3-DIMENSIONAL FINITE-ELEMENT MODELING OF BONE - EFFECTS OF ELEMENT SIZE
3-DIMENSIONAL FINITE-ELEMENT MODELING OF BONE - EFFECTS OF ELEMENT SIZE
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DOI：
10.1016/0141-5425(92)90100-y
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发表时间：
1992-11-01
期刊：
影响因子：
--
通讯作者：
SKINNER, HB
中科院分区：
文献类型：
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作者：
KEYAK, JH;SKINNER, HB
本研究量化了元素尺寸对骨有限元（FE）模型应力/应变结果的影响，这些模型是用先前描述的自动化方法生成的。该方法采用立方体六面体单元，使单元形状和长宽比保持恒定，同时研究了单元尺寸的影响。三个人体股骨近端模型，每个模型具有不同的单元尺寸（3. 1 mm、3.8 mm和4.8 mm）。模型在应变能上的收敛性已在前人的工作中得到验证。使用线性回归分析逐点比较模型预测的应力和应变。当单元尺寸增加时，应力和应变水平普遍下降，即使应变能收敛已经实现。单元宽度从3.1 mm增加到3.8 mm，预测应力总体下降了13%至29%;对于单元尺寸相同的增加，预测应变下降了4%至20%。这些结果表明，线性立方体六面体单元必须非常小（边长为3 mm或更小），以表示骨中存在的机械性能的急剧变化，并且使用较大的单元会降低预测的应力和应变。本研究中使用的元素与传统（非自动化）FE建模方法中通常用于表示松质骨的元素相似。因此，对于骨小梁发现的应力/应变结果对单元尺寸的敏感性也适用于这种骨的常规建模。这种对元素尺寸的敏感性意味着，如果这些模型中的元素尺寸不同，则通过不同FE模型预测的骨小梁中的应力/应变的定量比较可能没有意义。所有三个模型的定性结果是一致的，但是，表明定性比较FE模型可以。
This study quantifies the effects of element size on the stress/strain results of finite element (FE) models of bone that are generated with a previously described automated method. This method uses cube-shaped hexahedral elements, which enabled element shape and aspect ratio to be held constant while the effects of element size were studied. Three models of a human proximal femur, each with a different element size (3. 1 mm, 3.8 mm and 4.8 mm), were analysed. Convergence in strain energy of the models had been verified in previous work. The stresses and strains predicted by the models were compared on a pointwise basis using linear regression analysis. There was a general decrease in the level of stress and strain when element size was increased, even though convergence in strain energy had been achieved An increase in element width from 3.1 mm to 3.8 mm decreased the predicted stresses by 13% to 29% overall; the predicted strains decreased by 4% to 20% for the same increase in element size. These results indicate that linear cube-shaped hexahedral elements must be very small (3 mm on a side or smaller) to represent the sharp variations in mechanical properties that exist in bone, and that use of larger elements decreases the predicted stresses and strains. The elements used in this study are similar to those typically used to represent trabecular bone in conventional (non-automated) FE modelling methods. Therefore, the sensitivity of the stress/strain results to element size that was found for trabecular bone also applies to conventional modelling of such bone. This sensitivity to element size implies that quantitative comparisons of the stresses/strains predicted in trabecular bone by different FE models may not be meaningful if the elements in those models are not the same size. The qualitative results of all three models were in agreement, however, indicating that qualitative comparisons of FE models may be made.