Computational Study of Wolff's Law Utilizing Design Space Topology Optimization: A New Method for Hip Prosthesis Design
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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 maximize mechanical efficiency, thereby creating a naturally optimum structure. The primary objective of the research was to utilize an advanced structural optimization algorithm, called design space optimization (DSO), to create a numerical framework to perform a micro-level three-dimensional finite element bone remodeling simulation on the human proximal femur and analyze 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 result is a "fully stressed" structure with minimized compliance and increased stiffness. The large-scale computational simulation utilized a 175µm mesh resolution and the routine daily loading activities of walking and stair climbing. The resulting anisotropic human trabecular architecture was compared to both Wolff's trajectory hypothesis and natural femur data from the literature using a variety of visualization techniques, including radiography and computed tomography (CT). The remodeling predictions qualitatively revealed several anisotropic trabecular regions comparable to the natural human femurs. Quantitatively, the various regional bone volume fractions from the computational results were consistent with CT analyses. The strain energy proceeded to become more uniform during optimization; implying increased mechanical efficiency was achieved. The realistic simulated trabecular geometry suggests that the DSO method can accurately predict three-dimensional bone adaptation due to mechanical loading and that the proximal femur is an optimum structure as Wolff hypothesized. The secondary objective was to revise this computational framework to perform the first in-silico hip replacement considering micro-level bone remodeling. Two different commercially available hip prostheses were quantitatively analyzed using stress, strain energy, and bone mineral density as performance criteria and qualitatively visualized using the techniques above. Several important factors for stable fixation, determined from clinical evaluations, were evident: high levels of proximal bone loss, distal bone growth, and medial densification. The results suggest the DSO method can be utilized for comparative prosthetic implant stem design, uniquely considering post-operation bone remodeling as a design criterion.