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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. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2010-08-16 15:30:55.144

Trabecular bone forms the internal scaffolding of most bones, and consists of a microscopic lattice-like structure of interconnected bony struts. Experimental work has demonstrated that trabecular bone adapts its structural rigidity and orientation in response to the strains placed upon the skeleton during life, a concept popularly known as “Wolff’s Law” or “bone functional adaptation”. Anthropological work has focused on correlating variation in primate trabecular bone to locomotor and masticatory function, to provide a context for the interpretation of fossil morphology. However, intraspecies variation and its underlying mechanisms are still poorly understood. In this thesis, variation in trabecular bone structure is examined in the human foot in four archaeological populations. The aim is to tease apart the factors underlying variation in human trabecular microstructure to determine whether it may be a suitable proxy for inferring terrestrial mobility in past populations. μCT scanning is used to image the three-dimensional trabecular structure of the talus, calcaneus, and first metatarsal in samples from four archaeological populations. Trabecular structure is quantified in seventeen volumes of interest placed throughout the foot. Trabecular bone is influenced by a variety of factors including body mass, age, diet, temperature, genetics, sex, and mechanical loading. Before trabecular structure can be used to infer habitual behaviour, the effects of these factors need to be understood and ideally statistically accounted for. Therefore, the effects of variation in bone size and shape, body mass, age, and sex on human trabecular structure are examined in four populations. Significant effects of body mass and age are reported, but little sexual dimorphism was found within populations. Taking these results into account, variation in trabecular structure is compared between archaeological populations that were divided into high and low mobility categories. Results demonstrate that the four populations show similar patterns of trabecular variation throughout the foot, with a signal of terrestrial mobility level superimposed upon it. Terrestrial mobility is associated with greater bone volume fraction and thicker, more widely spaced, and less interconnected trabeculae. Ontogeny of trabecular bone in the human calcaneus is investigated in two archaeological populations in the final chapter of the thesis. Results indicate that calcaneal trabecular bone adapts predictably to changes in loading associated with phases of gait maturation and increases in body mass. This opens the possibility of using trabecular structure to serve as a proxy of neuromuscular development in juvenile hominins. This work demonstrates that trabecular bone may serve as a useful proxy of habitual behaviour in hominin fossils and past populations when all contributing factors are carefully considered and ideally statistically controlled for.