Prof. Dr. Christoph Bourauel
Oral Technology (OT)
Center of Dento-Maxillo-Facial Medicine
University of Bonn
Prof. Dr. Rolf Krause
Institute for Numerical Simulation (INS)
Faculty of Mathematics and Natural Science
Institute of Computational Science
Faculty of Informatics
Università della Svizzera Italiana
First Funding Period
Development of Mathematical Models and Efficient Algorithms to Simulate the Loading Conditions of the Periodontium in Dental Biomechanic
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, 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.
Second Funding Period
Development of mathematical models and efficient algorithms to simulate the loading conditions of the periodontium in dental biomechanics: clinical and experimental validation
In the first project phase of this subproject #5, newly developed in-vivo- and in-vitro-experimental devices have been constructed and new developments for the mathematical modeling and the numerical simulation of the periodontal ligament (PDL) have been performed. One of the central results of this first period is that a complete measurement - modeling - simulation - validation chain has been established as feedback loop. Particular focus was placed on the time-dependant behavior and the impact of varying health status of the periodontium. First in-vitro-tests together with ongoing in-vitro- and in-vivo-studies and simulations revealed an extreme influence of the loading velocity on the force/deflection characteristics, as reported earlier by several authors. However, accuracy and velocity range could be extended significantly. The main focus of the second project phase will be the clinical application of the developed methods and devices and further refinement of the developed mathematical und numerical models on the basis of the data acquired by in-vitro- and in-vivo-measurements. Tooth mobilities of patients will be measured with different periodontal status using the intraoral measurement device. The clinical work groups of the subprojects #2, #4, #7 and #8 will be asked for support in the clinical study phase.