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This paper presents the multi-scale stress analysis of trabecular bone by the homogenization method bridging nano-micro-macro scales. Three-dimensional microstructure of trabeculae is obtained by the X-ray CT and the image-based modeling technique. Biological apatite (BAp) crystallite orientation is considered in the microstructure model by means of the anisotropic mechanical properties. The c-axis of BAp is set up as the maximum principal stress direction under the long term macroscopic stress condition. These properties are automatically assigned to each voxel element. To determine appropriately the microstructure model, the trabeculae morphology is analyzed and quantified as the trabecular density distribution. The proposed method is applied to pig's femur. It was revealed by the morphology analysis and homogenized macroscopic properties that the trabecular bone has plate-like characteristics. The predicted anisotropic level of the macroscopic properties was quantitatively coincident with the measured value by the X-ray diffraction analysis.

Multi-Scale Stress Analysis of Trabecular Bone Considering Trabeculae Morphology and Biological Apatite Crystallite Orientation