Introduction

Ultimate strength-density relationships for bone have been reported with widely varying results. Reliable bone strength predictions are crucial for many applications that aim to assess bone failure. Bone density and bone morphology have been proposed to explain most of the variance in measured bone strength. If this holds true, it could lead to the derivation of a single ultimate strength-density-morphology relationship for all anatomical sites.

Methods

All relevant literature was reviewed. Ultimate strength-density relationships derived from mechanical testing of human bone tissue were included. The reported relationships were translated to ultimate strength-apparent density relationships and normalized with respect to strain rate. Results were grouped based on bone tissue type (cancellous or cortical), anatomical site, and loading mode (tension vs. compression). When possible, the relationships were compared to existing ultimate strength-density-morphology relationships.

Results

Relationships that considered bone density and morphology covered the full spectrum of eight-fold inter-study difference in reported compressive ultimate strength-density relationships for trabecular bone. This was true for studies that tested specimens in different loading direction and tissue from different anatomical sites. Sparse data was found for ultimate strength-density relationships in tension and for cortical bone properties transverse to the main loading axis of the bone.

Conclusions

Ultimate strength-density-morphology relationships could explain measured strength across anatomical sites and loading directions. We recommend testing of bone specimens in other directions than along the main trabecular alignment and to include bone morphology in studies that investigate bone material properties. The lack of tensile strength data did not allow for drawing conclusions on ultimate strength-density-morphology relationships. Further studies are needed. Ideally, these studies would investigate both tensile and compressive strength-density relationships, including morphology, to close this gap and lead to more accurate evaluation of bone failure.

中文翻译：

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骨密度与极限强度之间的经验关系：文献综述。

介绍

据报道，骨骼的最终强度-密度关系具有广泛变化的结果。可靠的骨强度预测对于旨在评估骨衰竭的许多应用至关重要。已经提出了骨密度和骨形态来解释测得的骨强度的大多数变化。如果这成立，则可能导致所有解剖部位的最终极限强度-密度-形态关系推导。

方法

所有相关文献进行了审查。包括从人体骨组织的机械测试得出的极限强度-密度关系。将报告的关系转换为极限强度-表观密度关系，并就应变率进行标准化。根据骨组织类型（松质或皮质），解剖部位和负荷模式（张力与压缩）对结果分组。在可能的情况下，将该关系与现有的最终强度-密度-形态关系进行比较。

结果

考虑骨密度​​和形态的关系涵盖了报道的小梁骨最终抗压强度-密度关系的八倍研究间差异。对于在不同的加载方向和不同解剖部位的组织中测试标本的研究而言，这是正确的。稀疏的数据发现了最终的拉伸强度强度-密度关系以及横向于骨主载荷轴的皮质骨特性。

结论

最终的强度-密度-形态关系可以解释跨解剖部位和加载方向测得的强度。我们建议在沿骨小梁排列方向以外的其他方向测试骨骼标本，并在研究骨骼材料特性的研究中纳入骨骼形态。缺乏抗张强度数据无法得出关于最终强度-密度-形态关系的结论。需要进一步研究。理想情况下，这些研究将研究包括形态在内的拉伸强度和压缩强度-密度关系，以缩小这一差距并导致更准确地评估骨衰竭。