Modelling and reconstructing the respiratory motion of the liver

Respiratory organ motion is a complicating factor in tumour treatment. For dose delivery, the aim is to obtain a possibly static target in the beam's eye view whenever the beam is on. Such a reduction of motion allows for reducing the safety margins or for delivering a higher dose in a shorter time. This thesis proposes a statistical, population-based model that covers all modes of deformation such as the perpetual breathing motion and organ drift. It furthermore provides a mathematical tool to estimate the current organ position based on sparse and low-dimensional measurements, with the goal to use ultrasound for obtaining the respiratory signal directly from the liver. The model can describe complex variations of the liver in shape and position without knowing the underlying physical mechanisms. To achieve this, 4D-MRI is acquired for a number of subjects. From these images, deformation fields are extracted, inter-subject correspondence is established and the model is learned from the data. The prediction accuracy is evaluated in various simulations where partial information of the organ in 3d, 2d or only 1d is known. Furthermore, an experiment is described where simultaneous 4D-MRI and ultrasound is acquired for six subjects in order to evaluate the approach in a clinically relevant scenario. The prediction is driven by tracked points in the ultrasound images and then compared to the ground-truth obtained from 4D-MRI. The results show that a statistical motion model can significantly reduce the uncertainty with respect to organ position during respiration.