Vienna University of Technology, Institute of Lightweight Design and Structural Biomechanics, Austria.
Biomech Model Mechanobiol. 2010 Oct;9(5):499-510. doi: 10.1007/s10237-010-0190-1. Epub 2010 Feb 5.
The key parameters determining the elastic properties of an unidirectional mineralized bone fibril-array decomposed in two further hierarchical levels are investigated using mean field methods. Modeling of the elastic properties of mineralized micro- and nanostructures requires accurate information about the underlying topology and the constituents' material properties. These input data are still afflicted by great uncertainties and their influence on computed elastic constants of a bone fibril-array remains unclear. In this work, mean field methods are applied to model mineralized fibrils, the extra-fibrillar matrix and the resulting fibril-array. The isotropic or transverse isotropic elastic constants of these constituents are computed as a function of degree of mineralization, mineral distribution between fibrils and extra-fibrillar matrix, collagen stiffness and fibril volume fraction. The linear sensitivity of the elastic constants was assessed at a default set of the above parameters. The strain ratios between the constituents as well as the axial and transverse indentation moduli of the fibril-array were calculated for comparison with experiments. Results indicate that the degree of mineralization and the collagen stiffness dominate fibril-array elasticity. Interestingly, the stiffness of the extra-fibrillar matrix has a strong influence on transverse and shear moduli of the fibril-array. The axial strain of the intra-fibrillar mineral platelets is 30-90% of the applied fibril strain, depending on mineralization and collagen stiffness. The fibril-to-fibril-array strain ratio is essentially ~1. This study provides an improved insight in the parameters, which govern the fibril-array stiffness of mineralized tissues such as bone.
使用平均场方法研究了在进一步的两个层次上分解的单向矿化骨原纤维阵列的弹性特性的关键参数。矿化微纳结构弹性性能的建模需要有关基础拓扑结构和组成材料特性的准确信息。这些输入数据仍然存在很大的不确定性，并且它们对计算骨原纤维阵列的弹性常数的影响仍不清楚。在这项工作中，平均场方法被应用于模拟矿化原纤维、纤维外基质和由此产生的原纤维阵列。这些组成部分的各向同性或横向各向同性弹性常数被计算为矿化度、纤维间和纤维外基质之间的矿物质分布、胶原蛋白刚度和原纤维体积分数的函数。在一组默认参数下评估了弹性常数的线性灵敏度。还计算了组成部分之间的应变比以及原纤维阵列的轴向和横向压痕模量，以与实验进行比较。结果表明，矿化度和胶原蛋白刚度主导着原纤维阵列的弹性。有趣的是，纤维外基质的刚度对原纤维阵列的横向和剪切模量有很大的影响。原纤维内的矿物质板的轴向应变取决于矿化度和胶原蛋白刚度，为原纤维应变的 30-90%。原纤维之间的应变比基本上约为 1。这项研究提供了对控制矿化组织（如骨）中原纤维阵列刚度的参数的深入了解。
