%0 Generic
%A Kihn, Martina Christine
%C Heidelberg, Germany
%D 2013
%F heidok:14602
%R 10.11588/heidok.00014602
%T Analysis of Bone Remodeling  An Application for Tooth Movement
%U https://archiv.ub.uni-heidelberg.de/volltextserver/14602/
%X Abstract  This thesis investigates a mathematical model that tries to consider most processes  involved in bone formation and bone resorption. It takes the solid bone matrix  and the fluid phase as bone marrow into account as well as the influences of bone  cell populations on the bone remodeling cycle. The role of parathyroid hormone  and calcium homeostasis and the signaling pathways between bone cells are also  studied.  A complex mathematical model is derived which results in a free boundary problem  as bone is constantly changing its shape and architecture. We find in the model on  the macroscopic level equations for linear elasticity and Navier-Stokes equation.  On the basic unit level we study equations for diffusion and transport, chemotaxis  and partial differential equations for bone cell populations.  The general complex model for bone remodeling is then simplified and applied to  a chosen problem in orthodontics, the movement of a tooth through bone. Tooth  movement caused by braces is a possible application of our general model. Here  the equations of Biot for a porous medium, the periodontal ligament, are used and  combined with a free boundary. We use the homogenized system and are able to  derive effective equations for the displacement and pressure.  We suggest for the analysis the Rothe method and prove in this thesis the existence  of solutions for the Rothe iteration step. The full convergence proof for the free  boundary problem is a problem for itself.