Synopsis

Balanced SSFP is an SNR-efficient sequence with unique T₂/T₁ contrast, but suffers from banding artifacts due to B₀ sensitivity. These artifacts can be mitigated through RF phase-cycling at a cost of significant increase in scan time. Here, we propose Joint L1-SPIRiT to jointly reconstruct highly accelerated/undersampled phase-cycled images and convert the different banding artifacts of these images into additional spatial encoding. This enables highly accelerated 2D and Simultaneous Multi-Slice imaging, thus mitigating scan time burden of phase-cycled bSSFP while producing banding-free images. In particular, Joint L1-SPIRiT provides around 2-fold decrease in both the average g-factor and RMSE relative to GRAPPA.

Introduction

Balanced steady state free precession (bSSFP) is an SNR-efficient technique that has found widespread use in cardiac, abdominal and brain imaging. Despite being a rapid sequence with unique T₂/T₁ contrast, it suffers from banding artifacts due to B₀ sensitivity. To mitigate these artifacts, multiple image data with different RF phase-cycling that shifts the B₀ sensitivity band are acquired and combined through maximum intensity projection (MIP). Such phase-cycling increases scan time, counteracting the inherent efficiency of bSSFP. To alleviate this, parallel imaging [1,2] and Simultaneous Multi-Slice (SMS) [3] have been deployed in phase-cycled bSSFP [4,5] for up to 4-fold acceleration. Moreover, Joint-GRAPPA [6] has recently been proposed to permit joint reconstruction of phase-cycled images and provided improvement over conventional GRAPPA reconstruction.

Herein, we propose Joint L1-SPIRiT, which extends and improves upon Joint-GRAPPA by enforcing consistency across both sampled and estimated k-space and exploiting gradient sparsity. This approach permits: up to 2.5-fold decrease in maximum g-factor, 2.3-fold decrease in average g-factor, and 1.9-fold reduction in RMSE relative to GRAPPA. Such improvement is achieved through Total Variation (TV) regularization together with SPIRiT kernels [2] that are fitted jointly across channels and phase-cycles, analogous to k-t and virtual coil approaches in dynamic and diffusion imaging [7,8].

Matlab code that reproduces the results is available at: bit.ly/2eyWfAT

Methods

Joint L1-SPIRiT creates virtual coils by stacking phase-cycles along the channel axis, where all coils and all cycles contribute to the reconstruction of a particular channel. Similar to k-t acquisition, sampling pattern is shifted across the cycles to provide complementary k-space coverage. By creating virtual coils out of the phase-cycles, Joint L1-SPIRiT makes use of intensity and phase modulations due to B₀ inhomogeneity, and converts these artifact sources into useful, additional spatial encoding. With Joint L1-SPIRiT reconstruction is regularized by gradient sparsity as follows:

$$\min_{x} \parallel (G-I)x \parallel_2^2 + \lambda \parallel \nabla F^{-1}x \parallel_1 \hspace{5mm} s.t. \hspace{5mm} Dx=y$$

Here $$$x$$$ represents k-space from all coils and cycles, $$$G$$$ are SPIRiT kernels, $$$\nabla$$$ is the gradient operator, $$$F^{-1}$$$ is the inverse Fourier transform, $$$y$$$ denotes sampled data and $$$D$$$ selects acquired samples. The constraint $$$Dx=y$$$ can be absorbed into the data consistency via $$$x=D^{T}y+D_c^T \tilde{x}$$$, where $$$D^T$$$ and $$$D_c^T$$$ insert the acquired and nonacquired samples into the full k-space grid, and $$$\tilde{x}$$$ denotes only the missing samples:

$$\min_{\tilde{x}} \parallel (G-I) D_c^T \tilde{x} +(G-I)D^T y \parallel_2^2 + \lambda \parallel \nabla F^{-1} D^T y+ \nabla F^{-1} D_c^T \tilde{x} \parallel_1$$

Optimization is performed using nonlinear CG [9].

To test Joint L1-SPIRiT, three datasets were acquired on a healthy volunteer at 3T with four phase-cycled bSSFP (0, π/2, π, 3π/2) for the following 2D and SMS cases:

i) 2D abdominal imaging at R=6×: FOV=380×380mm², mtx=160×160, 5mm slice, TR/TE=3.3/1.54ms, FA=37°, BW=822Hz/px, 34-channel reception.

ii) 2D brain imaging at R=6×: FOV=240×240mm², mtx=160×160, 4.5mm slice, TR/TE=3.37/1.57ms, FA=47°, BW=845Hz/px, 32-channel reception.

iii) SMS brain imaging at MB-8: Eight slices were acquired using parameters from case ii). To simulate SMS acquisition, these slices were shifted by multiples of FOV/4 and collapsed retrospectively. Since alternating the RF phase leads to a shift in both FOV and frequency [5], a collapsed slice group has contribution from all phase-cycles. As such, slices from appropriate cycles were shifted and collapsed.

GRAPPA, Joint-GRAPPA and Joint L1-SPIRiT were employed for reconstruction of the 2D acquisition cases, while Slice- and Joint Slice-GRAPPA, both with leak-block [10], were used to reconstruct the SMS data. All experiments used 32 ACS lines, 12 GCC compressed channels [7] and 300 Monte-Carlo iterations for g-factor calculation [8]. Kernel sizes, under-sampling pattern staggering between phase-cycles, and regularization parameters were selected for optimal RMSE in each case (parameters in Fig4).

Results

Fig1 shows reconstructed MIP images, error and g-factor maps for 2D abdominal imaging at R=6×. With GRAPPA, significant image artifacts are observed (blue arrows) along with a marked reduction in SNR, as reflected by the high g-factor. The image reconstruction improves with Joint-GRAPPA, and improve further still with Joint L1-SPIRiT to provide high quality reconstruction at ~2× lower RMSE and g-factor penalty.

Fig2 shows results for 2D brain imaging at R=6×, where Joint L1-SPIRiT also provides a similar reconstruction quality boost.

Fig3 shows results for SMS brain imaging at MB-8, where joint reconstruction via Joint Slice-GRAPPA provides 1.3× reduction in RMSE and 1.5× reduction in g-factor.

Discussion

Joint L1-SPIRiT employed banding artifacts as additional spatial encoding along with TV regularization. This provided up to 2-fold reduction in RMSE and noise amplification for highly accelerated phase-cycled 2D and SMS bSSFP acquisitions. Such reconstruction approach should enable rapid imaging of banding-free, high-SNR bSSFP images.

Acknowledgements

References

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