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

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.

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.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.