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A novel iterative approach to reap the benefits of multi-tissue CSD from just single-shell (+b=0) diffusion MRI data

Authors:

Abstract

Constrained spherical deconvolution (CSD) is a robust approach to resolve the fibre orientation distribution (FOD) from diffusion MRI data. However, the FOD from CSD only aims to represent "pure" white matter (WM) and is inappropriate/distorted in regions of (partial voluming with) grey matter (GM) or cerebrospinal fluid (CSF). Multi-shell multi-tissue CSD was proposed to solve this issue by estimating WM/GM/CSF components, but requires multi-shell data to do so. In this work, we provide the first proof that similar results can also be obtained from only simple single-shell (+b=0) data, and propose a novel specialised optimiser that achieves this goal.
Proc. Intl. Soc. Mag. Reson. Med. 24 (2016) 3010
A novel iterative approach to reap the benefits of multi-tissue CSD
from just single-shell (+b=0) diffusion MRI data
Thijs Dhollander1 and Alan Connelly1,2
1The Florey Institute of Neuroscience and Mental Health, Melbourne, Australia
2The Florey Department of Neuroscience, University of Melbourne, Melbourne, Australia
Synopsis
Constrained spherical deconvolution (CSD) is a robust approach to resolve the fibre orientation distribution (FOD)
from diffusion MRI data. However, the FOD from CSD only aims to represent "pure" white matter (WM) and is
inappropriate/distorted in regions of (partial voluming with) grey matter (GM) or cerebrospinal fluid (CSF). Multi-
shell multi-tissue CSD was proposed to solve this issue by estimating WM/GM/CSF components, but requires
multi-shell data to do so. In this work, we provide the first proof that similar results can also be obtained from
only simple single-shell (+b=0) data, and propose a novel specialised optimiser that achieves this goal.
Purpose
Constrained spherical deconvolution (CSD) is a robust approach to resolve the fibre orientation distribution (FOD)
from diffusion MRI (dMRI) data[1]. The FOD from single-shell single-tissue (SSST)-CSD only models white matter
(WM); it will be distorted/inappropriate when other tissue types are (partially) present; i.e., grey matter (GM) and
cerebrospinal fluid (CSF). Multi-shell multi-tissue (MSMT)-CSD was proposed to solve this issue[2], but requires multi-
shell data. We aim to achieve similar results/benefits, by using only single-shell (+b=0) data.
Data acquisition & preprocessing
Single subject dMRI data were acquired on a Siemens 3T scanner, with voxel size 2.5×2.5×2.5mm³, and a multi-shell
scheme (b=0,1000,2000,3000s/mm² respectively for 5,17,31,50 directions + additional b=0 volume with reversed-
phase encoding). The data were corrected for susceptibility-induced distortions[3], eddy-current-induced distortions
and motion[4], and bias-fields[5].
We use these terms to refer to subsets of the data:
MS-data (multi-shell data): all images over all 3 dMRI shells + b=0 data.
SS-data (single-shell data): the 50 directions at b=3000s/mm².
B0-data: b=0 images.
SS+B0-data: combination of the latter 2. (often informally called "single-shell" data)
MSMT-CSD & SSST-CSD
Conservative regions or individual voxels deemed to contain "pure" samples of single-fibre-WM,GM,CSF were
selected to estimate the tissue response functions (guided by FA and ADC maps). MSMT-CSD results are shown in
Fig.1, first column. The WM-tissue outcome is presented using FOD-based directionally-encoded colour (DEC),
weighted by the WM-FOD integral[6]. SSST-CSD results are shown in the second column: WM is overestimated,
because GM/CSF parts are not estimated. Both results match the findings of [2].
Proc. Intl. Soc. Mag. Reson. Med. 24 (2016) 3010
Naive multi-tissue approaches for SS+B0-data
First naive approach: applying MSMT-CSD directly to SS+B0-data. Even under non-negativity constraints, given
isotropy of GM and only two b-values, GM can be (and is) fitted by a WM+CSF mixture (Fig.1, third column). The
WM is still grossly overestimated; most fundamental problems of SSST-CSD results remain.
Second naive approach: applying MSMT-CSD, but using only WM+GM. This yields a more aggressive "cleanup" of
WM (Fig.1, fourth column). CSF gets fitted as "hyper-GM" (far beyond the 0-to-1 range): the only/best means to fit
its high B0-data. But this also (partially) happens in WM+CSF mixtures, resulting in an overly aggressive cleanup;
e.g., enlarged ventricles, eroded nearby WM... even at the cost of GM not being able to represent the non-B0 WM
anisotropy!
Iterative 2-shell 3-tissue (2S3T)-CSD for SS+B0-data
The naive approaches' results provide important insights. GM sits "in the range between WM and CSF". Fitting only
WM+GM provides an underestimate of WM. A similar property holds for fitting only CSF+GM: this yields an
underestimate of CSF.
This inspired us to design a specialised optimiser to tease out the WM-GM-CSF parts from SS+B0-data. Without
going into details, the overall strategy is:
1.Initialise WM to 0.
2.Fit only CSF+GM, given WM as prior constraint. This yields an underestimate of CSF.
3.Fit only WM+GM, given CSF as prior constraint. Since CSF is an underestimate, the resulting WM will be as well.
This marks the end of an iteration, yielding underestimates of CSF/WM, and consequently an overestimate of GM.
The next iteration is initialised with the current (under)estimate of WM.
In the theory of MSMT-CSD[2], the B0-data are regarded like any other b-value/shell; so "formally", SS+B0-data is a
case of 2-shell data (even though often informally called "single-shell" data). Retaining consistency, we refer to our
specialised strategy as a 2-shell 3-tissue CSD approach; 2S3T-CSD for short.
Results & discussion
We performed 2S3T-CSD on the SS+B0-data for 4 iterations (this took 13 minutes for the whole volume, on a
standard desktop computer). The final result is shown in Fig.1, fifth column. Note how closely the outcome
resembles the MSMT-CSD (on MS-data) result. Fig.2 shows the WM-GM-CSF estimates after each iteration. Note
how, even after iteration #1, the WM estimate is already informed by the initial (under)estimate of CSF; e.g., the
fornix starts to reappear. Over iterations, the WM/CSF are recovered. This is most apparent at, e.g., the ventricle
borders, where excess GM is swiftly eliminated; but also happens in other regions. Figs.3-4 present tractography
results, to further support the benefits of 2S3T-CSD for SS+B0-data. Fig.5 shows further 2S3T-CSD results, offering all
typical outputs previously only offered by MSMT-CSD[2].
Informed CSD[7] attempts this as well, but requires acquisition of a high-resolution T1-image, subvoxel-accuracy
registration and intricate spatial segmentation. 2S3T-CSD leverages the full potential of dMRI.
Conclusion
While it was initially believed that multiple tissue types could not be distinguished using single-shell data[2], we
hereby provide the first proof of the contrary. Leveraging (relative) properties of the 3 common brain tissue types
(WM,GM,CSF), we obtain close to the same results/benefits as MSMT-CSD, yet from single-shell (+b=0) data and
without any external spatial/anatomical priors, using a novel iterative method: 2-shell 3-tissue CSD (2S3T-CSD).
Proc. Intl. Soc. Mag. Reson. Med. 24 (2016) 3010
Fig.1: results from different techniques on SS(+B0)-data, compared to MSMT-CSD on MS-data. The WM results are
presented using FOD-based DEC maps (intensity = WM-FOD integral). All images are windowed equally; from 0
(black) to 1 (white or full DEC intensity). The 2S3T-CSD results are very similar to MSMT-CSD on MS-data.
Proc. Intl. Soc. Mag. Reson. Med. 24 (2016) 3010
Fig.2: evolution of 2S3T-CSD over iterations. The result at iteration #4 is also presented in Fig.1. Initially, the
WM/CSF parts are always a "safe" underestimate, and the GM an overestimate; especially in WM/CSF partial
volumed voxels (e.g., ventricle borders and fornix). The "excess GM" is eliminated in favour of WM/CSF.
Proc. Intl. Soc. Mag. Reson. Med. 24 (2016) 3010
Fig.3: tractography results (2mm slab) after MSMT-CSD on MS-data, versus SSST-CSD and 2S3T-CSD on SS(+B0)-data.
A low (0.06) FOD threshold was used; this allows to exploit a maximum amount of information from MSMT-CSD
results. SSST-CSD yields many false positives, while 2S3T-CSD closely replicates the quality previously ony expected
from MSMT-CSD.
Fig.4: detail of tractography results in a coronal slab, comparing MSMT-CSD (on MS-data) and 2S3T-CSD (on SS+B0-
data). Both results show similar qualities: little to no spurious tracks, while large coherent bundles of tracks nicely
fan out into cortical regions. 2S3T-CSD achieves this using data from a standard "single-shell" (+b=0) acquisition.
Proc. Intl. Soc. Mag. Reson. Med. 24 (2016) 3010
Fig.5: a range of 2S3T-CSD results. Upper row: tissue maps of several axial slices. Middle row: WM FOD-based DEC
maps of the same slices. Bottom row: WM-FODs in part of a coronal slice, overlaid on the FOD-based DEC (left) and
tissue (right) maps. Clean FODs nicely "penetrate" into the cortex.
Proc. Intl. Soc. Mag. Reson. Med. 24 (2016) 3010
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... For the diffusion scans, images were preprocessed using established methods to remove artifacts 53 , the white matter fiber orientation distribution was resolved using single-shell constrained spherical deconvolution 54 , and a whole brain connectome was created using probabilistic tractography and the AAL atlas parcellation 55,56 . Tracts from each participant's connectome were used in analysis if they terminated in the right or left amygdala and in the ROI overlapping the search region defined in the fMRI analysis. ...
... For a full description of preprocessing steps as well as reliability of metrics derived from this diffusion processing pipeline see Newman et., al 2020 53 . The white matter fiber orientation distribution (FOD) was then resolved at the voxel-wise level by processing the outermost b-value shell (b=3000s/mm 2 ) using single-shell constrained spherical deconvolution, a technique to separate directional axonal signal from intracellular and extracellular isotropic diffusion 54 . Probabilistic tractography was performed by applying the iFOD2 algorithm which propagates streamlines between voxels based on the direction and amplitude of the underlying FOD 87 . ...
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Diffusion-weighted (DW) magnetic resonance imaging (MRI) is a noninvasive imaging method, which can be used to investigate neural tracts in the white matter (WM) of the brain. However, the voxel sizes used in DW-MRI are relatively large, making DW-MRI prone to significant partial volume effects (PVE). These PVEs can be caused both by complex (e.g. crossing) WM fiber configurations and non-WM tissue, such as gray matter (GM) and cerebrospinal fluid. High angular resolution diffusion imaging methods have been developed to correctly characterize complex WM fiber configurations, but significant non-WM PVEs are also present in a large proportion of WM voxels. In constrained spherical deconvolution (CSD), the full fiber orientation distribution function (fODF) is deconvolved from clinically feasible DW data using a response function (RF) representing the signal of a single coherently oriented population of fibers. Non-WM PVEs cause a loss of precision in the detected fiber orientations and an emergence of false peaks in CSD, more prominently in voxels with GM PVEs. We propose a method, informed CSD (iCSD), to improve the estimation of fODFs under non-WM PVEs by modifying the RF to account for non-WM PVEs locally. In practice, the RF is modified based on tissue fractions estimated from high-resolution anatomical data. Results from simulation and in-vivo bootstrapping experiments demonstrate a significant improvement in the precision of the identified fiber orientations and in the number of false peaks detected under GM PVEs. Probabilistic whole brain tractography shows fiber density is increased in the major WM tracts and decreased in subcortical GM regions. The iCSD method significantly improves the fiber orientation estimation at the WM-GM interface, which is especially important in connectomics, where the connectivity between GM regions is analyzed.
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