On incorporating bone microstructure in macro- nite-element models
Donaldson, Finn Euan
Bone is porous and has a complex microstructure. This study considers the effect of microstructural morphology on the macrolevel mechanical properties of bone. Improved incorporation of such properties is required to advance current finite element approximations of bone behaviour. A technique to computationally generate realistic trabecular bone microstructures is developed. This provides the possibility of examining the effect of different microstructures on the macrolevel mechanical behaviour of bone. They would also permit direct incorporation of bone microstructure in macroscale finite element analyses without the prohibitive computational and experimental costs of donor-image based mesh generation. Micro- finite-element analyses are used for the first time to evaluate the macrolevel orthotropic elastic constants of cortical bone resulting from variations of microstructural morphology. It is concluded that the ratio of canal volume to tissue volume is the most powerful predictor of cortical bone elastic constants and that considerable periosteal-endosteal variations in these constants can develop with bone loss. The role of microstructure in cortical bone toughness is investigated using nano- finite-element analyses of murine cortical bone samples to simulate the initiation and propagation of microcracks. Results confirm the experimentally observed ability of canal and lacuna pores to act as stress raisers, thereby guiding the growth of microcracks. A novel and numerically efficient strain-based plasticity algorithm is presented which permits easy incorporation of strength anisotropy in finite element analyses of bone. The previously evaluated elastic properties of cortical bone are combined with the developed plasticity algorithm to conduct a detailed macro-finite-element investigation of external fixation of tibial midshaft fractures. Old patients are found to be at considerably higher risk of implant loosening under both unilateral and Ilizarov fixation, compared to younger patients.