Linear Multi-scale Modeling (LMM) of diffusion MRI data is a recently developed DWI analysis technique for separating orientation distributions of restricted and hindered diffusion water compartments over a range of length scales, thereby allowing more detailed characterization of tissue microstructure. Here, we apply the LMM framework to characterize a low-grade oligodendroglioma prior to resection. We use the distinct microstructural signature of the tumor to delineate tumor extent and use results from pathology and numerical simulations to refine our understanding of the tumor microstructure.
Data acquisition. With approval from the institutional review board, a pre-surgical patient with a left frontal oligodendroglioma (WHO grade II) was scanned on a dedicated high-gradient 3T MRI scanner (MAGNETOM CONNECTOM, Siemens Healthcare) with a maximum gradient strength of 300mT/m using a custom-made 64-channel head coil [4]. Sagittal 2-mm isotropic resolution diffusion-weighted spin echo EPI images were acquired using simultaneous multislice(SMS) [5] imaging and zoomed/parallel imaging [6] for high-resolution whole-brain coverage. The following parameters were used: δ/Δ=8/19,8/49ms, 4-5diffusion gradient increments linearly spaced from 55-293mT/m per Δ, TE/TR=77/3600ms, GRAPPA acceleration factor R=2, and SMS MB factor=2. Diffusion gradients were applied in 32/64/128non-collinear directions with interspersed b=0 images every 16 directions. The maximum b-value at Δ was 10,000s/mm2. Sagittal T1-MPRAGE and T2-SPACE-FLAIR images were also acquired. Total acquisition time was approximately 60min. Following resection, the tumor was processed with standard pathology and H&E staining.
LMM analysis. Following preprocessing to correct for gradient nonlinearity, motion and eddy currents[7], spherical harmonics expansion of order 6/8 with Laplace-Beltrami regularization[8] (λ=0.006) was used to interpolate the diffusion signal on each q-shell. To obtain the orientation distribution and corresponding volume fraction estimates, the linear multi-scale deconvolution inverse problem, as described in Fig.1, was solved by standard least-squares estimation with Tikhonov regularization. Profiles of restricted, hindered and free volume fractions for normal white, gray matter were derived by averaging volume fraction estimates over all white and cortical gray matter voxels in the normal right hemisphere(Freesurfer-segmentation). The tumor region was segmented manually by an experienced neuroradiologist using T1/T2 anatomic images. A microstructural signature specific for tumor was defined by calculating the difference between pathologic white/gray matter voxels within the tumor and normal white/gray matter profiles. Using the derived profiles as predictors, voxel wise linear least-squares regression was performed in order to decompose the estimated volume fractions into a white, gray matter and tumor component (Fig.4).
Simulation. To understand the biophysical basis underlying the estimated volume fraction profiles, synthetic MRI data was generated using the Camino Monte Carlo diffusion simulator[9] for diffusion within permeable/impermeable cylinders and spheres of different sizes and packing densities. Simulation results were compared to the experimental LMM tumor profiles as well as to histology.
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Fig. 4 Using the derived profiles for (A) white matter, (B) gray matter and (C) tumor as predictors, voxel wise constrained linear least-squares regression allows for decomposing the estimated volume fractions into a white matter, gray matter and tumor components.
The maps show linear regression coefficients for white matter, gray matter and tumor in solving the linear least-squares equation:
A · White Matter Profile + B · Gray Matter Profile + C · Tumor Profile = Volume fraction estimate in voxel, subject to A,B,C≥0.