On Smoothing Surfaces in Voxel Based Finite Element Analysis of Trabecular Bone

The (micro-)finite element analysis based on three-dimensional computed tomography (CT) data of human bone takes place on complicated domains composed of often hundreds of millions of voxel elements. The finite element analysis is used to determine stresses and strains at the trabecular level of bone. It is even used to predict fracture of osteoporotic bone. However, the computed stresses can deteriorate at the jagged surface of the voxel model. There are algorithms known to smooth surfaces of voxel models. Smoothing however can distort the element geometries. In this study we investigate the effects of smoothing on the accuracy of the finite element solution, on the condition of the resulting system matrix, and on the effectiveness of the smoothed aggregation multigrid preconditioned conjugate gradient method.