Anisotropic mechanical characterization of trabecular bone with linear and non-linear voxel-based finite elements...

Bone structural and mechanical properties predict fragility fractures, but unexplained variance remains. A better quantification of the anisotropic nature of bone, and an improved model-based prediction of bone failure load could fill in this gap. Yet, quantifying mechanical anisotropy requires high-resolution imaging modalities, which are often lacking in clinical practice. This study used voxel-based finite element (FE) models from high-resolution photon-counting CT (PCCT) and conventional energy-integrating detector CT (EIDCT) to mechanically characterize trabecular bone samples from vertebrae. Ten trabecular cubical samples from bovine lumbar vertebrae were scanned with PCCT, EIDCT and micro-CT (μCT), calibrated to bone mineral density values, and images were converted to voxel-based FE meshes. A density-scaled linear-elastic material model was employed to calculate the apparent stiffness tensor in the orthotropic direction, and results from PCCT and EIDCT were compared to μCT-based reference values. Anisotropy of the resulting linear-elastic material parameters was quantified as the ratio of axial to transverse moduli. Next, a non-linear density-scaled material model that included a plastic and strain-softening phase was used to quantify failure load. Anisotropy of failure load in the orthotropic directions was compared between PCCT and EIDCT, and axial failure load was compared to experimental measurements. For PCCT, all apparent Young's and shear moduli showed no systematic bias with respect to μCT; in contrast, EIDCT systematically overestimated all transverse moduli, and underestimated the axial Young's modulus. As a result, the anisotropic nature of bone was better quantified with PCCT (1.71 ± 0.28) than with EIDCT (1.22 ± 0.14). Similarly, PCCT demonstrated higher anisotropy of failure loads in the orthotropic directions (1.75 ± 0.27) than EIDCT did (1.28 ± 0.17). Compared to experimental measurements, all voxel-based FE models underestimated failure load, yet, adjusted R² was higher for PCCT (0.91) than for EIDCT (0.84). For multivariate linear models that incorporated both FE failure load and trabecular bone microarchitecture, adjusted R² increased to 0.98 for PCCT, and 0.91 for EIDCT. We conclude that the increased resolution of PCCT enables a better linear-elastic characterization as compared to EIDCT, and that PCCT is more predictive of failure load than EIDCT. This could aid in clinically relevant fracture risk predictions.