Uniaxial yield strains for bovine trabecular bone are isotropic and asymmetric

Abstract

Although evidence suggests that yield strains for trabecular bone are isotropic, i.e., independent of loading direction, decisive support for this hypothesis has remained elusive. To explicitly test whether yield strains for trabecular bone are isotropic, compressive and tensile yield strains of 51 specimens of bovine tibial trabecular bone (0.41 +/- 0.08 g/cm3 [mean apparent density +/- SD]) were measured without end artifacts in on-axis (along the principal trabecular orientation) and off-axis (30-40 degrees oblique to on-axis) orientations. Yield strains for the on-axis and off-axis orientations were similar in tension (0.80 +/- 0.03% compared with 0.85 +/- 0.04%, p = 0.21) and compression (0.97 +/- 0.05% compared with 0.96 +/- 0.07%, p > 0.99); as expected, modulus and strength depended on loading direction. When considered with an ancillary experiment on bovine tibial trabecular bone that showed yield strains to be similar between on-axis and 90 degrees off-axis bone, these results firmly establish the isotropy of uniaxial yield strains for bovine tibial trabecular bone. This bone is of high density and has a strong, plate-type, anisotropic architecture. Therefore, yield strains for uniaxial loading are expected to be isotropic, or nearly so, for other types of dense trabecular bone, although further work is required to confirm this and to establish this behavior for bone of lower density.

Contribution of inter-site variations in architecture to trabecular bone apparent yield strains

“…This had the effect of lowering both the compressive and tensile apparent yield strains for these data as compared to our previously published values (Chang et al, 1999;Keaveny et al, 1994b). The reprocessed mean (7SD) apparent compressive and tensile yield strains for this site were 0.79 (70.06)% and 0.61 (70.06)%, respectively.…”

“…In each loading mode, computed apparent yield strains were compared across anatomic site and against experimental data (Chang et al, 1999;) using a two-factor ANOVA and Tukey post hoc test (JMP 5.0, SAS Institute, Cary, NC). Although the comparison of computed values across site was the primary comparison in this study design, the comparison against experimental values was important for two reasons.…”

Subject-specific finite element models implementing a maximum principal strain criterion are able to estimate failure risk and fracture location on human femurs tested in vitro

“…A maximum principal strain criterion, including asymmetry in the tensile/compressive limit values, was selected because it incorporates many of the fundamental bone elastic limit characteristics reported in the literature: isotropy in mono-axial loading conditions (Chang et al, 1999), invariance with respect to density (Kopperdahl and Keaveny, 1998;Keaveny et al, 2001), at least for the same anatomical site , and tensile/ compressive asymmetry Niebur et al, 2000); it can be easily implemented in an automated subject-specific FE model maintaining the highest possible degree of automation. The tensile and compressive elastic limit strain values adopted (Table 3) were the mean values reported in a recent study on cortical and trabecular tissue (Bayraktar et al, 2004b), applying a well-standardised protocol that minimises experimental errors.…”

“…Recent advances in basic bone biomechanics proved the effectiveness of strain-based criteria to describe yield or failure of bone tissue (at least in normal bone, showing normal degree of mineralisation and no genetic alterations): bone failure has been shown to be driven by deformation (Nalla et al, 2003;Taylor, 2003), there is a growing consensus on the substantial isotropy of yield strain and on its invariance to density (Bayraktar et al, 2004b;Chang et al, 1999;Cowin and He, 2005;Currey, 2004;Kopperdahl and Keaveny, 1998), and a strain-based criteria managed to well fit mono-and multi-axial experimental data (Bayraktar et al, 2004a). Thus, it seems advisable to implement strain-based criteria in FE models of bone for the prediction of fracture risk.…”

Incorporating uncertainty in mechanical properties for finite element-based evaluation of bone mechanics

“…Experimental studies have shown yield strain to be isotropic (Chang et al, 1999) and uniform within an anatomic site (Morgan and Keaveny, 2001). The probabilistic platform could be similarly applied to modulus and yield strain, based on, for example, standard deviations associated with yield strain (Chang et al, 1999).…”