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TECHNICAL PAPERS: Bone/Orthopedic

A Model for Prediction of Bone Stiffness Using a Mechanical Approach of Composite Materials

[+] Author and Article Information
Dominique M. Perreux1

Department of Materials Science & Engineering, Georgia Institute of Technology, Atlanta, GA 30332; Laboratoire de Mécanique Appliquée R. Chaléat, University of Franche-Comté, 25000 Besançon, Francedominique.perreux@univ-fcomte.fr

W. Steven Johnson

Department of Materials Science & Engineering, Georgia Institute of Technology, Atlanta, GA 30332

1

Corresponding author. Current address: Laboratoire de Mécanique Appliquée R. Chaleat, FEMTO-ST, University of Franche-Comté, 24 rue de l’ Epitaphe 25000 Besançon, France.

J Biomech Eng 129(4), 494-502 (Jan 22, 2007) (9 pages) doi:10.1115/1.2746370 History: Received June 21, 2006; Revised January 22, 2007

A model to predict the bone stiffness is presented in this paper. The objective is to obtain a description of bone stiffness of a representative elementary volume (REV) based on a small set of physical parameters. The main idea is to use measurable information related to the orientation and the density of a basic elementary submicrostructure (ESMS). This ESMS is the first arrangement of the basic components. A simple rule-of-mixtures approach is used to provide the elastic properties for the ESMS. The basic properties are dependent on the volume fraction of the mineralized phase. The orientation and the density of the ESMS is described by a tensor and a scalar, respectively. The model is used to obtain the elastic properties of both the cortical and trabecular bones. Data from femoral bone are used to verify this approach.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Orientation of ESMS

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Figure 2

Representation of F

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Figure 3

Isotropic REV: A matrix with random distribution of hollow spheres

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Figure 4

(a) Comparison between present model and homogenization models for prediction of the Young’s modulus and (b) comparison between the present model and homogenisation model for prediction of the Poisson ratio

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Figure 5

Comparison between the prediction of the model (continuous line), and data from the Lotz (21) in axial direction of cortical femoral bone. The dashed line is the data fitting proposed by Wirtz (8).

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Figure 6

Comparison between the prediction of the model (continuous line), and data from the Lotz (21) in transversal direction of cortical femoral bone

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Figure 7

Simple vision of compact REV and REV with porosity

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