Combining statistical and biomechanical models for estimation of anatomical deformations

Approaches that combine the use of biomechanical and statistical models to estimate or predict the deformation of anatomical soft tissues are explored. Through training samples generated via biomechanical simulations or extracted from medical images, statistical models can learn the relationships between a deformation of interest and variables that affect this deformation. This allows a variety of paradigms for estimating these deformations and fitting them to imaging data in a number of important clinical applications. This work presents several important contributions. First, the developed methods are demonstrated primarily through their use to register brain atlases to radiological images of brain tumor patients with gross deformities and topological changes introduced by the tumor. Solving this largely unexplored deformable registration problem makes the rich information collected from a large number of individuals available for aiding neurosurgical planning on individual patients. Second, an accurate three-dimensional finite element model of brain tissue deformation induced by growing tumors is developed. Unlike similar models in the literature, the presented model includes the mass-effect of peri-tumor edema as well as the bulk tumor, and includes methods that allow the simulation of the large deformations caused by some real tumors. Although the developed statistical methods may depend on biomechanical models for training, the former provide the advantages of being faster and being able to solve ill-posed inverse problems which are otherwise not possible to solve using forward biomechanical models. Furthermore, to address some of the problems associated with statistical learning in high dimensional shape spaces based on a relatively small number of training samples, a multi-scale analysis approach using the wavelet packets library and best basis selection is proposed. Through the natural idea of analyzing shapes at multiple scales independently, the accuracy of the proposed statistical estimators is improved.