Modeling patterns of anatomical deformations in prostate patients undergoing radiation therapy with an endorectal balloon

External beam radiation therapy (EBRT) treats cancer by delivering daily fractions of radiation to a target volume. For prostate cancer, the target undergoes day-to-day variations in position, volume, and shape. For stereotactic photon and for proton EBRT, endorectal balloons (ERBs) can be used to limit variations. To date, patterns of non-rigid variations for patients with ERB have not been modeled. We extracted and modeled the patient-specific patterns of variations, using regularly acquired CT-images, non-rigid point cloud registration, and principal component analysis (PCA). For each patient, a non-rigid point-set registration method, called Coherent Point Drift, (CPD) was used to automatically generate landmark correspondences between all target shapes. To ensure accurate registrations, we tested and validated CPD by identifying parameter values leading to the smallest registration errors (surface matching error 0.13±0.09 mm). PCA demonstrated that 88±3.2% of the target motion could be explained using only 4 principal modes. The most dominant component of target motion is a squeezing and stretching in the anterior-posterior and superior-inferior directions. A PCA model of daily landmark displacements, generated using 6 to 10 CT-scans, could explain well the target motion for the CT-scans not included in the model (modeling error decreased from 1.83±0.8 mm for 6 CT-scans to 1.6±0.7 mm for 10 CT-scans). PCA modeling error was smaller than the naive approximation by the mean shape (approximation error 2.66±0.59 mm). Future work will investigate the use of the PCA-model to improve the accuracy of EBRT techniques that are highly susceptible to anatomical variations such as, proton therapy