Advantage of topological texture measures derived from Minkowski functionals (MF) and scaling index method (SIM) in comparison with biomechanical finite elements method (FEM) for the prediction of osteoporosis

Abstract

The assessment of trabecular bone microarchitecture by numerical analysis of high resolution magnetic resonance (HRMR) images provides global and local structural characteristics, which improve the understanding of the progression of osteoporosis and its diagnosis. In the present work we apply the finite elements method (FEM), which models the biomechanical behaviour of the bone, the scaling index method (SIM), which describes the topology of the structure on a local level, and Minkowski Functionals (MF), which are global topological characteristics, for analysing 3D HRMR images of 48 distal radius specimens in vitro. Diagnostic performance of texture measures derived from the numerical methods is compared with regard to the prevalence of vertebral fractures. Both topological methods show significantly better results than those obtained using bone mineral density (BMD) measurement and the failure load estimated by FEM. The receiver operating characteristic analysis for differentiating subjects with and without fractures reveals area under the curve of 0.63 for BMD, 0.66 for maximum compressive strength as determined in a biomechanical test, 0.72 for critical load estimated by FEM, 0.79 for MF₄ and 0.86 for SIM, i.e. local topological characteristics derived by SIM suit best for diagnosing osteoporosis. The combination of FEM and SIM on tissue level shows that in both weak and strong bones the plate-like substructure of the trabecular network are the main load bearing part of the inner bone and that the relative amount of plates to rods is the most important characteristic for the prediction of bone strength.