Automated rejection of motion-corrupted slices and optimised retrospective ghost correction for multi-shot DTI
Malte Hoffmann1 and Stephen J Sawiak1,2

1Wolfson Brain Imaging Centre, University of Cambridge, Cambridge, United Kingdom, 2Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge, United Kingdom

### Synopsis

DTI sequences based on EPI allow rapid acquisitions of image slices by traversing k-space lines in opposite directions following a single RF excitation. During long acquisition trains, phase errors caused by field inhomogeneity can lead to distortion. Acquiring slices in multiple shots can mitigate this effect. Motion between shots, however, results in ghosting that cannot be corrected. We show that slice-wise phase correction by entropy minimisation reduces ghosting compared to the manufacturer software (ParaVision 4.0, Bruker). Second, we propose an algorithm to automatically detect and reject slices with residual motion-induced ghosting, and validate it in a large cohort of mice.

### Purpose

Improving multi-shot in-vivo DTI data in two ways: (1) optimisation of zero- and first-order phase correction to reduce residual ghosting from k-space trajectory errors due to field inhomogeneity, and (2) automated detection and removal of remaining motion-induced ghosts on a slice-by-slice basis.

### Methods

DTI was performed in 177 mice (TR/TE 3000/35ms, voxel size 0.3×0.3mm2, 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.

### Results

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 atlas2.

### Discussion

Slice-wise phase correction based on entropy minimisation reduced the amount of ghosting in the data substantially (by 27.6% as compared to the manufacturer software). We presented an automated motion detection and rejection strategy for multi-shot DTI capable of decreasing the mean angular uncertainty on the principal diffusion direction by 26.7% in voxels with FA>0.5. Typically, only a few directions were rejected per slice, so that the possibility of affecting the diffusion parameters was low.3 After ghost correction, we observed a shift of FA towards lower values with a higher concentration of low to medium FA (see Figure 3A). This behaviour is in good agreement with results from Chang LC et al., who simulated the effect of outlier points in diffusion data.4 In DTI colour maps such as Figure 4, we observed that fine structures, in particular the dentate gyrus of the hippocampal formation, became more distinguished after motion correction

### Conclusion

We showed that slice-wise phase correction by entropy minimisation reduces ghosting considerably, and presented a novel approach for automated ghost correction of multi-shot DTI that successfully reduces the angular uncertainty on the primary diffusion direction. While the technique is easily implemented, it does not enforce a model onto the data. Our findings may be particularly interesting to users of older scanner platforms.

### Acknowledgements

We would like to thank the authors of the Cambridge MRI database for animal models of Huntington disease (Sawiak SJ et al. NeuroImage 2015) for providing the data.

### References

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.

### Figures

Figure 1 Image slice before (A) and after (B) phase correction. A slice from the same data set with motion-induced ghosting is shown in (C). Regions used for ghost intensity estimation are highlighted in green.

Figure 2 Distribution of rejected diffusion-encoded directions (out of 30, with $b>0$) per image slice across all 177 data sets.

Figure 3 (A) Distribution of fractional anisotropy (FA) across all 177 data sets. The black lines indicate the position of the most frequent value. (B) Distribution of angular uncertainty across all data sets. The black lines indicate quartiles.

Figure 4 DTI colour maps for the same image slice before (A) and after (B) the optimisation scheme. A corresponding image slice from the SPMMouse atlas2 is displayed in (C). (D-F) show the dentate gyrus of the hippocampus from (A-C) in more detail. The magnified region is highlighted in green.

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