Department of Mechanical Engineering, University of California, Berkeley, CA, USA.
Department of Mechanical Engineering, University of California, Berkeley, CA, USA; Department of Osteology and Biomechanics, University Medical Center Hamburg-Eppendorf, Hamburg, Germany.
Bone. 2020 Aug;137:115445. doi: 10.1016/j.bone.2020.115445. Epub 2020 May 23.
Although the ductility of bone tissue is a unique element of bone quality and varies with age and across the population, the extent to which and mechanisms by which typical population-variations in tissue-level ductility can alter whole-bone strength remains unclear. To provide insight, we conducted a finite element analysis parameter study of whole-vertebral (monotonic) compressive strength on six human L1 vertebrae. Each model was generated from micro-CT scans, capturing the trabecular micro-architecture in detail, and included a non-linear constitutive model for the bone tissue that allowed for plastic yielding, different strengths in tension and compression, large deformations, and, uniquely, localized damage once a specified limit in tissue-level ultimate strain was exceeded. Those strain limits were based on reported (mean ± SD) values from cadaver experiments (8.8 ± 3.7% strain for trabecular tissue and 2.2 ± 0.9% for cortical tissue). In the parameter study, the strain limits were varied by ±1 SD from their mean values, for a combination of nine analyses per specimen; bounding values of zero and unlimited post-yield strain were also modeled. The main outcomes from the finite element analysis were the vertebral compressive strength and the amount of failed (yielded or damaged) tissue at the overall structure-level failure. Compared to a reference case of using the mean values of ultimate strain, we found that varying both trabecular and cortical tissue ultimate strains by ±1 SD changed the computed vertebral strength by (mean ± SD) ±6.9 ± 1.1% on average. Mechanistically, that modest effect arose because the proportion of yielded tissue (without damage) was 0.9 ± 0.3% of all the bone tissue across the nine cases and the proportion of damaged tissue (i.e. tissue exceeding the prescribed tissue-level ultimate strain) was 0.2 ± 0.1%. If the types of variations in tissue-level ductility investigated here accurately represent real typical variations in the population, the consistency of our results across specimens and the modest effect size together suggest that typical variations in tissue-level ductility only have a modest impact on vertebral compressive strength, in large part because so few trabeculae are damaged at the load capacity of the bone.
尽管骨组织的延展性是骨质量的一个独特元素，并且随年龄和人群而变化，但典型人群组织延展性变化可以改变整体骨强度的程度和机制仍不清楚。为了提供深入了解，我们对六个人类 L1 椎体进行了整体（单调）压缩强度的有限元分析参数研究。每个模型都是从微 CT 扫描生成的，详细捕获了小梁微观结构，并包括用于骨组织的非线性本构模型，该模型允许塑性屈服、拉伸和压缩强度不同、大变形，以及唯一的局部损伤，一旦达到组织水平极限应变的指定限制。这些应变极限是基于尸体实验报告的（平均值 ± 标准差）值（小梁组织为 8.8 ± 3.7%应变，皮质组织为 2.2 ± 0.9%应变）。在参数研究中，应变极限在其平均值的 ±1 SD 范围内变化，每个标本进行了九次分析的组合；还模拟了零和无限后屈服应变的边界值。有限元分析的主要结果是椎体压缩强度和整体结构失效时失效（屈服或损坏）组织的量。与使用极限应变平均值的参考情况相比，我们发现，将小梁和皮质组织极限应变的平均值分别变化 ±1 SD，会导致计算出的椎体强度平均变化 ±6.9 ± 1.1%。从机制上讲，这种适度的影响是由于屈服组织（无损伤）的比例在 9 种情况下为所有骨组织的 0.9 ± 0.3%，而受损组织（即超过规定的组织水平极限应变的组织）的比例为 0.2 ± 0.1%。如果这里研究的组织延展性变化类型准确代表了人群中的典型变化，那么我们的结果在标本之间的一致性和适度的效应大小表明，组织延展性的典型变化对椎体压缩强度只有适度的影响，在很大程度上是因为在骨骼的承载能力下，只有很少的小梁受损。
