Regularized diffusion tensor MRI for high angular resolution ODF estimation and fibre tractography

J. S. Campbell, P. Savadjiev, G. B. Pike, K. Siddiqi Montreal Neurological Institute, Montreal, Quebec, Canada, McGill Centre for Intelligent Machines, Montreal, Quebec, Canada Introduction High angular resolution diffusion (HARD) MRI can be used to infer multiple subvoxel fibre directions [1-2], and this information can be used to improve the precision of fibre tractography over that achieved with the single diffusion tensor model [3]. Acquisition schemes suitable for HARD reconstruction typically require 100-500 diffusion encoding directions and b≥3000 s/mm. We have developed a regularization method [4] for inferring high angular resolution orientation distribution functions (ODFs) directly from the diffusion ODF field calculated using a single-tensor model, by considering information from neighbouring voxels. This is a powerful technique in that it allows us to infer multiple subvoxel fibre directions from a diffusion MRI acquisition that has either (i) sparse diffusion encoding directions or (ii) low b values. It allows us to obtain more precise diffusion ODF estimates in each voxel using an acquisition that is otherwise optimized for single-tensor fitting. We compare the regularized diffusion ODFs to those obtained using q-ball reconstruction [1], and investigate the use of these regularized ODFs in fibre tractography. Methods MRI data were acquired on a Siemens 3T Trio MR scanner (Siemens Medical Systems, Erlangen, Germany) using an 8-channel phased-array head coil. Diffusion encoding was achieved using a single-shot spin-echo echo planar sequence with twice-refocused balanced gradients. Two coregistered datasets were acquired, both with 99 diffusion encoding directions, 2mm isotropic voxel size, and 63 slices. The first dataset was acquired using a single-tensor optimized b value of 1000 s/mm, while the second was designed for q-ball reconstruction, using b=3000 s/mm (q=0.35 μm). A 1mm isotropic resolution T1 weighted anatomical scan was also acquired (TR=9.7ms, TE=4ms, α=12). For the first dataset, the diffusion ODF, Ψ, given by , with P the diffusion probability density function, was calculated using the single diffusion tensor (DT) model [5]. For the second, the diffusion ODF was calculated using q-ball (QB) reconstruction [1]. Both ODFs were normalized to unit volume. The regularization algorithm [4] was run on the diffusion tensor derived ODF field. The algorithm models fibre tracts locally as segments of 3D helix curves. This allows for curvature and torsion to vary along a tract. For each voxel (i), for each of N isotropic ODF sampling directions (u), the average local support (s) was calculated by considering all pairs of voxels in a local neighbourhood of the voxel i. The average local support for direction um at voxel i is given by , where j and k are voxel indices that range over the local neighbourhood of voxel i; n and p are direction indices that range from 1 to N, and rijk(um, un, up) is 1 if the three orientations um, un, up are cohelical at voxels i,j,k (i≠j≠k), respectively, and 0 if they are not. Ψi(um) is the ODF value in direction um at voxel i. Local support for each ODF sampling direction was maximized using a relaxation labeling algorithm [6]. In this implementation, a neighbourhood of radius 8mm and N=100 ODF sampling directions were considered. The ODFs obtained from the regularized diffusion tensor (r-DT) and QB approaches were compared qualitatively in regions of partial volume averaging of large, known fibre pathways: the corpus callosum (cc) and cingulum (cg), the corticospinal tract (cst) and the cc, the superior longitudinal fasciculus (slf) and the cst, and the pontine crossing tract (pct) and the coricopontine tract (cpt). Streamline fibre tractography was run using the DT ODF dataset and the r-DT ODF dataset. In the tensor case, the maximum of the diffusion ODF (the principal eigenvector) was calculated. In the r-DT case, all maxima of the ODF that rose more than 3σ/2 above their intermediate minima, with σ the ODF standard deviation, were calculated. These maxima correspond to the tangents to the most likely curves (fibres) in the voxel. Tracking followed all maxima of the ODF that gave curves with radius of curvature 2mm or greater (directions that generated paths with higher curvature were assumed to be crossing fibres and were not followed). FACT integration was used, and all curves were initiated on a subvoxel grid of 3x3x3 seed points per seed voxel in order to facilitate branching even with single-maximum ODFs. Results