12 May 2004 Application of the Minkowski functionals in 3D to high-resolution MR images of trabecular bone: prediction of the biomechanical strength by nonlinear topological measures
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Abstract
Multi-dimensional convex objects can be characterized with respect to shape, structure, and the connectivity of their components using a set of morphological descriptors known as the Minkowski functionals. In a 3D Euclidian space, these correspond to volume, surface area, mean integral curvature, and the Euler-Poincaré characteristic. We introduce the Minkowski functionals to medical image processing for the morphological analysis of trabecular bone tissue. In the context of osteoporosis-a metabolic disorder leading to a weakening of bone due to deterioration of micro-architecture-the structure of bone increasingly gains attention in the quantification of bone quality. The trabecular architecture of healthy cancellous bone consists of a complex 3D system of inter-connected mineralised elements whereas in osteoporosis the micro-structure is dominated by gaps and disconnections. At present, the standard parameter for diagnosis and assessment of fracture risk in osteoporosis is the bone mineral density (BMD) - a bulk measure of mineralisation irrespective of structural texture characteristics. With the development of modern imaging modalities (high resolution MRI, micro-CT) with spatial resolutions allowing to depict individual trabeculae bone micro-architecture has successfully been analysed using linear, 2- dimensional structural measures adopted from standard histo-morphometry. The preliminary results of our study demonstrate that due to the complex - i.e. the non-linear - network of trabecular bone structures non-linear measures in 3D are superior to linear ones in predicting mechanical properties of trabecular bone from structural information extracted from high resolution MR image data.
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Holger F. Boehm, Holger F. Boehm, Thomas M. Link, Thomas M. Link, Roberto A. Monetti, Roberto A. Monetti, Dirk Mueller, Dirk Mueller, Ernst J. Rummeny, Ernst J. Rummeny, David Newitt, David Newitt, Sharmila Majumdar, Sharmila Majumdar, Christoph W. Raeth, Christoph W. Raeth, } "Application of the Minkowski functionals in 3D to high-resolution MR images of trabecular bone: prediction of the biomechanical strength by nonlinear topological measures", Proc. SPIE 5370, Medical Imaging 2004: Image Processing, (12 May 2004); doi: 10.1117/12.532835; https://doi.org/10.1117/12.532835
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