3D FRONSAC with PSF reconstruction

Abstract

Purpose: This study extends the Fast ROtary Nonlinear Spatial ACquisition (FRONSAC) method to include 3D acquisitions and reconstructions. It uses a transform domain reconstruction which is needed to make 3D reconstructions practical and provides new insights into how parallel imaging performance is enhanced by FRONSAC encoding.

Methods: This work developed the first examples of FRONSAC incorporated into a 3D acquisition. 3D FRONSAC was tested on human subjects with both simple gradient echo and MPRAGE Cartesian acquisitions. The quality of the 3D FRONSAC images was evaluated using structural similarity index measure (SSIM), and normalized root mean square error (NRMSE).

Results: FRONSAC encoding did not significantly modify the contrast obtained in either sequence, but it substantially improves the image quality of undersampled reconstruction. FRONSAC images have reduced undersampling ghosts and consistently improved SSIM and NRMSE.

Conclusions: Acquisition and reconstruction of 3D FRONSAC images are feasible, and the additional FRONSAC encoding improves image quality in highly undersampled images.

Keywords: Accelerated imaging; Nonlinear gradients; Parallel imaging.

Figure 1.

Point spread functions (magnitude only, cropped along the frequency axis to improve visualization) for four aliasing voxels when acquired by 4 different coils are shown for (a) Cartesian and (b) FRONSAC encoding. (a) With Cartesian encoding, the PSF of each voxel follows a different pattern across coils, which allows for separate identification of these voxels in a set of aliased images. (b) With FRONSAC encoding, each voxel also has a unique ghosting pattern (constant across coils), which aids in the separation of voxels. Even within a single coil, the PSFs are linearly independent, which aids in the separation of aliased voxel. (c,d) For better characterization of blurring induced by FRONSAC encoding, log plots of these PSFs are also shown. Panel (e) shows the fields used for FRONSAC encoding in this work, as well as the placement of voxels whose PSFs are shown in panels (a)-(d).

Figure 2.

(a) In previous FRONSAC reconstructions, the entire image volume is related to the entire dataset by a very large and dense encoding matrix (generally ${\text{N}}_{\text{read}}\text{NP}{\text{E}}_{\text{y}}\text{NP}{\text{E}}_{\text{z}}{\text{N}}_{\text{coil}}\text{x}{\text{N}}_{\text{x}}{\text{N}}_{\text{y}}{\text{N}}_{\text{z}}$ though only one coil is shown in illustration). For most problems, inversion of this matrix, E, is not computationally feasible, and even iterative approaches become impractically slow for 3D volumes and high channel counts. (b) After Fourier transform of the data, a far more local relationship is evident, which is analytically derived in the Theory section. This allows one row of data (across coils) to be related to one row (or set aliased rows) in the reconstruction volume via the matrix ${\text{E}}_{\text{PSF}}$. (c) While this smaller matrix inversion must be solved for every row of acquired data, it is equivalent to diagonalization of the encoding matrix, leading to significantly better efficiency.

Figure 3.

First demonstrations of 3D FRONSAC imaging show very consistent contrast with traditionally acquired GRE and MP-RAGE images

Figure 4.

Reconstructions of 32 channel data at various undersampling factors show that structural similarity is consistently higher and NRMSE is consistently lower in images enhanced with FRONSAC encoding. In particular, it is notable that the unregularized 2×4 and 4×2 FRONSAC images show relatively modest undersampling artifacts that could possibly be reduced with more sophisticated reconstruction strategies. In contrast, the traditionally encoded Cartesian images fall apart at these high undersampling factors.

Figure 5.

Undersampled reconstructions from a simple 8 channel azimuthally arranged coil show surprisingly good image quality even at relatively high undersampling factors. As previously described, FRONSAC induces a ghosting pattern for aliased voxels that allows some separation even in the absence of coil encoding. Results are similar to the higher channel reconstructions shown in Figure 4.

Figure 6:

g-factor maps shown at FOVz/4, FOVz/2 and 3FOVz/4 are shown for the 8-channel coil. Note that different color scales were needed for some visualizations.