The sensitivity of nonlinear computational models of trabecular bone to tissue level constitutive model

Abstract

Microarchitectural finite element models have become a key tool in the analysis of trabecular bone. Robust, accurate, and validated constitutive models would enhance confidence in predictive applications of these models and in their usefulness as accurate assays of tissue properties. Human trabecular bone specimens from the femoral neck (n = 3), greater trochanter (n = 6), and lumbar vertebra (n = 1) of eight different donors were scanned by μ-CT and converted to voxel-based finite element models. Unconfined uniaxial compression and shear loading were simulated for each of three different constitutive models: a principal strain-based model, Drucker–Lode, and Drucker–Prager. The latter was applied with both infinitesimal and finite kinematics. Apparent yield strains exhibited minimal dependence on the constitutive model, differing by at most 16.1%, with the kinematic formulation being influential in compression loading. At the tissue level, the quantities and locations of yielded tissue were insensitive to the constitutive model, with the exception of the Drucker–Lode model, suggesting that correlation of microdamage with computational models does not improve the ability to discriminate between constitutive laws. Taken together, it is unlikely that a tissue constitutive model can be fully validated from apparent-level experiments alone, as the calculations are too insensitive to identify differences in the outcomes. Rather, any asymmetric criterion with a valid yield surface will likely be suitable for most trabecular bone models.

Keywords::

• trabecular bone
• constitutive model
• finite element method
• yield
• nonlinear

Notes

^1. Email: [email protected]

^2. Email: [email protected]

^3. Email: [email protected]

Additional information

Funding

This work was partially supported by the National Institutes of Health [grant number AR052008]; and U.S. Army Telemedicine & Advanced Technology Research Center [grant number W81XWH-09-1-0741].