Finite element dependence of stress evaluation for human trabecular bone
Résumé
Numerical simulation using finite element models (FEM) has become more and more
suitable to estimate the mechanical properties of trabecular bone. The size and kind of
elements involved in the models, however, may influence the results. The purpose of this
study is to analyze the influence of hexahedral elements formulation on the evaluation of
mechanical stress applied to trabeculae bone during a compression test simulation.
Trabecular bone cores were extracted from 18 L2 vertebrae (12 women and 6 men, mean
age: 76711, BV/TV¼7.571.9%). Samples were micro-CT scanned at 20 mm isotropic voxel
size. Micro-CT images have been sub-sampled (20, 40 and 80 mm) to create 5.6mm cubic
FEM. For each sample, a compression test FEM has been created, using either 8-nodes
linear hexahedral elements with full or reduced integration or 20-nodes quadratic
hexahedral elements fully integrated, resulting in nine models per samples. Bone
mechanical properties have been assumed isotropic, homogenous and to follow a linear
elastic behavior law (Young modulus: 8 GPa, Poisson ratio: 0.3).
Despite micro-architecture modifications (loss of connectivity, trabeculae thickening)
due to voxel size increase, apparent mechanical properties calculated with low resolution
models are significantly correlated with high resolution results, no matter the element
formulation. However, stress distributions are more sensitive to both resolution and
element formulation modifications. With linear elements, increasing voxel size leads to
an alteration of stress concentration areas due to stiffening errors. On the opposite, the use
of reduced integration induces severe smoothing and underestimation of stress fields
resulting in stress raisers loss. Notwithstanding their high computational cost, quadratic
elements are most appropriate for stress prediction in low resolution trabecular bone FEM.
These observations are dependent on trabecular bone micro-architecture, and are more
significant for low density sample displaying low trabecular thickness.
In conclusion, we found that element formulation is almost important as element size
when evaluating trabecular bone mechanical behavior at trabeculae scale. Therefore,
element type should be chosen carefully when evaluating trabecular bone behavior
using FEM.