Professor of Biomedical Engineering Vanderbilt University, United States
Introduction:: Diffusion of water in the white matter of the brain is constrained by axonal and other cellular membranes; hence, diffusion weighted magnetic resonance imaging (DMRI) provides a way to estimate the orientation and distribution of neuronal fiber bundles in the white matter of the brain, modeled as fiber orientation distribution functions (FODFs). Each discrete peak of the FODF corresponds to a uniquely oriented fiber population. Current methods to elucidate fiber bundle orientations from FODFs extract only one fiber bundle element (fixel) per FODF lobe. These approaches offer an angular resolution of ~45° between fixels (1).
It is estimated that approximately 90% of white matter voxels contain more than one fiber element (1), but with their angular resolution, lobe-based fixel segmentation methods can identify multiple fixels in only ~41% of voxels. This implies the true complexity of fiber angular distributions is underestimated. This loss in geometric complexity limits the accuracy of downstream analyses, such as fiber tract reconstruction and brain connectomics. Most attempts at improving angular resolution focus on a robust signal to FODF conversion (1, 2, 3). We propose an alternate, novel super-resolution approach for the detection of unresolved fixels. Our method allows for the identification of more than one fixel per FODF lobe and is based on the following observation: FODFs of parallel fiber populations demonstrate cylindrical symmetry about the fiber axis (1), so cylindrical asymmetry in FODF lobes suggests the presence of non-parallel fiber populations.
Materials and Methods:: Conventional FODFs were calculated using constrained spherical deconvolution, as implemented in the MRtrix3 software library (4), from single shell (diffusion weighting b=3000 s/mm^2 applied in 50 directions), whole brain (at 2.5 mm isotropic resolution), 3T MRI data from the BATMAN neuroimaging project hosted by the Open Science Framework [https://osf.io/fkyht/]. The full voxel (‘target’) FODFs were segmented into constituent fixels by iteratively fitting a cylindrically symmetric, single-fixel FODF model (referred to as F1) to the target FODF. F1 was estimated by averaging the rotated FODFs of all voxels used to estimate the white matter signal response function. To maintain cylindrical symmetry, only m=0 spherical harmonic coefficients were kept.
Fixels were segmented from the target FODF using these steps: 1) A cylindrically symmetric, elevation-restricted cap of points centered around the highest peak in the FODF was identified by comparing the eigenvalues of the second moment of the point coordinates. 2) F1 was rotated and scaled to align with this cap, then subtracted across the entire unit sphere. Figure 1 illustrates this process. These two steps iterate until the maximum peak is smaller than a threshold (= 0.1, consistent with standard practice (4)), or when there exists no cylindrically symmetric cap of points about the maximum peak.
The fixel models were validated using a continuity constraint and fiber information from the nearest-neighbor voxels. The model was considered acceptable when each candidate fixel deviated < 35° from 2 + fixels in nearest-neighbor voxels (5). Figure 2 shows an example of this geometric validation.
Results, Conclusions, and Discussions:: Results
Algorithm performance was evaluated on a full brain dataset. We compared the algorithm’s performance to both the ‘peak finding’ fixel segmentation method (4), and the method proposed in SIFT (6). All three fixel segmentation protocols were identically constrained (minimum fixel height = 0.1). Our algorithm was able to identify 89,140 viable fixels, finding multiple fixels in 48.5% of WM voxels. The geometric continuity filter (at 35 degrees) identified ~4,300 (4.7%) fixels as erroneous. Meanwhile, the best performing lobe-based method, SIFT, could only find 81,806 fixels, with multiple fixels in 41.9% of WM voxels (Fig 4). Improved fixel segmentations are shown in Figure 5. Our algorithm was able to detect fixels less than 40 degrees apart in 18.01% of WM voxels, compared to 1.7% of WM voxels with ‘peak finding’ and 0.8% of WM voxels with SIFT. Figure 6 illustrates the distribution of minimum interfixel angles in multifixel voxels. With simulated FODFs, our algorithm showed an interfiber angular resolution of ~20-25 degrees (varying with constituent fixel magnitude ratio), which is consistent with the experimental data in Figure 6. Conclusions The proposed algorithm offers marked improvements in interfixel angular resolution over conventional lobe based segmentation methods. The new algorithm identifies more fixels per voxel on average and those fixels are supported by concordant fixel geometry in neighboring voxels. This increased angular resolution has the potential to improve the accuracy of fiber tractography and tissue characterization, which in turn may increase reliability of fiber tracking in neurosurgical and other clinical applications.
Acknowledgements (Optional): :
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