A 3D generative structural model of trabecular bone using a novel probabilistic approach

This study aims to develop a three-dimensional (3D) generative trabecular bone model capable of rendering digital models that closely resemble real trabecular bone microstructures. This model was constructed based on a previously proposed probability-based framework, integrating image processing, Voronoi tessellation, inverse Monte Carlo simulation, and computer graphics techniques. To evaluate its efficacy, the microstructural and mechanical properties of the synthesized digital models were compared with those of target real bone samples in pairs. The target real bone samples consisted of a total of 542 trabecular cubes, extracted from different anatomical locations of six human cadaver proximal femurs of different ages and sexes. A set of scalar and random variables defining the microstructural features were measured from the target real bone samples and used as inputs for the generative model to synthesize digital models. The results demonstrated that: (1) The microstructural features of the synthesized digital models closely matched those of the target real bone samples in terms of trabecular orientation, size, and spatial arrangement, with mean Hellinger Distance ranging from 0.051 to 0.187. (2) The synthesized digital models captured the histomorphometric parameters of the target real bone samples in terms of BV/TV, PN, RN, R-P Junc.D, R-R Junc.D, and P-P Junc.D. (3) The digital models effectively captured the anisotropic mechanical behavior of the target real bone samples, with R² values ranging from 0.93 to 0.97 for the stiffness tensor and 0.90 to 0.93 for yield stress. These findings confirm the proposed generative model's efficacy in mimicking the microstructural and mechanical properties of trabecular bone.