Institute of Biomechanics, Trauma Center Murnau, Murnau am Staffelsee, Germany.
J Biomech. 2013 Sep 3;46(13):2152-7. doi: 10.1016/j.jbiomech.2013.06.035. Epub 2013 Jul 26.
In a previous study on subject-specific finite-element-models, we found that appropriate density-elasticity relationships to compute the mechanical behavior of femurs seem to be subject-specific. The purpose of this study was to test the hypothesis that the predictive error of a cohort of subject-specific finite element-models is lower with subject-specific density-elasticity relationships than with a cohort-specific density-elasticity relationship. Finite-element-analysis and inverse optimization based on response surface methodology were employed to test the hypothesis. Subject-specific FE-models of 17 human femurs and corresponding experimental data from biomechanical tests were taken from a previous study. A power function for the relation between radiological bone density and elastic modulus was set up with the optimization variables a and b: E(MPa)=aρqCT(b)(gK2HPO4/cm(3)). The goal of the optimization was to minimize the root-mean-square error in percent (RMSE%) between computational and experimental results. A Wilcoxon test (p=0.05) was performed on all absolute relative errors between the two groups (subject-specific functions vs. cohort-specific function). The subject-specific functions resulted in a 6% lower overall prediction error and a 6% lower RMSE% than the cohort-specific function (p<0.001). The determined subject-specific relations were mostly linear, with variable a ranging from 9307 to 15673 and variable b ranging from 0.68 to 1.40. For the cohort-specific relation, the following power law was obtained: E(MPa)=12486ρqCT(1.16)(gK2HPO4/cm(3)). We conclude that individual density-elasticity relationships improve the accuracy of subject-specific finite element models. Future subject-specific finite-element-analyses of bones should include the individuality of the elastic properties by a stochastic density-elasticity relationship with mean and standard deviation of a and b.
在之前的针对特定于个体的有限元模型的研究中，我们发现，计算股骨力学行为的适当密度-弹性关系似乎是特定于个体的。本研究的目的是检验以下假设：与特定于群体的密度-弹性关系相比，特定于个体的密度-弹性关系可降低队列特定于个体的有限元模型的预测误差。使用有限元分析和基于响应面方法的逆优化来检验该假设。使用先前研究中 17 个人类股骨的特定于个体的有限元模型和相应的生物力学测试实验数据。使用优化变量 a 和 b 建立了放射学骨密度与弹性模量之间的幂函数关系：E（MPa）=aρqCT(b)(gK2HPO4/cm(3))。优化的目标是最小化计算和实验结果之间的均方根误差百分比（RMSE%）。对两组之间的所有绝对相对误差（特定于个体的函数与群体特定函数）进行了 Wilcoxon 检验（p=0.05）。与群体特定函数相比，特定于个体的函数总体预测误差降低了 6%，RMSE%降低了 6%（p<0.001）。确定的特定于个体的关系主要是线性的，变量 a 的范围从 9307 到 15673，变量 b 的范围从 0.68 到 1.40。对于群体特定的关系，得到了以下幂律：E（MPa）=12486ρqCT(1.16)(gK2HPO4/cm(3))。我们得出结论，个体密度-弹性关系可提高特定于个体的有限元模型的准确性。未来针对骨骼的特定于个体的有限元分析应该通过具有 a 和 b 的均值和标准差的随机密度-弹性关系来包含弹性特性的个体性。
