# Real-time non-rigid 3D respiratory motion estimation for MR-guided radiotherapy using MR-MOTUS

arXiv: https://arxiv.org/abs/2104.07957 · HTML: https://mlsanity.com/paper/2104.07957/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Apr 2021.

## Built on by (most cited first, 3 of 3)

- [Spatiotemporal Gaussian representation-based dynamic reconstruction and motion estimation framework for time-resolved volumetric MR imaging (DREME-GSMR)](https://mlsanity.com/paper/2604.06482/) (2026)
- [Highly efficient non-rigid registration in k-space with application to cardiac Magnetic Resonance Imaging](https://mlsanity.com/paper/2410.18834/) (2024)
- [Low-Rank Velocity Fields as a Structural Prior for Unsupervised 4D Medical Image Interpolation](https://mlsanity.com/paper/2608.24025/) (2026)

## Abstract (arXiv)

The MR-Linac is a combination of an MR-scanner and radiotherapy linear accelerator (Linac) which holds the promise to increase the precision of radiotherapy treatments with MR-guided radiotherapy by monitoring motion during radiotherapy with MRI, and adjusting the radiotherapy plan accordingly. Optimal MR-guidance for respiratory motion during radiotherapy requires MR-based 3D motion estimation with a latency of 200-500 ms. Currently this is still challenging since typical methods rely on MR-images, and are therefore limited by the 3D MR-imaging latency. In this work, we present a method to perform non-rigid 3D respiratory motion estimation with 170 ms latency, including both acquisition and reconstruction. The proposed method called real-time low-rank MR-MOTUS reconstructs motion-fields directly from k-space data, and leverages an explicit low-rank decomposition of motion-fields to split the large scale 3D+t motion-field reconstruction problem posed in our previous work into two parts: (I) a medium-scale offline preparation phase and (II) a small-scale online inference phase which exploits the results of the offline phase for real-time computations. The method was validated on free-breathing data of five volunteers, acquired with a 1.5T Elekta Unity MR-Linac. Results show that the reconstructed 3D motion-field are anatomically plausible, highly correlated with a self-navigation motion surrogate (R = 0.975 +/- 0.0110), and can be reconstructed with a total latency of 170 ms that is sufficient for real-time MR-guided abdominal radiotherapy.