Is yield strain in cancellous bone isotropic?

Abstract

In science, one must never publish raw data lest someone reanalyze it and reach different conclusions. Several years ago (Turner, 1989), I demonstrated, quite convincingly (I thought), that yield strain in cancellous bone was not dependent upon trabecular anisotropy and, therefore, virtually isotropic. This finding has important implications conceming failure modes and adaptation of cancellous bone (Turner, 1992). However, Keaveny et al. (1994b) reanalyzed my original data and came to the opposite conclusion as mine, yield strain in cancellous bone depends upon loading direction and, therefore, is anisotropic. what is most puzzling about this debate is that both Keaveny et al. and I are correct in our analyses if not in our interpretations. In my original study, I showed that a stereological measure of trabecular anisotropy called mean intercept length was not statistically correlated to the yield strain in femoral bone specimens. Thus, trabecular orientation does not affect yield strain, unlike yield stress which is strongly affected by the trabecular orientation (Turner, 1992). Consequently, these results suggest that a single yield strain value defines compressive failure in cancellous bone regardless of the trabecular architecture. This simple result suggests a fundamental rule in cancellous bone’s design: the structure will sustain exactly the same level of strain regardless of the direction of loading. It is at this point that Keaveny et al. step in to confuse the issue. They point out that my data show significant differences in yield strains measured in different testing directions. This result is correct, but possibly irrelevant. The distal femur, from where I obtained my specimens, has the property of shape-dependent anisotropy, i.e. the trabecular orientation in the condyle resembles spokes of a wheel and generally does not align with anatomical direction. Of course, the specimens were cut and tested along anatomical axes so the trabecular orientation was somewhat random relative to the testing direction. fUrthi?more, the specimens tested in one direction did not necessarily come from the same region of bone as specimens tested in the other directions. This is reflected in the statistical differences in specimen densities between the testing groups (Turner, 19&9). Thus, the differences in yield strains measured in different testing directions could reflect the fact that samples from diRerent regions were used in each testing direction and have nothing to do with material anisotropy. For these reasons, I find the arguments made by Keaveny et al. unconvincing. In sum, the argument of Keaveny et al. is this: yield strain varies with testing direction and is therefore anisotropic. I counter with the argument that, in my experiment, testing direction related very poorly to the true cancellous anisotropy, whereas mean intercept length was a direct measure of anisotropy specific to each specimen. Therefore, the proper measure of material anisotropy is mean intercept length which did not correlate with yield strain. I will leave it to the readers to determine which argument is valid. This is difficult task since both arguments were derived from the same data. Considering that the experimental techniques used to measure the data are now antiquated, one might suggest further study of this issue using the superior experimental techniques developed by Keaveny et al. (1994a, b).