Reproducibility of Fiber Bundles from Different Subsampled q-space DSI Data Set

Introduction: Diffusion spectral imaging (DSI) has the potential to resolve crossing fibers. However, acquisition of the DSI data involves long scan times, making it impractical for routine scanning. A simple way to reduce the scan time is to limit the number of q-space points sampled and fill the q-space by exploiting its symmetry. However, the smallest number of q-space points needed to generate nearly artifact free tractography is not clear. In this study we have compared the fiber pathways generated using three subsample data sets of different sizes derived from the fully sampled q-space with those obtained with the full data set. Materials and Methods: Data Acquisition: Brain DSI data was acquired on 10 normal subjects on a 3T MRI scanner (Achieva, Philips Medical Systems, Best, Netherlands) with a maximum gradient amplitude of 80 mT/m and a slew rate of 200 mT/m/ms. An 8 channel SENSE coil was used for data acquisition. Multi-slice, diffusion-weighted images were acquired using a single shot spin echo EPI sequence with 257 DSI diffusion encodings, comprising of q-space points of a cubic lattice within the sphere of 4 lattice units in radius, q = (qx, qy, qz) where the qx, qy, and qz are integers with |q| = (q·q)≤4. The sequence parameters were: FOV= 240x240 mm, slice thickness=4mm, TR/TE = 11400/95, bmax=9700 s/mm2, corresponding to diffusion resolution of 1/|qmax|=12 μm. The total DSI data acquisition time for 28 slices was 48 min. Data Processing: The most fundamental relationship between the diffusion MRI signal E(q) and the diffusion propagator P(r) is given by the Fourier transform: P(r) = ∫E(q) exp (-ir●q), where r is the real space vector and q is the q-space vector defined by q = γτg (γ is the gyro magnetic ratio, τ is the diffusion sensitizing gradient duration and g is the diffusion sensitizing gradient vector) [1]. Hanning window was used to pre multiply the signal E(q) before Fourier Transformation to ensure the signal attenuation for large |q| values [2]. The diffusion probability density function (PDF) was reconstructed by taking the discrete 3D Fourier transform of the signal in q-space. The orientation distribution function (ODF), Ф, was obtained from the PDF by taking the radial summation of the 3D PDF P(r): Φ(u) = ∫P(ρu)ρdρ, where ρ is the radius and u is the unit direction vector [2]. The data sets with 129,153 and 198 points were generated from the original 257 data set using the spherical symmetry along the y-axis. Tracking Method: DSI tractography was adapted from the streamline tracking method [3, 4]. Three possible high diffusion direction vectors were chosen from the ODF using local maximum method [4]. For tracking the fornix and cingulum fibers, the seed points were placed near the splenium of the corpus callosum (purple color in Fig. I) and the posterior region for cingulum (blue color in Fig. II). For each data set and subject, the tracts were reconstructed from one set of seed points using Euler-trapezoidal (predictorcorrector) method: rn+1 = rn +h[f(rn+1) ) + f(rn) ] /2, where rn+1 = rn +hf(rn) is the predictor and h is a variable step length which depends on the maximum norm of the tracking direction vector f(rn) [5]. For fornix bundle tracking we set two typical ROI’s around the mammillary body and hippocampus to separate from other bundles with the same seed point but for cingulum we used only one ROI at the mid coronal plane. At each step of the tracking we considered the vector with maximum inner product with the incoming vector. For each data set and subject tracking was performed using 35,41 and 45 threshold angles. The fiber tracts were displayed using visualization toolkit (VTK) library functions (http://www.vtk.org/). Results: Reconstruction of Fornix and Cingulum fiber bundles with different sub samples of one subject are shown in Fig. I and Fig. II. Tractography from the original 257 q-space encoding data set (A, E, I) was used as the gold standard. From the figures we can observe and compare qualitatively how each subsample have reproduced the bundles. The mean ± SD in Table I shows the ratio of pathways for each sample data set with respect to the gold standard. A ratio of one implies a closer agreement with the fully sampled data. For the cingulum bundles the coefficient of variation (SD/Mean) is smaller than for fornix for all three samples. For angles 41 and 45 the ratio for the fornix and cingulum fiber bundles is close to unity with minimum coefficient of variation in the 198 q-space encoding samples. The ratio for the 129 samples is also close to unity, but the coefficient of variation is relatively high. Qualitatively we have also observed for 129 samples that some pathways do not appear to be part of the bundles. Discussion and Conclusion: For both fornix and cingulum fiber bundles, qualitatively and quantitatively the 198 q-space encoding samples with angles of threshold between 41 and 45 have shown a results that are close to the gold standard. This translates into a reduction in the scan time by 11 minutes. While 129 data also produced fiber tracks close to the full data set, in some instances we have observed extraneous fibers with this subsample set. Since the curvature of the pathways in fornix is high, low angle of threshold (35) gives very poor results. The local truncation error of the predictor-corrector numerical integration method which is used for our adapted tracking method is four times less than that of the Euler’s method for h=0.5. Choosing variable step length and using predictor-corrector integration method improves stoppage of the pathways because of curvature.