Three-dimensional finite element modelling of bone: effects of element size

Abstract

This study quantifies the effects of element size on the stress/strain results of finite element (FE) models of bone that are generated with a previously described automated method. This method uses cube-shaped hexahedral elements, which enabled element shape and aspect ratio to be held constant while the effects of element size were studied. Three models of a human proximal femur, each with a different element size (3.1 mm, 3.8 mm and 4.8 mm), were analysed. Convergence in strain energy of the models had been verified in previous work. The stresses and strains predicted by the models were compared on a pointwise basis using linear regression analysis. There was a general decrease in the level of stress and strain when element size was increased, even though convergence in strain energy had been achieved. An increase in element width from 3.1 mm to 3.8 mm decreased the predicted stresses by 13% to 29% overall; the predicted strains decreased by 4% to 20% for the same increase in element size. These results indicate that linear cube-shaped hexahedral elements must be very small (3 mm on a side or smaller) to represent the sharp variations in mechanical properties that exist in bone, and that use of larger elements decreases the predicted stresses and strains. The elements used in this study are similar to those typically used to represent trabecular bone in conventional (non-automated) FE modelling methods. Therefore, the sensitivity of the stress/strain results to element size that was found for trabecular bone also applies to conventional modelling of such bone. This sensitivity to element size implies that quantitative comparisons of the stresses/strains predicted in trabecular bone by different FE models may not be meaningful if the elements in those models are not the same size. The qualitative results of all three models were in agreement, however, indicating that qualitative comparisons of FE models may be made.