TECHNICAL PAPERS: Bone/Orthopedics

Prediction of Cortical Bone Elastic Constants by a Two-Level Micromechanical Model Using a Generalized Self-Consistent Method

[+] Author and Article Information
X. Neil Dong1

Bone Bioengineering Laboratory, Department of Biomedical Engineering,  Columbia University, New York, NY 10027

X. Edward Guo2

Bone Bioengineering Laboratory, Department of Biomedical Engineering,  Columbia University, New York, NY 10027


Present address: Orthopaedic Research Laboratories, University of California, Davis, 4635 Second Avenue, Room 2000, Sacramento, CA 95817; e-mail: xndong@ucdavis.edu


Corresponding author; e-mail: exg1@columbia.edu

J Biomech Eng 128(3), 309-316 (Nov 17, 2005) (8 pages) doi:10.1115/1.2187039 History: Received May 12, 2005; Revised November 17, 2005

A two-level micromechanical model of cortical bone based on a generalized self-consistent method was developed to take into consideration the transversely isotropic elasticity of many microstructural features in cortical bone, including Haversian canals, resorption cavities, and osteonal and interstitial lamellae. In the first level, a single osteon was modeled as a two-phase composite such that Haversian canals were represented by elongated pores while the surrounding osteonal lamellae were considered as matrix. In the second level, osteons and resorption cavities were modeled as multiple inclusions while interstitial lamellae were regarded as matrix. The predictions of cortical bone elasticity from this two-level micromechanical model were mostly in agreement with experimental data for the dependence of transversely isotropic elasticity of human femoral cortical bone on porosity. However, variation in cortical bone elastic constants was greater in experimental data than in model predictions. This could be attributed to variations in the elastic properties of microstructural features in cortical bone. The present micromechanical model of cortical bone will be useful in understanding the contribution of cortical bone porosity to femoral neck fractures.

Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Microstructural components in osteonal cortical bone

Grahic Jump Location
Figure 2

A two-level micromechanical model of osteonal cortical bone

Grahic Jump Location
Figure 3

Variation between the elastic properties of cortical bone and its porosity. (a) longitudinal Young’s modulus (EL); (b) longitudinal shear modulus (GL); (c) transverse Young’s modulus (ET); and (d) transverse shear modulus (GT).




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