  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 1mm 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.
