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首页> 外文期刊>Journal of Biomechanics >Numerical errors and uncertainties in finite-element modeling of trabecular bone.
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Numerical errors and uncertainties in finite-element modeling of trabecular bone.

机译：小梁骨有限元建模中的数值误差和不确定性。

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Although micromechanical finite-element models are being increasingly used to help interpret the results of bio-mechanical tests, there has not yet been a systematic study of the numerical errors and uncertainties that occur with these methods. In this work, finite-element models of human L1 vertebra have been used to analyze the sensitivity of the calculated elastic moduli to resolution, boundary conditions, and variations in the Poisson's ratio of the tissue material. Our results indicate that discretization of the bone architecture, inherent in the tomography process, leads to an underestimate in the calculated elastic moduli of about 20% at 20 microm resolution; these errors vary roughly linearly with the size of the image voxels. However, it turns out that there is a cancellation of errors between the softening introduced by the discretization of the bone architecture and the excess bending resistance of eight-node hexahedral finite elements. Our empirical finding is that eight-node cubic elements of the same size as the image voxels lead to the most accurate calculation for a given number of elements, with errors of less than 5% at 20 microm resolution. Comparisons with mechanical testing are also hindered by uncertainties in the grip conditions: our results show that these uncertainties are of comparable magnitude to the systematic differences in mechanical testing methods. Both discretization errors and uncertainties in grip conditions have a smaller effect on relative moduli, used when comparing between different specimens or different load directions, than on an absolute modulus. The effects of variations in the Poisson's ratio of the bone tissue were found to be negligible.
机译：尽管越来越多地使用微机械有限元模型来帮助解释生物机械测试的结果，但尚未对这些方法所产生的数值误差和不确定性进行系统的研究。在这项工作中，人类L1椎骨的有限元模型已用于分析计算的弹性模量对分辨率，边界条件和组织材料的泊松比变化的敏感性。我们的结果表明，断层扫描过程中固有的骨骼结构离散化导致在20微米分辨率下计算出的弹性模量低估了约20％;这些误差随图像体素的大小大致线性变化。然而，事实证明，在骨骼结构离散化所引起的软化与八节点六面体有限元的过度抗弯性之间存在误差消除。我们的经验发现是，对于给定数量的元素，与图像体素大小相同的八节点立方元素将导致最准确的计算，在20微米分辨率下的误差小于5％。与机械测试的比较也受到抓地力条件不确定性的阻碍：我们的结果表明，这些不确定性与机械测试方法中的系统差异具有可比性。离散误差和抓地力条件的不确定性对在不同样本或不同载荷方向之间进行比较的相对模量的影响要小于对绝对模量的影响。发现骨组织的泊松比的变化的影响可以忽略。

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