Development of Mathematical Models and Efficient Algorithms to Simulate the Loading Conditions of the Periodontium in Dental Biomechanics
The biomechanical behaviour of the periodontal ligament (PDL) is of crucial relevance for the transfer of the mechanical loading to the anatomi¬cal structures surrounding the teeth, i.e. alveolar bone, PDL and the mucosa covering the alveolar bone. Due to the complex structure of the PDL, a highly non-linear, anisotropic and time-dependent behaviour is to be assumed. Until now, a closed mathematical description of the biomechanical response of the tooth supporting system, covering the full range of short to long-term loading (chewing, clenching, orthodontic force system) could not be presented. It is the aim of the current proposal to 1.) develop a closed mathematical representation of the multiphase, time-dependent constitutive law of the PDL, 2.) develop robust and efficient discretisation techniques and parallel solution methods for the arising non-linear systems, 3.) apply these methods for biomechanical models of teeth and tooth supporting structures, and 4.) validate the developed models using experimental biomechanical results and clinical studies. Mathematical modelling and their efficient implementation on a parallel cluster-server will be carried out at the Institute for Numerical Simulation. Experimental and clinical work will be carried out at the Endowed Chair of Oral Technology in collaboration with the clinical departments of the Dental School.