General analysis of mathematical models for bone remodeling

TL;DR

This paper systematically analyzes mathematical models of bone remodeling using generalized modeling, revealing the critical role of osteoblast precursors, the proximity to bifurcations in natural regimes, and potential links to Paget's disease.

Contribution

It introduces a systematic generalized modeling approach to analyze bone remodeling models, highlighting the importance of osteoblast precursors and bifurcation proximity in dynamics.

Findings

Osteoblast precursors significantly influence bone remodeling regulation.

Natural parameter regimes are close to bifurcation points, affecting stability.

Proximity to bifurcations may lead to dynamical transitions linked to Paget's disease.

Abstract

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 find 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.