Stack-of-stars sampling is an attractive 3D MRI acquisition scheme combining radial and Cartesian trajectories ¹. The radial encoding in the k_x-k_y plane offers reduced sensitivity to motion ² and increased incoherence for the application of compressed sensing methods ³, while the Cartesian-encoding along the slice dimension (k_z) ensures sufficient fat suppression, low sensitivity to eddy currents, and parallel reconstruction of different slices after performing a FFT along k_z. GRASP (Golden-angle RAdial Sparse Parallel MRI ³) has been previously proposed for rapid and continuous free-breathing imaging combining multicoil sparse reconstruction with a golden-angle stack-of-stars sampling scheme; and it has been further extended into XD-GRASP (eXtra-Dimensional GRASP ⁴), where an extra motion-resolved dynamic dimension is reconstructed using a multidimensional sparse technique. However, the conventional stack-of-stars trajectory used in these cases was implemented with fully-sampled Cartesian phase-encoding; and therefore slice resolution had to be sacrificed in order to maintain sufficient slice coverage and in-plane resolution in dynamic MRI applications. Meanwhile, the exploitation of incoherence was also limited to the k_x-k_y plane for sparse reconstruction. Although XD-GRASP has also been extended to 3D radial sampling implemented with a “kooshball” pattern ⁵ for isotropic spatial resolution and coverage, challenges for such a sampling pattern (in this case a spiral phyllotaxis pattern ⁶) suffers from insufficient fat saturation and increased sensitivity to eddy currents, as well as reduced SNR due to intrinsically isotropic spatial resolution, all of which may preclude some clinical applications such as DCE-MRI. In this work, we propose a new XD-GRASP framework using a stack-of-stars sampling scheme with variable-density k_z-undersampling. This new imaging framework, called variable-density XD-GRASP, integrates the advantages of conventional stack-of-stars sampling and 3D radial sampling, enabling motion-resolved continuous 3D imaging with flexible slice resolution within a given scan time.

(i) Variable-Density Stack-of-Stars Sampling: Fig.1a shows the k_z-t sampling patterns corresponding to conventional stack-of-stars (left) and variable-density stack-of-stars (right) trajectories for the same number of k-space points, where an in-plane (k_x-k_y) radial spoke rotating at golden-angle (111.25^o) ⁷ is acquired for each k_z-t point. The varying k_z random undersampling pattern in the variable-density stack-of-stars pattern breaks the regularity of conventional stack-of-stars, thus higher slice resolution can be achieved within the same scan time using a multidimensional sparse reconstruction that exploits additional sparsity and incoherence along the slice dimension. The central region (e.g., 12 lines) in the variable-density stack-of-stars pattern is fully sampled, so that respiratory motion can be extracted from the corresponding z-direction projection profiles (Fig.1b-c), which is obtained by performing a FFT along the fully sampled central k_z points (red lines in Fig.1b). XD-GRASP reconstruction, as described in ref [4], can then be performed to reconstruct a motion-resolved image set exploiting correlations along all the spatial dimensions and the extra motion dimension.

(ii) Image Acquisition and Reconstruction: IRB-approved liver MRI was performed on 4 healthy volunteers in transverse orientation using a GRE sequence on a 3T scanner (Siemens Prisma). Three volunteers underwent non-contrast scans using both conventional golden-angle stack-of-stars sampling (Fig.2, imaging protocol a) and variable-density golden-angle stack-of-stars sampling with different z-direction resolutions (Fig.2 imaging protocol b&c). The same number of spokes were acquired with constant acquisition time (protocols a-c). For the fourth volunteer, DCE-MRI of the liver was performed with variable-density golden-angle stack-of-stars sampling using imaging protocol d (Fig.2). For non-contrast imaging, XD-GRASP reconstruction was performed with 4 respiratory motion phases, resulting in a 4D image set (x-y-z-respiration). For contrast-enhanced imaging, XD-GRASP reconstruction was performed with 12 contrast phases and 4 respiratory motion phases, resulting in a 5D image set (x-y-z-contrast-respiration). GRASP reconstruction without motion sorting was performed with 12 contrast phases on the DCE dataset for a head-to-head comparison.

Fig.3 compares conventional XD-GRASP to variable-density XD-GRASP with two different slice resolutions. Although respiratory motion can be resolved in all the images, improved sharpness can clearly be appreciated in variable-density XD-GRASP. Fig.4 shows the variable-density XD-GRASP images at different respiratory states from another volunteer, with significantly improved image quality comparing to standard NUFFT reconstruction without motion sorting. Fig.5 shows DCE-liver images at two contrast-enhancement phases, which demonstrate superior delineation of liver vessels when compared with variable-density GRASP without motion sorting.Variable-density XD-GRASP represents a robust method for rapid and continuous volumetric MRI. The new sampling approach combines the benefits of both stack-of-stars radial sampling and kooshball-type 3D radial sampling, enabling flexible slice resolution with robust and sufficient fat suppression and low sensitivity to eddy currents. Respiratory motion can be extracted directly from k-space data for motion-resolved sparse reconstruction.