Modeling bone resorption using mixture theory with chemical reactions

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 biothemomechanical 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.