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

Abstract

In order to analyze theoretically the dynamics of osteoblast and osteoclast cells in the bone remodeling process we first consider a simplified Komarova model. The existence of periodic solutions, which is consistent with the biophysical phenomenon, has been observed only numerically for the general model. By a stability analysis of the simplified model we provide sufficient conditions to obtain existence and uniqueness of positive periodic solutions. Considering recent biological evidence about the participation of another cells like osteocytes in the regulation of bone remodeling, we incorporate to the simplified model a new term as a way to model the signaling of external agents in the remodeling process. Finally, we demonstrate that this new model has stable positive non-periodic solutions. All the theoretical results are accompanied by computational simulations.