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Modeling bone
resorption using Mixture Theory with chemical reactions
Gholamreza Rouhi, Marcelo Epstein, Leszek Sudak and Walter Herzog |
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Vol. 2 (2007), No. 6, 1141–1155
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Abstract |
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The increasing rate of osteoporosis in an aging population calls for a greater understanding of the cellular mechanism of bone resorption. We propose a biphasic mixture model. The solid phase (matrix) is assumed to be elastic and isotropic, and the fluid phase is assumed to be a linear viscous fluid. We give conservation equations for each constituent and for the whole mixture, and write new constitutive equations for the system. The rate of mass supply to constituents, caused by chemical reactions, is taken from an empirical relation of dissolution kinetics. We derive the biochemomechanical affinity in terms of biological, chemical, and mechanical factors. The strain energy density, hydrostatic pressure, and concentration of different ions present in the mixture are shown to affect the rate of bone resorption. |
Keywords
bone resorption, mixture theory, chemical reactions,
osteoporosis
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Milestones
Received: 28 September 2006
Revised: 6 March 2007
Accepted: 3 April 2007
Published: 1 August 2007
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Authors |
| Gholamreza Rouhi | |
| Department of Mechanical
Engineering University of Ottawa 161 Louis Pasteur Room A017 Ottawa Ontario, Canada K1N 6N5 Canada |
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| Marcelo Epstein | |
| Department of Mechanical and
Manufacturing Engineering University of Calgary 2500 University Dr. NW Calgary, Alberta T2N 1N4 Canada |
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| Leszek Sudak | |
| Department of Mechanical and
Manufacturing Engineering University of Calgary 2500 University Dr. NW Calgary, Alberta T2N 1N4 Canada |
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| Walter Herzog | |
| Faculty of Kinesiology University of Calgary 2500 University Drive NW Calgary, Alberta T2N 1N4 Canada |
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