Nonrigid 3D motion estimation at high temporal resolution from prospectively undersampled k-space data using low-rank MR-MOTUS

Purpose With the recent introduction of the MR-LINAC, an MR-scanner combined with a radiotherapy LINAC, MR-based motion estimation has become of increasing interest to (retrospectively) characterize tumor and organs-at-risk motion during radiotherapy. To this extent, we introduce low-rank MR-MOTUS, a framework to retrospectively reconstruct time-resolved nonrigid 3D+t motion fields from a single low-resolution reference image and prospectively undersampled k-space data acquired during motion. Theory Low-rank MR-MOTUS exploits spatiotemporal correlations in internal body motion with a low-rank motion model, and inverts a signal model that relates motion fields directly to a reference image and k-space data. The low-rank model reduces the degrees-of-freedom, memory consumption, and reconstruction times by assuming a factorization of space-time motion fields in spatial and temporal components. Methods Low-rank MR-MOTUS was employed to estimate motion in 2D/3D abdominothoracic scans and 3D head scans. Data were acquired using golden-ratio radial readouts. Reconstructed 2D and 3D respiratory motion fields were, respectively, validated against time-resolved and respiratory-resolved image reconstructions, and the head motion against static image reconstructions from fully sampled data acquired right before and right after the motion. Results Results show that 2D+t respiratory motion can be estimated retrospectively at 40.8 motion fields per second, 3D+t respiratory motion at 7.6 motion fields per second and 3D+t head-neck motion at 9.3 motion fields per second. The validations show good consistency with image reconstructions. Conclusions The proposed framework can estimate time-resolved nonrigid 3D motion fields, which allows to characterize drifts and intra and inter-cycle patterns in breathing motion during radiotherapy, and could form the basis for real-time MR-guided radiotherapy.