Xucheng Zhu^{1,2}, Kevin Johnson^{3,4}, and Peder Larson^{1,2}

^{1}Radiology and Biomedical Imaging, University of California, San Francisco, San Francisco, CA, United States, ^{2}UC Berkeley-UCSF Graduate Program in Bioengineering, University of California, San Francisco and University of California, Berkeley, Berkeley, CA, United States, ^{3}Medical Physics, University of Wisconsin, Madison, Madison, WI, United States, ^{4}Radiology, University of Wisconsin, Madison, Madison, WI, United States

Center-out sequence has natural spoiling effect, called “self” spoiling. By leveraging this idea, the standard large spoiler gradient could be reduced or removed without sacrificing the image quality. In this study, we investigated how 3D radial trajectory ordering affects spoiling, and proposed a reordered 2D golden angle scheme to maximize “self” spoiling effect and retain robustness to free breathing scan. We evaluated the proposed ordering scheme on both phantom and volunteer. Proposed scheme without or with small spoiler gradient can reduce up to 40% scan time to get comparable image quality.

A basic center-out sequence and its corresponding k-space trajectory are in Fig.1(a,b), where the k-space sampling space is within the mesh sphere. In each TR, k-space sampling starts from center to edge of the k-space boundary. In the next TR, effectively, the previous spatial encoding gradient serves as a natural spoiler gradient, named “self” spoiling, with spoiling moment $$$\pi$$$. In a continuous acquisition, “self” spoiling is affected by trajectory pattern design of adjacent TRs. For instance, two 3D randomly generated sampling patterns with similar k-space coverages are plotted in Fig.1(c) and (d). According to the spoiling moment plots, the more continuous trajectory(d) creates larger spoiling moments in the subsequent TRs compared to random ordering(c).

In this work, we focus on the small-tip(<6°) center-out radial ultra-short TE(UTE) sequence application. Two major criteria should be considered in trajectory ordering design. Firstly, residual transverse magnetization should be spoiled in the following TRs. Secondly, pseudo-random k-space sampling ordering should be used to tolerate subject motion. We propose a reordered 2D golden angle(r2DGA) scheme to fulfill the two criteria. Firstly, a 3D sequentially sampling pattern is designed. Then, the acquisition orders are binned in different 2D golden angle groups(kx-ky plan). In each group, subgroup spokes are sorted by kz location. Sequential acquisition and 3D golden angle(3DGA) are used for comparison. The pseudo-code for all three schemes are summarized in Fig.2(a).1000 spokes from the full scan(100k spokes) with different sampling schemes are plotted in Fig.2(b), r2DGA scheme more uniformly samples the k-space, compared to sequential scheme, but less uniformly than 3DGA. However, reordered r2DGA scheme has the largest “self” spoiling moments among the three schemes, Fig.2(c).

Experiments were run on 3T GE Signa 750 (General Electric, Milwaukee, WI) with an 8-channel cardiac coil. An optimized variable density readout center-out radial sequence with 100,000 radial spokes was used in all experiments. For phantom study, data were acquired with isotropic FOV 20cm, image matrix size 200x200x200, TE=100μs, sampling bandwidth=125kHz, image was reconstructed by NUFFT. For volunteer study, data were acquired with isotropic FOV 32cm, image matrix size 256x256x256, image is reconstructed by soft-gated reconstruction

Fig.4 shows the effects of different levels spoiling moments on the image with r2DGA ordering. The apparent SNR(aSNR) largely increases when a very small spoiler gradient is added to the sequence, and the previous noise-like artifacts are largely suppressed. As the spoiler gradient moment increases, aSNR slightly increases, however the total scan time(TA) largely increases. Line profiles(red dash line in (a)) from each scan are plotted in (b). With the proposed ordering, spoiler gradient could be largely reduced by leveraging the “self” spoiling.

Fig.5 shows the volunteer studies. The r2DGA scheme without spoiler can reduce 40% scan time to get comparable image quality compared to the reference in (a), however, some small structures are invisible in maximum intensity projection(MIP), (b). By adding $$$\pi$$$ moment spoiler gradient, the noise-like artifacts are suppressed in (a) and smaller vessels could be delineated even compared to reference. In addition, 20% less scan time is required compared to the reference scan.

[1] Pipe, J. G. (1999). An optimized center‐out k‐space trajectory for multishot MRI: comparison with spiral and projection reconstruction. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, 42(4), 714-720.

[2] Johnson, K. M., Fain, S. B., Schiebler, M. L., & Nagle, S. (2013). Optimized 3D ultrashort echo time pulmonary MRI. Magnetic resonance in medicine, 70(5), 1241-1250.

[3] Feng, L., Grimm, R., Block, K. T., Chandarana, H., Kim, S., Xu, J., ... & Otazo, R. (2014). Golden‐angle radial sparse parallel MRI: combination of compressed sensing, parallel imaging, and golden‐angle radial sampling for fast and flexible dynamic volumetric MRI. Magnetic resonance in medicine, 72(3), 707-717.

[4] Chan, R. W., Ramsay, E. A., Cunningham, C. H., & Plewes, D. B. (2009). Temporal stability of adaptive 3D radial MRI using multidimensional golden means. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, 61(2), 354-363.

[5] Piccini, D., Littmann, A., Nielles‐Vallespin, S., & Zenge, M. O. (2011). Spiral phyllotaxis: the natural way to construct a 3D radial trajectory in MRI. Magnetic resonance in medicine, 66(4), 1049-1056.

[6] Leupold, J., Hennig, J., & Scheffler, K. (2008). Moment and direction of the spoiler gradient for effective artifact suppression in RF‐spoiled gradient echo imaging. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, 60(1), 119-127.

[7] Jiang, W., Ong, F., Johnson, K. M., Nagle, S. K., Hope, T. A., Lustig, M., & Larson, P. E. (2018). Motion robust high resolution 3D free‐breathing pulmonary MRI using dynamic 3D image self‐navigator. Magnetic resonance in medicine, 79(6), 2954-2967.

Figure1.Center-out radial sequence and “self” spoiling effect mechanism. Simple center-out spoiled gradient sequence is plotted in (a). The corresponding k-space trajectories are shown in (b). N^{th} excitation k-space sampling starts from center(blueline) and ends on the sphere, in (n+1)^{th} excitation, the spatial encoding gradient creates $$$\pi$$$ spoiling moment(yellow line). Two different 3D acquisition trajectory ordering, and their corresponding sequence and cumulative spoiling moments are plotted in (c) and (d).

Figure2. Trajectory design and ordering scheme and the ”self” spoiling effect. Pseudo code to generate acquisition trajectory schemes are summarized in (a). 1000 continuous spokes are plotted in (b), sequential acquisition only covers small part of k-space, however, r2DGA and 3DGA schemes cover the k-space more uniformly. Cumulative spoiling moment created by different schemes in the subsequent TRs are plotted in (c), sequential and r2DGA schemes creates much larger spoiling moments than 3DGA.

Figure3. Phantom study. Image acquired with 3DGA with $$$4\pi$$$ spoiling moment spoiler is shown in (a), with r2DGA without spoiler gradient in (b), 3DGA without spoiler gradient in (c). Compared to reference scan, image acquired with r2DGA ordering has very light noise-like artifacts, 3DGA without spoiler gradient shows strong artifacts compared to the other two.

Figure4. Phantom study with different spoiler gradient using r2DGA scheme. In (a), spoiler gradient with different spoiling moments are compared, as spoiling moment scale increases, scan time and apparent SNR increases. Line profile(red dash line plotted in (a)) are compared in (b).

Figure5. Volunteer study result. One coronal slice of 3D volume with different ordering schemes are shown in (a), r2DGA w/o spoiler is slightly noisier than the reference scan, but reduce 40% total scan time. 30 coronal slices maximum intensity projection(MIP) from each volume are plotted in (b), r2DGA with small spoiling gradient delineates most small vessels and has a relative shorter scan time.