An MR-Linac integrates an MR scanner with a radiotherapy delivery system, providing non-ionizing real-time imaging of the internal anatomy before, during and after radiotherapy treatments. Due to spatio-temporal limitations of MR imaging, only high-resolution 2D cine-MR images can be acquired in real-time during MRI-guided radiotherapy (MRIgRT) to monitor the respiratory-induced motion of lung tumours and organs-at-risk.

However, temporally-resolved 3D anatomical information is essential for accurate MR guidance of beam delivery and dose estimation of the actually delivered dose. Surrogate-driven respiratory motion models can estimate the 3D motion of the internal anatomy from surrogate signals, producing the required information.

The overall aim of this thesis was to tailor a generalized respiratory motion modelling framework for lung MRIgRT. This framework can fit the model directly to unsorted 2D MR images sampling the 3D motion, and to surrogate signals extracted from the 2D cine-MR images acquired on an MR-Linac. It can model breath-to-breath variability and produce a motion compensated super-resolution reconstruction (MCSR) 3D image that can be deformed using the estimated motion.

In this work novel MRI-derived surrogate signals were generated from 2D cine-MR images to model respiratory motion for lung cancer patients, by applying principal component analysis to the control point displacements obtained from the registration of the cine-MR images. An MR multi-slice interleaved acquisition potentially suitable for the MR-Linac was developed to generate MRI-derived surrogate signals and build accurate respiratory motion models with the generalized framework for lung cancer patients. The developed models and the MCSR images were thoroughly evaluated for lung cancer patients scanned on an MR-Linac. The results showed that respiratory motion models built with the generalized framework and minimal training data generally produced median errors within the MCSR voxel size of 2 mm, throughout the whole 3D thoracic field-of-view and over the expected lung MRIgRT treatment times.