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Proceedings Paper

Application of the Minkowski functionals in 3D to high-resolution MR images of trabecular bone: prediction of the biomechanical strength by nonlinear topological measures
Author(s): Holger F. Boehm; Thomas M. Link; Roberto A. Monetti; Dirk Mueller; Ernst J. Rummeny; David Newitt; Sharmila Majumdar; Christoph W. Raeth
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Paper 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.

Paper Details

Date Published: 12 May 2004
PDF: 9 pages
Proc. SPIE 5370, Medical Imaging 2004: Image Processing, (12 May 2004); doi: 10.1117/12.532835
Show Author Affiliations
Holger F. Boehm, Technische Univ. Muenchen (Germany)
Max-Planck-Institut für extraterrestrische Physik (Germany)
Thomas M. Link, Technische Univ. Muenchen (Germany)
Roberto A. Monetti, Max-Planck-Institut fur extraterrestrische Physik (Germany)
Dirk Mueller, Technische Univ. Munchen (Germany)
Max-Planck-Institut für extraterrestrische Physik (Germany)
Ernst J. Rummeny, Technische Univ. Munchen (Germany)
David Newitt, Magnetic Resonance Science Ctr., Univ. of California/San Francisco (United States)
Sharmila Majumdar, Magnetic Resonance Science Ctr., Univ. of California/San Francisco (United States)
Christoph W. Raeth, Max-Planck-Institut fur extraterrestrische Physik (Germany)


Published in SPIE Proceedings Vol. 5370:
Medical Imaging 2004: Image Processing
J. Michael Fitzpatrick; Milan Sonka, Editor(s)

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