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Dresden 2011 – scientific programme

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BP: Fachverband Biologische Physik

BP 5: Tissue Dynamics \& Developmental Processes

BP 5.6: Talk

Monday, March 14, 2011, 15:45–16:00, ZEU 250

General analysis of mathematical models for bone remodeling — •Martin Zumsande1, Dirk Stiefs1, Stefan Siegmund2, and Thilo Gross11Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany. — 2Department of Mathematics, Dresden University of Technology, 01062 Dresden, Germany.

Bone remodeling is a complex process by which the skeleton of vertebrates is rebuilt continuously throughout their life. It is based on the interplay of two cell types, bone-resorbing osteoclasts and bone-forming osteoblasts and regulated by various cytokines, hormones and other signaling agents. In this work, we apply the method of generalized modelling to systematically analyse a large class of mathematical models of bone remodeling that are based on ODEs. Our analysis shows that the precursors of osteoblast play an important role in the regulation of bone remodeling. Further, we find that stability of the steady state, which is required in the physiological state, is not a self-evident properties of the models. In contrast, the parameter regime that is most likely realized in nature based on experimental input is situated close to bifurcation lines, marking qualitative changes in the dynamics. Although proximity to a bifurcation facilitates adaptive responses to changing external conditions, it entails the danger of losing dynamical stability. These dynamical transitions can possibly be related to diseases of bone such as Paget's disease.

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