Vol. 2, No. 6, 2007

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ISSN: 1559-3959
Modeling bone resorption using Mixture Theory with chemical reactions

Gholamreza Rouhi, Marcelo Epstein, Leszek Sudak and Walter Herzog

Vol. 2 (2007), No. 6, 1141–1155
Abstract

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
Milestones
Received: 28 September 2006
Revised: 6 March 2007
Accepted: 3 April 2007
Published: 1 August 2007
Authors
Gholamreza Rouhi
Department of Mechanical Engineering
University of Ottawa
161 Louis Pasteur
Room A017 Ottawa
Ontario, Canada K1N 6N5
Canada
Marcelo Epstein
Department of Mechanical and Manufacturing Engineering
University of Calgary
2500 University Dr. NW
Calgary, Alberta T2N 1N4
Canada
Leszek Sudak
Department of Mechanical and Manufacturing Engineering
University of Calgary
2500 University Dr. NW
Calgary, Alberta T2N 1N4
Canada
Walter Herzog
Faculty of Kinesiology
University of Calgary
2500 University Drive NW
Calgary, Alberta T2N 1N4
Canada