Three‐dimensional Yarnball k‐space acquisition for accelerated MRI

Abstract

To introduce an efficient sampling technique named Yarnball, which may serve as a direct alternative to 3D Cones. Methods: Yarnball evolves through 3D k-space with increasing loop size, and the differential equations defining this flexible trajectory are presented in detail. The sampling efficiencies of Yarnball and 3D Cones were compared through point spread function analysis and simulated imaging (which highlights undersampling in the absence of other scanning effects). The feasibility of Yarnball implementation was demonstrated for fully sampled T 1-weighted images of the human head at 3 T. Results: The mostly large 3D loops of the Yarnball trajectory facilitate rapid sampling under peripheral nerve stimulation constraint, an advantage that increases with readout duration (T RO). Point spread function analysis yielded 89% (T RO = 2 ms) and 77% (T RO = 10 ms) of Yarnball voxels with magnitude less than 0.01% of the point spread function peak. For 3D Cones, these values were only 52% and 29%. The 3D-Cones technique required 1.4 times (T RO = 2 ms) and 1.8 times (T RO = 10 ms) more trajectories than Yarnball to produce simulated images of a sphere free from undersampling artifact. For a prolate spheroidal (head-like) object, 1.75 times and 2.6 times more trajectories were required for 3D Cones. Yarnball produced 0.72 mm (1/2k max) isotropic T 1-weighted human brain images free from undersampling artifact in only 98 seconds at 3 T. Conclusion: Yarnball demonstrated greater k-space sampling efficiency than directly comparable 3D Cones, and may have value wherever 3D Cones has been considered. Yarnball may also have value in the context of rapid T 1-weighted brain imaging.

Quantification of lung water density with UTE Yarnball MRI

“…The length of each Yarnball trajectory through k‐space is controlled with the design parameter ρ . Smaller ρ yields longer k‐space trajectories with more winds and increased k‐space coverage per excitation, as previously described 24 . Maximum gradient slew rates and peripheral nerve stimulation constrain ρ for a given readout duration (T RO ), where increased T RO improves efficiency (more sampling per excitation) but is limited by signal decay and artifacts from off‐resonance effects.…”

“…2.1 | Yarnball k-space trajectories for lung imaging: design and numerical simulations Yarnball trajectories wind outward from the center of 3D kspace with sampling immediately following excitation to facilitate UTE acquisitions similar to 3D radial acquisitions. 24 The use of nonlinear trajectories enables increased k-space sampling per excitation, yielding improved acquisition efficiency as compared with 3D radial acquisitions. The length of each Yarnball trajectory through k-space is controlled with the design parameter ρ.…”

“…Smaller ρ yields longer k-space trajectories with more winds and increased k-space coverage per excitation, as previously described. 24 Maximum gradient slew rates and peripheral nerve stimulation constrain ρ for a given readout duration (T RO ), where increased T RO improves efficiency (more sampling per excitation) but is limited by T * 2 signal decay and artifacts from off-resonance effects. Thus, the Yarnball approach offers trajectories that use the maximum available gradient performance at all readout times and consideration of acceptable T RO to offer maximum sampling efficiency for targeted applications.…”

“…Yarnball trajectories wind outward from the center of 3D kspace with sampling immediately following excitation to facilitate UTE acquisitions similar to 3D radial acquisitions. 24 The use of nonlinear trajectories enables increased k-space sampling per excitation, yielding improved acquisition efficiency as compared with 3D radial acquisitions. The length of each Yarnball trajectory through k-space is controlled with the design parameter ρ.…”

“…A recently developed optimized k‐space sampling approach called Yarnball was illustrated for application in the brain 24 with improved efficiency as compared with other trajectories such as 3D radial and 3D cones 25 . The goal of the current study was to develop a Yarnball UTE k‐space pulse sequence for efficient and quantitative imaging of LWD.…”