BioND — Dynamics of Biological Networks

General analysis of mathematical models for bone remodeling

Martin Zumsande, Dirk Stiefs, Stefan Siegmund, and Thilo Gross
Bone 48(4), 910-917, 2011.
arXiv:1010.1239

Abstract

Bifurcation Diagram

Bone remodeling is regulated by pathways controlling the interplay of osteoblasts and osteoclasts. In this work, we apply the method of generalized modelling to systematically analyse a large class of models of bone remodeling. Our analysis shows that osteoblast precursors can play an important role in the regulation of bone remodeling. Further, we fi nd that the parameter regime most likely realized in nature lies very close to bifurcation lines, marking qualitative changes in the dynamics. Although proximity to a bifurcation facilitates adaptive responses to changing external conditions, it entails the danger of losing dynamical stability. Some evidence implicates such dynamical transitions as a potential mechanism leading to forms of Paget's disease.

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