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Layered water in crystal interfaces as source for bone viscoelasticity: arguments from a multiscale approach
Extracellular bone material can be characterised as a nanocomposite where, in a liquid environment, nanometre-sized hydroxyapatite crystals precipitate within as well as between long fibre-like collagen fibrils (with diameters in the 100 nm range), as evidenced from neutron diffraction and transmiss...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Taylor & Francis
2012
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3877913/ https://www.ncbi.nlm.nih.gov/pubmed/22563708 http://dx.doi.org/10.1080/10255842.2012.670227 |
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author | Eberhardsteiner, Lukas Hellmich, Christian Scheiner, Stefan |
author_facet | Eberhardsteiner, Lukas Hellmich, Christian Scheiner, Stefan |
author_sort | Eberhardsteiner, Lukas |
collection | PubMed |
description | Extracellular bone material can be characterised as a nanocomposite where, in a liquid environment, nanometre-sized hydroxyapatite crystals precipitate within as well as between long fibre-like collagen fibrils (with diameters in the 100 nm range), as evidenced from neutron diffraction and transmission electron microscopy. Accordingly, these crystals are referred to as ‘interfibrillar mineral’ and ‘extrafibrillar mineral’, respectively. From a topological viewpoint, it is probable that the mineralisations start on the surfaces of the collagen fibrils (‘mineral-encrusted fibrils’), from where the crystals grow both into the fibril and into the extrafibrillar space. Since the mineral concentration depends on the pore spaces within the fibrils and between the fibrils (there is more space between them), the majority of the crystals (but clearly not all of them) typically lie in the extrafibrillar space. There, larger crystal agglomerations or clusters, spanning tens to hundreds of nanometers, develop in the course of mineralisation, and the micromechanics community has identified the pivotal role, which this extrafibrillar mineral plays for tissue elasticity. In such extrafibrillar crystal agglomerates, single crystals are stuck together, their surfaces being covered with very thin water layers. Recently, the latter have caught our interest regarding strength properties (Fritsch et al. 2009 J Theor Biol. 260(2): 230–252) – we have identified these water layers as weak interfaces in the extrafibrillar mineral of bone. Rate-independent gliding effects of crystals along the aforementioned interfaces, once an elastic threshold is surpassed, can be related to overall elastoplastic material behaviour of the hierarchical material ‘bone’. Extending this idea, the present paper is devoted to viscous gliding along these interfaces, expressing itself, at the macroscale, in the well-known experimentally evidenced phenomenon of bone viscoelasticity. In this context, a multiscale homogenisation scheme is extended to viscoelasticity, mineral-cluster-specific creep parameters are identified from three-point bending tests on hydrated bone samples, and the model is validated by statistically and physically independent experiments on partially dried samples. We expect this model to be relevant when it comes to prediction of time-dependent phenomena, e.g. in the context of bone remodelling. |
format | Online Article Text |
id | pubmed-3877913 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2012 |
publisher | Taylor & Francis |
record_format | MEDLINE/PubMed |
spelling | pubmed-38779132014-01-17 Layered water in crystal interfaces as source for bone viscoelasticity: arguments from a multiscale approach Eberhardsteiner, Lukas Hellmich, Christian Scheiner, Stefan Comput Methods Biomech Biomed Engin Research Article Extracellular bone material can be characterised as a nanocomposite where, in a liquid environment, nanometre-sized hydroxyapatite crystals precipitate within as well as between long fibre-like collagen fibrils (with diameters in the 100 nm range), as evidenced from neutron diffraction and transmission electron microscopy. Accordingly, these crystals are referred to as ‘interfibrillar mineral’ and ‘extrafibrillar mineral’, respectively. From a topological viewpoint, it is probable that the mineralisations start on the surfaces of the collagen fibrils (‘mineral-encrusted fibrils’), from where the crystals grow both into the fibril and into the extrafibrillar space. Since the mineral concentration depends on the pore spaces within the fibrils and between the fibrils (there is more space between them), the majority of the crystals (but clearly not all of them) typically lie in the extrafibrillar space. There, larger crystal agglomerations or clusters, spanning tens to hundreds of nanometers, develop in the course of mineralisation, and the micromechanics community has identified the pivotal role, which this extrafibrillar mineral plays for tissue elasticity. In such extrafibrillar crystal agglomerates, single crystals are stuck together, their surfaces being covered with very thin water layers. Recently, the latter have caught our interest regarding strength properties (Fritsch et al. 2009 J Theor Biol. 260(2): 230–252) – we have identified these water layers as weak interfaces in the extrafibrillar mineral of bone. Rate-independent gliding effects of crystals along the aforementioned interfaces, once an elastic threshold is surpassed, can be related to overall elastoplastic material behaviour of the hierarchical material ‘bone’. Extending this idea, the present paper is devoted to viscous gliding along these interfaces, expressing itself, at the macroscale, in the well-known experimentally evidenced phenomenon of bone viscoelasticity. In this context, a multiscale homogenisation scheme is extended to viscoelasticity, mineral-cluster-specific creep parameters are identified from three-point bending tests on hydrated bone samples, and the model is validated by statistically and physically independent experiments on partially dried samples. We expect this model to be relevant when it comes to prediction of time-dependent phenomena, e.g. in the context of bone remodelling. Taylor & Francis 2012-05-08 2014-01 /pmc/articles/PMC3877913/ /pubmed/22563708 http://dx.doi.org/10.1080/10255842.2012.670227 Text en © 2012 Lukas Eberhardsteiner, Christian Hellmich and Stefan Scheiner. Published by Taylor & Francis. http://www.informaworld.com/mpp/uploads/iopenaccess_tcs.pdf This is an open access article distributed under the Supplemental Terms and Conditions for iOpenAccess articles published in Taylor & Francis journals (http://www.informaworld.com/mpp/uploads/iopenaccess_tcs.pdf) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This is an Open Access article. Non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly attributed, cited, and is not altered, transformed, or built upon in any way, is permitted. The moral rights of the named author(s) have been asserted. |
spellingShingle | Research Article Eberhardsteiner, Lukas Hellmich, Christian Scheiner, Stefan Layered water in crystal interfaces as source for bone viscoelasticity: arguments from a multiscale approach |
title | Layered water in crystal interfaces as source for bone viscoelasticity: arguments from a multiscale approach |
title_full | Layered water in crystal interfaces as source for bone viscoelasticity: arguments from a multiscale approach |
title_fullStr | Layered water in crystal interfaces as source for bone viscoelasticity: arguments from a multiscale approach |
title_full_unstemmed | Layered water in crystal interfaces as source for bone viscoelasticity: arguments from a multiscale approach |
title_short | Layered water in crystal interfaces as source for bone viscoelasticity: arguments from a multiscale approach |
title_sort | layered water in crystal interfaces as source for bone viscoelasticity: arguments from a multiscale approach |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3877913/ https://www.ncbi.nlm.nih.gov/pubmed/22563708 http://dx.doi.org/10.1080/10255842.2012.670227 |
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