Jessica A McKay^{1}, Steen Moeller^{2}, Lei Zhang^{3}, Edward J Auerbach^{2}, Michael T Nelson^{2}, and Patrick J Bolan^{2}

Three-line navigator correction of Nyquist ghosts in spin-echo
echo-planar imaging (SE-EPI) diffusion weighted imaging (DWI) often fails in
body imaging. Several alternative strategies have been proposed including *referenceless methods*, which do not require any type of reference information but
instead minimize a cost function based on the data itself. The purpose of this
work is to assess ghost correction of undersampled (R=3) breast DWI using
several referenceless methods, including minimization of SVD in k-space, image
entropy, a ghost/object ratio of the image, and a combination. All four referenceless
strategies outperform the standard navigator correction, providing higher
quality images and unbiased ADC maps.

**Introduction**

**Methods**

*Acquisition*

Single-shot 2D SE-EPI DWI was acquired under IRB-approved
protocols from 41 female subjects, including healthy volunteers and patients undergoing MRI for screening or treatment monitoring (Table 1). DWI was
performed on a Siemens Prisma^{fit} 3T system with a Sentinelle
16-channel breast coil, using a protocol derived from the ACRIN 6698 clinical
trial^{5}: TR=8 s, TE=51/74 ms (monopolar/bipolar diffusion, N=12/29),
GRAPPA acceleration R=3, acquisition time ≤ 5 min. Three-scan traces were
acquired (2-3 averages) with b-values between b=0-800 s/mm^{2}. Three-line
navigators were acquired with each acquisition.

*Reconstruction
and ghost correction*

First-order ghost correction requires estimation of a linear shift and phase correction to alternating lines of k-space of the form $$$S_{corrected}(k_x,k_{y,odd}) = S_{ghost}(k_x-\kappa,k_{y,odd}) * e^{-i \phi}$$$. Method A represents the standard correction, in which the phase difference between alternating echoes of the 3-line navigator is filtered, weighted, and fit to estimate κ and ϕ.

The referenceless methods minimize a cost function $$$f_{cost}(\kappa, \phi)$$$ using a simplex minimization in Matlab (fminsearch). In method
B (“Entropy”) the cost function is the image entropy^{2,3}; in method C (“SVD”)
f_{cost} is the summation over the tail of singular values after
rearranging k-space into GRAPPA-like kernels^{4}; in method D (“Ghost/Object”) f_{cost}
is the summation of the ratio between the image and its FOV/2-shifted replica^{6}. The final method (E, “Median”) combines the referenceless
methods as $$$\kappa_{median} = \text{median}(\kappa_B, \kappa_C, \kappa_D)$$$ and $$$\phi_{median} = \text{median}(\phi_B, \phi_C, \phi_D)$$$. For all referenceless methods, the GRAPPA autocalibration (ACS)
data were used to estimate initial correction parameters for the undersampled data. The solutions were dynamically refined by
minimizing f_{cost} on single-channel data after unaliasing with
ghost-corrected ACS lines. ADC maps were generated using a pixel-by-pixel log-linear
fit over the b-values.

*Analysis*

The severity of ghost artifacts was assessed by measuring
the signal intensity in the background of the images determined by
semi-automatic thresholding and dilation of T_{1}-weighted anatomical
images (3D GRE). The background to noise ratio (BNR) was defined as the mean background
signal compared to a case-specific noise measurement in the corner of the image.
To compare method performance, the per-volume BNR measurements were fit to a
linear mixed model including the effects of method, b-value, and subject BMI. All
five methods were compared in a pairwise manner, adjusting for multiple
comparisons using Tukey-Kramer’s method.

All referenceless methods yielded reduced ghosts compared to the standard approach. Whole volume BNRs are plotted in Figure 1a on a per-slice and b-value basis. Similarly, individual BNR values were compared between the referenceless methods and standard navigator in Figure 1b. The distributions of per-volume BNRs are shown for each b-value in Figure 2.

According to the linear mixed model, the method (p<0.0001), b-value (p<0.0001), and BMI (p=0.0256) significantly affect the BNR; however, the interaction between b-value and method is not significant. The pairwise comparisons between each method are reported in Table 2. All four referenceless methods yielded lower BNR values (p<0.0001) than method A. There was no statistically significant difference between the referenceless methods (B,C,D,E), although the median method (E) yielded the lowest ghost level at all b-values.

Figure
3 shows images of a single b=0 s/mm^{2} average and ADC maps from a
single slice of two cases that represent successful and failed corrections by the
linear navigator.

**Discussion**

NIH P41 EB015894

NIH R21 CA201834

- Heid, O. (2000). Method for the phase correction of nuclear magnetic resonance signals.
- Clare, S. (2003). Iterative Nyquist ghost correction for single and multi-shot EPI using an entropy measure. In Proceedings of the 16th Annual Meeting of ISMRM, Toronto, Canada, p. 1041.
- Skare, S., Clayton, D.B., Newbould, R., Moseley, M., and Bammer, R. (2006). A fast and robust minimum entropy based non-interactive Nyquist ghost correction algorithm. In Proc. Intl. Soc. Mag. Reson. Med, (Seattle, Washington), p. 2349.
- Peterson, E., Aksoy, M., Maclaren, J., and Bammer, R. (2015). Acquisition-free Nyquist ghost correction for parallel imaging accelerated EPI. In Proc. Intl. Soc. Mag. Reson. Med., (Toronto, Ontario), p. 0075.
- Partridge SC, Zhang Z, Newitt DC, Gibbs JE, Chenvert TL, Rosen MA, Bolan PJ, Marques HS, Esserman LJ, Hylton NM. ACRIN 6698 Trial: Quantitative Diffusion-Weighted MRI to Predict Pathologic Response in Neoadjuvant Chemotherapy of Breast Cancer. In Proceedings of ASCO, Chicago, 2017
- McKay JA, Moeller S, Ramanna S, Auerbach EJ, Metzger GJ, Ryder JR, Ugurbil K, Yacoub E, Bolan, PJ. (2017) Novel Image-based Nyquist Ghost Correction of Diffusion-Weighted Echo Planar Imaging with Ghost/Object Minimization. In Proceedings of the 26th Annual Meeting of ISMRM [Submitted]

Table
1.
Summary of subjects. A total of 41 female subjects were scanned including women undergoing MRI breast cancer screening, patients with biopsy-proven breast cancer, and healthy female volunteers.

Figure
1. Ghost measurements for every subject and every acquisition over whole
volumes. **a)** BNR **b)** pair-wise difference
in BNR between method A and referenceless methods (B, C, D, E). In (a) lower values indicate more complete ghost suppression; in (b), negative values indicate cases in which the given referenceless method outperformed the linear navigator. Referenceless methods generally produce reduced ghosts compared to the standard approach.

Figure 2. Boxplots of BNR values over full volumes for every method separated by b-value. Circles indicate median, numbers indicate outliers. All four referenceless methods outperform the standard navigator for every b-value. Although not statistically significant, the median combination (E) yields lower median BNR values than the other referenceless methods (B, C, D) for every b-value.

Table
2. P-values for pairwise comparisons between each method according to the
linear mixed model including effects of method, b-value, and BMI. Adjustment for multiple
comparisons were made by Turkey-Kramer’s method. The linear mixed model estimates that all referenceless methods (B, C, D, E) yielded lower BNR values than the standard navigator approach (A) with statical significance of p < 0.0001.

Figure
3. b = 0 s/mm^{2} images and ADC maps from two example
cases that represent navigator success (top) and failure (bottom). Cases were chosen objectively based on the bottom and top 25th
percentiles of difference between BNRs from a b = 0 s/mm^{2}
image corrected using linear navigator and referenceless methods. PE
is in the right-left direction.