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J. Panyasantisuk, D. H. Pahr, T. Gross, P.K. Zysset:
"Comparison of Mixed and Kinematic Uniform Boundary Conditions in Homogenized Elasticity of Femoral Trabecular Bone Using Microfinite Element Analyses";
Journal of Biomechanical Engineering - Transactions of the ASME, 137 (2015), 1; 011002(7).

Mechanical properties of human trabecular bone play an important role in age-related bone fragility and implant stability. Microfinite element (μFE) 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 5.3 mm were extracted from three proximal femora and analyzed using μFE 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 Zysset-Curnier 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 Zysset-Curnier 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.

http://dx.doi.org/10.1115/1.4028968