Xiaoxi Liu^{1}, Di Cui^{1}, Edward S. Hui^{1,2}, Queenie Chan^{3}, and Hing-Chiu Chang^{1}

Multi-shot diffusion-weighted echo-planar imaging (DW-EPI) with multiplexed sensitivity encoding (MUSE) is a self-navigated technique that can achieve high resolution diffusion-tensor imaging (DTI) without the need of navigator echo. However, even with multi-shot acquisition, the effective echo spacing is still relatively long for acquisition of high resolution DTI, leading to significant geometric distortion. In this study, we aim to reduce the geometric distortion of multi-shot DW-EPI by 1) integrating the reversed gradient acquisition in multi-shot DW-EPI, and 2) developing a joint reconstruction method that can reconstruct non-uniform k-space data by taking the off-resonance effect into account.

**Purpose**

**Methods**

**Pulse sequence
design**:
The multi-shot DW-EPI sequence was modified to enable RG acquisition as shown
in the Figure 1a. All odd segments were acquired with forward phase-encoding (PE)
direction, and even segments with reversed PE direction. Figure 1b shows the
design of non-uniform k-space sampling for 4-shot DW-EPI with RG acquisition
for simulation study.

**Data reconstruction**: Figure
2 shows the flowchart of data reconstruction. First, the k-space data with reversed
PE was realigned (Figure 1a). Second, all segment data were respectively
reconstructed by using SENSE to estimate the inter-shot phase variations [4]. Third,
odd and even segment data were respectively reconstruction with MUSE framework
for producing two images with opposite PE direction. Fourth, the displacement
map (DM) was derived from two images with opposite PE direction using RG method
[6]. Fifth, the SPACE-RIP algorithm [7] was modified to jointly reconstruct all
segment data by taking into account phase variations and off-resonance effect
estimated from DM.

**In-vivo
experiments**: Human brain data were acquired at 3.0T MRI scanner (Philips,
Achieva) using a modified 4-shot DW-EPI sequence with RG acquisition (matrix size = 256x256 (TE/TR = 91/5000ms) and matrix size = 384x384 (TE/TR = 92/5000ms), partial Fourier factor = 60%, FOV = 240x240mm,
b-value = 800/mm^{2}, DTI directions = 6). A turbo-spin echo data set was
acquired for reference (TE/TR = 80/3000ms matrix size = 512x512). For comparison,
two conventional 4-shot DW-EPI data sets with opposite PE direction were
acquired to produce images with three pipelines: 1) the data with either
forward or reversed PE direction was respectively reconstructed using MUSE, 2) the
RG method was applied to MUSE reconstructed images with opposite PE directions
for distortion correction, and 3) the data with either forward or reversed PE
direction was respectively reconstructed using MUSE with acceleration factor of
2 (i.e., two out of four segments), and then applied RG correction.

**Simulation
study**:
A 384x384 data with non-uniform k-space sampling was simulated following the
design shown in figure 1b. The off-resonance effects associated with
non-uniform k-space sampling was considered to produce the distorted images
with either forward or reversed PE direction. Data reconstruction followed the
same pipeline for in-vivo data, expect that only low frequency part were used
for phase measurement and DM calculation.

**Discussion**

[1] Chen, NK; Wyrwicz, AM. Optimized distortion correction technique for echo planar imaging. Magn Reson Med 2001; 45:525–528.

[2] Chang HC and Chen NK, "Joint correction of Nyquist artifact and minuscule motion-induced aliasing artifact in interleaved diffusion weighted EPI data using a composite two-dimensional phase correction procedure", Magnetic Resonance Imaging, 2016;34(7):974-9.

[3] Morgan, Paul S.; Bowtell, Richard W.; Mcintyre, Dominick J. O.; Worthington, Brian S. Correction of Spatial Distortion in EPI Due to Inhomogeneous Static Magnetic Fields Using the Reversed Gradient Method. Journal of Magnetic Resonance Imaging, April 2004, Vol.19(4), pp.499-507.

[4] Pruessmann, Klaas P.; Weiger, Markus; Scheidegger, Markus B.; Boesiger, Peter. SENSE: Sensitivity encoding for fast MRI. Magnetic Resonance in Medicine, November 1999, Vol.42(5), pp.952-962.

[5] Jenkinson, Mark; Beckmann, Christian F.; Behrens, Timothy E.J.; Woolrich, Mark W.; Smith, Stephen M. FSL. NeuroImage, 15 August 2012, Vol.62(2), pp.782-790.

[6] Chang, H.C.; Chuang, T.C.; Lin, Y.R.; Wang, F.N. et al. Correction of geometric distortion in Propeller echo planar imaging using a modified reversed gradient approach Quant Imag Med Surg, 3(2) (2013), p.73.

[7] Kyriakos, Walid E.; Panych, Lawrence P.; Kacher, Daniel F.; Westin, CarlāFredrick; Bao, Sumi M.; Mulkern, Robert V.; Jolesz, Ferenc A. Sensitivity profiles from an array of coils for encoding and reconstruction in parallel (SPACE RIP). Magnetic Resonance in Medicine, August 2000, Vol.44(2), pp.301-308.

[8] Chen, Nan-Kuei; Guidon, Arnaud; Chang, Hing-Chiu; Song, Allen W. A robust multi-shot scan strategy for high-resolution diffusion weighted MRI enabled by multiplexed sensitivity-encoding (MUSE). NeuroImage, 15 May 2013, Vol.72, pp.41-47.

Fig.1: a) The
multi-shot DW-EPI sequence was modified to enable RG acquisition. All odd segments were acquired with forward phase-encoding (PE) direction,
and even segments with reversed PE direction. b) shows the design of
non-uniform k-space sampling for 4-shot DW-EPI with RG acquisition for
simulation study. The oversampling is 64 lines and the ETL of high frequency region is 1.5 times higher than the k-space center region.

The
reconstruction flowchart of data reconstruction process.

Fig.3: With the resolution of 256x256, T2W images, DW images, and corresponding cFA maps for different acquisition
and reconstruction methods. (a) The 4-shot DW-EPI data with forward PE
direction reconstructed using MUSE. (b) Two 4-shot DW-EPI data sets with
opposite PE direction respectively reconstructed using MUSE and subsequent
applied RG correction. (c) Two 4-shot DW-EPI data sets with opposite PE
direction respectively reconstructed using MUSE with acceleration factor of 2, and
subsequent applied RG correction. (d) The 4-shot DW-EPI data with RG acquisition
reconstructed by proposed method. (e) Gold-standard TSE-T2W image.

Fig.4: With the resolution of 384x384, T2W images, DW images, and corresponding cFA maps for different acquisition and reconstruction methods. (a) The 4-shot DW-EPI data with forward PE direction reconstructed using MUSE. (b) Two 4-shot DW-EPI data sets with opposite PE direction respectively reconstructed using MUSE and subsequent applied RG correction. (c) Two 4-shot DW-EPI data sets with opposite PE direction respectively reconstructed using MUSE with acceleration factor of 2, and subsequent applied RG correction. (d) The 4-shot DW-EPI data with RG acquisition reconstructed by proposed method. (e) Gold-standard TSE-T2W image.

Fig.5: The simulated T2WI and DWI images of non-uniform k-space sampling data with (a) forward PE direction, and (b) reversed PE direction. The arrows show the artifacts associated with discontinuous off-resonance effects due to non-uniform k-space sampling. (c) The reconstruction result with proposed method. (d) The original data for simulation.