A comparison of enhanced continuum FE with micro FE models of human vertebral bodies.

Continuum finite element (FE) models are standard tools for determination of biomechanical properties of bones and bone-implant systems. This study investigates the accuracy of an enhanced continuum FE model by taking muFE as the gold standard. The enhanced continuum models account for trabecular bone morphology (density and fabric) as well as for an anatomically correct cortical shell. Vertebral body slice models are extracted from high-resolution CT images using an algorithm proposed in [Pahr and Zysset, 2008b. From high-resolution CT data to FE models: development of an integrated modular framework. Computer Methods in Biomechanics and Biomedical Engineering, in press.]. Three different models are generated: the proposed enhanced density-fabric-based model with a subject-specific cortex and two classical isotropic density-only models, with and without explicit modeling of the cortical shell. The material property errors of the used morphology-elasticity relationship are minimized by using elasticity tensors from 60 cubical muFE models which are cropped from the trabecular centrums of the investigated vertebral bodies. Two different boundary conditions-kinematic [Van Rietbergen et al., 1995. A new method to determine trabecular bone elastic properties and loading using micromechanical FE models. Journal of Biomechanics 28 (1), 69-81] and mixed [Pahr, D.H., Zysset, P.K., 2008a. Influence of boundary conditions on computed apparent elastic properties of cancellous bone. Biomechanics and Modeling in Mechanobiology 7, 463-476.]-are used in these FE models. After removal of the endplates, compressive and antero-posterior shear loading is applied on the investigated vertebral bodies. Individual error sources are studied in more detail by loading also the trabecular centrum (removed shell) and the cortical shell alone. It is found that the cortex-only models need a correction of the shell thickness when transforming from a voxel to a smooth description. The trabecular centrum alone gives too stiff and too soft a response using material calibration with kinematic and mixed boundary conditions, respectively. A comparison of the whole vertebral body stiffnesses shows that an orthotropic cancellous bone material calibrated with kinematic boundary conditions corresponds best with muFE. Taken together, the proposed enhanced homogenized surface-based FE model is structurally more accurate than density-only models.