We are dealing with the simulation of maxillo-facial surgeries, especially with distraction osteogenesis. During this treatment the surgeon cuts free the patient's upper jaw (maxilla), which is subsequently relocated into a new position in the course of several weeks, using a distraction device.
The presented simulation toolchain is set up to predict the displacements of the facial tissues during and after the pulling process and is based on individual CT images of the patient's head before treatment. Its purpose is to support the surgeon in optimizing the treatment plan and avoiding additional post operative plastic surgeries.
The input data for the simulation toolchain is generated by adding the suggested cuts, the geometry of the distraction device and the suggested forces to the CT data of the patient's head. From these data we generate a Finite Element mesh of the head and perform a Finite Element analysis of the distraction process. In order to achieve sufficient accuracy we have to resolve most of the geometrical features of the human head, which leads to a large number of unknowns, typically several millions. In addition to that the computational costs are significantly increased by the size of the displacements and the visco-elastic behaviour of the materials, which can only be properly approximated by non-linear modelling. The image processing, the meshing and the analysis of the model are run via a grid service on an HPC resource.
Focusing on the efficiency of the simulation, the linear solvers used to solve the arising systems of equations play the most crucial role. In our case standard iterative solvers like Krylov methods or ILU methods fail, as we will show in our presentation. Therefore we will focus on the use of Multigrid solvers.
But the complex geometry of the human head in combination with large jumps of the material parameters -- Young's modulus jumps about 5 orders of magnitude between bone and soft tissues -- prevents standard multigrid approaches from converging at a sufficient rate. In theory convergence can be dramatically improved by computing the "near null space" of the systems, consisting of quasi-rigid body modes, and treating it separately. We will show the limitations of this approach for highly complex geometries, like the human head.
In our presentation we will demonstrate the performance of the only two solvers we have found to work on our problems so far, which are BoomerAMG from LLNL's hypre package and ML from Sandia's Trilinos package. We will show the results of our intensive parameter studies and discuss the extensibility of our perfomance results for elasto-mechanical Finite Element simulations in general.