Digital Modeling of Trabecular Bones: Structural Analysis and Probabilistic Modeling Techniques
Structural changes in trabecular bone related to aging and/or disease are a primary cause of bone fragility fractures. However, the effect of specific structural changes on the mechanical competency of the structure is not fully understood. Mathematical models of trabecular bone, developed to illuminate this relationship, have been hindered by the complexity and randomness of the structure. In order to establish a representative model, underlying commonality among the diverse trabecular structures must be elucidated. Recent advances in image processing (e.g. Individual Trabeculae Segmentation) have yielded results that seem to suggest the underlying distributions of individual trabecular features may be common among trabecular architectures. Based on these previous experiments, it was hypothesized that the size, spatial arrangement, and orientation of individual trabeculae follow a set of common underlying distributions that are not sensitive to individual differences among donors (i.e. age, gender, bone volume fraction, and anatomic location). An innovative m/n bootstrap Kolmogorov-Smirnov test was used to test this hypothesis, by which it was found that the underlying distributions of the eight trabecular features considered in this research are statistically similar. Furthermore, using these underlying distributions as the targets of an Inverse Monte Carlo optimization process within a Voronoi tessellation cellular solids framework, a digital model of the trabecular structure can be generated. Building on the development of the previous trabecular bone model, this research incorporated two additional trabecular features and implemented novel probabilistic techniques in order to improve the convergence of the model to real trabecular structures.