Trabecular bone (TB) consists of a network of interconnected struts and plates occurring near the joints of long bones and in the axial skeleton. In response to mechanical stresses it remodels such that trabeculae are aligned with the major stress lines, thus leading to a highly anisotropic network. Beside bone volume fraction, anisotropy and topological indices are known to be strong predictor of the TB mechanical competence. In osteoporosis, the most common bone disorder, the remodeling balance is perturbed due to increased resorption, resulting in net bone loss accompanied by architectural deterioration, leading to fragile bone and increased fracture risk. In vertebral osteoporosis, preferential loss of transverse trabeculae leads to increased anisotropy and change in topology, hence exact measurements of these parameters are of paramount interest. Current in vivo imaging yields voxel size comparable to TB thickness, thus resulting in inherently fuzzy representations. The commonly used methods for anisotropy require binarization which is difficult to achieve in the limited spatial resolution regime where the intensity histogram is mono-modal. Here, we present a new tensor scale (t-scale) based TB architectural measures that (1) obviates binarization, and (2) yields localized measures. We evaluate the performance of this method on micro-CT images of vertebral bone and test the hypothesis that the method, along with BMD and other structural parameters, allows prediction of TB's mechanical competence. Toward this goal, we estimate Young's modulus (YM) of (13mm)3 vertebral TB samples under uniaxial loading and examine linear correlation of different t-scale parameters computed via micro-CT imaging .
