Orthopaedic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740, USA.
J Biomech. 2013 Apr 26;46(7):1293-9. doi: 10.1016/j.jbiomech.2013.02.011. Epub 2013 Mar 14.
The role of tissue-level post-yield behavior on the apparent-level strength of trabecular bone is a potentially important aspect of bone quality. To gain insight into this issue, we compared the apparent-level strength of trabecular bone for the hypothetical cases of fully brittle versus fully ductile failure behavior of the trabecular tissue. Twenty human cadaver trabecular bone specimens (5mm cube; BV/TV=6-36%) were scanned with micro-CT to create 3D finite element models (22-micron element size). For each model, apparent-level strength was computed assuming either fully brittle (fracture with no tissue ductility) or fully ductile (yield with no tissue fracture) tissue-level behaviors. We found that the apparent-level ultimate strength for the brittle behavior was only about half the value of the apparent-level 0.2%-offset yield strength for the ductile behavior, and the ratio of these brittle to ductile strengths was almost constant (mean±SD=0.56±0.02; n=20; R(2)=0.99 between the two measures). As a result of this small variation, although the ratio of brittle to ductile strengths was positively correlated with the bone volume fraction (R(2)=0.44, p=0.01) and structure model index (SMI, R(2)=0.58, p<0.01), these effects were small. Mechanistically, the fully ductile behavior resulted in a much higher apparent-level strength because in this case about 16-fold more tissue was required to fail than for the fully brittle behavior; also, there was more tensile- than compressive-mode of failure at the tissue level for the fully brittle behavior. We conclude that, in theory, the apparent-level strength behavior of human trabecular bone can vary appreciably depending on whether the tissue fails in a fully ductile versus fully brittle manner, and this effect is largely constant despite appreciable variations in bone volume fraction and microarchitecture.
组织级后屈服行为对松质骨表观水平强度的作用是骨质量的一个潜在重要方面。为了深入了解这一问题，我们比较了松质骨在完全脆性和完全延性组织失效行为情况下的表观水平强度。我们对 20 个人体尸体松质骨标本（5mm 立方；BV/TV=6-36%）进行了微 CT 扫描，以创建 3D 有限元模型（22-微米单元尺寸）。对于每个模型，我们假设组织水平的行为完全脆性（无组织延性的断裂）或完全延性（无组织断裂的屈服），计算了表观水平强度。我们发现，脆性行为的表观极限强度仅为延性行为的表观 0.2%-偏移屈服强度的一半左右，并且这些脆性与延性强度的比值几乎恒定（平均值±标准差=0.56±0.02；n=20；两个测量值之间的 R(2)=0.99）。由于这种小的变化，尽管脆性与延性强度的比值与骨体积分数（R(2)=0.44，p=0.01）和结构模型指数（SMI，R(2)=0.58，p<0.01）呈正相关，但这些影响很小。从力学上讲，完全延性行为导致更高的表观水平强度，因为在这种情况下，组织失效所需的组织数量是完全脆性行为的 16 倍以上；此外，对于完全脆性行为，组织水平上的失效模式更多是拉伸模式而不是压缩模式。我们的结论是，理论上，人类松质骨的表观水平强度行为可以根据组织是完全延性还是完全脆性失效而有很大差异，尽管骨体积分数和微结构有很大变化，但这种影响基本保持不变。
