Quantifying Changes in the Bone Microarchitecture using Minkowski-Functionals and Scaling Vectors: a Comparative Study

摘要

Osteoporosis is a metabolic bone disease leading to de-mineralization and increased risk of fracture. The two major factors that determine the biomechanical competence of bone are the degree of mineralization and the micro-architectural integrity. Today, modern imaging modalities exist that allow to depict structural details of trabecular bone tissue. Recently, non-linear techniques in 2D and 3D based on the scaling vector method (SVM) and the Minkowski functionals (MF) have been introduced, which show excellent performance in predicting bone strength and fracture risk. However, little is known about the performance of the various parameters with respect to monitoring structural changes due to progression of osteoporosis or as a result of medical treatment. We test and compare the two methodologies 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 parameter of the system, become discernible by applying both the MF and the locally adapted scaling vector method. The results obtained with SVM are superior to those obtained with the Minkowski functionals. An additive combination of both measures drastically increases the sensitivity to slight changes in bone structures. 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.