Estimation of the effective yield properties of human trabecular bone using nonlinear micro-finite element analyses.

Micro-finite element ([Formula: see text]FE) analyses are often used to determine the apparent mechanical properties of trabecular bone volumes. Yet, these apparent properties depend strongly on the applied boundary conditions (BCs) for the limited size of volumes that can be obtained from human bones. To attenuate the influence of the BCs, we computed the yield properties of samples loaded via a surrounding layer of trabecular bone ("embedded configuration"). Thirteen cubic volumes (10.6 mm side length) were collected from [Formula: see text]CT reconstructions of human vertebrae and femora and converted into [Formula: see text]FE models. An isotropic elasto-plastic material model was chosen for bone tissue, and nonlinear [Formula: see text]FE analyses of six uniaxial, shear, and multi-axial load cases were simulated to determine the yield properties of a subregion (5.3 mm side length) of each volume. Three BCs were tested. Kinematic uniform BCs (KUBCs: each boundary node is constrained with uniform displacements) and periodicity-compatible mixed uniform BCs (PMUBCs: each boundary node is constrained with a uniform combination of displacements and tractions mimicking the periodic BCs for an orthotropic material) were directly applied to the subregions, while the embedded configuration was achieved by applying PMUBCs on the larger volumes instead. Yield stresses and strains, and element damage at yield were finally compared across BCs. Our findings indicate that yield strains do not depend on the BCs. However, KUBCs significantly overestimate yield stresses obtained in the embedded configuration (+43.1 ± 27.9%). PMUBCs underestimate (-10.0 ± 11.2%), but not significantly, yield stresses in the embedded situation. Similarly, KUBCs lead to higher damage levels than PMUBCs (+51.0 ± 16.9%) and embedded configurations (+48.4 ± 15.0%). PMUBCs are better suited for reproducing the loading conditions in subregions of the trabecular bone and deliver a fair estimation of their effective (asymptotic) yield properties.

Not only stiffness, but also yield strength of the trabecular structure determined by non-linear µFE is best predicted by bone volume fraction and fabric tensor.

The micro-architecture of cancellous bone is considered a major determinant of the fracture risk. Yet, if morphometry tells about alterations of the trabecular network, its elastic behaviour is best described by bone volume fraction (BV/TV) and the fabric tensor, which gives the anisotropy of the trabecular structure. This remains to be proven for yield strength, the onset of bone failure. The microstructure of 126 samples extracted from femoral heads of two female subjects was evaluated on micro-computed tomography scans via 25 structural indices. Parameters such as plate and rod decomposition via ITS and textural analyses by ISV, similar to the trabecular bone score, were also examined. The degree of collinearity between indices was assessed. The indices considered sufficiently independent were included in multi-linear regression models predicting stiffness or yield strength measured via nonlinear micro finite element analyses. The models' accuracy was checked and the contributions of all explanatory variables to the prediction were compared. Our results show that BV/TV alone explained most of the predicted yield strength (76%) and stiffness (89%). BV/TV together with the fabric tensor explained more than 98% of both measures! The fabric tensor also had a larger impact on yield strength (23%) than on the stiffness predictions (9%). On the other hand, the predictive value of the other independent factors (Tb.Th.SD, Tb.Sp.SD, rTb.Th, RR.Junc.D, ISV) was negligible (<1%). In conclusion, just as stiffness, yield strength of femoral trabecular bone is also best explained by BV/TV and trabecular anisotropy, the latter being even more relevant in its post-elastic behaviour.

Comparison of mixed and kinematic uniform boundary conditions in homogenized elasticity of femoral trabecular bone using microfinite element analyses.

Mechanical properties of human trabecular bone play an important role in age-related bone fragility and implant stability. Microfinite element (lFE) analysis allows computing the apparent elastic properties of trabecular bone for use in homogenized FE (hFE) analysis,but the results depend unfortunately on the type of applied boundary conditions(BCs). In this study, 167 human femoral trabecular cubic regions with a side length of 5.3mm were extracted from three proximal femora and analyzed using lFE analysis to compare systematically their stiffness with kinematic uniform BCs (KUBCs) and periodicity-compatible mixed uniform BCs (PMUBCs). The obtained elastic constants were then used in the volume fraction and fabric-based orthotropic Zysset­Curnier model to identify their respective model parameters. As expected, PMUBCs lead to more compliant apparent elastic properties than KUBCs, especially in shear. The differences in stiffness decreased with bone volume fraction and mean intercept length (MIL). Unlike KUBCs, PMUBCs were sensitive to heterogeneity of the biopsies. The Zysset­Curnier model fitted the apparent elastic constants successfully in both cases with adjusted coefficients of determination (r2adj) of 0.986 for KUBCs and 0.975 for PMUBCs. The proper use of these BCs for hFE analysis of whole bones will need to be investigated in future work.