A Robust Reconstruction Method for High Resolution Multishot DWI: SPIRiT-based SYMPHONY
Zijing Dong1, Fuyixue Wang1, Xiaodong Ma1, Erpeng Dai1, Zhe Zhang1, and Hua Guo1

1Center for Biomedical Imaging Research, Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing, China, People's Republic of

### Synopsis

SYnergistic iMage reconstruction using PHase variatiOns and seNsitivitY (SYMPHONY) is a reconstruction method for multi-shot DWI which can provide high resolution diffusion weighted images. In this study, we proposed a SPIRiT-based SYMPHONY method in which a self-consistency constraint is applied instead of the conventional GRAPPA kernel to further improve the robustness of SYMPHONY. Simulation and in-vivo experiment validated the benefits of the proposed method which can improve the accuracy of reconstruction with less navigator data.

### Target Audience

Researchers and clinicians interested in high resolution diffusion weighted imaging (DWI).

### Purpose

Multi-shot EPI could provide high resolution diffusion weighted images with less artifacts and distortions. However, multi-shot DWI suffers from phase variations among different shots due to minuscule motions during diffusion encoding gradients. Recently, our group developed a k-space based reconstruction method for 2D navigated multi-shot DWI, SYnergistic iMage reconstruction using PHase variatiOns and seNsitivitY (SYMPHONY)1, which can obtain artifact-free multi-shot diffusion weighted images. In this study, we proposed a SPIRiT-based SYMPHONY method in which a self-consistency constraint is applied instead of the conventional GRAPPA kernel to further improve the robustness of SYMPHONY and the quality of diffusion weighted images.

### Methods

The basic idea of original SYMPHONY is to utilize shot-to-shot phase variations as encoding information like coil sensitivity encoding. This encoding information can be obtained from 2D navigator echoes. Then, the auto-calibration method GRAPPA2 is performed to reconstruct images. The interpolation process for the data of shot i and channel j in the original SYMPHONY is represented by

$$x_{i,j}^*=\sum_{j=1}^{Nc}\sum_{i=1}^{Ns}w_{i,j}(S_{i}x_{i,j})$$

where $x_{i,j}$ is the k-space data, $S_{i}$ is the operator to choose sampled points in kernel, $w_{i,j}$ is the interpolation weight of the kernel obtained by 2D navigators. $x_{i,j}^*$ represents the undersampled points in k-space which are synthesized by neighboring points from all shots and coils.

SPIRiT3 is a parallel imaging reconstruction method which is more robust than traditional GRAPPA by enforcing consistency constraints. Inspired by SPIRiT, a modified SYMPHONY reconstruction method is developed. Instead of using GRAPPA kernel interpolation, a SPIRiT-based kernel $g_{i,j}$ is applied:

$$x_{i,j}=\sum_{j=1}^{Nc}\sum_{i=1}^{Ns}g_{i,j}(x_{i,j})$$

Note that the SPIRiT-based kernel is applied to the whole k-space instead of only acquired points to satisfy the self-consistency constraint. The iteration procedure is shown in Fig. 1. Data from all coils and shots are aligned first. Then SPIRiT-based SYMPHONY reconstruction with the self-consistency constraint and data consistency projection are performed to shot-coil dimension to get final images.

A simulation was designed to compare the proposed method with the original SYMPHONY. Non-diffusion weighted 8-shot EPI images were acquired with a 32-channel coil. Third-order spatially random phases were added to 8 shots respectively, which imitated motion-induced phase variations in DWI. The matrix size of the data was 240×232. 32 channels were compressed to 4 channels while 98% of the information was preserved 4. SPIRiT-based SYMPHONY and the original SYMPHONY were performed with navigator size of 240×32 (32-echo) and 240×21 (21-echo) respectively.

In-vivo brain DWI data were acquired from a healthy volunteer on a Philips 3T scanner (Philips Healthcare, Best, The Netherlands), using a 2D-navigated interleaved EPI sequence. The multi-shot diffusion images were acquired with the following parameters: number of shot=8, FOV=240×240 mm2, slice thickness=4 mm, TR/TE=2500/77 ms, in-plane image resolution=1×1 mm2, the number of diffusion directions=12 with b value=800 s/mm2, Navigator size=240×19, Number of Signals Averaged (NSA)=2. Single shot EPI DWI images were acquired with in-plane resolution of 2×2 mm2 as references.

### Results

The simulation results are shown in Fig. 2. SPIRiT-based SYMPHONY is more effective to reconstruct images with less errors compared with the original SYMPHONY, especially when the navigator echo train length is 21, because the original SYMPHONY based on the GRAPPA kernel requires more calibration data than the SPIRiT-based kernel when the number of shot is large. Fig. 3 shows the comparison of the in-vivo images between the two methods. Blurring and contrast degradation appeared in the images reconstructed by the original SYMPHONY. The FA map (Fig. 4) of the proposed method is closer to the single shot reference but provides higher resolution than the single shot acquisition.

### Discussion and Conclusion

The SPIRiT-based SYMPHONY approach was described and validated in the simulation and the in-vivo experiment for high resolution multi-shot diffusion imaging. It is a more robust approach than the original method, because the self-consistency constraint was applied. The experiment proved that SPIRiT-based SYMPHONY could reconstruct relatively accurate diffusion images with less navigator echoes, which can increase the acquisition efficiency and reduce distortions of navigators.

### Acknowledgements

Grant sponsor: This work was supported by National Natural Science Foundation of China (61271132, 61571258) and Beijing Natural Science Foundation (7142091).

### References

1. Xiaodong M, Zhe Z, et al. High Resolution Spine Diffusion Imaging using 2D-navigated Interleaved EPI with Shot Encoded Parallel-imaging Technique (SEPARATE). In Proceedings of the 23th Annual Meeting of ISMRM, Montreal, Canada, 2015. p. 2799.

2. Griswold M A, Jakob P M, Heidemann R M, et al. Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magnetic resonance in medicine, 2002, 47(6): 1202-1210.

3. Lustig M, Pauly J M. SPIRiT: Iterative self-consistent parallel imaging reconstruction from arbitrary k-space. Magnetic Resonance in Medicine, 2010, 64(2): 457-471.

4. Zhang T, Pauly J M, Vasanawala S S, et al. Coil compression for accelerated imaging with Cartesian sampling. Magnetic Resonance in Medicine, 2013, 69(2): 571-582.

### Figures

FIG. 1. Illustration of the SPIRiT-based SYMPHONY reconstruction process. As an example, 3-shot-2-channel data were aligned to shot-coil dimension. In each iteration, SPIRiT-based kernel interpolation and data consistency projection are performed to exert the consistency constraint. At the end, full k-space data of all shots and channels are reconstructed.

FIG. 2. Reconstructed images and the corresponding error maps (×5) in the simulation are shown. The proposed method and the original SYMPHONY were compared when two different navigator echo sizes were used. The nRMSEs are listed at the bottom right of each reconstructed image. IG

FIG. 3. In-vivo reconstructed diffusion weighted images of 4 directions out of 12. The proposed method results in more clear and artifact-free image (white arrows).

FIG. 4. FA maps of single shot EPI acquisition, SYMPHONY and the proposed SPIRiT-based SYMPHONY. The zoomed FA maps of the selected region are listed in the lower right of each image. SPIRiT-based SYMPHONY provides a closer FA map to that of single shot than the original SYMPHONY.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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