Dynamics of bone cell signaling and PTH treatments of osteoporosis

David S. Ross; Christina Battista; Antonio Cabal; Khamir Mehta

doi:10.3934/dcdsb.2012.17.2185

Article Contents

2012, Volume 17, Issue 6: 2185-2200. Doi: 10.3934/dcdsb.2012.17.2185

This issue Previous Article Dynamics of a two-receptor binding model: How affinities and capacities translate into long and short time behaviour and physiological corollaries Next Article Lyapunov-Schmidt reduction for optimal control problems

Dynamics of bone cell signaling and PTH treatments of osteoporosis

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

Received: August 31, 2011

Revised: January 31, 2012

Published: August 2012

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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.

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Mathematics Subject Classification: Primary: 34D23, 37C75; Secondary: 92C45, 92C50.

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