We propose a method to compute a 4D statistical model of respiratory lung motion which consists of a 3D shape atlas, a 4D mean motion model and a 4D motion variability model. Symmetric diffeomorphic image registration is used to estimate subject-specific motion models, to generate an average shape and intensity atlas of the lung as anatomical reference frame and to establish inter-subject correspondence. The Log-Euclidean framework allows to perform statistics on diffeomorphic transformations via vectorial statistics on their logarithms. We apply this framework to compute the mean motion and motion variations by performing a Principal Component Analysis (PCA) on diffeomorphisms. Furthermore, we present methods to adapt the generated statistical 4D motion model to a patient-specific lung geometry and the individual organ motion. The prediction performance is evaluated with respect to motion field differences and with respect to landmark-based target registration errors. The quantitative analysis results in a mean target registration error of 3,2 ± 1,8 mm. The results show that the new method is able to provide valuable knowledge in many fields of application.
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