Using the axis of rotation of polar navigator echoes to rapidly measure 3D rigid‐body motion

Abstract

An improved technique to prospectively correct three-dimensional rigid-body motion using polar spherical navigator (pNAV) echoes is presented. The technique is based on acquiring pNAVs of an object in a baseline and rotated position and determining the axis of rotation (AOR) between data sets, thereby reducing 3D rotations to a 2D, planar rotation. Finding the AOR is simplified by prerotating the baseline trajectory, which forces the axis to lie within a specific polar region of a spherical shell in k-space. Orbital navigator echoes are interpolated from the pNAV data in planes orthogonal to the AOR and cross-correlated to determine the 2D rotation. The rotation about the AOR is used in conjunction with its orientation to calculate the overall 3D rotation. The pNAV-AOR technique was tested for its precision, accuracy, and processing speed in detecting compound rotations and translations of varying magnitude. In comparison to the spherical navigator echo technique, the pNAV-AOR technique is noniterative, fast, and independent of rotation magnitude and direction. At low SNR, the technique can detect compound rotations to 0.5 degrees accuracy in an estimated 100 msec, indicating that prospective 3D rigid-body motion correction may be feasible with this technique.