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Bone morphology allows estimation of loading history in a murine model of bone adaptation


Bone adapts its morphology (density/micro- architecture) in response to the local loading conditions in such a way that a uniform tissue loading is achieved (‘Wolff’s law’). This paradigm has been used as a basis for bone remodeling simulations to predict the formation and adaptation of trabecular bone. However, in order to predict bone architectural changes in patients, the physiological external loading conditions, to which the bone was adapted, need to be determined. In the present study, we developed a novel bone loading estimation method to predict such external loading conditions by calculating the loading history that produces the most uniform bone tissue loading. We applied this method to murine caudal vertebrae of two groups that were in vivo loaded by either 0 or 8 N, respectively. Plausible load cases were sequentially applied to micro-finite element models of the mice vertebrae, and scaling factors were calculated for each load case to derive the most uniform tissue strain-energy density when all scaled load cases are applied simultaneously. The bone loading estimation method was able to predict the difference in loading history of the two groups and the correct load magnitude for the loaded group. This result suggests that the bone loading history can be estimated from its morphology and that such a method could be useful for predicting the loading history for bone remodeling studies or at sites where measurements are difficult, as in bone in vivo or fossil bones.


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Funding from the European Union for the osteoporotic virtual physiological human project (VPHOP FP7-ICT2008-223865) is gratefully acknowledged.

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Correspondence to Bert van Rietbergen.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Christen, P., van Rietbergen, B., Lambers, F.M. et al. Bone morphology allows estimation of loading history in a murine model of bone adaptation. Biomech Model Mechanobiol 11, 483–492 (2012). https://doi.org/10.1007/s10237-011-0327-x

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  • Bone loading estimation
  • Bone adaptation
  • Micro-finite element analysis
  • Bone remodeling algorithm
  • Murine caudal vertebra