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September  2012, 17(6): 2185-2200. doi: 10.3934/dcdsb.2012.17.2185

## Dynamics of bone cell signaling and PTH treatments of osteoporosis

 1 School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, United States, United States 2 ESD - Modeling and Simulations, Merck and Co., West Point, PA 19486, United States 3 Applied Computer Science and Mathematics, Merck and Co., West Point, PA 19486, United States

Received  September 2011 Revised  February 2012 Published  May 2012

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.
Citation: David S. Ross, Christina Battista, Antonio Cabal, Khamir Mehta. Dynamics of bone cell signaling and PTH treatments of osteoporosis. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 2185-2200. doi: 10.3934/dcdsb.2012.17.2185
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