Unsupervised 3-tissue response function estimation from single-shell or multi-shell diffusion MR data without a co-registered T1 image
, David Raffelt
, and Alan Connelly
The Florey Institute of Neuroscience and Mental Health, Melbourne, Australia,
The Florey Department of Neuroscience, University of Melbourne, Melbourne, Australia
Target audience: people interested in obtaining multi-tissue CSD results from single-shell or multi-shell data without any hassle
Purpose: To overcome the fact that the fibre orientation distribution (FOD) from constrained spherical deconvolution (CSD)
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)
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 . We refer to this method as “single-shell 3-tissue CSD” (SS3T-CSD). Both MSMT-CSD
and SS3T-CSD require WM, GM and CSF response functions. These can be obtained from manually selected exemplary voxels of
the tissue classes, or via the procedure described in , which relies on a highly accurately co-registered T1 image. We propose an
unsupervised procedure that does not depend on a T1 image, nor registration, and works for both single-shell and multi-shell data.
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
and a single-shell scheme (60 directions at b = 3000 s/mm
and 7 b=0 images) as well as a
separate multi-shell scheme (30, 45, 60 directions respectively at b = 1000, 2000, 3000 s/mm
and 16 b=0 images). A T1 dataset
with voxel size 0.9 × 0.9 × 0.9 mm
was also acquired. All data were jointly 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.
Methods: Fig.1 shows the 4 main steps of our method, running on the single-shell data. In the 1
step, a brain mask is computed as
follows: for each separate b-value (including b=0), all images are averaged and an optimal threshold
is computed; all b-value
masks are combined; a median filter is applied to the combined mask; the largest connected component is selected and holes are
filled. The following steps use 2 metrics: a fractional anisotropy (FA) map and a simple signal decay metric (SDM). For single-shell
data, the SDM is defined as the (natural) logarithm of the ratio of the average b=0 to the average diffusion-weighted image. For
multi-shell data, this is done for each shell and an average across shells, weighted by the number of images per shell, is obtained. In
step, crude WM-GM-CSF segmentations are computed: the brain mask is eroded (by 3 voxels); the WM is separated from
the rest by a low FA threshold (0.2); the remaining voxels are split in GM and CSF by an optimal threshold
computed on the SDM
values. In the 3
step, the WM-GM-CSF segmentations are refined and made more conservative, to remove the bulk of multi-tissue
partial volumed voxels. High WM SDM outliers above Q
) are removed. For both the voxels below and above the GM SDM
median, optimal thresholds
are computed and both parts closer to the initial GM median are retained. The high SDM outliers that
were removed from the WM are reconsidered for the CSF if they have higher SDM than the current minimal CSF SDM. An optimal
is computed for the resulting CSF and only the higher SDM valued voxels are retained. In the 4
step, a number of final
best single-fibre (SF) WM, GM and CSF voxels are selected, as a percentage of the current conservative WM, GM and CSF masks;
respectively 0.5%, 2% and 10%. For the WM, a modified version of the algorithm in  is used to obtain the best SF WM voxels. For
the GM, the voxels closest to the GM SDM median are selected. For the CSF, the highest SDM valued voxels are selected.
We compare our algorithm to the one in , which is based on a probabilistic WM-GM-CSF segmentation of a co-registered T1
image. It retains voxels with more than 95% tissue probability and applies an additional upper FA threshold (0.2) for both GM and
CSF. Both algorithms are applied on the multi-shell and single-shell data. The obtained response functions are then used to perform
MSMT-CSD on the multi-shell data and SS3T-CSD on the single-shell data.
Results & discussion: The algorithm took about 35 sec. on a standard desktop computer (mostly spent on the selection of SF WM
voxels using ). The resulting response functions as obtained from the multi-shell and single-shell data are shown respectively in
Fig.2 and Fig.3, and compared to those obtained using the algorithm in . The WM and GM responses from both algorithms—as
well as the angular profiles of the b≠0 WM responses (not shown)—are very similar. Surprisingly, the CSF responses do differ
significantly: compared to our proposed method, the algorithm in  appears to underestimate the b=0 CSF intensity by more than
30%. There are several possible explanations here: the method in  may easily suffer from even the slightest (T1) registration
inaccuracies (and hence include nearby WM or GM partial volume in the diffusion MR data); it may also miss out on several good
CSF voxels due to the FA threshold, which our method recovers at step 3 (Fig.1). Finally, our algorithm only retains the best 10%
voxels of the CSF in step 4. The MSMT-CSD and SS3T-CSD results are shown respectively in Fig.2 and Fig.3. The results using the
responses from the  algorithm (top) are similar to those using the responses from our method (bottom); except for the fact that
the former overestimate the CSF. This causes, e.g., underestimation of the WM FOD in voxels containing free water partial volume.
SS3T-CSD appears to be more resilient to the CSF miscalibration caused by . The most WM is recovered by combining the proposed method with SS3T-CSD (Fig.3., bottom).
Conclusion: We propose a method for unsupervised estimation of WM-GM-CSF responses from single-shell or multi-shell data that doesn’t require a co-registered T1 image.
Combined with SS3T-CSD, this allows for fast and fully automated 3-tissue CSD processing of simple single-shell diffusion MR data without any other external prerequisites.
References:  Tournier et al, NeuroImage 2007;35(4):1459–1472.  Jeurissen et al, NeuroImage 2014;103:411–426.  Dhollander et al, Proc ISMRM 2016;24:3010.
 Ridgway et al, NeuroImage 2009;44(1):99–111.  Tournier et al, NMR Biomed 2013;26(12):1775–1786.
the 4 m
ain steps of the algorithm,
running on the single-shell dataset. Two
slices are shown. The numbers below
each step indicate how many voxels are
still left in the WM – GM – CSF masks.
: the method in
full line: our method. Middle: SS3T-CSD results using responses from the method
: FODs in region at arrow tip
: the method in
full line: our method. Middle: MSMT-CSD results using responses from the method
: FODs in region at arrow
0 1000 2000 3000