Keaveny T M, Borchers R E, Gibson L J, Hayes W C
Department of Orthopaedic Surgery, Charles A. Dana Research Institute, Beth Israel Hospital, Boston, MA 02215.
J Biomech. 1993 Aug;26(8):991-1000. doi: 10.1016/0021-9290(93)90059-n.
We performed a series of uniaxial compression tests on wet bovine trabecular bone to compare both modulus and strength when measured using 2:1 aspect ratio (10 mm long, 5 mm diameter) cylinders (n = 30) and 5 mm cubes (n = 29). We also compared the correlation coefficients in the resulting modulus-density and strength-density regressions and the standard errors of the estimate. When comparing the mean values of modulus and strength for each group, the confounding variations in apparent density were accounted for with an analysis of covariance. The Fisher's Z transformation was used to compare the correlation coefficients statistically. Results from the analysis of covariance indicated that the modulus and strength of the cubes were higher by 36% (p < 0.01) and 18% (p < 0.05), respectively, with respect to the 2:1 cylinder values. The correlation coefficients in the modulus-density and strength-density regressions were not sensitive to the regression model (linear versus power law). However, correlation coefficients for both modulus-density and strength-density regressions were higher (p < 0.05) for the 2:1 cylinders (r = 0.90, modulus; r = 0.94, strength) than for the cubes (r = 0.57, modulus; r = 0.82, strength). In addition, the standard errors of the estimate in both modulus and strength were substantially lower for the 2:1 cylinders. These data indicate that both modulus and strength can depend on the specimen geometry when using conventional compression testing techniques. We conclude, therefore, that inter-study comparisons of modulus and strength may be invalid if these confounding effects of different specimen geometries are not addressed. Our data also indicate that density can better explain the observed variance in modulus and strength when 2:1 cylinders are used as opposed to cubes. Using this phenomenon as a rationale for choosing a standard specimen gometry, we recommend that the 2:1 cylinder be used as a standard specimen in studies designed to determine the effects of various treatments on the uniaxial compressive modulus and strength of trabecular bone.
我们对湿牛松质骨进行了一系列单轴压缩试验,以比较使用长宽比为2:1(长10毫米,直径5毫米)的圆柱体(n = 30)和5毫米立方体(n = 29)测量时的模量和强度。我们还比较了所得模量 - 密度和强度 - 密度回归中的相关系数以及估计的标准误差。在比较每组的模量和强度平均值时,通过协方差分析考虑了表观密度的混杂变化。使用费舍尔Z变换对相关系数进行统计学比较。协方差分析结果表明,相对于2:1圆柱体的值,立方体的模量和强度分别高出36%(p < 0.01)和18%(p < 0.05)。模量 - 密度和强度 - 密度回归中的相关系数对回归模型(线性与幂律)不敏感。然而,2:1圆柱体的模量 - 密度和强度 - 密度回归的相关系数(p < 0.05)高于立方体(模量r = 0.90;强度r = 0.94)(模量r = 0.57;强度r = 0.82)。此外,2:1圆柱体的模量和强度估计标准误差都要低得多。这些数据表明,使用传统压缩测试技术时,模量和强度都可能取决于试样几何形状。因此,我们得出结论,如果不解决不同试样几何形状的这些混杂效应,模量和强度的研究间比较可能无效。我们的数据还表明,与立方体相比,使用2:1圆柱体时,密度能更好地解释观察到的模量和强度方差。以这种现象作为选择标准试样几何形状的依据,我们建议在旨在确定各种处理对松质骨单轴压缩模量和强度影响的研究中,使用2:1圆柱体作为标准试样。