Introduction

Diffusion Weighted Imaging (DWI) is important for many neuroscientific and clinical applications¹. Multi-b-value DWI offers an improved accuracy for Apparent Diffusion Coefficients (ADC) and Diffusion Tensor Imaging (DTI)², and provides data for IntraVoxel Incoherent Motion (IVIM) mapping³. Typically, DWI is acquired by single-shot EPI, which only samples a limited number of k-space lines causing limited resolution. Recent works have shown that multi-shot EPI based on Locally Low-Rank (LLR) reconstruction is able to achieve high-resolution DWI at a single b-value, provided that the algorithm is initialized by parallel imaging⁴. However, in multi-b-value imaging, repeated multi-shot EPI over multiple b-values would cause a linearly increasing scan time. Here we propose the use of multi-shot keyhole-EPI (EPIK) with continuously-changing b values and adoption of a different LLR algorithm to achieve robust reconstruction for highly undersampled multi-b-value DWI.

Methods

EPI-keyhole was initially developed by Zaitsev et al. to achieve EPI imaging with a high temporal resolution.⁵ In their work, they showed that EPIK resulted in a distortion less than single-shot EPI provided that a reasonable shimming was performed. In this work, EPIK was combined with interleaved k-space sampling to achieve multi-shot DWI. Furthermore, the b-values are increased at each shot of the EPIK acquisition, facilitating an accelerated multi-shot multi-b-value imaging (Figure 1). The main reason for using EPIK instead of EPI is to bypass the need for a careful initialization of the LLR reconstruction⁴. This is critical for intra-shot undersampling rates higher than 4, since parallel imaging at higher undersampling rates induces severe noise.

Reconstruction of the proposed method involves minimization of the following cost function:
$$\min_x\sum_{b=1}^{Nb}{\frac{1}{2}\lVert E_bFSx_b-y_b \rVert}_{2}^{2}+\lambda \lVert x \rVert _{LLR}\ \left( 1 \right) $$
Where $$$Nb$$$ is the number of b-values,$$$E_b$$$ the sampling operator,$$$F$$$ the DFT matrix,$$$S$$$ the sensitivity maps, $$$x=\left[ \begin{matrix} x_1& \cdots& x_{Nb}\\\end{matrix} \right] ^T$$$ the multi-b-value DWI images,$$$y=\left[ \begin{matrix} y_1& \cdots& y_{Nb}\\\end{matrix} \right] ^T$$$the acquired multi-b-value k‐space signal, $$$\lVert \cdot \rVert _{LLR}$$$ the LLR constraint, which is defined in [9].

To solve Eq 1, we developed an algorithm based on the Alternating Direction Method of Multipliers (ADMM), which is similar to that proposed by Lima da Cruz et al.⁶ for MR fingerprinting. The LLR-ADMM algorithm supports a densely-overlapped LLR enforcement, which was found by us to generate better reconstruction quality than non-overlapped LLR used by POCS⁷, SPA-LLR⁴ and several other groups ^{8, 9}. In this work, we compared our LLR-ADMM algorithm with LLR-POCS and SPA-LLR for reconstruction accuracy.

Imaging was performed in two healthy subjects (age 23±2, 1 male) in a 3T scanner (United Imaging uMR790) with a 32-channel head coil after obtaining written informed consent. A spin-echo single-shot DW EPI sequence was performed with full sampling to acquire 21 b-values ranging from 0 to 1000s/mm² in an increment of 50 s/mm². Three DW encoding directions were used. Other parameters were FOV/image size/TR/TE/bandwidth/NEX/flip-angle =240×240mm²/128×128/3000ms/132.3ms/1790Hz/1/90°. Afterwards, a 2-shot with R=1, 2-shot with R=2, and 4-shot with R=2 multi-b-value EPIK sequence with the same resolution and b-values was performed. The intra-shot undersampling rate for these sequences was 2, 4, and 8, respectively, entailing sampling of 76, 50 and 37 k-space lines in each shot, and a corresponding TE of 70.4ms, 69.2ms and 60.1ms, respectively. To validate the method for high-resolution DWI, the 2-shot EPIK with intra-shot R=2 was performed again with 1mm isotropic resolution and TE=100.4ms.

Results

Figure 2 shows the reconstructed DWI image (b-value = 1000s/mm²) for retrospectively undersampled EPIK with different intra-shot undersampling rates. For 2-shot, all three methods achieved similar quality compared with the gold standard. For 4-shot, however, SPA-LLR generated strong artifacts potentially due to a suboptimal SENSE initialization with intra-shot 8-fold undersampling. LLR-ADMM showed reduced noise amplification, improved NRMSE, and reduced aliasing artifacts (green arrows) compared with LLR-POCS.

Figure 3 shows reconstruction of the ADC and M₀ maps and associated fractional difference maps for the 3 reconstruction methods given retrospective 4-shot acquisition (R=2). The difference between the 3 methods was more apparent in these maps. LLR-ADMM showed the best suppression of image artifacts compared with LLR-POCS and SPA-LLR.

Figure 4 shows reconstruction of the ADC maps in the second healthy subject with prospective undersampling. SPA-LLR showed considerable artifacts with 8-fold intra-shot undersampling. LLR-POCS showed better quality than SPA-LLR, yet there were still some residual aliasing artifacts (green arrows). LLR-ADMM showed the best reconstruction quality. All methods led to increasing loss of fine details with higher undersampling rates.

Figure 5 shows the 1mm isotropic-resolution multi-shot multi-b-value DWI images and the resultant ADC maps reconstructed by the three methods. The intra-shot undersampling rate was 4. LLR-ADMM led to reduced aliasing artifacts compared with LLR-POCS and SPA-LLR.

Discussion and conclusions

We demonstrate a novel acceleration method based on multi-shot EPIK and LLR-ADMM to accelerate multi-b-value DWI. The proposed method showed a reasonable accuracy at intra-shot undersampling rates of 2,4, and 8. By sampling the central k-space in every shot and b-value, the algorithm does not need a “warm-start” based on parallel imaging, which was needed by SPA-LLR and error-prone at higher undersampling rate. Although more experiments are needed to fully validate the method, the preliminary results showed that the method is promising to achieve high-resolution multi-b-value imaging with an efficient acquisition.

Acknowledgements

No acknowledgement found.

References

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