Phase Encoded xSPEN: A High-Definition Approach to Volumetric MRI with Unusually High Acceleration Factors
Zhiyong Zhang1, Michael Lustig2, and Lucio Frydman1

1Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot, Israel, 2Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA, United States


xSPEN is a single-shot MRI approach whose timing and pre-acquisition hyperbolic phase, endow it with exceptional resilience to offsets. We recently introduced multi-scan, phase-encoded (PE) 3D xSPEN MRI which preserves this while increasing resolution along the PE (y) and slab-selection (z) dimensions. It is here shown that parallel receivers endow this 3D approach with unprecedented PE downsampling performances. This reflects xSPEN’s unusual kernel, whose hyperbolic phase couples the directly-sampled kz information with the y coil sensors. This mitigates the artifacts associated with a highly undersampled ky axis, as demonstrated by highly accelerated in vitro and human scans.


xSPEN (Fig. 1a) is a new approach to single-scan imaging endowed with unprecedented resilience to field distortions 1. xSPEN uses frequency-swept pulses under the action of bipolar ±Gy and constant Gz gradients, to impart a hyperbolic phase eiCyz modulation. This encoding kernel leads to a unique situation whereby Gz reads out y-axis profiles –and vice-versa. Phase-encoded xSPEN (Fig. 1b) is an extension of this single-shot protocol to volumetric 3D imaging 2, incorporating an additional ky loop. This simultaneously yields ky/kz data containing low and high frequency components, as well as transposed, low-resolution z/y images 2 (Figs. 1c, 1d). This study demonstrates that when multiple receivers are available, the method’s redundant information results in unique ky downsampling capabilities with minimal artifacts and excellent SNR. This allows one to complete 3D spin-echo-based brain scans with full Fourier multiplexing and sub-millimeter isotropic resolution in ≤2 min, using conventional, commercial scanners and coils.


xSPEN’s eiCyz pre-encoding leads to a situation whereby the k-space sampling spreads from the localized 2D sinc of traditional MRI (Fig. 1c) into a 2D box-like shape (Fig. 1d). In traditional k-space acquisitions, the spatial dimensions are thus de-coupled, and the number of effective coil elements along a spatial dimension limits the downsampling that can be afforded along that axis: beyond this limit, SNR will rapidly drop and visible artifacts appear. By contrast, in xSPEN acquisitions where ky,kz are coupled by a bilinear phase, a particular kz value gives (low-resolution) insight about a specific position along the y profile. This kz-based y-information mitigates the aliasing artifacts that will appear if downsampling is applied in the ky dimension. Figure 2 demonstrates this by comparing the GRAPPA-based reconstruction3 of traditional k-space and of xSPEN acquisitions, using simulations that assume an acceleration factor of 6 along the PE dimension using a generic 8-channel head coil. In the traditional case, this ky downsampling leads to overlapping replicas of the full object, which are beyond the separation ability of multi-coil harmonics even after GRAPPA3. By contrast, the coupling arising in xSPEN means that for a specific kz, only local y contributions will be acquired by ky. Downsampling this variable will thus result, for a particular kz, in replicas of local y contributions and not of the full object. This filtering allows the GRAPPA reconstruction to yield artifact-free images, despite a highly downsampled (i.e., a highly accelerated) acquisition. (Notice that throughout this discussion xSPEN’s third, EPI-like ±kx sampling was ignored as it is conventionally sampled and decoupled form the other domains; it is intriguing to think what opportunities would arise if this weren’t the case).

Results and Discussion

Experimental tests of these considerations were carried out on a 3T Siemens TrioTIM® using a 32-channels head coil on phantoms and on human volunteers; the latter following suitable written consent. Figure 3 compares the effects of downsampling in TSE4 vs PE xSPEN 3D acquisitions, using water and a human head as test cases. A slab thickness FOVz=12mm with 29 kz encodings was used, achieving an oversampling factor of 1.2 along this dimension. The echo train length in PE xSPEN was thus set 29, while the TSE turbo factor was also set to 29 in order to keep similar acquisition times for both sets of tests. The Figure clearly exemplifies what would happen if scan times were reduced in these experiments from 9.6 to 1.7 min, by increasing the ky downsampling. Notice the significant artifacts that appear in 3D TSE when downsampling exceeds ≈3. By contrast PE xSPEN remains nearly artifact-free till downsampling ca. 5x for the phantom, and brain scans remain artifact-free till reaching a downsampling factor of 7. Figure 4 exemplifies another aspect of PE xSPEN’s extreme downsampling ability, by comparing its g-maps5 with those of a 2D TSE acquisition for an acceleration of 6. Figure 4b clearly demonstrates the weaker artifacts appearing in the PE xSPEN (x,y) plane upon acceleration, while Fig. 4c rationalizes this by showing the much smaller g-factors of this new scheme. Figure 4d completes this picture by showing how these g-factor maps change for different kz acquisition points; although spatially- and kz-dependent, these g-factors always remain lower than those of TSE downsampled acquisitions.


A new, highly accelerated approach to 3D MRI acquisitions based on phase encoded xSPEN was introduced, capable of delivering sub-millimeter resolutions in whole head 3D images within 2 min, with excellent SNR and free of aliasing artifacts. Further improvements including compressed sensing, SENSE-based reconstruction and multibanding, are currently in progress.


Funding by the Israel Science Foundation grant 2508/17, ERC-2016-PoC grant # 751106, and the Kimmel Institute of Magnetic Resonance (Weizmann Institute) is acknowledged. ZZ thanks Israel’s Council of Higher Education and the Koshland Foundation for postdoctoral fellowships. ML acknowledges a Visiting Faculty Program Fellowship (Weizmann). We are also grateful to Dr. Sagit Shushan (Wolfson MC) and to the Weizmann MRI team (Edna Furman-Haran, Fanny Attar and Nachum Stern).


1. Zhang Z., Seginer A ., Frydman L., Single-scan magnetic resonance imaging with exceptional resilience to field heterogeneities, Magn Reson Med 2017;77: 623–634

2. Zhang Z, Lustig M. Frydman L., High resolution imaging by phase encoded xSPEN MRI, Proceedings of 25th ISMRM, Honolulu, USA, April 22-27, 2017; Zhang Z, Lustig M. Frydman L., Phase-encoded xSPEN: A novel high-resolution volumetric alternative to RARE and spin-echo EPI, Magn Reson Med 2017 (in revision).

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Fig. 1 Single-shot xSPEN sequence1 delivering x-axis profiles via an EPI-like oscillation and y-axis information using a Gz constant readout gradient. (b) Extension to a multi-scan, phase-encoded xSPEN sequence2 capable of delivering quality 3D images by Fourier analysis along all k-axes. (c,d) Relation between an object and its k-space response in a conventional acquisition (c) versus the k-space response for the same object subject to xSPEN’s hyperbolic-phase kernel encoding. Notice the low-resolution, 90˚-rotated rendition of the object being imaged given by xSPEN’s k-space data.

Fig. 2 Differences between a conventional GRAPPA reconstruction3 applied on a traditional (a) and on xSPEN (b) k-space acquisitions. These simulations (based on rotating a Shepp-Logan phantom along the z axis) assumed an acceleration factor of 6 along PE (ky) dimension on an 8-channel head coil setting. Notice the remarkable artifact-free images reconstructed from PE xSPEN imaging despite the significant downsampling.

Fig. 3 Comparisons between the multi-slab 3D TSE and 3D PE xSPEN acquisitions on a water phantom and on a human head. All the downsampling acquisitions were retrospectively produced from the fully sampled counterparts collected at a resolution of 1×1×0.5 mm3. Reconstruction was done by GRAPPA3, keeping in all cases full sampling of the 12 central ky lines for self-calibration.

Fig. 4 Geometry factor performance on 2D TSE and PE xSPEN acquisition with an acceleration of 6. (a) Fully-sampled reference images collected with an isotropic resolution of 0.75 mm3 for PE xSPEN and of 0.75×0.75×3 mm3 for 2D TSE (to make up for its inferior SNR). (b) Reconstructed images for an acceleration of 6. (c) g-factor maps based on the pseudo-replica method5. While a single g-factor map is obtained in 2D TSE, g-factor maps are different for different kz lines in PE xSPEN acquisition (d). The PE xSPEN g-factor map shown in (c) corresponds to the central kz line.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)