An accurate estimation of bone density improves the accuracy of subject-specific finite element models

Abstract 

An experimental–numerical study was performed to investigate the relationships between computed tomography (CT)-density and ash density, and between ash density and apparent density for bone tissue, to evaluate their influence on the accuracy of subject-specific FE models of human bones.

Sixty cylindrical bone specimens were examined. CT-densities were computed from CT images while apparent and ash densities were measured experimentally. The CT/ash-density and ash/apparent-density relationships were calculated. Finite element models of eight human femurs were generated considering these relationships to assess their effect on strain prediction accuracy.

CT and ash density were linearly correlated (R²=0.997) over the whole density range but not equivalent (intercep t <0, slope >1). A constant ash/apparent-density ratio (0.598±0.004) was found for cortical bone. A lower ratio, with a larger dispersion, was found for trabecular bone (0.459±0.100), but it became less dispersed, and equal to that of cortical tissue, when testing smaller trabecular specimens (0.598±0.036). This suggests that an experimental error occurred in apparent-density measurements for large trabecular specimens and a constant ratio can be assumed valid for the whole density range. Introducing the obtained relationships in the FE modelling procedure improved strain prediction accuracy (R²=0.95, RMSE=7%).

The results suggest that: (i) a correction of the densitometric calibration should be used when evaluating bone ash-density from clinical CT scans, to avoid ash-density underestimation and overestimation for low- and high-density bone tissue, respectively; (ii) the ash/apparent-density ratio can be assumed constant in human femurs and (iii) the correction improves significantly the model accuracy and should be considered in subject-specific bone modelling.

Keywords: Bone biomechanics, Bone density, Computed tomography, CT calibration, Subject-specific finite element model, Validation