A two-parameter model of the effective elastic tensor for cortical bone
A two-parameter model of the effective elastic tensor for cortical bone
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DOI：
10.1016/j.jbiomech.2011.03.006
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发表时间：
2011-05-17
影响因子：
2.4
通讯作者：
Laugier, Pascal
中科院分区：
文献类型：
--
作者：
Grimal, Quentin;Rus, Guillermo;Laugier, Pascal
皮质骨弹性的多尺度模型需要大量的参数来描述组织的组织和组成。我们假设，可以对不同骨骼的宏观尺度各向异性弹性属性进行建模，只保留两个变量参数，并将其他参数设置为对所有骨骼都相同的通用值。皮质骨被认为是一种两相复合材料：致密的矿化基质(超微结构)和软相(孔洞)。超微结构假定为均匀的横观各向同性组织，其弹性性质在不同方向上是相互依赖的，并且可以用驱动整体刚度的单个参数来衡量。这个参数被认为是矿物f(Ha)的体积分数。孔隙网络被模拟为充满水的圆柱体的系综，仅用孔隙率p来描述。有效宏观弹性张量C-ij(f(Ha)，p)是从现有模型出发用多尺度细观力学方法计算的。所建模型的刚度系数与选择的四个文献数据集相比是有利的，因为它们提供了人体样本组的全部刚度张量。由于f(Ha)和p的物理对应值对于数据集是未知的，因此通过优化确定了它们的值，从而允许通过建模的张量来最好地拟合实验张量。F(Ha)和p的最佳值是唯一和现实的。这些结果表明，双参数模型可能足以模拟不同样本的人股骨和胫骨的弹性。这种模型在骨机械响应的大规模参数研究中尤其有用。(C)2011爱思唯尔有限公司。保留所有权利。
Multiscale models of cortical bone elasticity require a large number of parameters to describe the organization and composition of the tissue. We hypothesize that the macro-scale anisotropic elastic properties of different bones can be modeled retaining only two variable parameters, and setting the others to universal values identical for all bones. Cortical bone is regarded as a two-phase composite material: a dense mineralized matrix (ultrastructure) and a soft phase (pores). The ultrastructure is assumed to be a homogeneous and transversely isotropic tissue whose elastic properties in different directions are mutually dependent and can be scaled with a single parameter driving the overall rigidity. This parameter is taken to be the volume fraction of mineral f(ha). The pore network is modeled as an ensemble of water-filled cylinders and described only by the porosity p. The effective macroscopic elasticity tensor C-ij(f(ha),p) is calculated with a multiscale micromechanics approach starting from existing models. The modeled stiffness coefficients compare favorably to four literature datasets which were chosen because they provide the full stiffness tensors of groups of human samples. Since the physical counterparts of f(ha) and p were unknown for the datasets, their values which allow the best fit of experimental tensors by the modeled ones were determined by optimization. Optimum values of f(ha) and p are found to be unique and realistic. These results suggest that a two-parameter model may be sufficient to model the elasticity of different samples of human femora and tibiae. Such a model would in particular be useful in large-scale parametric studies of bone mechanical response. (C) 2011 Elsevier Ltd. All rights reserved.