Application of homogenization theory to the study of trabecular bone mechanics.
Application of homogenization theory to the study of trabecular bone mechanics.
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DOI：
10.1016/0021-9290(91)90308-a
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发表时间：
1991
影响因子：
2.4
通讯作者：
S. Hollister;D. Fyhrie;K. Jepsen;S. Goldstein
中科院分区：
文献类型：
--
作者：
S. Hollister;D. Fyhrie;K. Jepsen;S. Goldstein
人们普遍认为，骨小梁的微结构对骨小梁的强度和刚度有很大的影响。也有人假设，骨小梁的应力诱导适应性受骨小梁组织水平、应力和/或应变的影响。然而，目前还没有普遍接受的(或容易实现的)技术来预测微结构对骨小梁表观硬度和强度的影响，或估计组织水平的应力或应变。本文提出了一种新发展起来的专门用于分析微结构材料的力学理论--均匀化理论，并将其应用于骨小梁力学分析。利用均化理论，可以分别进行微结构分析和连续分析，然后以系统的方式将它们结合在一起。两种不同微观结构的骨小梁模型的刚度预测与实验结果符合得很好，取决于干骺端区域，(R2>；0.5对于肱骨近端标本，R2<；0.5对于股骨远端和胫骨近端标本)。对微观结构应变能密度(SED)和表观应变能密度(SED)的估计表明，表观SED(由标准连续介质有限元分析计算)与最大微结构或组织SED之间存在很大差异(最大可达30倍)。此外，对于相同的骨体积分数(BV TV)，支柱微结构和球形空洞微结构给出了非常不同的最大组织SED估计。在10-20%BV Tv时，球形空洞组织的估计值是支撑组织的2-20倍。
It is generally accepted that the strength and stiffness of trabecular bone is strongly affected by trabecular microstructure. It has also been hypothesized that stress induced adaptation of trabecular bone is affected by trabecular tissue level stress and/or strain. At this time, however, there is no generally accepted (or easily accomplished) technique for predicting the effect of microstructure on trabecular bone apparent stiffness and strength or estimating tissue level stress or strain. In this paper, a recently developed mechanics theory specifically designed to analyze microstructured materials, called the homogenization theory, is presented and applied to analyze trabecular bone mechanics. Using the homogenization theory it is possible to perform microstructural and continuum analyses separately and then combine them in a systematic manner. Stiffness predictions from two different microstructural models of trabecular bone show reasonable agreement with experimental results, depending on metaphyseal region,(R 2> 0.5 for proximal humerus specimens, R 2< 0.5 for distal femur and proximal tibia specimens). Estimates of both microstructural strain energy density (SED) and apparent SED show that there are large differences (up to 30 times) between apparent SED (as calculated by standard continuum finite element analyses) and the maximum microstructural or tissue SED. Furthermore, a strut and spherical void microstructure gave very different estimates of maximum tissue SED for the same bone volume fraction (BV TV). The estimates from the spherical void microstructure are between 2 and 20 times greater than the strut microstructure at 10–20% BV TV.