Mathematical rendering of trabecular bone microarchitecture using stochastic geometry and Voronoi tessellation methods

The architecture of trabecular bone is important to the overall stability and strength of load-bearing bones. Recently, numerical simulations of mechanical performance of vertebrae and long bones under different loading conditions have become a promising approach to predict bone fragility failures. However, determination of trabecular architecture is still relying on imaging modalities from individual patients or donors, which is extremely time-consuming and costly. As an effort to quantify the complex architecture of trabecular (cancellous) bone, we proposed a novel approach that combines stochastic and Voronoi tessellation techniques to numerically generate 3-D trabecular architecture that can mimic real trabecular bones.

This thesis is the first step to establish such mathematical model, in which we focus on one aspect of trabecular microarchitecture: i.e. the spatial distribution of rod-rod and rod-plate joints. Our eventual goal is to develop a mathematical tool that can be used to accurately predict bone fragility fractures under different circumstances.