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

Thijs Dhollander^{1} and Alan Connelly^{1,2}

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

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)

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!*

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

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.

**[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)

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