BIOPHYSICAL THEORY AND MODELING |
Hierarchical Modeling of the Elastic Properties of Bone at Submicron Scales: The Role of Extrafibrillar Mineralization
Svetoslav Nikolov 1* and Dierk Raabe 1
1 Max-Planck-Institute fur Eisenforschung
* To whom correspondence should be addressed. E-mail: s.nikolov{at}mpie.de.
Submitted on November 9, 2007
Revised on December 27, 2007
Accepted on 31 December 2007
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Abstract |
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We model the elastic properties of bone at the level of mineralized collagen fibrils via step-by-step homogenization from the staggered arrangement of collagen molecules up to an array of parallel mineralized fibrils. A new model for extrafibrillar mineralization is proposed, assuming that the extrafibrillar minerals are mechanically equivalent to reinforcing "rings" coating each individual fibril. Our modeling suggests that no more than 30% of the total mineral content is extrafibrillar and the fraction of extrafibrillar minerals grows linearly with the overall degree of mineralization. It is shown that the extrafibrillar mineralization considerably reinforces the fibrils’ mechanical properties in the transverse directions and the fibrils' shear moduli. The model predictions for the elastic moduli and constants are found to be in a good agreement with the experimental data reported in the literature.
Key Words:
biominerals, bone, collagen fibrils, mechanical properties, modeling, structure
