We also tested our method using the MGH HCP data set acquired on the Siemens
3T Connectome scanner with maximum gradient strength of 300 mT/m. The spatial resolution of this data set was 1.5
× 1.5
× 1.5 mm
3. The experimental parameters were
TR/TE = 8800/57 ms,
δ = 12.9 ms and Δ = 21.8 ms. The data set consisted of four b-values with
b = 1000, 3000, 5000 and 10000 s/mm
2. The number of gradient directions at each b-shell were 64, 64, 128 and 256, respectively. More detailed information about data acquisition and pre-processing steps can be found in (Setsompop et al., 2013 (
link)).
The maximum q-value that can be reached in this data set is about 0.7559 rad
/μm, which allows for probing short-range disturbances as well. In order to incorporate short-range disturbances, we extend the model (
34) to the three-dimensional case as follows:
where
M2 and
D are both 3
× 3 positive semidefinite tensors as before. Similar to the previous experiment, we assume that
Û2,
Û4 and
D0 all have the same set of eigenvectors. From
M2 and
M4, we define
Û2 :=
M2D and
Û4 =
M4D. The eigenvalues for the three tensors are denoted by {
û2,‖,
û2,⊥,
û2,⊥}, {
û4,‖,
û4,⊥,
û2,⊥} and {
d‖,
d⊥,
d⊥}, respectively.
Ning L., Özarslan E., Westin C.F, & Rathi Y. (2016). Precise Inference and Characterization of Structural Organization (PICASO) of tissue from molecular diffusion. NeuroImage, 146, 452-473.