Elizabeth Powell^{1,2}, Torben Schneider^{3}, Marco Battiston^{2}, Matthew Clemence^{3}, Ahmed Toosy^{2}, Jonathan Clayden^{4}, and Claudia A.M. Wheeler-Kingshott^{2,5,6}

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.

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 present^{2}. Importantly,
quantitative MRI methods based on EPI readout, such as diffusion
weighted imaging (DWI), may be affected by incomplete corrections^{3}.
Several 2D phase correction methods have been proposed^{4,5,6}; 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.

*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/mm^{2} and 30 diffusion directions per shell; 9 volumes
were acquired with b=0s/mm^{2}. SENSE acceleration=2 was used, with
resolution=2x2x2mm^{3}, 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) maps^{7} 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 DKI^{8}, and
orientation dispersion index (ODI) from the NODDI model^{9}, were generated
as test metrics for each reconstruction method and evaluated against
the reference dual acquisition using the relative difference:

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

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.

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

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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)

Figure 1: Overview of reconstruction methods

Figure 2: Reconstructions of the DW-EPI with b=[0,3000] s/mm^{2} 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.