利用松质骨理想化模型对骨小梁刚度的研究

INVESTIGATION OF THE STIFFNESS OF TRABECULAE BY REPRESENTATIVE VOLUME ELEMENT (RVE) APPROACH

利用结构张量的概念建立了考虑松质骨结构各向异性的理想模型，将杆型与板型两种传统模型统一起来．采用均匀化理论，通过有限单元的数值计算建立了松质骨弹性常数与结构张量、固体体积比之间的数值关系，并预测了骨小梁的弹性模量．结果表明，本文模型较好地体现了松质骨的各向异性力学性质．对骨小梁的计算结果表明，骨小梁的弹性模量在６７６ＧＰａ～１０９ＧＰａ范围内，平均意义上的结果是９２１ＧＰａ．

Based on the concept of the fabric tensor to represent the microstructure of the cancellous bone, a more sophisticated idealized representative volume element (RVE) model is introduced for cancellous bone. It is assumed that the trabeculae distribution in the principal direction of the fabric tensor is proportional to the associated eigenvalue of the tensor. With this understanding, the present model provides a consistent and quantitative way to describe various kinds of microstructures from rod like trabeculae (corresponding to smaller eigenvalue) to platelike trabeculae (corresponding to larger eigenvalues). Homogenization theory is applied here to establish the relation between the properties of continuum level bone and the trabecuale. Unlike former studies that used the homogenization theory to predict the macro mechanical property from the assumed microstructure and mechanical property of the constituents of the composite, the present study focuses on the investigation of the stiffness of the trabeculae, by the comparison of the calculated results with the continuum level experimental data by Turner et al. The results show that the modulus of the trabeculae is in the range 6 76～10 9 GPa, and the mean value is 9 21 GPa. These values are in good agreement with the experimentally established modulus for the trabeculae.