Development of a simple numerical model for trabecular bone structures.

PURPOSE: Advances in additive manufacturing processes are enabling the fabrication of surrogate bone structures for applications including use in high-resolution anthropomorphic phantoms. In this research, a simple numerical model is proposed that enables the generation of microarchitecture with similar statistical distribution to trabecular bone. METHODS: A human humerus, radius, ulna, and several vertebrae were scanned on the Imaging and Medical beamline at the Australian Synchrotron and the proposed numerical model was developed through the definition of two complex functions that encode the trabecular thickness and position-dependant spacing to generate volumetric surrogate trabecular structures. The structures reproduced those observed at 19 separate axial locations through the experimental bone volumes. The applicability of the model when incorporating a two-material approximation to absorption- and phase-contrast CT was also investigated through simulation. RESULTS: The synthetic structures, when compared with the real trabecular microarchitecture, yielded an average mean thickness error of 2 µm, and a mean difference in standard deviation of 33 µm for the humerus, 24 µm for the ulna and radius, and 15 µm for the vertebrae. Simulated absorption- and propagation-based phase contrast CT projection data were generated and reconstructed using the derived mathematical simplifications from the two-material approximation, and the phase-contrast effects were successfully demonstrated. CONCLUSIONS: The presented model reproduced trabecular distributions that could be used to generate phantoms for quality assurance and validation processes. The implication of utilizing a two-material approximation results in simplification of the additive manufacturing process and the generation of synthetic data that could be used for training of machine learning applications