions can be pulled from the library.

Figure 2:

Global fiber tractography (a,d) and identified fiber directions (b,c,e,f) in a dataset simulated with the Phantomas-software. The fiber directions are detected by local maximum search (DSIStudio, top row) and ODF-Fingerprinting (ODF-FP, bottom row). Areas where ODF-FP performed better are indicated with a yellow arrow (e,f).

Figure 3:

Local fiber tractography of selected fiber tracts (top row) in a dataset simulated with the Phantomas-software using fiber directions detected by local maximum search (DSIStudio, middle row) and ODF-Fingerprinting (ODF-FP, bottom row). The orange ROIs in each image were used to initiate the tractography.

Figure 4:

Average number of fibers found (a,b,c) and error on the detected crossing angles (d,e,f) of simulated pairs of crossing fibers (random angle) as identified by local maximum search (DSIStudio), Newton search (MRtrix3), probabilistic estimation (FSL, bedpostx), constrained spherical deconvolution (MRtrix3, dwi2fod msmt_csd), and ODF-fingerprinting. The results are plotted as a function of the simulated crossing angle with no added noise (a,d, b_max = 4000 mm/s²), with SNR 50 (b,e, b_max = 4000 mm/s²) and with SNR 25 (c,f, b_max = 3000 mm/s²). (a) and (d) include results of simulated pairs of crossing fibers with an intra-voxel fiber orientation dispersion of 20°.

Figure 5:

Angular precision (a,b,c) and dispersion (d,e,f) of simulated crossing fibers (random angle) as identified by local maximum search (DSIStudio), Newton search (MRtrix3), probabilistic estimation (FSL, bedpostx), constrained spherical deconvolution (MRtrix3, dwi2fod msmt_csd), and ODF-fingerprinting. The results are plotted as a function of the simulated crossing angle with no added noise (a,d, b_max = 4000 mm/s²), with SNR 50 (b,e, b_max = 4000 mm/s²) and with SNR 25 (c,f, b_max = 3000 mm/s²). (a) and (d) include results of simulated pairs of crossing fibers with an intra-voxel fiber orientation dispersion of 20°.

Figure 6:

In vivo ODFs and fiber directions identified from the ODFs by local maximum search (DSIS-tudio), Newton search (MRtrix3), probabilistic estimation (FSL, bedpostx), constrained spherical deconvolution (MRtrix3, dwi2fod msmt_csd, and ODF-Fingerprinting (ODF-FP) in voxels selected from an RDSI acquisition. ODFs are rotated for visibility, their position is indicated in the bottom left QA-map.

Figure 7:

Fiber directions identified in a subsection of a transversal slice in both high and low resolution versions of a HCP dataset. In the low resolution datasets, the fibers are identified by 5 algorithms: local maximum search (DSIStudio), Newton search (MRtrix3), probabilistic estimation (FSL, bedpostx), constrained spherical deconvolution (MRtrix3, dwi2fod msmt_csd, and ODF-Fingerprinting (ODF-FP). The arrows indicate one of the voxels where ODF-FP identified fiber directions which are missed by some of the other algorithms.

Figure 8:

Maps of the number of fibers identified in the high and low resolution versions of a HCP dataset (top row). The low resolution dataset was processed with 5 algorithms (local maximum search (DSIStudio), Newton search (MRtrix3), probabilistic estimation (FSL, bedpostx), constrained spherical deconvolution (MRtrix3, dwi2fod msmt_csd, and ODF-Fingerprinting (ODF-FP) and the number of correctly identified (true positive, second row), wrongly identified (false positive, third row) and missed (false negative, bottom row) fibers were calculated relative to the reference high resolution dataset. ODF-FP shows a larger number of true positive fibers at the cost of a somewhat higher number of false positive fibers.

Figure 9:

Reproducibility and noise sensitivity analysis of fiber identification in 300 bootstrapped RDSI datasets. Fibers are identified by local maximum search (DSIStudio, top row), Newton search (MRtrix3, 2nd row), probabilistic estimation (FSL, bedpostx, 3rd row), constrained spherical deconvolution (MRtrix3, dwi2fod msmt_csd, 4th row), and ODF-Fingerprinting (ODF-FP, bottom row). Displayed are the number of fibers identified and 95% confidence intervals (CI), coherence (κ) and Quantitative Anisotropy (QA) values for the first and second fiber.

Figure 10:

Fiber directions are identified by local maximum search (DSIStudio, a), Newton search (MR-trix3, shpeaks, b), probabilistic estimation (FSL, bedpostx, c), constrained spherical deconvolution (MRtrix3, dwi2fod msmt_csd, d) and ODF-Fingerprinting (ODF-FP, e) in a coronal slice of a whole brain in vivo dataset. Example areas where ODF-FP performed better are indicated with a yellow arrow; an example area where spurious fibers are detected are indicated with an orange arrow.

Figure 11:

Fiber tractography of the corticospinal tracts (a,e,i,m,q), the left arcuate fasciculus (b,f,j,n,r), the optic radiations (c,g,k,o,s) and the forceps minor (d,h,l,p,t) in a whole brain RDSI dataset. Fiber directions are identified by local maximum search (DSIStudio, a-d), Newton search (MRtrix3, shpeaks, e-h), probabilistic estimation (FSL, bedpostx, i-l), constrained spherical deconvolution (MRtrix3, dwi2fod msmt_csd, m-p) and ODF-Fingerprinting (ODF-FP, q-t).