Statistical Modeling to Investigate Anatomy and Function of the Knee

The natural knee is a hinge joint with significant functional requirements during activities of daily living; as a result, acute and chronic injuries can occur. Pathologies are influenced by joint anatomy and may include patellar maltracking, cartilage degeneration (e.g. osteoarthritis), or acute injuries such as meniscal or ligamentous tears. Population variability makes broadly applicable conclusions about etiology of these conditions from small-scale investigations challenging. The work presented in this dissertation is a demonstration of statistical modeling approaches to evaluate population variability in anatomy of the knee and function of its tibiofemoral (TF) and patellofemoral (PF) joints. Three-dimensional (3D) computational models of the bone and cartilage in the knee were characterized using a principal component analysis (PCA) algorithm to understand the primary sources of variability in shape and motion and make predictions from sparse data.;Statistical models were used to investigate relationships between natural knee anatomy and kinematics and make predictions of both shape and function from sparse data. A whole-joint characterization study identified key correlations between shape and function of the TF and PF joints, successfully recreating results from multiple studies and introducing new relationships under one unified approach. Results from this study were used in a subsequent investigation to build a statistical model of two-dimensional (2D) shape and alignment measures and 6 degree-of-freedom (DOF) kinematics to identify the key measures capable of predicting PF joint motion. The ability to reconstruct the 3D implanted patellar bone of a subject with a total knee replacement (TKR) was evaluated by a statistical shape model of the patella and simulated 2D edge profiles in a custom optimization algorithm. Lastly, a validated predictive algorithm was employed to assess the accuracy of subject-specific knee articular cartilage predictions from bony geometry. The utility of statistical modeling is elucidated by the population-based evaluations of the musculoskeletal system described in this work and could continue to inform characteristics related to pathological conditions and large-scale computational evaluations of implant performance.