A novel morphological model of trabecular bone based on the gyroid

Human trabecular bone is known to be structurally very complex. The geometrical distribution of trabecular bone has major effects on its ability to perform its physiological function of load-bearing efficiently. Idealized unit cell models are very helpful in understanding the significance of micro-level properties on macro-level behavior. There is a need for a simple method to model trabecular bone, such that micro-level phenomena (like buckling) can be studied. We investigate a new model for trabecular bone, based on a minimal surface solid called a gyroid. The gyroid-based model is computationally easy to implement, and generates structures that possess strong morphometric and mechanical resemblance to real trabecular bone. We generated gyroid models for a range of volume fractions, representing trabecular bone samples obtained from various anatomic sites and ages. Finite element analysis was performed to obtain the mechanical properties of the gyroid structures. We calculated the small-strain elastic moduli values for each of the gyroid models and plotted these against corresponding apparent density. A power-law relationship was obtained for the gyroid models, in accordance with published studies on real trabecular bone mechanical behavior. The results showed that the gyroid could provide a suitable model for studying the effects of variations in trabecular structure on macro-level bone behavior.