Automated rejection of motion-corrupted slices and optimised retrospective ghost correction for multi-shot DTI

Malte Hoffmann^{1} and Stephen J Sawiak^{1,2}

DTI was performed in 177 mice
(TR/TE 3000/35ms, voxel size 0.3×0.3mm^{2}, matrix 128×128, 17 0.8mm
slices, 0.2mm gap, 35 directions, 4 EPI segments). The first five volumes of
each data set were acquired without diffusion gradients $$$(b=0)$$$.

Data sets reconstructed with
manufacturer-provided phase correction in ParaVision 4.0 (Bruker, Billerica, MA)
were compared to phase correction by iterative slice-wise entropy minimisation
based on zero- and first-order phase shifts.^{1} Ghost intensities were assessed as
the ratio of the mean signal within two squares (16×16 voxels), centred (a) in
readout direction at the top border and (b) within the image, respectively (see
**Figure 1B**). Ghosting was evaluated across
all 5310 diffusion-encoded central slices.

Diffusion-encoded slices with entropy exceeding 105% of the median slice entropy $$$\overline{E}$$$ were labelled as motion-corrupted and excluded from the estimation of the tensor. An independent value for $$$\overline{E}$$$ was determined across all diffusion-encoded slices of each data set. The diffusion tensor was fitted using iterative non-linear least-squares minimisation in MATLAB (MathWorks, Natick, MA). The eigenvectors and functional anisotropy (FA) were calculated before and after rejection of motion-corrupted data. The angular uncertainty on the primary eigenvector $$$u$$$ was estimated from the standard deviations (SD) $$$\sigma_i$$$ of the tensor elements $$$d_i$$$ $$$(i=1,2,\dots,6)$$$: assuming the error on tensor elements is normally distributed (mean $$$d_i$$$, SD $$$\sigma_i$$$), we drew $$$N=10000$$$ sets of $$$d_i$$$ for each voxel to determine a primary eigenvector. The SD of the angles $$$\alpha$$$ $$$(0^\circ\leq\alpha\leq90^\circ)$$$ between each of these vectors and $$$u$$$ was taken as an estimate of angular uncertainty.

**Figure 1** shows an exemplary image slice before and after phase
correction. A slice from the same data set with motion-induced ghosting is shown
in **Figure 1C.** Ghost intensities of 6-352% (mean±SD
15±16%) were measured after manufacturer-provided phase correction. Instead, entropy
minimisation resulted in a reduced intensity range of 7-255% (mean 13±7%). For
comparison, ghosting was 7-521% (mean 17±23%) in the uncorrected data.

On average, 2.3±3.1 directions were
rejected per slice. The maximum number of rejections was 15, which occurred in 2.3%
of the data sets. **Figure 2** depicts
the distribution of rejected directions per slice. For voxels with FA>0.5,
the mean angular uncertainty on the principal diffusion direction was reduced
from 8.6° to 6.3° (26.7%). The distribution of angular uncertainty before and
after ghost removal is shown in **Figure
3B**. The mean ratio of the SD for each tensor element and its actual value
as estimated by the fitting algorithm dropped from 256.6% to 6.5%. Figure 3A shows the distribution of FA in all data sets before and
after motion correction.
A DTI colour map for the
same image slice before and after rejecting three ghosted diffusion directions
is displayed in **Figure 4**,
along with a corresponding slice from the SPMMouse atlas^{2}.

1. Skare S et al. A fast and robust minimum entropy based non-interactive Nyquist ghost correction algorithm. Proc ISMRM 2006. p. 2349.

2. Sawiak SJ et al. Voxel-based morphometry in the R6/2 transgenic mouse reveals differences between genotypes not seen with manual 2D morphometry. Neurobiol Dis. 2009;33(1):20-7.

3. Chen Y et al. Effects of rejecting diffusion directions on tensor-derived parameters. NeuroImage 2015;109:160-170.

4. Chang LC et al. RESTORE: robust estimation of tensors by outlier rejection. Magn Reson Med 2005;53(5):1088-1095.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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