The Role of Cortical Shell and Trabecular Fabric in Finite Element Analysis of the Human Vertebral Body

Classical finite element (FE) models can estimate vertebral stiffness and strength with much lower computational costs than $μFE$ analyses, but the accuracy of these models rely on calibrated material properties that are not necessarily consistent with experimental results. In general, trabecular bone material properties are scaled with computer tomography (CT) density alone, without accounting for local variations in anisotropy or micro-architecture. Moreover, the cortex is often omitted or assigned with a constant thickness. In this work, voxel FE models, as well as surface-based homogenized FE models with topologically-conformed geometry and assigned with experimentally validated properties for bone, were developed from a series of 12 specimens tested up to failure. The effects of changing from a digital mesh to a smooth mesh, including a cortex of variable thickness and/or including heterogeneous trabecular fabric, were investigated. In each case, FE predictions of vertebral stiffness and strength were compared with the experimental gold-standard, and changes in elastic strain energy density and damage distributions were reported. The results showed that a smooth mesh effectively removed zones of artificial damage locations occurring in the ragged edges of the digital mesh. Adding an explicit cortex stiffened and strengthened the models, unloading the trabecular centrum while increasing the correlations to experimental stiffness and strength. Further addition of heterogeneous fabric improved the correlations to stiffness $(R2=0.72)$ and strength $(R2=0.89)$ and moved the damage locations closer to the vertebral endplates, following the local trabecular orientations. It was furthermore demonstrated that predictions of vertebral stiffness and strength of homogenized FE models with topologically-conformed cortical shell and heterogeneous trabecular fabric correlated well with experimental measurements, after assigning purely experimental data for bone without further calibration of material laws at the macroscale of bone. This study successfully demonstrated the limitations of current classical FE methods and provided valuable insights into the damage mechanisms of vertebral bodies.