Adaptive bone remodeling in the proximal head of femur

Abstract

Bone is a living tissue with continuous structural transformations. Wolff (1982-1986) proposed a law that asserts that every change in the internal structure of bone is in response to external loads. Many researchers have considered Wolff's law to obtain the bone density distribution in the proximal femur. However, most of these researches have either considered the trabecular bone as a continuous material while it actually consists of a porous structure made of rods and plates, or their models are computationally inefficient. In this study, we have developed a model of the femur which resembles bone natural structure. The model initially consists of a solid shell representing cortical bone encompassing a cubical network of interconnected rods with circular cross-sections representing the trabecular bone. A computational efficient program has been developed which iteratively changes the structure of trabecular bone by keeping the local stress in the structure within a defined stress range. The stress is controlled by adding or removing beams to the initial trabecular frame structure. Analyses are performed for two cases by considering beams as homogenous isotropic or homogenous transversely isotropic. It is shown that trabecular bone tissue material properties do not have a significant effect on the converged structure of trabecular bone. Trabecular bone structure is obtained for three load cases: walking, stair climbing, and stumbling. It is shown that as the magnitude of the loads increases, the internal structure gets denser in critical zones. The highest density is achieved using loading associated with the stumbling. Walking which is considered as a routine daily activity, results in the least internal density in different regions of the bone among three load cases studied. The results show the converged bone architectures consisting of rods and plates are comparable with the natural bone morphology of the femur. Furthermore, the bone volume fraction at the critical regions of the converged results is in good agreement with previously measured data obtained from combinations of Dual X-ray Absorptiometry (DXA) and Computed Tomography (CT). --Author's abstract