Theoretical aspects of bone remodeling and resorption processes
Date
2006
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Abstract
The ability of living bone to adapt its material structure and form to its mechanical loading is very well-known. Resorption of extra-cellular matrices by osteoclasts is followed by osteoblastic invasion of the cavity, and subsequent secretion of extra-cellular matrix. These sequential processes continuously occur in healthy bone in a balanced manner, and these are called bone remodeling. Optimal remodeling of bone is responsible for bone health and strength throughout life. Bone resorption and apposition are caused by chemical reactions that occur between bone matrix and bone cells. There is a need to develop a theory (or theories) that can help elucidate features of this complex process. Adaptive elasticity theory is one of the most rigorous and well-known mathematical models of bone remodeling. The theory of adaptive elasticity was developed as a model for the mechanical load induced adaptation of bone. It describes an elastic material that adapts its structure to applied loading. The strain adapting properties of living bone are represented by a strain-controlled chemical reaction that transfers mass, momentum, entropy and energy to and from the porous elastic solid. In the constitutive equations, volume fraction of the solid phase is used as one of the independent variables. But, knowing that all of the resorption and deposition of bone occur on the bone free surfaces, we propose free surface density instead of volume fraction in the constitutive equations. On the basis of this assumption, a new set of remodeling equations is derived. In this model, one can observe the effect of bone internal geometry and mass distribution on the rate of remodeling. Surface remodeling equation can be extracted from this model, also the effects of mechanical stimuli and bone internal geometry can be studied simultaneously. In the second phase of our research, a microcrack factor is introduced in the governing equations, and a new model is developed. This model agrees with experimental evidence and suggests that mechanical stimuli, their rates, and also their cumulative effects regulate the process. Considering the new remodeling equation, one can conclude that the rate of remodeling is not a function of the rate of damage production but rather a function of the damage factor. In the third step of this research, a mixture theory approach with chemical reactions is used to model the bone resorption process. Mechanical and chemical factors are considered, simultaneously, in this model. Rates of mass transferred by the chemical reactions between the solid and fluid phases are assumed from an empirical relation. Degree of saturation is assumed to be a function of the chemical affinity. The analysis is consistent with experimental observations that strain energy density and hydrostatic pressure are two mechanical stimuli which effect the rate of resorption. With increasing microcracks the rates of bone resorption and remodeling are expected to increase. Our model suggests that by increasing the concentration of calcium ions rate of resorption decreases.
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Bibliography: p. 198-221
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Citation
Rouhi, G. (2006). Theoretical aspects of bone remodeling and resorption processes (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/278