Computational study of Wolffʹs law with trabecular architecture in the human proximal femur using topology optimization

In the field of bone adaptation, it is believed that the morphology of bone is affected by its mechanical loads, and bone has self-optimizing capability; this phenomenon is well known as Wolffʹs law of the transformation of bone. In this paper, we simulated trabecular bone adaptation in the human proximal femur using topology optimization and quantitatively investigated the validity of Wolffʹs law. Topology optimization iteratively distributes material in a design domain producing optimal layout or configuration, and it has been widely and successfully used in many engineering fields. We used a two-dimensional micro-FE model with 50 μm pixel resolution to represent the full trabecular architecture in the proximal femur, and performed topology optimization to study the trabecular morphological changes under three loading cases in daily activities. The simulation results were compared to the actual trabecular architecture in previous experimental studies. We discovered that there are strong similarities in trabecular patterns between the computational results and observed data in the literature. The results showed that the strain energy distribution of the trabecular architecture became more uniform during the optimization; from the viewpoint of structural topology optimization, this bone morphology may be considered as an optimal structure. We also showed that the non-orthogonal intersections were constructed to support daily activity loadings in the sense of optimization, as opposed to Wolffʹs drawing.