Computational Simulation of Bone Remodeling using Design Space Topology Optimization

Abstract The law of bone remodeling, commonly referred to as Wolff's Law, asserts that the internal trabecular bone adapts to external loadings, reorienting with the principal stress trajectories to optimize mechanical efficiency creating a naturally optimum structure. The current study utilized an advanced structural optimization algorithm, called design space toptimization (DSO), to perform a three‐dimensional computational bone remodeling simulation on the human proximal femur and analyse the results to determine the validity of Wolff's hypothesis. DSO optimizes the layout of material by iteratively distributing it into the areas of highest loading, while simultaneously changing the design domain to increase computational efficiency. The large‐scale simulation utilized a 175 µm mesh resolution with over 23.3 million elements. The resulting anisotropic trabecular architecture was compared to both Wolff's trajectory hypothesis and natural femur samples from literature using radiography. The results qualitatively showed several anisotropic trabecular regions that were comparable to the natural human femur. The realistic simulated trabecular geometry suggests that the DSO method can accurately predict bone adaptation due to mechanical loading and that the proximal femur is an optimum structure as Wolff hypothesized. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)