The shape of a bone affects the dynamics of the musculoskeletal system by influencing muscle length, tendon and ligament moment arms, and skeletal kinematics and cartilage contact patterns. In addition, variations in bone shape are symptomatic of orthopedic disease and markers of human evolution. Thus, the primary goal of this thesis was to create a deformable modeling methodology based on a multiple vector burst (MVB) system that could describe shape and, by combining with nonrigid registration, could quantify shape variation in a hierarchical manner by defining both the global and local shape information in a MVB system. Unique aspects of this MVB method are its ability to maintain anatomical meaning in its description of shapes, its quantification of shape variations and its multi-step non-rigid registration scheme. The latter allows the MVB model to be deformable in order to best fit into different shapes accurately and automatically, which provides time efficiency and the ability to quantify and remove global shape parameters prior to quantifying local shape variations, resulting in improved precision and accuracy.

Combing the MVB model and non-rigid registration solves the difficult problem of accurate shape description and the quantification of shape variations for a complicated shape. To validate the utility of this method, a group of normal femoral shapes was studied. Average femoral shapes were created using both a classical method and the new hierarchical deformation model. The deformable model method generated an average femur with lower surface variability than the classical method and yielded a set of global parameters with improved precision compared to previous studies. Synthetic shapes with artificial deformation were generated and the accuracy of the registration was investigated by analyzing the resultant shape variation. In addition, pathological femoral shapes, altered by cerebral palsy, were investigated to demonstrate the ability of this method to automatically quantify global and local shape variations.