14 April 2012 Similarities and differences in the mass-structure scaling relations of the trabecular bone taken from different locations in the femur
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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. Consequently, the inner bone structure should show signs of adaptation to external forces acting on the bone. To test this paradigm, we investigate the relations between bone volume and structure for the trabecular bone using 3D μCT images taken from two different sites in the femur in vitro, namely from the femoral neck (88 specimens) and femoral trochanter (126 specimens). We determine the local structure of the trabecular network as well as its alignment with the direction of the external force acting on the bone by calculating isotropic (α) and anisotropic scaling indices (αz). Comparing global structure measures derived from the scaling indices (mean, variance) with the bone mass (BV/TV) we find that all correlations obey very accurately power laws with scaling exponents of 0.48 and 0.45 (<α>), -1.45 and -1.59 (var(μz)), 0.50 and 0.44 (<α>) and -1,47 and -1.32 (var(μz)) (neck and trochanter respectively). Thus, the relations for the isotropic scaling indices turn out to be siteindependent, albeit the mechanical stress to which the femoral neck is exposed is much larger than that for the trochanter. We find, however, differences in the degree of alignment of the trabeculae as reflected by the moments of the distribution of the anisotropic scaling indices. In summary, the mass-structure scaling relations of the bone probes taken from the two different sites of the femur show surprisingly small variations. Thus, a naïve interpretation of Wolff's law may not universally valid.
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Christoph Räth, Thomas Baum, Irina Sidorenko, Roberto Monetti, Felix Eckstein, Maiko Matsuura, Eva-Maria Lochmüller, Philippe K. Zysset, Jan Bauer, "Similarities and differences in the mass-structure scaling relations of the trabecular bone taken from different locations in the femur", Proc. SPIE 8317, Medical Imaging 2012: Biomedical Applications in Molecular, Structural, and Functional Imaging, 831718 (14 April 2012); doi: 10.1117/12.911815; https://doi.org/10.1117/12.911815
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