Nazemi S Majid, Kalajahi S Mehrdad Hosseini, Cooper David M L, Kontulainen Saija A, Holdsworth David W, Masri Bassam A, Wilson David R, Johnston James D
Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Canada.
Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Canada.
J Biomech. 2017 Jul 5;59:101-108. doi: 10.1016/j.jbiomech.2017.05.018. Epub 2017 May 31.
Previously, a finite element (FE) model of the proximal tibia was developed and validated against experimentally measured local subchondral stiffness. This model indicated modest predictions of stiffness (R=0.77, normalized root mean squared error (RMSE%)=16.6%). Trabecular bone though was modeled with isotropic material properties despite its orthotropic anisotropy. The objective of this study was to identify the anisotropic FE modeling approach which best predicted (with largest explained variance and least amount of error) local subchondral bone stiffness at the proximal tibia.
Local stiffness was measured at the subchondral surface of 13 medial/lateral tibial compartments using in situ macro indentation testing. An FE model of each specimen was generated assuming uniform anisotropy with 14 different combinations of cortical- and tibial-specific density-modulus relationships taken from the literature. Two FE models of each specimen were also generated which accounted for the spatial variation of trabecular bone anisotropy directly from clinical CT images using grey-level structure tensor and Cowin's fabric-elasticity equations. Stiffness was calculated using FE and compared to measured stiffness in terms of R and RMSE%.
The uniform anisotropic FE model explained 53-74% of the measured stiffness variance, with RMSE% ranging from 12.4 to 245.3%. The models which accounted for spatial variation of trabecular bone anisotropy predicted 76-79% of the variance in stiffness with RMSE% being 11.2-11.5%.
Of the 16 evaluated finite element models in this study, the combination of Synder and Schneider (for cortical bone) and Cowin's fabric-elasticity equations (for trabecular bone) best predicted local subchondral bone stiffness.
此前，已开发出胫骨近端的有限元（FE）模型，并根据实验测量的局部软骨下骨刚度进行了验证。该模型对刚度的预测效果一般（R = 0.77，归一化均方根误差（RMSE%）= 16.6%）。尽管小梁骨具有正交各向异性，但在建模时采用的是各向同性材料属性。本研究的目的是确定能最佳预测（解释方差最大且误差最小）胫骨近端局部软骨下骨刚度的各向异性有限元建模方法。
使用原位宏观压痕测试，在13个胫骨内侧/外侧间室的软骨下表面测量局部刚度。针对每个标本生成有限元模型，假设具有均匀各向异性，采用从文献中获取的14种不同的皮质骨和胫骨特定密度 - 模量关系组合。还针对每个标本生成了两个有限元模型，它们直接利用灰度结构张量和考因织物弹性方程，根据临床CT图像考虑小梁骨各向异性的空间变化。使用有限元计算刚度，并根据R和RMSE%与测量的刚度进行比较。
均匀各向异性有限元模型解释了测量刚度方差的53 - 74%，RMSE%范围为12.4至245.3%。考虑小梁骨各向异性空间变化的模型预测了刚度方差的76 - 79%，RMSE%为11.2 - 11.5%。
在本研究评估的16个有限元模型中，斯奈德和施耐德（用于皮质骨）与考因织物弹性方程（用于小梁骨）的组合能最佳预测局部软骨下骨刚度。
