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


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.


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)


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].

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.


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).


No acknowledgement found.


[1] Tournier JD, Calamante F, Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution. NeuroImage 2007;35(4):1459-1472.

[2] Jeurissen B, Tournier JD, Dhollander T, Connelly A, Sijbers J. Multi-tissue constrained spherical deconvolution for improved analysis of multi-shell diffusion MRI data. NeuroImage 2014;103:411-426.

[3] Andersson JLR, Skare S, Ashburner J. How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging. NeuroImage 2003;20(2):870-888.

[4] Andersson JLR, Xu J, Yacoub E, Auerbach E, Moeller S, Ugurbil K. A comprehensive Gaussian Process framework for correcting distortions and movements in diffusion images. Proc ISMRM 2012;20:2426.

[5] Tustison NJ, Avants BB, Cook PA, Zheng Y, Egan A, Yushkevich PA, Gee JC. N4ITK: Improved N3 bias correction. IEEE TMI 2010;29(6):1310-1320.

[6] Dhollander T, Smith RE, Tournier JD, Jeurissen B, Connelly A. Time to move on: an FOD-based DEC map to replace DTI's trademark DEC FA. Proc ISMRM 2015;23:1027.

[7] Roine T, Jeurissen B, Perrone D, Aelterman J, Philips W, Leemans A, Sijbers J. Informed constrained spherical deconvolution (iCSD). Med Image Anal 2015;24(1):269-281.


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.

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.

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.

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)