Journal
MATHEMATICAL BIOSCIENCES
Volume 264, Issue -, Pages 29-37Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.mbs.2015.03.003
Keywords
Bone remodeling; External agents; Periodic solutions; Nonlinear stability analysis
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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. (C) 2015 Elsevier Inc. All rights reserved.
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