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 anatomical structures surrounding the teeth, i.e. alveolar bone and the mucosa covering the alveolar bone. Due to the complex structure of the PDL, a highly non-linear, anisotropic and time-dependent behaviour has to be assumed. 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) has not been presented yet. It is the aim of the current proposal to
- develop a closed mathematical model of the multiphase, time-dependent constitutive law of the PDL,
- develop robust and efficient discretisation techniques and parallel solution methods for the arising non-linear saddle-poit-like systems,
- apply these methods for biomechanical models of teeth and tooth supporting structures, and
- validate the developed models using experimental biomechanical results and clinical studies.
Model and computational methods are being tested in strict and constant collaboration with Endowed Chair of Oral Technology (Prof. Bourauel, University of Bonn) where experimental and clinical work are carried out.
This project is funded by the DFG within the framework of the Clinical Research Unit 208 "Aetiology and Sequelae of Periodontal Diseases - Genetic, Cell Biological and Biomechanical "Aspects
Prof. Dr. Rolf Krause; ; PI; ICS Institute of Computational Science