Bone strength is a fundamental contributor to fracture risk, and with the recent development of in vivo 3D bone micro-architecture measurements by high-resolution peripheral quantitative computed tomography, the finite element (FE) analysis may provide a means to assess patient bone strength in the distal radius. The purpose of this study was to determine an appropriate FE procedure to estimate bone strength by comparison with experimental data. Models based on a homogeneous tissue modulus or a modulus scaled according to computed tomography attenuation were assessed, and these were solved by linear and non-linear FE analyses to estimate strength.
The distal radius from fresh, human cadaver forearms (5 male/5 female, ages 55 to 93) was dissected free and four 9.1 mm sections were cut beginning at the subchondral plate to provide 40 test specimens. The sections were scanned using an in vivo protocol providing 3D image data with an 82 μm voxel size. All specimens were mechanically tested in uniaxial compression, and elastic and yield properties were determined. Linear FE analyses were performed on all specimens (N = 40), and non-linear analyses using an asymmetric, bilinear yield strain criteria were performed on a sub-sample (N = 10) corresponding to the normal clinical measurement site.
Experimentally determined apparent elastic properties correlated highly with ultimate stress (R2 = 0.977, p < 0.05, N = 31) for the 31 specimens tested to failure. Subsequently, a linear FE analysis estimating apparent elastic properties also correlated highly with failure, and the correlation was higher when moduli were determined from scaled CT-attenuation values than a homogeneous modulus (R2 = 0.983 vs. R2 = 0.972, p < 0.05, N = 31). A non-linear analysis based on tensile and compressive yield strains of 0.0295 and 0.0493 for homogeneous models, and 0.0127 and 0.0212 for scaled models directly estimated ultimate stress, and correlated highly (R2 = 0.951 vs. R2 = 0.937, p < 0.05, N = 5).
The linear relation between stiffness and strength may be unique to radius compressive loading. It supports the use of a linear FE analysis to determine bone strength by regression equations established here. Scaled tissue modulus models performed better than homogeneous modulus models, and the advantage of a scaled model is its potential to account for mineralization changes. The combined numerical–experimental procedure for FE model validation on the patient micro-CT technology demonstrated that bone strength can be estimated non-invasively, and this may provide important insight into fracture risk in patient populations.