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Proceedings Paper

Scaling relations between bone volume and bone structure as found using 3D µCT images of the trabecular bone taken from different skeletal sites
Author(s): Christoph Raeth; Dirk Müller; Irina Sidorenko; Roberto Monetti; Felix Eckstein; Maiko Matsuura; Eva-Maria Lochmüller; Philippe K. Zysset; Jan Bauer
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Paper Abstract

According to Wolff's law bone remodels in response to the mechanical stresses it experiences so as to produce a minimal-weight structure that is adapted to its applied stresses. Here, we investigate the relations between bone volume and structure for the trabecular bone using 3D μCT images taken from different skeletal sites in vitro, namely from the distal radii (96 specimens), thoracic (73 specimens) and lumbar vertebrae (78 specimens). We determine the local structure of the trabecular network by calculating isotropic and anisotropic scaling indices (α, αz). These measures have been proven to be able to discriminate rod- from sheet-like structures and to quantify the alignment of structures with respect to a preferential direction as given by the direction of the external force. Comparing global structure measures derived from the scaling indices (mean, standard deviation) with the bone mass (BV/TV) we find that all correlations obey very accurately power laws with scaling exponents of 0.14, 0.12, 0.15 (<α⪆), -0.2, -017, -0.17 (σ(αz)), 0.09, 0.05, 0.07 (⪅αz⪆) and -0.20, -0.11 ,-0.13 (σ(αz)); distal radius, thoracic vertebra and lumbar vertebra respectively. Thus, these relations turn out to be site-independent, albeit the mechanical stresses to which the bones of the forearm and the spine are exposed, are quite different. The similar alignment might not be in agreement with a universal validity of Wolff's law. On the other hand, such universal power law relations may allow to develop additional diagnostic means to better assess healthy and osteoporotic bone.

Paper Details

Date Published: 9 March 2010
PDF: 8 pages
Proc. SPIE 7626, Medical Imaging 2010: Biomedical Applications in Molecular, Structural, and Functional Imaging, 76261L (9 March 2010); doi: 10.1117/12.843779
Show Author Affiliations
Christoph Raeth, Max-Planck-Institut für extraterrestrische Physik (Germany)
Dirk Müller, Technische Univ. München (Germany)
Irina Sidorenko, Max-Planck-Institut für extraterrestrische Physik (Germany)
Roberto Monetti, Max-Planck-Institut für extraterrestrische Physik (Germany)
Felix Eckstein, Paracelsus Medizinische Privatuniv. (Austria)
Maiko Matsuura, Ludwig-Maximilians-Univ. München (Germany)
Eva-Maria Lochmüller, Ludwig-Maximilians-Univ. München (Germany)
Philippe K. Zysset, Technische Univ. Wien (Austria)
Jan Bauer, Technische Univ. München (Germany)


Published in SPIE Proceedings Vol. 7626:
Medical Imaging 2010: Biomedical Applications in Molecular, Structural, and Functional Imaging
Robert C. Molthen; John B. Weaver, Editor(s)

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