Nawathe Shashank, Yang Haisheng, Fields Aaron J, Bouxsein Mary L, Keaveny Tony M
Department of Mechanical Engineering, University of California, Berkeley, CA, USA.
Department of Basic Medical Sciences, Purdue University, IN, USA.
J Biomech. 2015 May 1;48(7):1264-9. doi: 10.1016/j.jbiomech.2015.02.066. Epub 2015 Mar 12.
The influence of the ductility of bone tissue on whole-bone strength represents a fundamental issue of multi-scale biomechanics. To gain insight, we performed a computational study of 16 human proximal femurs and 12 T9 vertebral bodies, comparing the whole-bone strength for the two hypothetical bounding cases of fully brittle versus fully ductile tissue-level failure behaviors, all other factors, including tissue-level elastic modulus and yield stress, held fixed. For each bone, a finite element model was generated (60-82 μm element size; up to 120 million elements) and was virtually loaded in habitual (stance for femur, compression for vertebra) and non-habitual (sideways fall, only for femur) loading modes. Using a geometrically and materially non-linear model, the tissue was assumed to be either fully brittle or fully ductile. We found that, under habitual loading, changing the tissue behavior from fully ductile to fully brittle reduced whole-bone strength by 38.3±2.4% (mean±SD) and 39.4±1.9% for the femur and vertebra, respectively (p=0.39 for site difference). These reductions were remarkably uniform across bones, but (for the femur) were greater for non-habitual (57.1±4.7%) than habitual loading (p<0.001). At overall structural failure, there was 5-10-fold less failed tissue for the fully brittle than fully ductile cases. These theoretical results suggest that the whole-bone strength of the proximal femur and vertebra can vary substantially between fully brittle and fully ductile tissue-level behaviors, an effect that is relatively insensitive to bone morphology but greater for non-habitual loading.
骨组织的延展性对全骨强度的影响是多尺度生物力学的一个基本问题。为了深入了解这一问题，我们对16例人类近端股骨和12个T9椎体进行了一项计算研究，比较了两种假设的边界情况，即完全脆性与完全延性的组织水平失效行为下的全骨强度，其他所有因素，包括组织水平的弹性模量和屈服应力均保持不变。对于每根骨头，生成了一个有限元模型（单元尺寸为60 - 82μm；多达1.2亿个单元），并在习惯性（股骨为站立位，椎体为压缩位）和非习惯性（侧向跌倒，仅针对股骨）加载模式下进行虚拟加载。使用几何和材料非线性模型，假设组织要么完全脆性要么完全延性。我们发现，在习惯性加载下，将组织行为从完全延性改变为完全脆性时，股骨和椎体的全骨强度分别降低了38.3±2.4%（平均值±标准差）和39.4±1.9%（部位差异p = 0.39）。这些降低在各骨头之间非常均匀，但（对于股骨）非习惯性加载（57.1±4.7%）比习惯性加载时降低得更多（p < 0.001）。在整体结构失效时，完全脆性情况的失效组织比完全延性情况少5 - 10倍。这些理论结果表明，近端股骨和椎体的全骨强度在完全脆性和完全延性的组织水平行为之间可能有很大差异，这种影响对骨形态相对不敏感，但在非习惯性加载时更大。
