Gaussian Processes for real-time 3D motion and uncertainty estimation during MR-guided radiotherapy

Respiratory motion during radiotherapy causes uncertainty in the tumor's location, which is typically addressed by an increased radiation area and a decreased dose. As a result, the treatments' efficacy is reduced. The recently proposed hybrid MR-linac scanner holds the promise to efficiently deal with such respiratory motion through real-time adaptive MR-guided radiotherapy (MRgRT). For MRgRT, motion-fields should be estimated from MR-data and the radiotherapy plan should be adapted in real-time according to the estimated motion-fields. All of this should be performed with a total latency of maximally 200 ms, including data acquisition and reconstruction. A measure of confidence in such estimated motion-fields is highly desirable, for instance to ensure the patient's safety in case of unexpected and undesirable motion. In this work, we propose a framework based on Gaussian Processes to infer 3D motion-fields and uncertainty maps in real-time from only three readouts of MR-data. We demonstrated an inference frame rate up to 69 Hz including data acquisition and reconstruction, thereby exploiting the limited amount of required MR-data. Additionally, we designed a rejection criterion based on the motion-field uncertainty maps to demonstrate the framework's potential for quality assurance. The framework was validated in silico and in vivo on healthy volunteer data (n=5) acquired using an MR-linac, thereby taking into account different breathing patterns and controlled bulk motion. Results indicate end-point-errors with a 75th percentile below 1 mm in silico, and a correct detection of erroneous motion estimates with the rejection criterion. Altogether, the results show the potential of the framework for application in real-time MR-guided radiotherapy with an MR-linac.

Real-Time Non-Rigid 3D Respiratory Motion Estimation for MR-Guided Radiotherapy Using MR-MOTUS

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.

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.

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.

Opening a new window on MR-based Electrical Properties Tomography with deep learning

In the radiofrequency (RF) range, the electrical properties of tissues (EPs: conductivity and permittivity) are modulated by the ionic and water content, which change for pathological conditions. Information on tissues EPs can be used e.g. in oncology as a biomarker. The inability of MR-Electrical Properties Tomography techniques (MR-EPT) to accurately reconstruct tissue EPs by relating MR measurements of the transmit RF field to the EPs limits their clinical applicability. Instead of employing electromagnetic models posing strict requirements on the measured MRI quantities, we propose a data driven approach where the electrical properties reconstruction problem can be casted as a supervised deep learning task (DL-EPT). DL-EPT reconstructions for simulations and MR measurements at 3 Tesla on phantoms and human brains using a conditional generative adversarial network demonstrate high quality EPs reconstructions and greatly improved precision compared to conventional MR-EPT. The supervised learning approach leverages the strength of electromagnetic simulations, allowing circumvention of inaccessible MR electromagnetic quantities. Since DL-EPT is more noise-robust than MR-EPT, the requirements for MR acquisitions can be relaxed. This could be a major step forward to turn electrical properties tomography into a reliable biomarker where pathological conditions can be revealed and characterized by abnormalities in tissue electrical properties.