We introduce acquisition and reconstruction strategies for robust, high-quality multi-shot EPI (msEPI) without phase navigators. We extend the MUSSELS low-rank constrained parallel imaging technique to perform Virtual Coil (VC) reconstruction, and demonstrate diffusion imaging with sub-millimeter in-plane resolution using 55% partial-Fourier (PF) sampling. We propose Blip Up-Down Acquisition (BUDA) using interleaved blip-up and -down phase encoding, and incorporate B0 forward-modeling into MUSSELS to enable distortion- and navigator-free msEPI. We improve the acquisition efficiency by developing Simultaneous MultiSlice (SMS-)MUSSELS, and combine it with machine learning (ML) to provide Rtotal=16-fold acceleration with 3-shots. Deploying this in a spin-and-gradient-echo (SAGE) scan with signal modeling allows for whole-brain T2 and T2* mapping with high geometric fidelity in 12.5 seconds.
msEPI allows high-resolution imaging with reduced distortion, but combining shots is prohibitively difficult because of shot-to-shot phase variations. Existing navigator-free approaches employ parallel imaging (PI) to reconstruct each shot, from which phase variations are estimated (1,2). This imposes a limit on the distortion reduction since PI breaks down beyond Rinplane>4 acceleration.
MUSSELS (3) is a low-rank constrained PI approach (4,5) which improves acceleration capability, but requires a large number of shots (Rinplane=8 with 4-shots). We propose SMS-MUSSELS acquisition/reconstruction to further accelerate msEPI, demonstrate its extension to VC concept (6) and obtain high-quality images from a PF=55% acquisition. We propose Blip Up-Down Acquisition (buda) where msEPI sampling is performed with interleaved blip-up and -down acquisitions, and combine these shots with B0 forward-modeling and MUSSELS to yield distortion-free images. Finally, we push the acceleration to Rtotal=16 (RinplanexSMS=8x2) and combine ML and SMS-MUSSELS to obtain 1x1x3mm3 whole-brain T2 and T2* maps from a 12.5sec acquisition.
Code/data: https://bit.ly/2qzhA1t
Acquisition: 0.85x0.85x3mm3 resolution diffusion data were acquired at b=1000s/mm2 using 32-channel reception at 3T with TE/TR=46/2000ms (7). 4-shots were collected at Rinplane=4 and PF=55%.
Reconstruction: In Fig1a, SENSE (8) was performed for each shot separately, followed by magnitude averaging over the 4-shots. MUSSELS in Fig1b was obtained via
$$min_x \sum_{t=1}^{N_s}\parallel F_t Cx_t-d_t\parallel_2^2+\lambda\parallel H\left(x\right)\parallel_*$$
where $$$F_t$$$ is the undersampled Fourier operator in shot $$$t$$$, $$$C$$$ are ESPIRiT sensitivities (9), and $$$d_t$$$ are the shot k-space data. $$$\parallel H\left(x\right)\parallel_*$$$ enforces low-rank prior on the block-Hankel representation of the multi-shot data $$$x$$$, which is formed by concatenating the images $$$x_t$$$ from $$$N_s$$$ shots. Proposed VC-MUSSELS (Fig1c) incorporates conjugate shot-images $$$x_t^*$$$ into the low-rank constraint, whereby conjugate-symmetric k-space helps estimate the missing data and improves the resolution (yellow boxes).
Blip Up-Down Acquisition (buda-) MUSSELS
Acquisition: 1x1x5mm3 spin-echo EPI at Rinplane=4 was acquired with TE/TR=75/3000ms, and two shots with blip-up and -down polarity were collected.
Reconstruction: Fig2a&b demonstrate separate SENSE for blip-up and -down acquisitions with significant distortion. Hybrid-space SENSE (10) jointly reconstructs the 2-shots by using their phase difference and B0 information from topup (9,10) (Fig2c). buda-MUSSELS obviates the need for phase estimation, and eliminates distortion by incorporating the fieldmap in PI to improve image quality and SNR (Fig2d, yellow boxes).
Network Estimated Artifacts for Tampered Reconstruction (NEATR) combines SMS-MUSSELS with ML
SMS-MUSSELS: is developed to combine MUSSELS with SMS using the readout-extended FOV concept (13). This represents SMS as undersampling in the kx-axis by concatenating the two slices along the readout (Fig3a). In-plane and slice acceleration could thus be captured using $$$F_t$$$ with kx-ky undersampling and push the acceleration to RinplanexSMS=8x2 for spin-and-gradient echo (SAGE (14)) msEPI.
Due to high acceleration, SMS-MUSSELS failed to provide clean images using 3-shots (Rnet=16/3, Fig3a&4a). A network with U-Net architecture (15) was utilized to mitigate the SMS-MUSSELS artifacts. To provide “fully-sampled” data to train the network, four volunteers were scanned with 8-shots at prospective Rinplane=8 (FOV=224x224x120mm3, 1x1x3mm3 resolution, TEs=26/61/61/130/165ms, TR=8.3sec). MUSSELS reconstruction of this Rnet=1 data yielded references images.
Residual U-Net (Fig3b): learned a mapping between the 3-shot SMS-MUSSELS and the error relative to the reference images. Three volunteers’ data were used for training and the fourth subject was reserved for testing. U-Net with 5 levels, $$$\ell_2$$$-loss, leaky-ReLU activation (16) and 64 filters at the highest level was trained on 64x64 patches. Real and imaginary parts of 3-shots were presented as channels for complex-valued processing.
Joint Virtual Coil (JVC-)SENSE: The refined U-Net magnitude $$$m_{unet}$$$ allows us to solve for the phase of $$$t^{th}$$$ shot $$$\phi_t$$$ with wavelet ($$$\Psi$$$) regularization (17) (Fig3c): $$min_{\phi_t} \sum_{t=1}^{N_s}\parallel F_t Cm_{unet}e^{i\phi_t}-d_t\parallel_2^2+\alpha\parallel \Psi \phi_t\parallel_1$$Shot-phases from the complex U-Net reconstruction were used to initialize this non-convex problem. We finally solve for the magnitude using data from all shots by including the estimated phase variations in the sensitivities via $$$C e^{i\phi_t}$$$ and create virtual coils $$$C^* e^{-i\phi_t}$$$ (Fig3d).
Results: Fig4 shows 2 echoes (out of 5) from a slice group where SMS-MUSSELS yielded 13.4% Rmse with ghosting/aliasing artifacts (arrows). U-Net mitigated these (8.7% error), allowing JVC-SENSE to provide clean images (7.6% Rmse). Using the SAGE signal equation yielded T2 and T2* maps with whole-brain coverage in 12.5 sec (Fig5).
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