Introduction

Echo Planar Time Resolved Imaging (EPTI) is a distortion-free rapid quantitative technique with exciting neuroimaging applications^1-5. Last year, we developed a 3D spherical-EPTI (sEPTI)⁶ achieving 1.4X additional acceleration compared to already-fast EPTI with improved image quality for the >100-echo T2*-weighted images and T2* maps. However, SNR has always been a problem for T2* and QSM due to the rapidly decreased signal intensity at long TE. Averages are usually necessary, resulting in doubled or tripled scan time. In this work, we further improved the image quality and reduced averages (scan time) innovatively from 3 aspects: (1) an improved data-driven B0 update pipeline for high-quality B0 map; (2) a widely-applicable eddy-current correction pipeline that significantly reduces the artifacts; (3) a physics-informed unrolled network for subspace reconstruction⁷ to improve the SNR by 2X times. The optimized sEPTI achieved whole-brain T2* and QSM quantifications at 0.75 mm resolution on 3T within a single-average 84-second scan.

Methods

Prototype acquisition and reconstruction: All data were acquired with gradient echo sequence with sEPTI sampling. The reconstruction was performed using low-rank subspace framework through two steps. First step is to obtain a data-updated high resolution B₀ map² from a low-resolution B_0,low from calibration data using:
$$\widehat{\mathbf{U}_{\boldsymbol{B}}}=\arg\min_{\mathbf{U}_{\boldsymbol{B}}}\left\|\Omega\mathrm{FSB_l}\mathbf{U}_{\boldsymbol{B}}\boldsymbol{\Phi}_{\boldsymbol{B}}-\mathbf{d}\right\|_2^2+R\left(\mathbf{U}_{\boldsymbol{B}}\right),(1)$$
where $$$\mathbf{d}$$$ is the acquired data, $$$\mathrm{B_l}$$$ is the B_0,low-induced phase, $$$\boldsymbol{\Phi}_{\boldsymbol{B}}$$$ is temporal subspace containing both T2* decay and phase evolution with off-resonance [-50,50]Hz, and $$$\mathbf{U}_{\boldsymbol{B}}$$$ is the spatial coefficients to be solved. The reconstructed images $$$\mathbf{U}_{\boldsymbol{B}}\boldsymbol{\Phi}_{\boldsymbol{B}}$$$ provides a residual phase of $$${\Delta}{B_0}$$$ to achieve $$$B_0=B_{0,low}+{\Delta}{B_0}$$$. In the second step, the reconstruction is performed as⁶:
$$\widehat{\mathbf{U}}=\arg\min_{\mathbf{U}}\|\Omega\mathrm{FSB}\mathbf{U}\boldsymbol{\Phi}-\mathbf{d}\|_2^2+R(\mathbf{U}),(2)$$
Improved B0 updating: Reduced SNR at 0.75 mm results in noisy $$${\Delta}{B_0}$$$ from Eq.(1) and even noisier images. Polynomial fitting can smooth $$${\Delta}{B_0}$$$, but tends to oversmooth the edge and leads to aliasing (Fig.1A). To resolve this issue, we developed an iterative B₀ updating-smoothing framework. In each iteration, a $$$\pm$$$20 Hz $$${\Delta}{B_0}$$$ is updated and smoothed through polynomial fitting; the last iteration without polynomial fitting is to preserve the sharp edge (Fig.1B).
Eddy current correction: Eddy current induced gradient non-linearity is a fundamental issue with all EPI-based sampling⁸ including EPTI. To compensate this effect, a phase difference $$$P$$$ between odd and even echoes was estimated from the low-resolution calibration data, which is four-echo GRE sequences providing sensitivity maps, initial B_0,low, and eddy current phase. The reconstruction model was then updated as (Fig.1C):
$$\widehat{\mathbf{U}}=\arg\min_{\mathbf{U}}\|\Omega\mathrm{FSPB}\mathbf{U}\boldsymbol{\Phi}-\mathbf{d}\|_2^2+R(\mathbf{U}),(3)$$
Unrolled network for subspace reconstruction (Figure 2): Data with 0.75-mm resolution suffers from 40% SNR loss compared to 1 mm. To further improve the SNR and reduce the need of averages, an unrolled network was developed for the subspace reconstruction⁹:
$$\widehat{\mathbf{U}}=\arg\min_{\mathbf{U}}\|\Omega\text{FSBPU}\mathbf{\Phi}-\mathbf{d}\left\|_2^2+\lambda\right\|\mathbf{U}-N(\mathbf{U};\theta)\|_2^2,(4)$$
where $$$N(\mathbf{U};\theta)$$$ is the convolutional neural network (CNN)-based denoiser with trainable parameters $$$\theta$$$. The network was trained through a supervised manner with the acquired single-average sEPTI as input and the spatial coefficients from multi-averaged sEPTI as ground truth (GT). To ensure the GT is of good quality, each average was reconstructed using Eq.(2) separately, co-registered to the same motion state, corrected with background phase differences¹⁰, and then averaged to boost SNR. The data were acquired at 1 mm and 0.75 mm, and the networks were trained on data with a single resolution or both.
In vivo experiments: Ten volunteers were studied on a 3T system (Premier, GE Healthcare) with a 48-channel head-coil. Sagittal images were acquired with: FOV=240x240x216mm³, TEs=5-60ms, TR=65ms, flip angle=20°. The 1.0-mm data was acquired 45 seconds per average and 6 averages were acquired; the 0.75-mm data was acquired 84 seconds per average and 8 averages were acquired. Data from 7 subjects were used for training, 1 for validating, and 2 for testing. To test generalizability, 1-mm data were acquired on a pediatric patient with epilepsy where the T2* contrast is different from training population.

Results

Figure 3 demonstrated visible SNR improvement and artifacts reduction from improved B₀ update and eddy current correction. The reconstruction of unrolled network further improves the SNR by 2 times (Fig.4), and the model trained on both resolution provides the best outcome. The test showed that the improvements in this work achieved better image quality compared to 2-average data (Fig.5A); the pipeline can be extended for wide applications with different contrasts (Fig.5B).

Conclusion

With the improvement in the B₀ update, eddy current correction, and integration of deep learning, sEPTI achieved additional 2-times acceleration for 0.75-mm T2* and QSM quantification on 3T within 84 seconds. This opens the potential for submillimeter T2* and QSM on clinical field strength.

Acknowledgements

This work is partially supported by R01MH116173, R01EB019437, U01EB025162, P41EB030006, R01EB033206, U24NS129893