Lieberman Daniel E, Polk John D, Demes Brigitte
Department of Anthropology, Peabody Museum, Harvard University, Cambridge, Massachusetts 02138, USA.
Am J Phys Anthropol. 2004 Feb;123(2):156-71. doi: 10.1002/ajpa.10316.
Long bone loading histories are commonly evaluated using a beam model by calculating cross-sectional second moments of areas (SMAs). Without in vivo strain data, SMA analyses commonly make two explicit or implicit assumptions. First, while it has long been known that axial compression superimposed on bending shifts neutral axes away from cross-sectional area centroids, most analyses assume that cross-sectional properties calculated through the area centroid approximate cross-sectional strength. Second, the orientation of maximum bending rigidity is often assumed to reflect the orientation of peak or habitual bending forces the bone experiences. These assumptions are tested in sheep in which rosette strain gauges mounted at three locations around the tibia and metatarsal midshafts measured in vivo strains during treadmill running at 1.5 m/sec. Calculated normal strain distributions confirm that the neutral axis of bending does not run through the midshaft centroid. In these animals, orientations of the principal centroidal axes around which maximum SMAs (Imax) are calculated are not in the same planes in which the bones experienced bending. Cross-sectional properties calculated using centroidal axes have substantial differences in magnitude (up to 55%) but high correlations in pattern compared to cross-sectional properties calculated around experimentally determined neutral axes. Thus interindividual comparisons of cross-sectional properties calculated from centroidal axes may be useful in terms of pattern, but are subject to high errors in terms of absolute values. In addition, cross-sectional properties do not necessarily provide reliable data on the orientations of loads to which bones are subjected.
长骨的加载历史通常使用梁模型通过计算截面面积二次矩（SMAs）来评估。在没有体内应变数据的情况下，SMA分析通常会做出两个明确或隐含的假设。首先，虽然长期以来人们都知道叠加在弯曲上的轴向压缩会使中性轴偏离截面质心，但大多数分析都假设通过截面质心计算的截面特性近似于截面强度。其次，最大抗弯刚度的方向通常被假定为反映骨骼所经历的峰值或习惯性弯曲力的方向。在绵羊身上对这些假设进行了测试，在绵羊的胫骨和跖骨中轴周围的三个位置安装了应变片，以测量其在跑步机上以1.5米/秒速度跑步时的体内应变。计算得出的法向应变分布证实，弯曲的中性轴并不穿过中轴质心。在这些动物中，计算最大SMA（Imax）所围绕的主质心轴方向与骨骼发生弯曲的平面并不相同。与围绕实验确定的中性轴计算的截面特性相比，使用质心轴计算的截面特性在大小上有很大差异（高达55%），但在模式上有高度相关性。因此，从质心轴计算得到的截面特性的个体间比较在模式方面可能是有用的，但在绝对值方面存在较大误差。此外，截面特性不一定能提供关于骨骼所承受载荷方向的可靠数据。
