3D rigid‐body motion information from spherical Lissajous navigators at small k‐space radii: A proof of concept

Purpose To demonstrate, for the first time, the feasibility of obtaining low‐latency 3D rigid‐body motion information from spherical Lissajous navigators acquired at extremely small k‐space radii, which has significant advantages compared with previous techniques. Theory and Methods A spherical navigator concept is proposed in which the surface of a k‐space sphere is sampled on a 3D Lissajous curve at a radius of 0.1/cm. The navigator only uses a single excitation and is acquired in less than 5 ms. Rotation estimations were calculated with an algorithm from computer vision that exploits a rotation theorem of the spherical harmonics transform and has minimal computational cost. The effectiveness of the concept was investigated with phantom and in vivo measurements on a commercial 3T MRI scanner. Results Scanner‐induced in vivo motion was measured with maximum absolute errors of 0.58° and 0.33 mm for rotations and translations, respectively. In the case of real, in vivo motion, the proposed method showed good agreement with motion information from FSL image registrations (mean/maximum deviations of 0.37°/1.24° and 0.44 mm/1.35 mm). In addition, phantom measurements indicated precisions of 0.014° and 0.013 mm. The computations for complete motion information took, on average, 24 ms on an ordinary laptop. Conclusions This work demonstrates a proof of concept for obtaining accurate motion information from small‐radius spherical navigators. The method has the potential to overcome several previously reported problems and could help increase the utility of navigator‐based motion correction both in research and in the clinic.