Joao Tourais^{1,2}, Guruprasad Krishnamoorthy^{1,2}, Marc Kouwenhoven^{1}, Jouke Smink^{1}, and Marcel Breeuwer^{1,2}

Radial sampling techniques are often used in dynamic MRI because they are robust to flow and motion, support short echo times, and have a diffuse aliasing pattern. However, standard implementations of radial imaging do not support in-plane anisotropic FOV, which leads to sampling redundancy when the object being imaged has anisotropic in-plane dimensions (e.g. abdomen, chest, spine, leg, etc.). In this work we demonstrate the feasibility of 3D golden angle stack-of-stars acquisition with an in-plane anisotropic FOV in abdominal acquisitions.

Larson et al.^{7} provided a scheme for supporting anisotropic FOV in 2D and 3D radial imaging and Wu et al.^{8} showed that conventional 2D golden angle sampling can be organized in an angle-normalized space and converted back to k-space such that the chosen non-uniform spoke density is preserved for arbitrary temporal window length. In conventional 3D GA-SOS, the angles have a uniform distribution because the consecutive acquired spokes are equally spaced (i.e. golden ratio Ɵ(i)=mod[2i/(1+√5),1]*π,i=0,…,N). By using the Larson method^{7}, a fully sampled radial anisotropic FOV is computed θ_{full}(n). Lastly, with Wu approach^{8} θ(i) of the i^{th} GA spoke was computed as θ(i)=θ_{full} [A(i)]+D(i)*∆θ_{full} [A(i)], where A(i)=floor[ind_{ga}(i)],D(i)=golden_{ratio}(i) - A(i). In the case of 3D GA-SOS the
computed radial angular distribution was repeated for every phase encoding step
in the slice direction.

We illustrate this generalized mapping approach using an elliptical in-plane FOV for 3D GA-SOS. Trajectory simulations, point-spread-function (PSF) and spoke density analysis was performed. The proposed sampling scheme approach was implemented on a 1.5T Ingenia (Philips Healthcare, Best, NL). Phantom data and in-vivo axial abdominal images were acquired using a T1-TFE fat-suppressed navigator-gated 3D GA-SOS sequence in three healthy volunteers. The proposed method with elliptical FOV were compared against the isotropic FOV. Imaging parameters: FOV: 450 x 450 x 400 mm^{3} (fully-sampled and undersampled isotropic FOV) or 450 x 200 x 400 mm^{3} (anisotropic FOV), Resolution: 1 x 1 x 3 mm^{3}, SENSE factor: 2, Half-scan factor: 0.8, Flip Angle: 10°, TR/TE: 3.3/1.34 ms, prescribed scan time was 2:03 min (fully-sampled isotropic FOV) and 1:06 min (anisotropic FOV and undersampled isotropic FOV). The sampling pattern generation and the reconstruction were performed online in the scanner. Sampling density compensation factor was calculated and taken into account during the reconstruction pipeline.

- Robson, M. D., Gatehouse, P. D., Bydder, M., Bydder, G. M. (2003). Magnetic resonance: an introduction to ultrashort TE (UTE) imaging. J Comput Assist Tomogr., 27(6):825-46.
- Nishimura, D. G., Jackson, J. I. and Pauly, J. M. (1991), On the nature and reduction of the displacement artifact in flow images. Magn. Reson. Med., 22: 481–492. doi:10.1002/mrm.1910220255
- Glover, G. H. and Pauly, J. M. (1992), Projection Reconstruction Techniques for Reduction of Motion Effects in MRI. Magn. Reson. Med., 28: 275–289. doi:10.1002/mrm.1910280209
- Han, F., Zhou, Z., Rapacchi, S., Nguyen, K.-L., Finn, J. P., & Hu, P. (2016). Segmented Golden Ratio Radial Reordering with Variable Temporal Resolution for Dynamic Cardiac MRI. Magnetic Resonance in Medicine, 76(1), 94–103. http://doi.org/10.1002/mrm.25861
- Feng, L., Axel, L., Chandarana, H., Block, K. T., Sodickson, D. K., & Otazo, R. (2016). XD-GRASP: Golden-Angle Radial MRI with Reconstruction of Extra Motion-State Dimensions Using Compressed Sensing. Magnetic Resonance in Medicine, 75(2), 775–788. http://doi.org/10.1002/mrm.25665
- Song, H. K., Yan, L., Smith, R. X., Xue, Y., Rapacchi, S., Srinivasan, S., … Wang, D. J. (2014). Non-Contrast Enhanced 4-D Dynamic MRA with Golden Angle Radial Acquisition and K-space Weighted Image Contrast (KWIC) Reconstruction. Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 72(6), 1541–1551. http://doi.org/10.1002/mrm.25057
- Larson PEZ, Gurney PT, Nishimura DG. "Anisotropic Field-of-Views in Radial Imaging." IEEE Transactions on Medical Imaging2008; 27(1): 47-57.
- Wu, Z., Han, F., Hu, P., & Nayak, K. S. (2016). Anisotropic Field-of-View support for Golden Angle Radial Imaging. Magnetic Resonance in Medicine, 76(1), 229–236. http://doi.org/10.1002/mrm.25898

Point Spread Functions (PSF) for the isotropic in-plane FOV with GA sampling (A) and for anisotropic (elliptical) FOV with GA sampling (B). In the anisotropic FOV (Figure 2B) is possible to observe the major and minor axis of the desired ellipse.

Simulations of the trajectories for 3D GA-SOS with isotropic in-plane FOV (A) and anisotropic (elliptical) in-plane FOV (B). C-D) Detail of one slice encoding for the same approaches. E-F) Trajectories obtained from the acquired raw data.

Abdominal
axial slices of one volunteer acquired using: A) the fully-sampled conventional isotropic FOV 3D
GA-SOS, B) the proposed anisotropic (elliptical) in-plane FOV
3D GA-SOS approach and C) the undersampled isotropic FOV 3D GA-SOS with matched scan time as in the case B. The white dotted line in the images represents
the effective field-of- view. The image quality between A and B is comparable although B is significantly faster. In C due to undersampling, streaking artifacts are more pronounced. The prescribed scan time for each acquisition is under the respective images.