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Generating a T1-like contrast using 3-tissue constrained spherical deconvolution results from single-shell (or multi-shell) diffusion MR data
Thijs Dhollander
1
and Alan Connelly
1,2
1
The Florey Institute of Neuroscience and Mental Health, Melbourne, Australia,
2
The Florey Department of Neuroscience, University of Melbourne, Melbourne, Australia
Target audience: people who wish to generate a contrast closely resembling a T1-weighted image from just
single-shell (or multi-shell) diffusion MR data, for various purposes—e.g., registration of their diffusion MR data
to an actual T1-weighted image, correction of susceptibility-induced and/or eddy-current distortions, etc.
Purpose: To overcome the fact that the fibre orientation distribution (FOD) from constrained spherical
deconvolution (CSD)
[1]
assumes a single-fibre white matter (WM) response function—and is thus inappropriate
and distorted in voxels containing grey matter (GM) or cerebrospinal fluid (CSF)—multi-shell multi-tissue CSD
(MSMT-CSD)
[2]
was proposed. MSMT-CSD can resolve WM, GM and CSF signal contributions, but requires multi-
shell data. Very recently, a novel method that can achieve the same results using just single-shell data was
proposed in [3]. We refer to this method as “single-shell 3-tissue CSD” (SS3T-CSD). Both MSMT-CSD as well as
SS3T-CSD yield tissue components that describe partial volume signal contributions of the tissue classes. As
individual tissue classes show a homogeneous intensity within each tissue class in a T1-weighted image, the 3-
tissue CSD components may be able to provide the necessary information to generate a T1-like contrast from the
diffusion MR data. In this work, we merely pursue a proof-of-concept of this hypothesis.
Data & preprocessing: Single-subject diffusion MR data were acquired on a Siemens Skyra 3T scanner using a 32-
channel head coil, with voxel size 2.5 × 2.5 × 2.5 mm
3
and a single-shell scheme (60 directions at b = 3000 s/mm
2
and 7 b=0 images). The data were corrected for susceptibility-induced distortions (using an extra pair of b=0
images acquired with opposite phase encodings), eddy-current distortions, motion, and bias fields. A T1-
weighted image with voxel size 0.9 × 0.9 × 0.9 mm
3
was also acquired. This image was independently corrected
for bias fields.
Methods: We obtained the WM, GM and CSF response functions for 3-tissue CSD by an unsupervised procedure
that does not depend on the T1-weighted image (not shown, this method is described in a separate abstract
submitted for this workshop). We then performed SS3T-CSD on the single-shell diffusion MR data. Next, we
normalised the resulting tissue components, so as to obtain tissue fractions that sum to 1. This step is crucial, as
CSD methods (e.g., CSD, MSMT-CSD and SS3T-CSD) seek to model the diffusion MR (and b=0) signal directly, and
hence the resulting components are not fractions by definition; e.g., portions of the corticospinal tracts typically
show a hyperintense WM component compared to their WM surroundings. The T1-weighted image, however,
does not show these (T2 related) intensity variations within tissue types, which motivates normalisation of the
tissue components for this specific application. Finally, we determined 3 constant weights that reproduce the T1-
weighted image as well as possible by means of a weighted sum of the 3 normalised tissue components. For the
sake of this experiment, we rely on the fact that the T1-weighted image and the diffusion MR data are already
corrected for motion, distortions and bias fields: we down-sample the T1-weighted image to the grid of the
diffusion MR data and recover the 3 weights as the least-squares solution across all voxels within a brain mask.
Results & discussion: The results are shown for two axial slices in Fig.1. Note the difference between Fig.1C and
Fig.1D; i.e., the tissue components before and after normalisation. The final T1-like contrast (Fig.1E) closely
resembles the actual T1-weighted contrast (Fig.1B). This is further supported by the bivariate histogram in Fig.2.
Note that the intensities in the T1-like contrast are capped between 2 values (which respectively occur in voxels
containing 100% CSF and 100% WM). The outliers in Fig.2 mostly concern voxels at the edge of the brain mask—
but may also reveal imperfections in the registration between the T1-weighted image and the diffusion MR data.
If the T1-like contrast were to be used for registration (motion and relative distortions) to a T1-weighted image,
the 3 constant weights could of course not be determined up-front by a voxel-wise least-squares fit as we did
here. A solution would be to fit the weights to reproduce the distribution of intensities in the T1-weighted image
(i.e., not requiring spatial correspondence). Alternatively, the weights could be jointly optimised with the spatial
transformation between both images. As the normalised tissue components do not suffer from bias fields, the
bias field on the T1-weighted image could be jointly corrected for as well. The “anisotropic power map”
[4]
also
resembles a T1-weighted image, but is not based on full tissue component partial volume as informed by all b-
values. Furthermore, as it is an absolute measure, it is not inherently free of potential bias fields.
Conclusion: We have shown that a T1-like contrast can be generated as a weighted sum of the normalised tissue
components from 3-tissue CSD methods such as SS3T-CSD; which can be useful in several processing applications.
References:
[1] Tournier et al,
NeuroImage 2007;35(4):1459–1472.
[2] Jeurissen et al,
NeuroImage 2014;103:411–426.
[3] Dhollander et al,
Proc ISMRM 2016;24:3010.
[4] Dell’Acqua et al,
Proc ISMRM 2014;22:370.
Fig.2
: Bivariate
histogram of the actual T1
-
weighted image
intensities (horizontal axis) versus the T1-like contrast intensities
generated from the normalised SS3T-CSD tissue components
(vertical axis). For reference, the identity line is shown in red.
A
B
C
D
E
Fig.1:
[A]: T1-weighted image
[B]: T1-weighted image, down-sampled to the grid
of the diffusion MR data, and brain-masked
[C]: WM-GM-CSF tissue components from SS3T-CSD
(relying only on the single-shell diffusion MR data)
[D]: WM-GM-CSF normalised tissue components
(i.e., tissue fractions which sum to 1)
[E]: T1-like contrast, generated as a weighted sum of
the normalised tissue components. The 3 weights
are constants for the entire brain volume.