The results of this nonlinear μFE analysis are plausible for a number of reasons. First, this μFE model was based on a high-resolution 3D model of acetabular trabecular bone scanned by μCT, indicating that this μFE model can be considered to represent an effective surrogate for real specimens.16,17 This kind of μFE model can successfully describe in detail the thickness, length, orientation of individual trabeculae and 3D microarchitecture of the trabecular bone. Second, the trabecular cube was scanned at 37 μm, and 37 μm is sufficiently high to obtain precise 3D images of the trabecular microstructure. Therefore, based on this high-resolution 3D model, the μFE analysis can accurately describe the tissue-level biomechanical properties and changes of the trabecular bone. A few previous studies that investigated the effects of voxel size on bone microstructural parameters calculated from μCT images and on the computed values of bone properties in μFE simulations proved that high-resolution scanning and reconstruction were important for achieving precise results using μFE analyses.18,19 Third, since this finite element formulation included geometric and material nonlinearity, the nonlinear μFE analyses could accurately describe the nonlinear behavior of the trabeculae and the strength asymmetry at the level of individual trabeculae.20 For highly porous bone, such as osteoporotic trabecular bone, the effects of geometric nonlinearity should be great. Owing to the material nonlinearity, our tissue-level constitutive model allowed strain softening (a negative modulus). Therefore, this approach included the physics essential for predicting apparent level strain softening. Finally, the results of our study agreed well with previous experimental studies on trabecular damage to human vertebral bone, which indicated that microdamage was the prevalent damage for modulus reduction versus small apparent strains.21,22
The micromechanics of our model dictate that loads at small apparent strains that are sufficiently large to cause microfractures would similarly induce severe amounts of microdamage in the trabecular bone of the osteoporotic acetabulum. Therefore, the biomechanical effects of microdamage dominated over those of microfracture, suggesting that microfracture should be viewed as an endpoint of microdamage accumulation with increasing apparent strains and providing an explanation for why microfractures were seldom observed in comparison to microdamage.21,22
Our data indicated that microdamage commenced at 0.2% apparent strain. When the relationship between modulus reduction and peak applied strain for human trabecular bone obtained in a previous compressive test is extrapolated,26 modulus reductions are predicted to commence at about 0.2% strain, which coincides with our result. Taken together, these findings may imply that the threshold of microdamage in trabecular bone should be 0.2% apparent strain regardless of differences in bone density, microstructure, anatomical site and age. The quartiles of the maximum principal logarithmic strains, minimum principal logarithmic strains and Von Mises stresses increased nonlinearly with the applied strains. In other words, these similarities imply that the continuous nonlinear increments in tissue-level strains and stresses result in nonlinear accelerated accumulation of microdamage in trabecular bone, whereby modulus reductions are initiated at an early point and then increase with apparent strain as microdamage propagates throughout the specimen.
Some limitations of this study should be mentioned. The first limitation is that the study does not have complementary experimental data regarding microdamage at small strains. With experimental measurements of microdamage, we would be able to gain insights into the physical deformation and bulking phenomena associated with the changes. However, it is very difficult, and perhaps impossible, to noninvasively quantify trabecular damage through biomechanical techniques at the tissue level.25 Some previous studies have indicated that nonlinear μFE analyses can precisely predict the tissue-level mechanical behavior of trabecular bone and that the results agree well with experimental data. Second, the computational requirements for these nonlinear μFE analyses are still excessive. For the analysis, the equivalent of 134 hours of CPU time was used. As a result, a parallel supercomputer is required to perform these analyses within a reasonable amount of wall-clock time. Finally, inhomogeneous FE models are more accurate representations of the heterogeneous distribution of tissue in trabecular bone. Hence, inhomogeneous FE analyses are expected to more precisely estimate the local stresses and strains in trabeculae than homogeneous FE analyses. However, a previous study found that there was less than 9% difference in the estimated stresses and strains between these two kinds of FE analyses.27
Biologically and clinically, the present results provide extra information about the tissue-level biomechanical nature of osteoporotic acetabular trabecular bone. From a biological perspective, our data indicate that microdamage and microfracture can take place in osteoporotic trabecular bone at relatively low apparent strains. As such small strains can be expected to happen during strenuous activity28 or daily life,8 it is possible that some form of subtle microdamage and microfracture can occur habitually, which subsequently induces biological responses that serve as a remodeling stimulus.29 On the contrary, such microdamage can decrease bone quality30 and increase fracture susceptibility31,32 if the microdamage accumulation is beyond the repair ability of the bone with aging. From a clinical perspective, since the trabeculae of cancellous bone have similar mechanical properties to those of cortical bone33,34 and cortical bone is often described as condensed trabeculae,35,36 such microdamage and microfracture may be doomed to occur in the cortical bone of the osteoporotic acetabulum at small apparent strains, which may play important roles in the aseptic loosening of acetabular prostheses. Therefore, further μFE analyses of the whole acetabular bone, including the cortical bone and trabecular bone, may help to provide insights into the biomechanical mechanism underlying the aseptic loosening of acetabular prostheses.
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