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Hybrid-space reconstruction with add-on distortion correction for simultaneous multi-slab DWI1Center for Biomedical Imaging Research, Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing, China, 2Philips Healthcare, Beijing, China
Synopsis
Keywords: Image Reconstruction, Diffusion Tensor Imaging
3D simultaneous multi-slab imaging (SMSlab) can achieve high-resolution DWI with high SNR efficiency. Recently, we integrated SMSlab DWI with blipped-CAIPI gradients (blipped-SMSlab) and proposed a hybrid-space reconstruction algorithm, REACH. In this study, REACH is extended for distortion correction, which is called DC-REACH. It can correct the image distortions and the phase interferences introduced by the blipped-CAIPI gradients simultaneously. It also distinctly reduces the g-factor penalty via the joint reconstruction of the blip-up/down data.
Introduction
3D simultaneous multi-slab (SMSlab) 1-4 excites multiple 3D slabs simultaneously. It can achieve high-resolution whole-brain DWI with high SNR efficiency 5. Recently, we integrated SMSlab imaging with blipped-CAIPI 6, which is named blipped-SMSlab, to reduce the g-factor penalty. However, EPI-related image distortions induced by B0 field inhomogeneities and eddy currents remain a problem. Typically, the topup method is used to estimate the off-resonance maps and correct for distortions 7-10. It has been reported that a joint reconstruction of the blip-up/down data can correct the distortions and reduce the g-factors simultaneously 11,12. This study aims to propose such a joint reconstruction algorithm with distortion correction (DC) for blipped-SMSlab.Theory and Methods
Blipped-SMSlab and the combination with blip-up/down acquisitionThe blipped-SMSlab sequence with blip-up/down acquisition is shown in Figure 1. Multiple 3D slabs are simultaneously excited for acceleration. A table of kz gradients is used to encode the intra-slab slices. Blipped-CAIPI gradients are added between different EPI sub-echoes along the slice direction for multi-band encoding. Then a 4D k-space framework (kx-ky-kz-km) is formulated to model the signal encoding, with km representing multi-band encoding. For each image, two in-plane shots with blip-up/down acquisition are acquired for each kz. To reduce the inter-shot motion between the blip-up/down pairs, they are acquired inside the kz loop.
Because the km gradients and the kz gradients share the same physical gradient direction, the blipped-CAIPI gradients introduce kz deviations from the nominal k-space location 13, which are referred to as the ramp phase,
$$\varphi_{\text {ramp }}=2 \pi \cdot \Delta z / F O V_m \cdot n_{k m} \cdot n_z . (1)$$
Δz is slice thickness. FOVm=Rmb∙zgap is the defined FOV in the multi-band dimension. Rmb is the MB factor, and zgap is the gap between the centers of the simultaneously excited slabs. nkm is the index of km encoding in k-space, and nz is the intra-slab slice index in the image domain.
Reconstruction in a hybrid space with distortion correction
For b=0 s/mm2 images, φramp can be directly removed after 1D iFFT along kz. However, for diffusion-weighted images, it should be corrected during the reconstruction. An algorithm called REconstruction with phAse Correction in a Hybrid space (REACH) was proposed to solve this problem, which is reported in the other abstract. In this study, REACH is extended to jointly reconstruct the blip-up/down data of blipped-SMSlab, which is called DC-REACH.
In this study, the 4D representation of a distorted blipped-SMSlab diffusion-weighted image is formulated as
$$\mathrm{F}_{\mathrm{u}} \Psi \Theta \mathrm{SPI}=\mathrm{d} . (2) $$
The k-space signals are transformed into the hybrid space (x-ky-kz-km) and represented by d, which enables a separate reconstruction for each x index 14. Fu is an undersampled 3D FFT operator on y, z, and m dimensions. The ramp phase is represented by Ψ(nkm,nz)=φramp. The phase accrual (causing image distortions) along the ky dimension is formulated as Θ(∆f,nky)=exp(i∙∆f∙(ESP∙nky)), where Δf represents the off-resonance and/or eddy-current-induced field map. S represents coil sensitivities. P represents motion-induced inter-kz phase variations. I is the full-sampled image.
The flowchart of DC-REACH is shown in Figure 2. In step 0, the blip-up and blip-down data are separately reconstructed using REACH without distortion correction. Then, in step 1, the image amplitudes of the blip-up/down pairs are used to estimate the field maps Δf using topup 7 from the FSL 15. In step 2, to jointly reconstruct the blip-up and blip-down data, the background phase difference D caused by the reverse PE polarities should be corrected 12. The motion-induced phase P is extracted from the recovered SMS navigators. Both D and P are distortion corrected16 and smoothed to reduce the impact of geometric mismatch. In step 3, DC-REACH is done by minimizing the following cost function.
$$\mathrm{I}_{\mathrm{DC}}=\operatorname{argmin}\left\|\mathrm{d}-\mathrm{F}_{\mathrm{u}} \Psi \Theta \mathrm{SDPI}\right\|_2^2. (3)$$
Results & Discussion
The effect of correction for background phase difference between blip-up and blip-down data is shown in Figure 3. Without the correction, inter-slab aliasing artifacts arise in both the b=0 s/mm2 image and the b=1000 s/mm2 image of DC-REACH (yellow arrows).Figure 4 shows the reconstructed blipped-SMSlab images with 1.5-mm isotropic resolution. Results from both REACH and DC-REACH are shown. In DC-REACH, the distortions are corrected, and the geometry is close to the T2W image. The mean values of 1/g-factor of REACH and DC-REACH are 0.42 and 0.59, respectively. Compared with the separate REACH reconstruction, DC-REACH utilizes the acquired data more effectively and distinctly increases the 1/g-factor, which means that a higher SNR is maintained.
A DTI dataset acquired with the blipped-SMSlab and blip-up/down acquisition is shown in Figure 5. 1.3-mm isotropic resolution, 2 b=0 images and 32 diffusion directions with b=1000 s/mm2 were used. With TR=1.8 s and 10 kz steps for each slab, it took 36 s to acquire one direction, and 20.4 mins for a distortion-corrected whole-brain dataset.
Conclusion
This study integrated a hybrid-space reconstruction algorithm, REACH, with distortion correction (DC-REACH), for blipped-SMSlab DWI computation. It can correct image distortions and the phase interferences introduced by the blipped-CAIPI gradients simultaneously. It also reduces the g-factor penalty via the joint reconstruction of blip-up/down data.Acknowledgements
No acknowledgement found.References
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Figures
Figure 1. SMSlab EPI with blipped-CAIPI (blipped-SMSlab) combined with the blip-up/down acquisition. (A) and (B) show the sequence diagram and the trajectory in 4D k-space, respectively. Some gradients are omitted in (A) for simplification, including the slice-selection gradients, the Gx gradients, and so on.
Figure 2. The flowchart of hybrid-space reconstruction with distortion correction (DC-REACH) for blip-up/down acquisitions.
Figure 3. Comparison between results of joint reconstruction of the blip-up and blip-down data with (DC-REACH) and without background phase correction. The results without background phase correction were generated by removing D from the cost function of DC-REACH. Blipped-SMSlab images with the blip-up/down acquisition and 1.5-mm isotropic resolution are shown.
Figure 4. The images were acquired using blip-up/down blipped-SMSlab with TR=1.9 s, Ry × MB=2×2, and 1.5-mm isotropic resolution. T2W TSE images were acquired as the distortion-free reference. The g-factors of b=0 images were calculated via a Monte-Carlo-based method with 128 repetitions 17. For the REACH reconstruction, only the 1/g-factor maps of blip-up images are shown.
Figure 5. The reconstructed images via DC-REACH for the DTI dataset from blipped-SMSlab with blip-up/down acquisition. Ry × MB=2×3, 1.3-mm isotropic resolution, b=1000 s/mm2, and 32 directions were used. Slab boundary artifacts were corrected using a deep-learning-based algorithm 18. The first column shows the distorted b=1000 s/mm2 images reconstructed by REACH. The other columns show the b=1000 s/mm2 images and the colored fractional-anisotropy (FA) maps of DC-REACH.