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 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.

Biomechanics of Osteoporosis: The Importance of Bone Resorption and Remodeling Processes

“…The treatment of the bone diseases is based on drugs that intend to restore the remodeling equilibrium. Most of the work on osteoporosis, probably the most important of these diseases, seems to be currently in the osteoclast inhibition side (Rodan & Martin, 2000;Teitelbaum, 2000;Rouhi et al, 2007). Peak bone mass (PBM) corresponds to the amount of bony tissue present at the end of skeletal maturation.…”

“…Cells, as live organs in the biological tissues, can dictate rate of growth and adaptation, and their activities are affected by different, including mechanical, chemical, and biological factors. Here a brief explanation about a recently proposed biphasic mixture model of bone resorption is presented (Rouhi et al, 2007). This model aims at shedding some light on the bone resorption process using a multi-constituents continuum mechanics model.…”

“…In the constitutive equations, it is assumed that dependent variables, such as free energy, are a function of temperature, deformation gradient, rate of deformation gradient, and the extent of chemical reactions (Rouhi et al, 2007). It should be noted that bone mineral (hydroxyapatite) and organic (collagen I) matrix are degraded independently.…”

Carbon Nanotubes in Bone Tissue Engineering

“…The treatment of these diseases is based on drugs that intend to restore the remodeling equilibrium. Most of the work on osteoporosis, probably the most important of these diseases, seems to be currently in the osteoclast inhibition side (Rodan & Martin, 2000;Teitelbaum, 2000;Rouhi et al, 2007). An early hypothesis about the dependence of the structure and form of bones on their mechanical function was proposed by Galileo in 1638 (Ascenzi, 1993).…”

Using a Truss-Inspired Model with the Uniform Strength Optimization Theory to Predict Spongy Bone Geometry in Proximal Femur

“…the fabric tensor [17]. Many theories, mostly phenomenological, have been proposed to explain the process of bone remodeling [19][20][21][22][23][24][25][26][27][28]. For example, the apparent density has been used to characterize the internal morphology of the bone and the strain energy density assumed as the stimulus for bone adaptation [19].…”