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Giving up the ghost: a systematic comparison of 2D phase correction algorithms in multi-shell high angular diffusion weighted imaging
Elizabeth Powell1,2, Torben Schneider3, Marco Battiston2, Matthew Clemence3, Ahmed Toosy2, Jonathan Clayden4, and Claudia A.M. Wheeler-Kingshott2,5,6

1Medical Physics and Biomedical Engineering, University College London, London, United Kingdom, 2Queen Square MS Centre, Department of Neuroinflammation, UCL Queen Square Institute of Neurology, Faculty of Brain Sciences, University College London, London, United Kingdom, 3Philips Healthcare UK, Guildford, Surrey, United Kingdom, 4Developmental Imaging and Biophysics Section, Great Ormond Street Institute of Child Health, University College London, London, United Kingdom, 5Department of Brain and Behavioural Sciences, University of Pavia, Pavia, Italy, 6Brain MRI 3T Research Center, IRCCS Mondino Foundation, Pavia, Italy

### Synopsis

The echo planar imaging (EPI) Nyquist ghost often requires complex 2D phase error corrections in order to be robustly removed. Several methods exist but have not yet been systematically evaluated in high b-value diffusion-weighted (DW) EPI, where lower signal-to-noise ratios may affect the phase error estimation. We explore here the influence of different 2D phase-error corrected reconstruction methods on quantitative parameters derived from DW-EPI, and demonstrate that errors in parameter estimations relating to the Nyquist ghost can persist even after 2D phase-error correction.

### Introduction

Echo planar imaging (EPI) suffers from Nyquist ghost artefacts owing to alternating readout gradient polarities: gradient system imperfections cause a phase shift between opposing k-space trajectories which produces a ghost image offset by half the field-of-view (FOV)1. The 1D phase correction methods commonly implemented only correct shifts along the readout direction, and as such are unable to fully suppress the artefact when higher order phase errors are present2. Importantly, quantitative MRI methods based on EPI readout, such as diffusion weighted imaging (DWI), may be affected by incomplete corrections3. Several 2D phase correction methods have been proposed4,5,6; however the associated scan time increase, noise amplification or requirement for off-line reconstruction can be problematic. Crucially, 2D phase-corrected reconstruction methods have not been systematically studied in multi-shell high angular DWI (HARDI) with high b-values, where a low signal-to-noise ratio (SNR) may impact phase error estimations. Their widespread use in standard reconstruction pipelines has therefore been limited.

This work explores the extent to which widely used diffusion model parameters are influenced by different 2D phase-corrected reconstruction methods with varying requirements for reference scans.

### Methods

Image Acquisition and Reconstruction. Multi-shell DW-EPI were acquired (3T Philips Ingenia CX) using the vendor’s 32-channel headcoil on 5 healthy volunteers (3 female; age=37±12years) with b=[1000,2000,3000]s/mm2 and 30 diffusion directions per shell; 9 volumes were acquired with b=0s/mm2. SENSE acceleration=2 was used, with resolution=2x2x2mm3, TR/TE=6848/85ms, bandwidth=3281Hz. A dual acquisition of each volume was acquired with opposing readout gradient polarities. Image reconstruction was performed off-line on the vendor’s 1D phase-corrected raw k-space data using Matlab; each dataset was reconstructed using five different methods (Figure 1). All datasets were inspected for artefacts: no corrections for motion or eddy currents were applied in order to avoid confounding the effects of post-processing with the reconstruction methods.

Image Analysis. SNR maps for each reconstruction were approximated using the non-DW volumes. Artefact power (AP) maps7 were generated for the same volumes, with S the voxel intensity and N the total voxel number:

$$AP=\Bigg|\left(\frac{\left( S-S_{dual}\right)^2}{S_{dual}^2}\right)^{\frac{1}{2}}-\frac{1}{N}\sum^N_{j=1}\left(\frac{\left(S\left( j\right)-S_{dual}\left( j\right)\right)^2} {S_{dual}\left( j\right)^2}\right)^{\frac{1}{2}}\Bigg|$$

Parameter maps, including fractional anisotropy (FA), mean diffusivity (MD) and mean kurtosis (MK) from DKI8, and orientation dispersion index (ODI) from the NODDI model9, were generated as test metrics for each reconstruction method and evaluated against the reference dual acquisition using the relative difference:

$$d = \frac{ S-S_{dual}}{S_{dual}}$$

### Results

DW-EPI reconstructed using each method, and corresponding SNR and AP maps, are given in Figure 2; parameter maps are shown in Figure 3. The AP maps show that the Nyquist ghost is effectively suppressed by all 2D phase-corrected methods compared to the standard 1D correction, although SENSE noise amplification in PAGE and PEC-SENSE is evident in both AP and SNR maps. However, differences in parameter estimates relative to the dual reconstruction (Figure 4) demonstrate that residual effects from the Nyquist ghost persist even after 2D phase correction. Parameter estimates, particularly in PAGE and PEC-SENSE, show spatial variability dependent on artefact location, while a tendency for overestimation of MD is evident for REFB0. Distributions of relative differences (Figure 5) suggest that PAGE and PEC-SENSE introduce greater errors in parameter estimations relative to no correction or REFB0.

### Discussion

Of the phase-corrected reconstructions implemented, REFB0 was most effective in reducing the influence of Nyquist ghost artefacts on parameter estimates. The additional scan time required for the reference image is minimal, and overall the correction is fast and easy to combine with simultaneous multi-slice acceleration without the need for complex reconstruction algorithms. The potential bias towards overestimation of MD requires further exploration, but could be related to the lack of correction applied to the DW volumes.

Optimisations to the PEC-SENSE method, such as phase maps estimated from low b-value data alone, could reduce the influence of SENSE noise amplification and improve the feasibility of this method. This could be relevant for different applications; intravoxel incoherent motion (IVIM) imaging, for example, utilises low b-value data that may require phase corrections that a non-DW reference scan cannot correct.

The influence of 2D phase-corrected reconstruction methods on diffusion parameters is therefore non-trivial: the tested parameters appear variably affected by the different reconstructions, and inconsistencies in expected estimates have the potential to mask pathologically relevant changes. This could impact multi-centre trials, where manifestations of the ghost may differ between centres.

### Conclusions

The appearance of the Nyquist ghost, not only in DW-EPI but more importantly in derived parameter maps, demonstrates the need for appropriate artefact suppression to improve parameter estimation reliability. Different 2D phase-corrected reconstruction methods show variable influence on parameter estimates, and may introduce additional errors owing to artefacts from the reconstruction algorithm itself.

### Acknowledgements

No acknowledgement found.

### References

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2. Aldefeld B, Börnert P. Effects of gradient anisotropy in MRI. Magn Reson Med. 1998;39(4):606-614.

3. Porter DA, Calamante F, Gadian DG, Connelly A. The effect of residual Nyquist ghost in quantitative echo-planar diffusion imaging. Magn Reson Med. 1999;42(2):385-392.

4. Kellman P, McVeigh ER. Ghost artifact cancellation using phased array processing. Magn Reson Med. 2001;46(2):335-343.

5. Xie VB, Lyu M, Liu Y, Feng Y, Wu EX. Robust EPI Nyquist ghost removal by incorporating phase error correction with sensitivity encoding (PEC-SENSE). Magn Reson Med. 2018;79(2):943-951.

6. Chen NK, Wyrwicz AM. Removal of EPI Nyquist ghost artifacts with two-dimensional phase correction. Magn Reson Med. 2004;51(6):1247-1253.

7. Wargo CJ, Moore J, Gore JC. A comparison and evaluation of reduced-FOV methods for multi-slice 7T human imaging. Magn Reson Imaging. 2013;31(8):1349-1359.

8. Veraart J, Sijbers J, Sunaert S, Leemans A, Jeurissen B. Weighted linear least squares estimation of diffusion MRI parameters: Strengths, limitations, and pitfalls. Neuroimage. 2013;81:335-346.

9. Zhang H, Schneider T, Wheeler-Kingshott CA, Alexander DC. NODDI: Practical in vivo neurite orientation dispersion and density imaging of the human brain. Neuroimage. 2012;61(4)

### Figures

Figure 1: Overview of reconstruction methods

Figure 2: Reconstructions of the DW-EPI with b=[0,3000] s/mm2 and maps of SNR and AP for a representative subject. The Nyquist ghost is indicated by the yellow arrows; the ghost offset is 1/4 FOV owing to a SENSE factor of 2. SENSE noise amplification is also visible in the PAGE and PEC-SENSE reconstructions.

Figure 3: DT, DKI and NODDI parameter maps for each reconstruction. The influence of the Nyquist ghost on parameter estimates is visible in all maps when no 2D phase correction is applied (yellow arrows).

Figure 4: Relative differences in DKI and NODDI parameter maps of reconstructions using no correction, REFB0, PAGE and PEC-SENSE respectively with the dual reconstruction; the colourbar indicates the difference for each parameter relative to the expected value from the dual reconstruction. Structure from the residual Nyquist ghost is apparent, suggesting that none of the methods fully correct the EPI phase misalignment from every DW volume.

Figure 5: Distributions of parameter differences relative to expected values from the dual reconstruction for each correction method, evaluated in white and gray matter voxels in all subjects combined.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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