Classification of trabeculae into three-dimensional rodlike and platelike structures via local inertial anisotropy

Trabecular bone microarchitecture is a significant determinant of the bone's mechanical properties and is thus of major clinical relevance in predicting fracture risk. The three-dimensional nature of trabecular bone is characterized by parameters describing scale, topology, and orientation of structural elements. However, none of the current methods calculates all three types of parameters simultaneously and in three dimensions. Here the authors present a method that produces a continuous classification of voxels as belonging to platelike or rodlike structures that determines their orientation and estimates their thickness. The method, dubbed local inertial anisotropy (LIA), treats the image as a distribution of mass density and the orientation of trabeculae is determined from a locally calculated tensor of inertia at each voxel. The orientation entropies of rods and plates are introduced, which can provide new information about microarchitecture not captured by existing parameters. The robustness of the method to noise corruption, resolution reduction, and image rotation is demonstrated. Further, the method is compared with established three-dimensional parameters including the structure-model index and topological surface-to-curve ratio. Finally, the method is applied to data acquired in a previous translational pilot study showing that the trabecular bone of untreated hypogonadal men is less platelike than that of their eugonadal peers.