Registering spherical navigators with spherical harmonic expansions to measure three-dimensional rotations in magnetic resonance imaging

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.

Combination of multidimensional navigator echoes data from multielement RF coil

Until now, only one-dimensional navigator-echo techniques have been implemented with multielement RF coils. For the multidimensional navigator echoes, which extract six-degree of freedom motion information from the raw k-space data, an efficient raw data combination approach is needed. In this work, three combination approaches, including summation of the complex raw data, summation following phase alignment, and summation of the squares of the k-space magnitude profiles, were evaluated with the spherical navigator echoes (SNAV) technique. In vivo brain imaging experiments were used to quantify accuracy and precision and demonstrated that SNAVs acquired with an eight-channel head coil can determine the rotation and translation in range up to 10° and 20 mm with subdegree and submillimeter accuracy, respectively. Results from a 3D brain volume realignment experiment showed excellent agreement between baseline images and SNAV-aligned follow-up volumes.

Rapid six-degree-of-freedom motion detection using prerotated baseline spherical navigator echoes

A new spherical navigator echo (SNAV) registration technique is presented. This technique starts by collecting a set of SNAV templates at a reference position. These templates are acquired by rotating the gradient system to result in rotation angles that uniformly cover a predefined range of rotation. The rotation angles between an unknown physically transformed position and the reference position are subsequently determined by finding the template with the lowest sum of squared differences with SNAV at the transformed position. Translations are calculated from the phase differences between the best-match SNAV template and the SNAV acquired at the transformed position. In comparison with the conventional SNAV registration technique, the proposed technique is noniterative, robust, and can detect 3-dimensional rigid body motion in less than 50 msec. The technique was verified with phantom and in vivo experiments, which demonstrated subdegree rotational and submillimeter translational accuracy over a range of simultaneous ±20° and ±10° mm of motion.