Bone remodelling is a lifelong process where mature bone tissue is removed from the skeleton and new bone tissue is formed. These processes also control the reshaping or replacement of bone following injuries like fractures but also micro-damage, which occurs during normal activity. We discuss adequate general classes of two- and three-dimensional population models for the cell types involved in this process and show that two populations are not enough to explain what biologists observe. A three-dimensional model class not only explains the observations but also explains what is called Paget’s disease of oscillating or disorganised bone remodeling. Main tools are the useful notion of elasticity from economy, as well as linearisation and bifurcation theory for ordinary differential equations. This is joint work with Thilo Gross, Martin Zumsande and Dirk Stiefs.
Stefan Siegmund received his Ph.D. in mathematics in 1999 from the University of Augsburg, Germany. He was Visiting Scholar at the Georgia Institute of Technology at Atlanta, at the University of California at Berkeley, at the University of Minnesota at Minneapolis and at Boston University, USA. Since 2008 he is Chair for Dynamics and Control at TU Dresden and since 2010 founding-director of the Center for Dynamics. Stefan Siegmund works on dynamical systems in a broad sense, his interests include geometric theory of dynamical systems, as well as applications in biology, fluid dynamics and meteorology.
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