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A determination of the minimum sizes of representative volume elements for the prediction of cortical bone elastic properties.
MedLine Citation:
PMID:  21267625     Owner:  NLM     Status:  Publisher    
Abstract/OtherAbstract:
At its highest level of microstructural organization-the mesoscale or millimeter scale-cortical bone exhibits a heterogeneous distribution of pores (Haversian canals, resorption cavities). Multi-scale mechanical models rely on the definition of a representative volume element (RVE). Analytical homogenization techniques are usually based on an idealized RVE microstructure, while finite element homogenization using high-resolution images is based on a realistic RVE of finite size. The objective of this paper was to quantify the size and content of possible cortical bone mesoscale RVEs. RVE size was defined as the minimum size: (1) for which the apparent (homogenized) stiffness tensor becomes independent of the applied boundary conditions or (2) for which the variance of elastic properties for a set of microstructure realizations is sufficiently small. The field of elastic coefficients and microstructure in RVEs was derived from one acoustic microscopy image of a human femur cortical bone sample with an overall porosity of 8.5%. The homogenized properties of RVEs were computed with a finite element technique. It was found that the size of the RVE representative of the overall tissue is about 1.5 mm. Smaller RVEs (~0.5 mm) can also be considered to estimate local mesoscopic properties that strongly depend on the local pores volume fraction. This result provides a sound basis for the application of homogenization techniques to model the heterogeneity of cortical microstructures. An application of the findings to estimate elastic properties in the case of a porosity gradient is briefly presented.
Authors:
Quentin Grimal; Kay Raum; Alf Gerisch; Pascal Laugier
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Publication Detail:
Type:  JOURNAL ARTICLE     Date:  2011-1-26
Journal Detail:
Title:  Biomechanics and modeling in mechanobiology     Volume:  -     ISSN:  1617-7940     ISO Abbreviation:  -     Publication Date:  2011 Jan 
Date Detail:
Created Date:  2011-1-26     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101135325     Medline TA:  Biomech Model Mechanobiol     Country:  -    
Other Details:
Languages:  ENG     Pagination:  -     Citation Subset:  -    
Affiliation:
UPMC Univ Paris 06, UMR 7623, Laboratoire d'Imagerie Paramétrique, 75005, Paris, France, quentin.grimal@upmc.fr.
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