Mathematical Modeling for Break Down of Dynamical Equilibrium in Bone Metabolism

Abstract

We study the break down of bone metabolism , using mathematical modeling. The principal part of this model is composed of two pathways of maturation, that is, from pre-osteoblast to osteoblast and from pre-osteoclast to osteoclast. There is also a pathway of acceleration to the formation of pre-osteoclast by pre-osteoblast. This pathway is evoked by a cytokine, called RANKL. Experimental data, on the other hand, suggest a differentiation annihilation factor to the maturation pathways above. Total mathematical modeling on these positive and negative feedback loops induces an insight, how the dynamical equilibrium of this metabolism breaks down, via mathematical analysis and numerical simulations. Then in vivo experiments are proposed to confirm actual existence of the above factor, together with the evaluation of medical manipulations.