Synopsis

Keywords: New Trajectories & Spatial Encoding Methods, New Trajectories & Spatial Encoding Methods

A new 3D Spatially Fourier Excited Acquisition and Reconstruction method (SFEAR) is introduced, in which double-RF pulses are used to excite sinusoidally-modulated slice profiles across a slab. Target spatial frequencies are achieved by varying the time shift between the two pulses, to construct the slice-phase-encode dimension of 3D k-space from Fourier excited acquisitions. SFEAR outperforms conventional GRAPPA in the slice-phase encode dimension, given its inherent ability to undersample sine or cosine components rather than whole planes of 3D k-space. Superior reconstruction of undersampled data and lower g-factor values are demonstrated in both 7T phantom and in vivo data.

Introduction

Spatially selective RF excitation pulses have been used to encode MR images using non-Fourier basis sets such as wavelet encoding and SVD decomposition^1,2,3 to spread MR signal’s energy in k-space in the context of Compressed Sensing^{4, 5}. In this work, we exploit the linear response model⁶ of selective excitation and introduce a Spatially Fourier Excited Acquisition and Reconstruction (SFEAR) technique that encodes magnetization using sinusoidally-modulated excitation and constructs a 3D k-space from the cosine- and sine-modulated, slab selective excitations. The 3D image volume is returned simply by inverse Fourier transform. Following proof-of-principle demonstration of SFEAR, the strength of SFEAR is demonstrated in slice-phase encode undersampling using a modified GRAPPA⁷ reconstruction algorithm. Rather than dropping whole planes in 3D k-space, SFEAR can selectively drop cosine- and sine-components, thus acquiring partial information at a greater number of 3D k-space planes. The robustness of SFEAR in slice-undersampled data is demonstrated on both 7T phantom and in-vivo datasets, without the need for Compressed Sensing sparsity regularization terms or other forms of penalty functions.

Theory

SFEAR Excitation: In 3D image acquisition, 3D k-space is encoded by readout, phase encode and slice-phase encode dimensions, k_x, k_y and k_z (assigned without loss of generality), respectively. Our proposal of Spatially Fourier Excited Acquisition uses Euler’s identity, $$$e^{-jk_z z}=cos(k_{z}z)-jsin(k_{z}z)$$$, to decompose the slice-phase encode dimension into its cosine and sine components, moving each to the RF excitation; double-RF pulses encode either a cosine or sine-modulation of the magnetization (Fig.1). The desired set of (N+1) k_z frequencies are obtained by a set of time shifts, Δ, between the double-RF pulses, calculated from $$$k_{z_i}=\gamma G_{ss}\Delta_i$$$, $$$i=0,\dots, \lfloor N/2\rfloor$$$, for a given slice select gradient magnitude, G_ss, with corresponding to a base pulse with twice the magnitude of the non-zero k_z frequencies. Sine-modulated profiles are achieved by applying phases of 90° and -90° to the first and second pulses, respectively, of the cosine-modulated case. Each SFEAR acquisition is a slab-selective excitation, with profile determined by the base pulse, followed by a 2D readout. SFEAR Reconstruction: The i^th positive and negative planes of the SFEAR 3D k-space, S^SFEAR, are constructed from S_c and S_s, the 2D k-space planes acquired under cosine- and sine-modulation, respectively, for variable time shift, $$$\Delta_i=k_{z_i}/{\gamma G_{ss}}$$$:
$$S^{SFEAR} (k_x, k_y, k_{z_i})=S_c(k_x, k_y, \Delta_i)-jS_{s}(k_x, k_y, \Delta_i), $$
and
$$S^{SFEAR}(k_x, k_y, -k_{z_i})=S_c(k_x, k_y, \Delta_i)+jS_{s}(k_x, k_y, \Delta_i).$$
Thus, SFEAR 3D k-space with (N+1)k_z planes is constructed by (N/2+1) cosine and N/2 sine encodings, analogous to a Fourier series representation of the data. Slice-phase encode acceleration: A modified GRAPPA algorithm estimates the fully-sampled k-space from undersampled SFEAR data (Fig. 2), using an undersampling pattern that can alternate sine- and cosine-modulated acquisitions. For an undersampling factor of R_z=2, no 3D k-space planes are left without partial acquisition of information, in contrast to the conventional approach of dropping entire planes of 3D k-space.

Methods

Experiments: An in-house 3D printed resolution phantom and a 27-year-old volunteer were scanned using SFEAR via a modified Flash sequence (slab thickness = 7 mm, 21 slices of thickness = 0.33 mm, G_ss=21.8 mT/m , Δ_i$$$\in$$${0, 156, 313, 469, 626, 782, 939, 1096, 1255,1409, 1558} μs , TE = 20 ms, TR = 300 ms, FA = 15°, in-plane resolution = 0.78 × 0.78 mm, scan time = 28 minutes). 3D FLASH acquisitions with the same parameters and same scan time were acquired for comparison. Slice acceleration: Data was retrospectively undersampled and reconstructed using a kernel size of 5×5×5 and an autocalibration space consisting of the 10 central k-space planes. To obtain g-factor measurements from the phantom, 100 noisy reconstructions were pseudo-replicated⁸ in simulation using the coil noise covariance matrix measured with a noise-only scan at the beginning of the experiment.

Results

Phantom: The reconstructed fully-sampled phantom images (Fig. 3) provide a proof-of-principle that SFEAR replicates the image quality and structural detail of 3D FLASH. In undersampling in the slice-phase encode dimension, SFEAR clearly outperforms GRAPPA. GRAPPA reconstructions contain noisy regions that are absent in the undersampled SFEAR images. The g-factor maps show consistently lower values in the undersampled 3DBEE reconstruction. In-vivo: As with the phantom results, fully sampled in-vivo SFEAR replicates 3D FLASH (Fig. 5). Undersampled SFEAR (R_z=2) maintains image quality, in contrast to the noisy regions present in the conventional GRAPPA reconstructions.

Discussion and Conclusion

Proof-of-principle of the Spatially Fourier Excited Acquisition and Reconstruction method, that moves the slice-phase encode dimension into the excitation, has been demonstrated in phantom and in-vivo experiments. SFEAR pulses have half the SAR of the slab selective pulses applied in conventional 3D acquisitions. Considering the small size of the autocalibration set, the noisy results achieved by GRAPPA are consistent with previous studies⁹, while SFEAR reconstructions returned smaller g-factors and markedly better unaliasing of the slices, despite there being only 21 slices in the exemplar volumes. Our current pilot results are promising for SFEAR outperforming GRAPPA at higher undersampling factors also. SFEAR undersampling can also be combined with in-plane GRAPPA to further accelerate acquisitions. The implicit property of SFEAR that permits robust undersampling of the slice-phase encode dimension without requiring regularization offers great promise for future combination of SFEAR and Compressed Sensing for further acceleration of 3D imaging.

Acknowledgements

We acknowledge the facilities, the scientific and technical assistance of the Australian National Imaging Facility, a National Collaborative ResearchInfrastructure Strategy (NCRIS) capability, at the Melbourne Brain Centre Imaging Unit of the University of Melbourne. The work is supported by a research collaboration agreement with Siemens Healthineers.

References

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