General analysis of mathematical models for bone remodeling

Abstract

Bone remodeling is regulated by pathways controlling the interplay of osteoblasts and osteoclasts. In this work, we apply the method of generalized modeling 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 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.

Generalized models for high-throughput analysis of uncertain nonlinear systems

“…This Jacobian can then analyzed analytically or numerically by a random sampling procedure. Both approaches are illustrated in a recent paper on bone remodeling [4].…”

Stability analysis of a Komarova type model for the interactions of osteoblast and osteoclast cells during bone remodeling

“…299 region. Given that the linear system under the condition γ 1 γ 2 < 1 303 has periodic solutions, then the nonlinear system (14) verifying this 304 condition has a unique positive non-oscillatory solution which tends 305 to an equilibrium point (15). 306 Taking into account realistic data, we present the behavior of the 307 solution for system (14).…”

“…For example, using the same system 318 coefficients considered in Fig. 6 with k = 0.00001 to solve (14), we 319 obtain the solution and the phase plane shown in Fig. 7.…”

“…34 Lemaire et al proposed a linear model in which more populations 35 of osteoclasts and osteoblasts are included, for example precursors, 36 active and apoptotic, and several activator and inhibitor substances 37 as RANK, RANKL, TGFβ, PTH, OPG, etc. More recent related works 38 are given in [12][13][14]. With some modifications to the first models, 39 there also have been modeling applications such as bone diseases, for 40 example such as myeloma [15] [17,18].…”

“…Osteoblasts then receive signals to start with the recon-13 struction. Experimental work on bone remodeling shows a compli- 14 cated interaction between several substances and receptors. Diverse 15 hypotheses have been proposed for the different signaling pathways 16 and the communication between osteoclast and osteoblast cells [3][4][5], 17 but the whole remodeling process is still not completely understood.…”