Knowledge of the anisotropic elastic properties of osteon and osteonal lamellae provides a better understanding of various pathophysiological conditions, such as aging, osteoporosis, osteoarthritis, and other degenerative diseases. For this reason, it is important to investigate and understand the elasticity of cortical bone. We created a bidirectional micromechanical model based on inverse homogenization for predicting the elastic properties of osteon and osteonal lamellae of cortical bone. The shape, the dimensions, and the curvature of osteon and osteonal lamellae are described by appropriately chosen curvilinear coordinate systems, so that the model operates close to the real morphology of these bone components. The model was used to calculate nine orthotropic elastic constants of osteonal lamellae. The input values have the elastic properties of a single osteon. We also expressed the dependence of the elastic properties of the lamellae on the angle of orientation. To validate the model, we performed nanoindentation tests on several osteonal lamellae. We compared the experimental results with the calculated results, and there was good agreement between them. The inverted model was used to calculate the elastic properties of a single osteon, where the input values are the elastic constants of osteonal lamellae. These calculations reveal that the model can be used in both directions of homogenization, i.e., direct homogenization and also inverse homogenization. The model described here can provide either the unknown elastic properties of a single lamella from the known elastic properties at the level of a single osteon, or the unknown elastic properties of a single osteon from the known elastic properties at the level of a single lamella.
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August 2015
Research-Article
Elastic Properties of Human Osteon and Osteonal Lamella Computed by a Bidirectional Micromechanical Model and Validated by Nanoindentation
Radim Korsa,
Radim Korsa
1
Department of Mechanics, Biomechanics
and Mechatronics,
e-mail: radim.korsa@gmail.com
and Mechatronics,
Czech Technical University in Prague
,Technicka 4
,Prague 166 07
, Czech Republic
e-mail: radim.korsa@gmail.com
1Corresponding author.
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Jaroslav Lukes,
Jaroslav Lukes
Department of Mechanics, Biomechanics
and Mechatronics,
e-mail: jaroslav.lukes@fs.cvut.cz
and Mechatronics,
Czech Technical University in Prague
,Technicka 4
,Prague 166 07
, Czech Republic
e-mail: jaroslav.lukes@fs.cvut.cz
Search for other works by this author on:
Josef Sepitka,
Josef Sepitka
Department of Mechanics, Biomechanics
and Mechatronics,
e-mail: Josef.Sepitka@fs.cvut.cz
and Mechatronics,
Czech Technical University in Prague
,Technicka 4
,Prague 166 07
, Czech Republic
e-mail: Josef.Sepitka@fs.cvut.cz
Search for other works by this author on:
Tomas Mares
Tomas Mares
Department of Mechanics, Biomechanics
and Mechatronics,
e-mail: tomas.mares@fs.cvut.cz
and Mechatronics,
Czech Technical University in Prague
,Technicka 4
,Prague 166 07
, Czech Republic
e-mail: tomas.mares@fs.cvut.cz
Search for other works by this author on:
Radim Korsa
Department of Mechanics, Biomechanics
and Mechatronics,
e-mail: radim.korsa@gmail.com
and Mechatronics,
Czech Technical University in Prague
,Technicka 4
,Prague 166 07
, Czech Republic
e-mail: radim.korsa@gmail.com
Jaroslav Lukes
Department of Mechanics, Biomechanics
and Mechatronics,
e-mail: jaroslav.lukes@fs.cvut.cz
and Mechatronics,
Czech Technical University in Prague
,Technicka 4
,Prague 166 07
, Czech Republic
e-mail: jaroslav.lukes@fs.cvut.cz
Josef Sepitka
Department of Mechanics, Biomechanics
and Mechatronics,
e-mail: Josef.Sepitka@fs.cvut.cz
and Mechatronics,
Czech Technical University in Prague
,Technicka 4
,Prague 166 07
, Czech Republic
e-mail: Josef.Sepitka@fs.cvut.cz
Tomas Mares
Department of Mechanics, Biomechanics
and Mechatronics,
e-mail: tomas.mares@fs.cvut.cz
and Mechatronics,
Czech Technical University in Prague
,Technicka 4
,Prague 166 07
, Czech Republic
e-mail: tomas.mares@fs.cvut.cz
1Corresponding author.
Manuscript received October 16, 2014; final manuscript received April 13, 2015; published online June 9, 2015. Assoc. Editor: David Corr.
J Biomech Eng. Aug 2015, 137(8): 081002 (11 pages)
Published Online: August 1, 2015
Article history
Received:
October 16, 2014
Revision Received:
April 13, 2015
Online:
June 9, 2015
Citation
Korsa, R., Lukes, J., Sepitka, J., and Mares, T. (August 1, 2015). "Elastic Properties of Human Osteon and Osteonal Lamella Computed by a Bidirectional Micromechanical Model and Validated by Nanoindentation." ASME. J Biomech Eng. August 2015; 137(8): 081002. https://doi.org/10.1115/1.4030407
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