A dynamical systems approach to bone remodeling

Abstract: 

Bone remodeling 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 population 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 disorganized bone remodeling. Main tools are the useful notion of elasticity from economy, as well as linearization and bifurcation theory for ordinary differential equations. This is joint work with Thilo Gross, Martin Zumsande and Dirk Stiefs.