Niebur G L, Feldstein M J, Yuen J C, Chen T J, Keaveny T M
Orthopaedic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, 6175 Etcheverry Hall, 94720-1740, Berkeley, CA, USA.
J Biomech. 2000 Dec;33(12):1575-83. doi: 10.1016/s0021-9290(00)00149-4.
The ability to predict trabecular failure using microstructure-based computational models would greatly facilitate study of trabecular structure-function relations, multiaxial strength, and tissue remodeling. We hypothesized that high-resolution finite element models of trabecular bone that include cortical-like strength asymmetry at the tissue level, could predict apparent level failure of trabecular bone for multiple loading modes. A bilinear constitutive model with asymmetric tissue yield strains in tension and compression was applied to simulate failure in high-resolution finite element models of seven bovine tibial specimens. Tissue modulus was reduced by 95% when tissue principal strains exceeded the tissue yield strains. Linear models were first calibrated for effective tissue modulus against specimen-specific experimental measures of apparent modulus, producing effective tissue moduli of (mean+/-S.D.) 18.7+/-3.4GPa. Next, a parameter study was performed on a single specimen to estimate the tissue level tensile and compressive yield strains. These values, 0.60% strain in tension and 1.01% strain in compression, were then used in non-linear analyses of all seven specimens to predict failure for apparent tensile, compressive, and shear loading. When compared to apparent yield properties previously measured for the same type of bone, the model predictions of both the stresses and strains at failure were not statistically different for any loading case (p>0.15). Use of symmetric tissue strengths could not match the experimental data. These findings establish that, once effective tissue modulus is calibrated and uniform but asymmetric tissue failure strains are used, the resulting models can capture the apparent strength behavior to an outstanding level of accuracy. As such, these computational models have reached a level of fidelity that qualifies them as surrogates for destructive mechanical testing of real specimens.
利用基于微观结构的计算模型预测小梁骨失效的能力，将极大地促进小梁骨结构 - 功能关系、多轴强度和组织重塑的研究。我们假设，在组织水平包含类似皮质骨强度不对称性的小梁骨高分辨率有限元模型，能够预测多种加载模式下小梁骨的表观水平失效。将一种在拉伸和压缩时具有不对称组织屈服应变的双线性本构模型应用于模拟七个牛胫骨标本的高分辨率有限元模型中的失效情况。当组织主应变超过组织屈服应变时，组织模量降低95%。首先针对有效组织模量，根据标本特定的表观模量实验测量值对线性模型进行校准，得出有效组织模量为（均值±标准差）18.7±3.4GPa。接下来，对单个标本进行参数研究，以估计组织水平的拉伸和压缩屈服应变。然后将这些值（拉伸应变0.60%和压缩应变1.01%）用于所有七个标本的非线性分析中以预测表观拉伸、压缩和剪切加载下的失效情况。与先前针对相同类型骨测量的表观屈服特性相比，在任何加载情况下，失效时应力和应变的模型预测在统计学上均无差异（p>0.15）。使用对称的组织强度无法匹配实验数据。这些发现表明，一旦校准了有效组织模量并使用均匀但不对称的组织失效应变，所得模型就能以极高的精度捕捉表观强度行为。因此，这些计算模型已达到一种逼真度水平，使其有资格作为真实标本破坏性力学测试的替代方法。
