Improving the textural characterization of trabecular bone structure to quantify its changes: the locally adapted scaling vector method

We extend the recently introduced scaling vector method (SVM) to improve the textural characterization of oriented trabecular bone structures in the context of osteoporosis. Using the concept of scaling vectors one obtains non-linear structural information from data sets, which can account for global anisotropies. In this work we present a method which allows us to determine the local directionalities in images by using scaling vectors. Thus it becomes possible to better account for local anisotropies and to implement this knowledge in the calculation of the scaling properties of the image. By applying this adaptive technique, a refined quantification of the image structure is possible: we test and evaluate our new method using realistic two-dimensional simulations of bone structures, which model the effect of osteoblasts and osteoclasts on the local change of relative bone density. The partial differential equations involved in the model are solved numerically using cellular automata (CA). Different realizations with slightly varying control parameters are considered. Our results show that even small changes in the trabecular structures, which are induced by variation of a control parameters of the system, become discernible by applying the locally adapted scaling vector method. The results are superior to those obtained by isotropic and/or bulk measures. These findings may be especially important for monitoring the treatment of patients, where the early recognition of (drug-induced) changes in the trabecular structure is crucial.