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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Dynamics of bone cell signaling and PTH treatments of osteoporosis

Pages: 2185 - 2200, Volume 17, Issue 6, September 2012      doi:10.3934/dcdsb.2012.17.2185

 
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David S. Ross - School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, United States (email)
Christina Battista - School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, United States (email)
Antonio Cabal - ESD - Modeling and Simulations, Merck and Co., West Point, PA 19486, United States (email)
Khamir Mehta - Applied Computer Science and Mathematics, Merck and Co., West Point, PA 19486, United States (email)

Abstract: In this paper we analyze and generalize the dynamical system introduced by Lemaire and co-workers [14] as a model of cell signaling in bone remodeling. We show that for large classes of parameter values, including the physically-realistic baseline values, the system has a unique physically relevant equilibrium which is a global attractor. We generalize that model, minimally, to incorporate a mechanism by which parathyroid hormone (PTH) retards osteoblast apoptosis. We show that with this mechanism, which is a simplified version of that proposed by Bellido and co-workers [4], the model exhibits a well-known phenomenon that has puzzled researchers: the system responds catabolically to the continuous administration of PTH and ally to appropriately pulsed administration of PTH.

Keywords:  Cell signaling, Lyapunov, global stability, osteoporosis, parathyroid hormone, PTH.
Mathematics Subject Classification:  Primary: 34D23, 37C75; Secondary: 92C45, 92C50.

Received: September 2011;      Revised: February 2012;      Available Online: May 2012.

 References