Keywords: multi-scale, finite element method, dynamic explicit method, mechanical properties, cancellous bone, trabecular bone.

Recently, the morphological measurement and material characterization technology of micro trabecular tissue has shown great progress, because of the development of micro optical measurement technology, such as three-dimensional µ-CT observation. In this paper, we define the femur as a two-scale structure, such as a macro cancellous structure with the size of mm and a micro trabecular tissue with one of µm. A two-scale finite element (FE) analysis scheme was developed to characterize macro-scale and micro-scale mechanical properties, such as the macro and micro elastic moduli and failure strengths of cancellous bone and trabecular bone tissue, respectively. It employs a representative volume element (RVE) of micro trabecular of the bovine femur bone, which is measured by µ-CT with the unit of 40 µm voxel. The porous cancellous bone structure can be characterized by the bone volume fraction (BVF) and the fabrication angle, because of its fibrous and shell structures.

In this paper, the micro FE model of the RVE was constructed using µ-CT measured at 40 µm voxel, which is used as the solid finite element. Stress and strain analyses were carried out. We identified the mechanical properties of the trabecular bone tissue at micro-scale by comparison with experimental results of compression tests using 10mm cube cancellous bones.

In this paper, three main subjects were discussed:

1. BVF and texture orientation characterizations of the femur bone by using the µ-CT analyzer: It elucidates that the right-hand side of the bovine femur has larger BVF and a lesser angle to the z axis.
2. Macro mechanical property evaluations of cancellous bone, such as elastic modulus and failure stress using the experimental results of compression tests. There is a strong correlation between the macro Young's modulus and the BVF, but not so much between the macro Young's modulus and the trabecular fiber orientation. A similar relationship is found in the case of failure strength.
3. Micro finite element analyses to evaluate the micro elastic modulus of trabecular bone tissue: Most of the micro Young's moduli appear to be around the average value 8GPa, but we found the largest value 27.9GPa and the lowest value 4.1GPa. We found the similar results in the case of failure strength.

We found significant differences between macro properties and micro ones. We investigated differences between macro elastic modulus and failure strength, and micro ones, and investigated how to evaluate the bone ossein. We concludes that the micro Young's modulus and the failure strength can be related to the bone ossein, and that our micro FE simulation can be a useful tool for the diagnoses of bone.

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