Introduction

Simultaneous multi-slab imaging (SMSlab) ^1-3 combines simultaneous multislice (SMS) ^4-10 and 3D multi-slab ^11-13 sampling. It can achieve high-resolution whole-brain DWI with high SNR efficiency ^1-3,14,15, but image distortions caused by B0 inhomogeneities remain a problem ¹⁶. Typically, two acquisitions with reversed phase-encoding (PE) directions are used to estimate the off-resonance maps and correct for distortions ¹⁷. Rather than correcting the images after reconstruction, joint reconstruction utilizing the blip-up/down data can correct for distortions and reduce g-factors intrinsically ^18,19. This study aims to propose such a framework to conduct joint reconstruction for SMSlab DWI.

Materials & Methods

Joint Reconstruction with Intrinsic Distortion Correction
The generation of a distorted under-sampled 3D image can be formulated as ^18,19
$$F_{u} W S \Phi x=A x=d, (1)$$
where F_u represents the 2D FFT operator with undersampling along ky and kz directions. W describes off-resonance-induced phase accrual causing image distortions. S represents coil sensitivities. Φ is the background phase difference between the blip-up/down acquisitions ¹⁹. x is the full-sampled distortion-corrected image. d is the acquired signals transformed to the x-ky-kz hybrid space ²⁰. For diffusion imaging, motion-induced inter-shot phase variations Θ should be included:
$$F_{u} W S \Phi \Theta x=d. (2)$$
The reconstruction framework is shown in Fig. 1. In step 1, motion-induced phase variations Θ are extracted from the reconstructed multi-band navigators. Then Θ is used to reconstruct the blip-up/down data separately via 3D SENSE ²¹. In step 2, the reconstructed b=0 s/mm² images are used to estimate the off-resonance maps using topup ¹⁷ from the FSL ²², which generate W. In step 3, background phase differences Φ between the blip-up/down acquisitions are extracted from the results of step 1. Both Φ and Θ are combined with S for the joint reconstruction ^19,23, which is done by computing the least-squares solutions of Eq. 1 or 2.

Blip-up/down Acquisitions for SMSlab
All images were acquired on a 3T scanner (Philips, Ingenia CX) using a 32-channel coil. The SMSlab acquisitions mainly followed ^1,2, except that the PE gradient polarity was alternated for the blip-up/down acquisitions. The resolution was 1.5 mm isotropic. The detailed parameters are listed in Table 1. Two-dimensional navigators (multi-band factor [MB] = 2) were acquired and unfolded to separate bands via SENSE ²¹. Sensitivity maps were estimated from a low-resolution GRE sequence using ESPIRiT ²⁴.
Three sampling patterns were compared (Fig. 2). Protocol A used a 4-shot acquisition with 2 shots undersampled (N_shot=2). Namely, for each shot, the undersampling factor R_shot=4. Then reversed PE directions were used in each kz plane without CAIPI sampling ²⁵. Protocol B was a single-shot acquisition (N_shot=1) with R_shot=2 CAIPI sampling, and the PE gradient polarity was alternated for odd/even kz encodings. Protocol C repeated A but with CAIPI sampling. The g-factors of the joint reconstruction were calculated as follows ^19,20.
$$g=\sqrt{X_{\text {cov}}^{\text {joint}} / X_{\text {cov}}^{\text {full}} / R_{\text {net}}}, (3)$$
where $$$X_{\text {cov}}^{\text {joint}} $$$ is the noise covariance matrix of the joint reconstruction matrix A. $$$X_{\text {cov}}^{\text {full}}$$$ is the noise covariance matrix for a full-sampled SENSE reconstruction without off-resonance effects. R_net is the final effective undersampling factor, which is 2 for all three protocols after combining blip-up/down data.

Results & Discussion

The levels of distortions and the 1/g maps of three sampling patterns are shown in Fig. 2. Protocol A shows higher g-factors compared with protocol B and C because CAIPI is not used. For protocol B, only N_shot=1 is used and the acquisition time is halved, but the reduced R_shot (=2) leads to stronger distortions (arrowheads), which introduces higher g-factors compared with protocol C. Protocol C uses R_shot=4, which reduces the distortion and thus reduces the g-factors. The 1/g map of protocol C but without off-resonance effects is shown in the lower right, which reflects the upper bound of 1/g because the phase accrual from off-resonance effects can affect the g-factors ¹⁸.
The b=0 mm/s² images of protocol B (R_shot=2) and C (R_shot=4) are shown in Fig. 3. Compared with protocol C, stronger distortions are found in protocol B, where more severe signal loss/pile-up exists (arrowheads). The correction performance at such regions is less satisfactory in protocol B compared with C. Therefore, for the proposed joint reconstruction method, multiple shots in each kz plane should be used to improve the R_shot and thus improve the performance of distortion correction.
Fig. 4 shows the b=0 mm/s² and b=800 mm/s² images from protocol C. The 1/g maps of step 1 and joint reconstruction are also shown. Compared with step 1, joint reconstruction utilizes the acquired data more completely and distinctly reduces the g-factors. Residual aliasing exists (arrowhead) due to imperfect correction for inter-shot phase variations. Advanced MUSE-like reconstruction ^14,26,27 can be implemented to solve this problem in the future.

Conclusion

In this study, we proposed a framework to jointly reconstruct blip-up/down SMSlab imaging with intrinsic distortion correction, which reduces the g-factors. We also used a large R_shot to improve the performance of distortion correction. Combined with the CAIPI sampling, it can further reduce the g-factors. In the future, receiving coil with more channels can be applied to increase the net acceleration factor.

Acknowledgements

No acknowledgement found.

References

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