Linear Elastic Modelling of the Human Mandible

Responsible: Cornelia Kober, Bodo Erdmann, Jens Lang, Peter Deuflhard

Cooperation R. Sader, H.-F. Zeilhofer, 
Technische Universit&t, Klinikum Rechts der Isar, München

Literature: B. Erdmann, C. Kober, J. Lang, P. Deuflhard, H.-F. Zeilhofer, R. Sader, Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible, Report ZIB 01-14, Konrad-Zuse-Zentrum für Informationstechnik Berlin, 2001.

A detailed understanding of the mechanical behaviour of the human mandible has been an object of medical and biomedical research for a long time. Better knowledge of the stress and strain distribution, e.g. concerning standard biting situations, allows an advanced evaluation of the requirements for improved osteosynthesis or implant techniques. In the field of biomechanics, FEM-Simulation has become a well appreciated research tool for the prediction of regional stresses.
The scope of this project is to demonstrate the impact of adaptive finite element techniques in the field of biomechanical simulation. Regarding to their reliability, computationlly efficient adaptive procedures are nowadays entering into real-life applications and starting to become a standard feature of modern simulation tools. Because of its complex geometry and the complicated muscular interplay of the masticatory system, modelling and simulaion of the human mandible are challenging applications.
Figure 1: The bone structure of the human mandible.

In general, simulation in structural mechanics requires at least a representation of the specimen's geometry, an appropriate material description, and a definition of the loading case. In our field, the inherent material is bone tissue, which is one of the strongest and stiffest tissues of the body. Bone itself is a highly complex composite material. Its mechanical properties are anisotropic, heterogeneous, and visco-elastic. At a macroscopic scale, two different kinds of bone can be distinguished in the mandible: cortical or compact bone is present in the outer part of bones, while trabecular, cancellous or spongious bone is situated at the inner, see Figure 1.
Figure 2: The separation of cortical and cancellous bone as realized in the simulations.
Computed tomography data (CT) are the base of the jawbone simulation. By this, the individual geometry is quite well reproduced, also the separation of cortical and trabecular bone, see Figure 2. In this project. we restrict ourselves to an isotropic, but inhomogeneous linear elastic material law. Figure 3 gives a view on a loading case, here the lateral biting situation.
Figure 3: Loading case.
For pre- and postprocessing including volumetric grid generation we use the visualization package AMIRA. After semiautomatic segmentation of the CT data, the algorithm for generation of non-manifold surfaces gives a quite satisfying reconstruction of the individual geometry. After some coarsening, we get a mesh (see Figure 4) which can be used as initial grid (11,395 tetrahedra resp.2,632 points) in the adaptive discretization process.
Figure 4: Initial grid for the adaptive finite element method.
Figure 5: Grid after three steps of adaptive refinement.
According to the required accuracy, the volumetric grid is adaptively refined from level 0 up to level 3. The finest grid is shown in Figure 5. In Figure 6, we present the maximum absolute values of deformation (occuring in the processus coronoidus) for both adaptive and uniform refinement of the grid. The comparison makes it comprehensible that the adaptive method is much more efficient if high accuracy is required.
Figure 6: Adaptive versus uniform mesh refinement: comparative maximum deformation results.
In the following, the results after adaptive calculation of a common postprocessing variable, the von Mises equivalent stress, is discussed. It represents the distortional part of the strain energy density for isotropic materials. Figure 7 and 8 show a comparison between the results from a calculation on the coarse (level 0) grid versus that from the finest (level 3) grid. In both calculations, the stress maximum occurs around the processus coronoidus of the working side whereas the condyles are nearly at the minimum level in spite of the conylar reaction forces. On the level 0, the observed stress maximum of 2.81 MPa is about 65 % less than the maximum stress of 4.34 MPa achieved on the level 4 calculation.
Figure 7: Von Mises equivalent stress on level 0, maximum: 2.81 MPa.
Figure 8: Von Mises equivalent stress on level 4, maximum: 4.34 MPa.

Last update: July 2007
© 2007 by Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)