Hierarchical eigenmodes to characterize bladder motion and deformation in prostate cancer radiotherapy

In radiotherapy for prostate cancer the bladder presents the largest inter-fraction shape variations during treatment resulting in random geometric uncertainties that may increase the risk of developing side-effects. In this setting, our interest is thus to propose a hierarchical population model, based on longitudinal data, to characterize bladder motion and deformation between fractions. This method is based on a principal component analysis (PCA) of bladder shapes to obtain the dominant eigenmodes that describe bladder geometric variations between fractions. However, PCA may not properly capture the latent structure of complex data like longitudinal data of organs with large inter and intra-patient shape variations. With this, we propose hierarchical modes to separate intra- and inter-patient bladder variability of the longitudinal data following a dimensionality reduction by means of spherical harmonics (SPHARM). The training data base was used to derive a top-level PCA model that describes the entire structure of the bladder surface space. This space was subsequently divided into subspaces by lower-level PCA models that describe their internal structures. The model was evaluated using a reconstruction error and compared with a conventional PCA model following leave-one-out cross validation.