Zwahlen Alexander, Christen David, Ruffoni Davide, Schneider Philipp, Schmolz Werner, Muller Ralph
J Biomech Eng. 2015 Jan;137(1). doi: 10.1115/1.4028991.
The local interpretation of microfinite element (μFE) simulations plays a pivotal role for studying bone structure–function relationships such as failure processes and bone remodeling.In the past μFE simulations have been successfully validated on the apparent level,however, at the tissue level validations are sparse and less promising. Furthermore,intra trabecular heterogeneity of the material properties has been shown by experimental studies. We proposed an inverse μFE algorithm that iteratively changes the tissue level Young's moduli such that the μFE simulation matches the experimental strain measurements.The algorithm is setup as a feedback loop where the modulus is iteratively adapted until the simulated strain matches the experimental strain. The experimental strain of human trabecular bone specimens was calculated from time-lapsed images that were gained by combining mechanical testing and synchrotron radiation microcomputed tomography(SRlCT). The inverse μFE algorithm was able to iterate the heterogeneous distribution of moduli such that the resulting μFE simulations matched artificially generated and experimentally measured strains.
微观有限元（μFE）模拟的局部解释对于研究诸如失效过程和骨重塑等骨结构 - 功能关系起着关键作用。过去，μFE模拟已在表观水平上成功得到验证，然而，在组织水平上的验证却很少且前景不佳。此外，实验研究表明小梁内材料特性存在异质性。我们提出了一种反向μFE算法，该算法迭代地改变组织水平的杨氏模量，以使μFE模拟与实验应变测量值相匹配。该算法设置为一个反馈回路，其中模量被迭代调整，直到模拟应变与实验应变相匹配。人小梁骨标本的实验应变是根据通过结合机械测试和同步辐射微计算机断层扫描（SRlCT）获得的时间推移图像计算得出的。反向μFE算法能够迭代模量的非均匀分布，从而使所得的μFE模拟与人工生成的和实验测量的应变相匹配。
