Institute for Surgical Technology and Biomechanics, University of Bern, Bern, Switzerland.
Biomech Model Mechanobiol. 2017 Dec;16(6):1925-1936. doi: 10.1007/s10237-017-0928-0. Epub 2017 Jun 22.
Micro-finite element ([Formula: see text]FE) analyses are often used to determine the apparent mechanical properties of trabecular bone volumes. Yet, these apparent properties depend strongly on the applied boundary conditions (BCs) for the limited size of volumes that can be obtained from human bones. To attenuate the influence of the BCs, we computed the yield properties of samples loaded via a surrounding layer of trabecular bone ("embedded configuration"). Thirteen cubic volumes (10.6 mm side length) were collected from [Formula: see text]CT reconstructions of human vertebrae and femora and converted into [Formula: see text]FE models. An isotropic elasto-plastic material model was chosen for bone tissue, and nonlinear [Formula: see text]FE analyses of six uniaxial, shear, and multi-axial load cases were simulated to determine the yield properties of a subregion (5.3 mm side length) of each volume. Three BCs were tested. Kinematic uniform BCs (KUBCs: each boundary node is constrained with uniform displacements) and periodicity-compatible mixed uniform BCs (PMUBCs: each boundary node is constrained with a uniform combination of displacements and tractions mimicking the periodic BCs for an orthotropic material) were directly applied to the subregions, while the embedded configuration was achieved by applying PMUBCs on the larger volumes instead. Yield stresses and strains, and element damage at yield were finally compared across BCs. Our findings indicate that yield strains do not depend on the BCs. However, KUBCs significantly overestimate yield stresses obtained in the embedded configuration (+43.1 ± 27.9%). PMUBCs underestimate (-10.0 ± 11.2%), but not significantly, yield stresses in the embedded situation. Similarly, KUBCs lead to higher damage levels than PMUBCs (+51.0 ± 16.9%) and embedded configurations (+48.4 ± 15.0%). PMUBCs are better suited for reproducing the loading conditions in subregions of the trabecular bone and deliver a fair estimation of their effective (asymptotic) yield properties.
微有限元 ([Formula: see text]FE) 分析常用于确定小梁骨体积的表观力学性能。然而，这些表观性质强烈依赖于可从人体骨骼获得的体积的有限大小的应用边界条件 (BC)。为了减轻 BC 的影响，我们通过计算加载的样品的屈服特性来计算 ("嵌入式配置")。从 [Formula: see text]CT 重建的人类椎骨和股骨中收集了 13 个立方体积 (10.6 毫米边长)，并将其转换为 [Formula: see text]FE 模型。选择各向同性弹塑性材料模型用于骨组织，模拟了六个单轴、剪切和多轴载荷情况的非线性 [Formula: see text]FE 分析，以确定每个体积的子区域 (5.3 毫米边长) 的屈服特性。测试了三种 BC。运动学均匀 BC (KUBC：每个边界节点受到均匀位移的约束) 和周期性兼容混合均匀 BC (PMUBC：每个边界节点受到模仿各向异性材料周期性 BC 的均匀位移和牵引力的约束) 直接应用于子区域，而嵌入式配置则通过在较大体积上应用 PMUBC 来实现。最后，在不同的 BC 下比较了屈服应力和应变，以及屈服时的元素损伤。我们的研究结果表明，屈服应变不依赖于 BC。然而，KUBC 会显著高估嵌入式配置下的屈服应力 (+43.1 ± 27.9%)。PMUBC 低估 (-10.0 ± 11.2%)，但不显著，嵌入式情况下的屈服应力。同样，KUBC 导致比 PMUBC 更高的损伤水平 (+51.0 ± 16.9%) 和嵌入式配置 (+48.4 ± 15.0%)。PMUBC 更适合再现小梁骨子区域的加载条件，并对其有效 (渐近) 屈服特性进行公平估计。
