Linear Multi-scale Modeling of diffusion MRI data: A framework for characterization of orientational structures across length scales

Barbara Wichtmann^{1,2}, Susie Huang^{1}, Qiuyun Fan^{1}, Thomas Witzel^{1}, Elizabeth Gerstner^{3}, Bruce Rosen^{1}, Lothar Schad^{2}, Lawrence Wald^{1,4}, and Aapo Nummenmaa^{1}

*Simulation.* Synthetic MRI data with
an SNR of 10 was generated using the Monte Carlo diffusion simulator of Camino^{3} for diffusion within impermeable, regular packed cylinders with
a range of diameters (2.5-20µm) and intra-axonal volume fractions (0.1-0.9).

*Data
acquisition.* With approval from the institutional review board, a healthy volunteer
and a patient with a resected left frontal anaplastic oligodendroglioma were
scanned on a dedicated high-gradient 3T MRI scanner (MAGNETOM CONNECTOM,
Siemens Healthcare) with a maximum gradient strength of 300mT/m and maximum
slew rate of 200T/m/s^{4}. Sagittal 2mm isotropic resolution diffusion-weighted spin
echo EPI images were acquired using simultaneous multislice (SMS) imaging^{4} and zoomed/parallel imaging^{5} for high-resolution whole-brain coverage. The following
parameters were used: δ/Δ=8/19, 8/30, 6/50 ms, 4-5 diffusion gradient increments
linearly spaced from 55-293mT/m per Δ, TE/TR=77/4400ms, GRAPPA acceleration
factor R=2, and SMS MB factor=2. Diffusion gradients were applied in 64 to 128
non-collinear directions with interspersed b=0 images every 16 directions. The
maximum b-value at the longest diffusion time was 10,350 s/mm^{2}.
Total acquisition time was 90 min.

*Data analysis.* Following preprocessing to correct for gradient nonlinearity, motion
and eddy currents^{6}, spherical harmonics expansion of order 6/8
with Laplace-Beltrami regularization^{7} was used to interpolate the diffusion signal on
each q-shell (regularization
parameter λ set to 0.006). The linear multi-scale forward model of different
sized restricted and hindered diffusion compartments was obtained by concatenating
two spectra of response functions (Fig. 1): 1)
a non-Gaussian diffusion response function^{8} for water restricted inside cylindrical
structures and 2) a Gaussian diffusion response function^{2} for hindered water and free water diffusion. For
a more compact and efficient linear implementation we parameterized the
orientation distribution of the hindered and restricted compartments with a set
of order 4 and 6 spherical harmonics, respectively. To obtain the orientation
distribution functions and corresponding volume fractions, the multi-scale
deconvolution inverse problem was solved by standard least-squares estimation
with Tikhonov regularization.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

0661