MR-MOTUS: model-based non-rigid motion estimation for MR-guided radiotherapy using a reference image and minimal k-space data

Time-resolved motion estimation from MRI data has received an increasing amount of interest due to the advent of the MR-Linac. The combination of an MRI scanner and a linear accelerator enables radiation plan adaptation based on internal organ motion estimated from MRI data. However, time-resolved estimation of this motion from MRI data still remains a challenge. In light of this application, we propose MR-MOTUS, a framework to estimate non-rigid 3D motion from minimal k-space data. MR-MOTUS consists of two main components: (1) a signal model that explicitly relates the k-space signal of a deforming object to non-rigid motion-fields and a reference image, and (2) model-based reconstructions of the non-rigid motion-fields directly from k-space data. Using an a priori available reference image and the fact that internal body motion exhibits a high level of spatial correlation, we represent the motion-fields in a low-dimensional space and reconstruct them from minimal k-space data that can be acquired very rapidly. The signal model is validated through numerical experiments with a digital 3D phantom and motion-fields are reconstructed from retrospectively undersampled in vivo head and abdomen data using various undersampling strategies. A comparison is made with state-of-the-art image registration performed on images reconstructed from the same undersampled data. Results show that MR-MOTUS reconstructs in vivo 3D rigid head motion from 474-fold retrospectively downsampled k-space data, and in vivo non-rigid 3D respiratory motion from 63-fold retrospectively undersampled k-space data. Preliminary results on prospectively undersampled data acquired with a 2D golden angle acquisition during free-breathing demonstrate the practical feasibility of the method.