Morgan Elise F, Bayraktar Harun H, Keaveny Tony M
Orthopaedic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, 6175 Etcheverry Hall, Berkeley, CA 94720-1740, USA.
J Biomech. 2003 Jul;36(7):897-904. doi: 10.1016/s0021-9290(03)00071-x.
One outstanding issue regarding the relationship between elastic modulus and density for trabecular bone is whether the relationship depends on anatomic site. To address this, on-axis elastic moduli and apparent densities were measured for 142 specimens of human trabecular bone from the vertebra (n=61), proximal tibia (n=31), femoral greater trochanter (n=23), and femoral neck (n=27). Specimens were obtained from 61 cadavers (mean+/-SD age=67+/-15 years). Experimental protocols were used that minimized end-artifact errors and controlled for specimen orientation. Tissue moduli were computed for a subset of 18 specimens using high-resolution linear finite element analyses and also using two previously developed theoretical relationships (Bone 25 (1999) 481; J. Elasticity 53 (1999) 125). Resultant power law regressions between modulus and density did depend on anatomic site, as determined via an analysis of covariance. The inter-site differences were among the leading coefficients (p<0.02), but not the exponents (p>0.08), which ranged 1.49-2.18. At a given density, specimens from the tibia had higher moduli than those from the vertebra (p=0.01) and femoral neck (p=0.002); those from the trochanter had higher moduli than the vertebra (p=0.02). These differences could be as large as almost 50%, and errors in predicted values of modulus increased by up to 65% when site-dependence was ignored. These results indicate that there is no universal modulus-density relationship for on-axis loading. Tissue moduli computed using methods that account for inter-site architectural variations did not differ across site (p>0.15), suggesting that the site-specificity in apparent modulus-density relationships may be attributed to differences in architecture.
关于松质骨弹性模量与密度之间的关系，一个突出问题是这种关系是否取决于解剖部位。为解决这一问题，对取自椎骨（n = 61）、胫骨近端（n = 31）、股骨大转子（n = 23）和股骨颈（n = 27）的142例人松质骨标本测量了轴向弹性模量和表观密度。标本取自61具尸体（平均±标准差年龄 = 67±15岁）。采用了能将端部伪影误差降至最低并控制标本取向的实验方案。使用高分辨率线性有限元分析以及两种先前开发的理论关系（《骨》25 (1999) 481；《弹性学杂志》53 (1999) 125），为18个标本的子集计算了组织模量。通过协方差分析确定，模量与密度之间的幂律回归确实取决于解剖部位。部位间差异存在于首项系数之间（p < 0.02），但指数之间无差异（p > 0.08），指数范围为1.49 - 2.18。在给定密度下，胫骨标本的模量高于椎骨标本（p = 0.01）和股骨颈标本（p = 0.002）；大转子标本的模量高于椎骨标本（p = 0.02）。这些差异可能高达近50%，当忽略部位依赖性时，模量预测值的误差增加高达65%。这些结果表明，对于轴向加载不存在通用的模量 - 密度关系。使用考虑部位间结构变化的方法计算的组织模量在各部位之间无差异（p > 0.15），这表明表观模量 - 密度关系中的部位特异性可能归因于结构差异。
