Assessing methods for characterising local and global structural and biomechanical properties of the trabecular bone network.

We apply noval techniques, the Scaling Index Method (SIM), which reveals local topology of the structure, and the Minkowski Functionals (MF), which provide four global topological characteristics, to assess strength of the trabecular network of the human bone. We compare capabilities of these methods with the standard analysis, biomechanical Finite Element Method (FEM) and morphological parameters, in prediction of bone strength and fracture risk. Our study is based on a sample of 151 specimens taken from the trabecular part of human thoracic and lumbar vertebrae in vitro, visualised using µCT imaging (isotropic resolution 26µm) and tested by uniaxial compression. The sample of donors is heterogeneous, consisting of 58 male and 54 female cadavers with a mean age of 80 ±10 years. To estimate the predictive power of the methods, we correlate texture measures derived from µCT images with the maximum compressive strength (MCS) as obtained in biomechanical tests. A linear regression analysis reveals that the failure load estimated by FEM shows the highest correlation with MCS (Pearson's correlation coefficient r=0.76). None of the methods in current study is superior to the FEM: morphometric parameters give r<0.5, global topological characteristics show r=0.73 for the first Minkowski Functional MF₁, which coincides with bone volume fraction BV/TV and r=0.61 for the second Minkowski functional MF₂, which coincides with bone surface BS. Although scaling indices provided by SIM correlate only moderately with MCS (r=0.55), texture measures based on the nonlinear combination of local (SIM) and global (MF) topological characteristics demonstrate high correlation with experimental MCS (r=0.74) and with failure load estimated by FEM (r=0.95). Additional advantage of the proposed texture measures is possibility to reveal the role of the topologically different trabecular structure elements for the bone strength.