Computational modeling of trabecular bone in lower extremity injuries due to impact

Abstract

Lower extremity injuries resulting from improvised explosive devices (IEDs) pose a serious threat to the safety of military troops. Reports from Operation Iraqi Freedom and Operation Enduring Freedom identify IEDs as the cause for a substantial number of lower extremity bone fractures. The Army Research Laboratory (ARL) concentrates part of its research efforts into better understanding impact related injuries. Despite a significant number of articles on bone mechanical behavior, only a few consider high strain rates. In collaboration with ARL, we propose in this thesis to capture via an in silico approach the dynamic and quasi-static responses of the trabecular bone. To achieve this goal, we conducted large scale parallel finite element simulations on biofidelic and biomimetic morphological models of trabecular bone. The biofidelic model was developed using an image-based tetrahedral meshing approach on [mu]CT images, courteously provided by Niebur's group at Notre Dame University, of a human femural sample. The biomimetic model was developed from an analytical model proposed by Wang and Cutiño [50] for a periodic unit cell. For the solid part of the trabecular, a visco-elastic visco-plastic constitutive model developed by Socrate's group [15] for cortical bone was applied. For the dynamic simulations, the effect of strain rate on the response of the bone microstructure was investigated and compared to published experimental results. We observed a structural softening on the stress-strain curve which takes its origins from the buckling that appears within the spongious trabeculae structure. Finally we included fracture in our dynamic simulations using the discontinuous Galerkin method developed by Radovitzky's group [37] to observe initiation and propagation of cracks within the trabecular and to capture the resulting material softening in the post-yield stress-strain response.