To what extent can cortical bone millimeter-scale elasticity be predicted by a two-phase composite model with variable porosity?
To what extent can cortical bone millimeter-scale elasticity be predicted by a two-phase composite model with variable porosity?
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DOI：
10.1016/j.actbio.2014.10.011
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发表时间：
2015-01-15
影响因子：
9.7
通讯作者：
Laugier, Pascal
中科院分区：
文献类型：
--
作者：
Granke, Mathilde;Grimal, Quentin;Laugier, Pascal
在充分理解和可靠地模拟在毫米尺度上观察到的人类皮质骨弹性各向异性的变化方面存在证据差距。已知孔隙率（孔隙体积分数）占弹性变化的大部分，但不是全部。这种效应可以通过由圆柱形孔遍布的均匀基体组成的两相微观力学模型来建模。虽然该模型已被广泛使用，但缺乏实验验证。本工作的目的是重新审视实验数据（弹性系数，孔隙度）先前获得的21个皮质骨标本从股骨中段骨干的10个捐助者和测试的有效性，提出了一个详细的讨论其假设模型。这包括调查在何种程度上的实验不确定性，孔隙网络建模，和矩阵的弹性性能影响模型的预测。结果支持的有效性的两相模型的皮质骨，假设在毫米级的弹性性能的变化的基本来源是血管孔隙的体积分数。我们建议，剩余的预测刚度系数和实验数据之间的差异（RMSE在6%和9%之间）的大部分是部分由于实验误差和部分由于血管外基质性质的小变化。更重要的是，虽然大多数的模型，已提出的皮质骨的基础上的几个均匀化步骤和大量的可变参数，我们表明，一个模型与一个单一的参数，即血管孔隙率的体积分数，是一个合适的表示皮质骨。本研究结果可为骨皮质骨模型的建立提供指导。这对于分析骨的结构与功能关系以及设计仿生骨材料具有重要意义。(C)2014 Acta Materialia Inc.由爱思唯尔有限公司出版。保留所有权利。
An evidence gap exists in fully understanding and reliably modeling the variations in elastic anisotropy that are observed at the millimeter scale in human cortical bone. The porosity (pore volume fraction) is known to account for a large part, but not all, of the elasticity variations. This effect may be modeled by a two-phase micromechanical model consisting of a homogeneous matrix pervaded by cylindrical pores. Although this model has been widely used, it lacks experimental validation. The aim of the present work is to revisit experimental data (elastic coefficients, porosity) previously obtained from 21 cortical bone specimens from the femoral mid-diaphysis of 10 donors and test the validity of the model by proposing a detailed discussion of its hypotheses. This includes investigating to what extent the experimental uncertainties, pore network modeling, and matrix elastic properties influence the model's predictions. The results support the validity of the two-phase model of cortical bone which assumes that the essential source of variations of elastic properties at the millimeter-scale is the volume fraction of vascular porosity. We propose that the bulk of the remaining discrepancies between predicted stiffness coefficients and experimental data (RMSE between 6% and 9%) is in part due to experimental errors and part due to small variations of the extravascular matrix properties. More significantly, although most of the models that have been proposed for cortical bone were based on several homogenization steps and a large number of variable parameters, we show that a model with a single parameter, namely the volume fraction of vascular porosity, is a suitable representation for cortical bone. The results could provide a guide to build specimen-specific cortical bone models. This will be of interest to analyze the structure-function relationship in bone and to design bone-mimicking materials. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.