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Echo Planar Time-Resolved Imaging (EPTI) with subspace constraint and optimized k-t trajectory

Zijing Dong^1,2, Fuyixue Wang^1,3, Timothy G. Reese¹, Berkin Bilgic¹, and Kawin Setsompop^1,3

¹A. A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, MA, United States, ²Electrical Engineering and Computer Science, MIT, Cambridge, MA, United States, ³Harvard-MIT Health Sciences and Technology, MIT, Cambridge, MA, United States

Synopsis

Echo planar time-resolved imaging (EPTI) is a multi-contrast quantitative imaging technique, which achieved fast acquisition of distortion- and blurring-free images at multiple echo times (TE). To improve the SNR and accuracy of EPTI at high-accelerations, in this study, we developed a subspace-constrained reconstruction for EPTI and proposed new k-t sampling trajectories to take advantage of this reconstruction. The subspace reconstruction is also augmented with phase-cycling to extract high-resolution phase data, without need of high-resolution B₀ calibration scan. Using the proposed approach, whole-brain 1.1mm-isotropic multi-echo images, and T₂* and B₀ maps are reconstructed from 3D-EPTI data acquired within 50 seconds.

Purpose

Echo planar time-resolved imaging^[1] is a multi-contrast quantitative imaging technique, which achieved rapid acquisition of distortion- and blurring-free images at multiple echo times (TE). In EPTI, a spatio-temporal CAIPI sampling^[1-3] is used to cover k-t space efficiently through customized multishot-EPI trajectory. The highly-undersampled k_y-t data is then recovered by exploiting signal correlation across the time and coil dimensions through a GRAPPA-like reconstruction. In such reconstruction, the edge of k_y-t space cannot be recovered accurately through kernel-based interpolation, reducing the number of echo images that can be reconstructed. Moreover, the SNR of the reconstruction can be low for high spatial resolution cases with high-undersampling. To address these issues, we develop a new reconstruction using the subspace-constrained approach^[4,5], and validated its improved performance on both 2D- and 3D-EPTI acquisitions. New EPTI sampling patterns were also designed and combined with subspace reconstruction to further improve highly-accelerated 3D-EPTI.

Methods

In EPTI, continuous EPI readouts are performed with spatio-temporal CAIPI-sampling to efficiently sample the desired signal evolution in k-t space. For instance, a 3D gradient-echo (GE) EPTI sequence shown in Fig.1a was used to acquire the T₂* signal decay. After each RF excitation, an EPTI readout is used to cover a small k_y-k_z block using highly-accelerated zigzag trajectory. Such spatio-temporal CAIPI trajectory has been demonstrated to enable effective use of coil sensitivity in recovering highly undersampled k_y-k_z-t data within each sampling block^[1]. Acquisition across k-space blocks are performed across TRs to fill k_y-k_z space. To recover the signal evolution from undersampled data, subspace reconstruction is developed for EPTI (Fig.1b). First, the desired signal evolution (T₂* decay in this study) within the possible parameter range is simulated based on the acquisition parameters. Then, several bases are extracted through PCA as Φ, which form a low-dimensional subspace used to approximate the signal space. Using these bases, the temporal image series can be calculated by Φc, where c is the coefficient map of the bases that needs to be estimated. Using this approach, the degrees of freedom of reconstruction is reduced from the number of time points to the number of bases, which improves conditioning of the reconstruction and image-SNR^[5]. The subspace-constrained reconstruction is solved by:

$$min_{c}\parallel UFSB\phi c-y \parallel_2^2+\lambda R(x)$$

where B is temporal B₀ phase-evolution, S is coil sensitivity, F is Fourier transform, U is undersampling mask, and y is the acquired undersampled k_x-k_y-k_z-t data. Regularization R(c) can be used to improve the conditioning and SNR for higher undersampling. After estimating c, we can generate the time-series images/volumes by computing Φc. The B₀ phase evolution and coil sensitivity in the forward model are both estimated using a fast-low-resolution calibration data with 6 GE echoes. High-resolution B₀ maps can be estimated by the phase-cycling approach^[6] using the reconstructed magnitude images and acquired signals.The following brain data were acquired at 3T using a 32-channel coil.

2D GE-SE EPTI acquisition was used to compare GRAPPA-like method and subspace reconstruction. Gradient- and spin-echo k-t data with FOV_xy = 220x220mm² and res_xyz =1.1×1.1×3mm³ were acquired with full 216 phase-encodings across 40 gradient-echo and 80 spin-echo time-points. The data were retrospectively undersampled along k_y-t by 24x to synthesize a 9-shot 2D-EPTI acquisition used for reconstruction comparison.

3D GE EPTI acquisition was used to evaluate subspace reconstruction under four different EPTI sampling strategies: i)&ii) regular CAIPI-like EPTI samplings, iii) variable density (VDS) random-sampling, and iv) VDS CAIPI-sampling. For VDS cases (iii&iv), locally low-rank (LLR) constraint was employed. GE k-t data at 1.1mm isotropic resolution were fully acquired across 50 echo-time points, with FOV_xyz = 220x220x110mm³. The data were retrospectively undersampled along k_y-k_z-t by 72x with a block size of R_yblock x R_zblock=12×6 for all sampling strategies to reduce acquisition time from 26-mins to 22s.

Results

Fig.2 shows the comparison between GRAPPA-like reconstruction and subspace reconstruction for 2D GE-SE EPTI. The edge echoes which are corrupted in GRAPPA reconstruction are well-recovered by the subspace reconstruction. Fig.3 shows the results of different 3D EPTI sampling strategies combined with subspace reconstruction. Through 72× acceleration, 3D brain volumes at 1.1mm isotropic resolution across 50 echoes time-points can be obtained in 22 seconds. Here, VDS CAIPI-sampling with LLR-subspace reconstruction achieves the best results with low errors. The reconstructed multi-echo images, T₂* and B₀ maps of 3D EPTI data at 36× acceleration with VDS CAIPI-sampling (44s scan) and LLR-constrained subspace reconstruction are shown in Fig.4.

Conclusion

Subspace reconstruction improves the performance of EPTI for better signal evolution recovery, and the designed 3D sampling strategy enables efficient high-resolution EPTI, providing a powerful technique for fast multi-contrast and quantitative imaging.

Acknowledgements

This work was supported in part by NIH research grants: R01MH116173, R01EB020613, R01EB019437, U01EB025162, P41EB015896, and the shared instrumentation grants: S10RR023401, S10RR019307, S10RR019254, S10RR023043.

References

1. Wang F, Dong Z, Reese T, Wald L, Setsompop K. Echo Planar Time-resolved Imaging. In Proceedings of the 26th Annual Meeting of ISMRM, Paris, France, 2018. p 0217.

2. Breuer FA, Blaimer M, Mueller MF, Seiberlich N, Heidemann RM, Griswold MA, Jakob PM. Controlled Aliasing in Volumetric Parallel Imaging (2D CAIPIRINHA). Magn Reson Med 2006; 55:549–556.

3. Setsompop K, Gagoski BA, Polimeni JR, Witzel T, Wedeen VJ, Wald LL. Blipped‐controlled aliasing in parallel imaging for simultaneous multislice echo planar imaging with reduced g‐factor penalty. Magn Reson Med 2012;67:1210-1224.

4. Liang Z P. Spatiotemporal imaging with partially separable functions. Biomedical Imaging: From Nano to Macro, 2007. ISBI 2007. 4th IEEE International Symposium on. IEEE, 2007: 988-991.

5. Tamir JI, Uecker M, Chen W, Lai P, Alley MT, Vasanawala SS, Lustig M. T2 shuffling: Sharp, multicontrast, volumetric fast spin‐echo imaging. Magn Reson Med. 2017;77:180-195.

6. Ong F, Cheng J Y, Lustig M. General phase regularized reconstruction using phase cycling. Magn Reson Med. 2018, 80: 112-125.

Figures

Figure 1. The graphic illustration of EPTI acquisition and subspace-constrained reconstruction. (a) The diagram of 3D GE-EPTI sequence and its block-wise sampling in k_y-k_z-t space per EPTI-shot. Spatio-temporal CAIPI trajectory is employed, which has been demonstrated to enable effective use of coil sensitivity information to recover highly undersampled k_y-k_z-t data. Data blocks of different k_y-k_z positions are acquired sequentially across TRs to fill k_y-k_z space. (b) Signal evolution curves with T₂* decay is simulated based on the tissue and acquisition parameters. The subspace bases are extracted and used to approximate the actual temporal signal evolution.

Figure 2. Comparison of 2D GE-SE EPTI results reconstructed by GRAPPA-like reconstruction and subspace reconstruction without regularization for a 9-shot 2D EPTI acquisition. Four images at different TEs (out of 120) are shown, where images at the early and late TEs show severe artifacts from the GRAPPA reconstruction while the subspace method provided clean images. The signal drops of GRAPPA at the edge echoes are also shown in the signal curve (indicated by blue arrows). In contrast, subspace reconstruction obtained accurate signal evolution without signal drop or fluctuation.

Figure 3. Comparison of different 3D-EPTI sampling combined with subspace reconstruction using a 3D GE-EPTI data at 1.1mm isotropic resolution. The FOV was 220×220×110mm³, TR=80ms, echo spacing=0.93ms, number of echoes=50, TE range=9-55ms. The 26-minute fully-sampled dataset was undersampled by a factor of 72 for all four cases, corresponding to a 22-second scan. Overall, the VDS CAIPI pattern with LLR-constrained subspace reconstruction achieved the lowest RMSEs for both echo-combined and single-echo images. The CAIPI-like EPTI pattern shows improved accuracy when compared to block-wise random sampling due to better utility of both coil sensitivity and temporal signal correlation.

Figure 4. The reconstructed multi-echo images, T₂* and B₀ maps by the VDS EPTI sampling and LLR-constrained subspace reconstruction. The reduction factor of the 3D-GE data was 36, corresponding to a 44-second scan at 1.1mm isotropic resolution. The high-resolution B₀ maps were estimated by the phase-cycling approach using the reconstructed magnitude images and undersampled k-space signals.

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

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