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Robust high-quality multi-shot EPI with low-rank prior and machine learning

Berkin Bilgic¹, Congyu Liao¹, Mary Kate Manhard¹, Qiyuan Tian¹, Itthi Chatnuntawech², Siddharth Srinivasan Iyer¹, Stephen F Cauley¹, Thorsten Feiweier³, Shivraman Giri⁴, Yuxin Hu⁵, Susie Y Huang¹, Jonathan R Polimeni¹, Lawrence L Wald¹, and Kawin Setsompop¹

¹Martinos Center for Biomedical Imaging, Charlestown, MA, United States, ²National Nanotechnology Center, Pathum Thani, Thailand, ³Siemens Healthcare, Erlangen, Germany, ⁴Siemens Healthcare, Charlestown, MA, United States, ⁵Department of Electrical Engineering, Stanford University, Stanford, CA, United States

Synopsis

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 R_total=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.

Introduction

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 R_inplane>4 acceleration.

MUSSELS (3) is a low-rank constrained PI approach (4,5) which improves acceleration capability, but requires a large number of shots (R_inplane=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 R_total=16 (R_inplanexSMS=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

Virtual Coil (VC-) MUSSELS

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 R_inplane=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

m i n_{x} \sum_{t = 1}^{N_{s}} ∥ F_{t} C x_{t} - d_{t} ∥_{2}^{2} + λ ∥ H (x) ∥_{*}

$min_x \sum_{t=1}^{N_s}\parallel F_t Cx_t-d_t\parallel_2^2+\lambda\parallel H\left(x\right)\parallel_*$

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 R_inplane=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 k_x-axis by concatenating the two slices along the readout (Fig3a). In-plane and slice acceleration could thus be captured using $F_t$ with k_x-k_y undersampling and push the acceleration to R_inplanexSMS=8x2 for spin-and-gradient echo (SAGE (14)) msEPI.

Due to high acceleration, SMS-MUSSELS failed to provide clean images using 3-shots (R_net=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 R_inplane=8 (FOV=224x224x120mm³, 1x1x3mm³ resolution, TEs=26/61/61/130/165ms, TR=8.3sec). MUSSELS reconstruction of this R_net=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.

: 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):

m i n_{ϕ_{t}} \sum_{t = 1}^{N_{s}} ∥ F_{t} C m_{u n e t} e^{i ϕ_{t}} - d_{t} ∥_{2}^{2} + α ∥ Ψ ϕ_{t} ∥_{1}

$min_{\phi_t} \sum_{t=1}^{N_s}\parallel F_t Cm_{unet}e^{i\phi_t}-d_t\parallel_2^2+\alpha\parallel \Psi \phi_t\parallel_1$ 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 ϕ_{t}}

$C e^{i\phi_t}$ and create virtual coils

C^{*} e^{- i ϕ_{t}}

$C^* e^{-i\phi_t}$ (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).

Conclusion

We incorporated VC, buda and SMS concepts into MUSSELS to push the limits of PF, in-plane and slice acceleration in msEPI, and enabled high in-plane resolution, rapid structural imaging with improved geometric fidelity. SMS-NEATR took advantage of ML for accurate estimates of shot-to-shot phase variations and provided 1.8x Rmse reduction over SMS-MUSSELS. This paves the way for full synergistic combination of ML and model-based reconstruction, where deep learning could provide rapid estimates of B0 inhomogeneity to be included in buda-NEATR, and eliminate distortion without the need for topup processing.

Acknowledgements

This work was supported in part by NIH research grants: R01EB020613, R01EB019437, R24MH106096, P41EB015896, and the shared instrumentation grants: S10RR023401, S10RR019307, S10RR019254, S10RR023043.

References

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Figures

msEPI diffusion acquisition at b=1000s/mm²with 0.85x0.85mm² in-plane resolution using 4-shots. (a) Separate SENSE reconstructions for each of the R_inplane=4-fold accelerated shots were averaged after computing their magnitude. Missing data due to 55% partial-Fourier acquisition led to substantial resolution loss in the phase-encoding direction. (b) MUSSELS permitted joint reconstruction of the shots without navigation, but underestimated the missing portion of k-space with visible loss of resolution. (c) Proposed Virtual Coil MUSSELS made use of conjugate symmetry and seamlessly incorporated partial-Fourier into the joint reconstruction to improve the resolution (yellow boxes).

Blip-up and blip-down spin-echo EPI acquisitions at R_inplane=4 with 1x1mm² in-plane resolution. (a&b) Performing separate SENSE reconstructions for the blip-up and -down acquisitions demonstrate severe geometric distortion at this lower slice, as well as voxel pile-ups and noise amplification. (c) Hybrid-space SENSE jointly reconstructs the 2-shots with B₀ forward-modeling to eliminate distortion, but requires explicit phase-estimation and exhibits some noise amplification (yellow box). (d) Proposed buda-MUSSELS obviates the need for phase-navigation, eliminates distortion and improves reconstruction quality.

Due to high acceleration (R_total=16), proposed SMS-MUSSELS in (a) fails to provide clean reconstruction when the number of shots is reduced to 3. To amend this, we propose SMS-NEATR and synergistically combine machine learning and physics reconstruction. In (b), we use a complex-valued deep network to estimate and mitigate the artifacts in SMS-MUSSELS, and use the improved data to initialize the non-convex physics-based reconstruction in (c). This helps refine the phase estimates of each shot, which are then included in a final Joint Virtual Coil SENSE reconstruction to solve for a common magnitude image in (d).

(a) We have deployed our SMS-MUSSELS in the multi-contrast spin-and-gradient echo (SAGE) msEPI sequence with 5 echoes (first and last TEs are shown). Due to high acceleration (R_total=16), there were residual artifacts/ghosts (yellow arrows). (b) These were largely mitigated after the subsequent U-Net processing, at the cost of some image blurring. (c) Using the U-Net solution to initialize a final physics-based reconstruction provided further improvement in the SMS-NEATR result.

SMS-NEATR synergistically combines machine learning and physics-based reconstruction to enable T₂ and T₂* mapping with whole-brain coverage at 1x1x3mm³ resolution. While R_inplane=8-fold acceleration provides high geometric fidelity, SMS=2 acceleration reduces the TR to 4.2 seconds per shot, leading to a 12.5 second acquisition with 3-shots.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)

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