Eric Kenneth Gibbons^{1}, Patrick LeRoux^{2}, Shreyas Vasanawala^{3}, John Mark Pauly^{4}, and Adam Bruce Kerr^{4}

This abstract presents a novel reconstruction for the nCPMG SS-FSE sequence. A theoretical justification for this approach is given. This reconstruction and sequence is demonstrated in phantom and *in vivo* and is shown to be quantitatively and qualitatively robust.

SS-FSE is a fast and robust method to acquire images in a single shot in regions of $$$B_0$$$ inhomogeneity without image distortion. SS-FSE sequences rely on a rigid phase modulation throughout the echo train known as CPMG. Because of these phase requirements, many contrast preparations (e.g., diffusion weighting) are typically unsuited for use in SS-FSE. Various methods have been proposed to work around the loss of the CPMG condition [1][2][3][4] though each comes with drawbacks in terms of SNR, motion from a multi-shot acquisitions, or a complicated reconstruction scheme. The nCPMG phase modulation approach[4] leads to a (1, -1, 1, -1…) amplitude modulation on the quadrature component of the signal and thus aliasing. This can be represented as [5]

$$Q_n = (A+b)X + (-1)^n (A-b)Y,$$

where $$$Q_n$$$ is the image signal at each n echo, $$$X$$$ is the in phase component of the image, and $$$Y$$$ is the out of phase component of the image. The coefficients $$$A$$$ and $$$b$$$ are complex valued and are slowly varying in the spatial domain if nutation angle is controlled[5]. We propose modifying the nCPMG SS-FSE sequence to include an accelerated self-calibrated reconstruction for body DWI applications.

The proposed reconstruction doubles the field of view by oversampling in k-space by a factor of 2 in a nCPMG sequence (Fig. 1). This necessarily doubles the number of phase encodes. From there the object can be reconstructed by taking the top quarter and bottom quarter of the image to generate the $$$Y$$$ component of the image. The center of the image can extracted to find $$$X$$$. Thus, the final image is found by combining

$$Q = X + jY$$

after
appropriate corrections to account for the $$$(A+b)$$$ and $$$(A-b)$$$ phase terms. Fig.
2 shows this procedure. Double phase encoding does lead to increased
SAR, TE, as well as phase encode direction blur. These effects can
be ameliorated by using a partial k-space reconstruction (which also
corrects for the phase errors introduced by the coefficients $$$A$$$ and $$$b$$$)
as well as parallel imaging. Here, partial k-space is used combined
with uniform sampling with $$$R=3$$$ in the periphery (Fig. 3).
Reconstruction is performed via the ESPIRiT algorithm. Agar ball
phantom and in
vivo
images were acquired using a 32-channel head and body coils,
respectively, on a GE 3T scanner. FOV varied from 20cm to 40cm,
matrix size 192x128, TR=600ms, TE=65ms, and b=700s/mm^{2}. *In vivo *images are pediatric abdominal cases. All in
*vivo
images* were scanned in the coronal plane to best match the coil
sensitivity patterns.

[1] Alsop, David C. "Phase insensitive preparation of single-shot RARE: Application to diffusion imaging in humans." *Magnetic Resonance in Medicine* 38.4 (1997): 527-533.

[2] Pipe, James G., Victoria G. Farthing, and Kirsten P. Forbes. "Multishot diffusion-weighted FSE using PROPELLER MRI."* Magnetic Resonance in Medicine *47.1 (2002): 42-52.

[3] Deng, Jie, Reed A. Omary, and Andrew C. Larson. "Multishot diffusion-weighted SPLICE PROPELLER MRI of the abdomen." *Magnetic Resonance in Medicine* 59.5 (2008): 947-953.

[4] Le Roux, Patrick. "Non-CPMG fast spin echo with full signal." *Journal of Magnetic Resonance* 155.2 (2002): 278-292.

[5] Gibbons, Eric, et al. "Body diffusion weighted imaging using non-CPMG fast spin echo." *IEEE Transactions on Medical Imaging *(2016).

Figure 1: nCPMG
SS-FSE sequence with diffusion weighting.

Figure 2: The proposed double FOV reconstruction method. This method allows
overcoming spatially varying phase terms as well as the (1, -1, 1,
-1) half FOV shift aliasing.

Figure 3: Double phase encoding can lead to increase SAR accumulation (and
consequently longer TRs), image blur, and SNR loss. This can be
ameliorated to a certain extent by using partial k-space and parallel
imaging reconstructions. Note: the red and blue lines indicate the
sign on the quadrature component of the image.

Figure 4: Agar ball phantom images with
diffusion weighting of b=700mm^{2}/s.
ADC maps for both SS-FSE and EPI for comparison. It is found that
the mean ADC values for SS-FSE and EPI match at roughly 0.00183
s/mm^{2}.

Figure 5: Abdominal
DWI in
vivo
images with b=700
mm^{2}/s. The arrow in the furthest right case highlights a lesion,
demonstrating the expected diffusion weighting contrast between the
mesenteric nodal metastasis
and normal tissue.