The influence of boundary conditions and loading mode on high-resolution finite element-computed trabecular tissue properties

A widely used technique for determining the material properties of trabecular tissue is to perform combined experimental and computational testing of trabecular structures in order to calibrate effective tissue properties. To better understand the nature of such properties, we tested n = 25 cores of human vertebral trabecular bone under two different boundary conditions (endcap and PMMA embedding) and loading modes (compression and torsion). High-resolution (20 µm) finite element models that explicitly modeled the different experimental conditions were constructed and sensitivity studies were performed to quantify errors arising from uncertainties between model and experiment. Mean (± S.D.) effective tissue modulus for the four groups ranged from 9.6 ± 1.9 to 11.5 ± 3.5 GPa, and the overall mean was 10.3 ± 2.4 GPa. For the endcap tests, mean values were the same regardless of loading mode, suggesting that the effective tissue modulus is representative of true material behavior. However, on a specimen-specific basis, the various repeated measures of effective tissue modulus were only moderately correlated with each other (R2 = 27% to 81%), indicating that the individual measures can be subject to appreciable random errors. The sensitivity studies on the endcap tests indicated that models using lower resolution (40 µm element size) and roller-type platens boundary conditions overestimated effective tissue modulus by 42% on average, although preliminary tests with higher-density femoral neck bone indicated less sensitivity to modeling issues. We conclude that effective tissue properties derived from micro-finite element models do have biomechanical significance if measured correctly, although individual measures of tissue properties may have poor precision.