A new design and rationale for 3D orthogonally oversampled k‐space trajectories

A novel center‐out 3D trajectory for sampling magnetic resonance data is presented. The trajectory set is based on a single Fermat spiral waveform, which is substantially undersampled in the center of k‐space. Multiple trajectories are combined in a “stacked cone” configuration to give very uniform sampling throughout a “hub,” which is very efficient in terms of gradient performance and uniform trajectory spacing. The fermat looped, orthogonally encoded trajectories (FLORET) design produces less gradient‐efficient trajectories near the poles, so multiple orthogonal hub designs are shown. These multihub designs oversample k‐space twice with orthogonal trajectories, which gives unique properties but also doubles the minimum scan time for critical sampling of k‐space. The trajectory is shown to be much more efficient than the conventional stack of cones trajectory, and has nearly the same signal‐to‐noise ratio efficiency (but twice the minimum scan time) as a stack of spirals trajectory. As a center‐out trajectory, it provides a shorter minimum echo time than stack of spirals, and its spherical k‐space coverage can dramatically reduce Gibbs ringing. Magn Reson Med, 2011. © 2011 Wiley Periodicals, Inc.