Trabecular bone is a flexible, lightweight bone tissue that exhibits hierarchical mechanisms of fracture resistance across scales. At the mesoscale, trabecular bone resembles a web of interconnected bone struts (trabeculae) that erode with age and diseases such as osteoporosis, resulting in increased fracture propensity. Recent ex vivo bone experiments have indicated that the traditional diagnostic marker of osteoporosis, bone mineral density (BMD), correlates poorly with bone strength when used as a sole predictor, but that it can explain much of the variation in bone strength when considered in conjunction with architectural features.
We introduce a novel approach to modeling trabecular bone that combines network analysis with simulations of mechanical loading and failure, enabling a unique characterization of how bone architecture contributes to robustness and resilience. Network science has been applied to a vast range of systems across biology and soft condensed matter physics, among many other fields, but has rarely been applied to the study of bone. Exploiting the disordered network resemblance of bone, we generate network models from tomographic images of real human vertebral bone. We simulate loading and deformation on finite element models in which edges are replaced by beams, resulting in a considerable reduction in computation time in comparison with fine-grained models used for in silico validation. The beam-element analysis facilitates direct comparison of mechanics and topology at multiple scales ranging from that of individual edges (beams) to the network as a whole.
To assess how variation in architecture impacts mechanical response, we also develop networked structures simulated via multi-objective topology optimization. We maximize a weighted combination of biologically motivated objectives: stiffness, surface area, and stability. By modulating the weights of the objectives, we analyze how tradeoffs in these quantities produce topologies of varying strength and robustness. Finally, we discuss implications of our work in the context of clinical application, facilitated by advances in data acquisition methods for assessing fine tissue structure, and we highlight future directions for integrating our results into a comprehensive characterization of bone that links its molecular constituents at the nanoscale to its architecture at large