Finite element analysis of a femur to deconstruct the paradox of bone curvature

Most long limb bones in terrestrial mammals exhibit a longitudinal curvature and have been found to be loaded in bending. Bone curvature poses a paradox in terms of the mechanical function of limb bones, for many believe the curvature in these bones increases bending stress, potentially reducing the bone's load carrying capacity (i.e., its mechanical strength). The aim of this study is to investigate the role of longitudinal bone curvature in the design of limb bones. In particular, it has been hypothesized that bone curvature results in a trade-off between the bone's mechanical strength and its bending predictability. We employed finite element analysis (FEA) of abstract and realistic human femora to address this issue. Geometrically simplified human femur models with different curvatures were developed and analyzed with a commercial FEA tool to examine how curvature affects the bone's bending predictability and load carrying capacity. Results were post-processed to yield probability density functions (PDFs) describing the circumferential location of maximum equivalent stress for various curvatures in order to assess bending predictability. To validate our findings, a finite element model was built from a CT scan of a real human femur and compared to the simplified femur model. We found general agreement in trends but some quantitative differences most likely due to the geometric differences between the digitally reconstructed and the simplified finite element models. As hypothesized by others, our results support the hypothesis that bone curvature can increase bending predictability, but at the expense of bone strength.