Convergence behavior of high-resolution finite element models of trabecular bone

The convergence behavior of finite element models depends on the size of el ements used, the element polynomial order, and on the complexity of the app lied loads. For high-resolution models of trabecular bone, changes in archi tecture and density may also be important. The goal of this study was to in vestigate the influence of these factors on the convergence behavior of hig h-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging f rom 20 to 80 mu m and subjected to both compressive and shear loading. Resu lts indicated that convergence behavior depended on both lending mode (axia l versus shear) and volume fraction of the specimen. Compared to the 20 mu m resolution, the differences in apparent Young's modulus at 40 mu m resolu tion were less than 5 percent for all specimens, and for apparent shear mod ulus were less than 7 percent. By contrast, differences at 80 mu m resoluti on in apparent modulus were up to 41 percent, depending on the specimen tes ted and loading mode. Overall, differences in apparent properties were alwa ys less than 10 percent when the ratio of mean trabecular thickness to elem ent size was greater than four. Use of higher order elements did not improv e the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points ra ther than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.