Particle methods

		Dynamic cutting sequence using the particles approach. Dumbbell surface driven by the mean curvature solved by a novel particle level set technique. The surface shrinks and approaches a mathematical singularity where it breaks off. The surface is colored according to the mean curvature. High resolution simulation of a compressible viscous vortex ring using 33 mio. particles distributed on 16 processors.

Volumetric Modeling of Organs

Our particle-based geometric models of human organs are based on triangle meshes which have been segmented from the "Visible Human Project" data set by the Computer Vision Lab, ETHZ (G. Szekely). Using a vertex-in-volume test, the interior of the organ is discretized into a uniformly distributed set of particles. Whereas the original topology data set typically consists of more than 100k faces, the reconstructed surface based on the particle map can contain only several hundred of faces and still provides a smooth representation of the topology.

Physical Modeling

Particle-based simulations are characterized by their adaptivity and flexibility, e.g. concerning complex and changing geometries and multi-physics simulations. A new feature of our approach is the reinitialisation or 'remeshing' to guarantee the convergence of the method. We have implemented a remeshed Smoothed Particle Hydrodynamics (SPH) approach for one, two and three dimensions for solving our physical models. To mimic the dynamic behavior of soft biological tissue we have developed a particle model which describes a linear visco-elastic solid. The mechanical parameters of the model are derived from the experimental measurements of the Institute of Mechanical Systems, ETHZ (E. Mazza), considering human liver and kidney. Currently, we are working on the validation of our particle-based tissue simulations. Another research topic is the simulation of fluid-solid interactions, which is important for many biological applications.

Surface Capturing

An important issue in this project is the surface reconstruction of the tissue represented by particles. Level set methods are established techniques to capture interfaces in Eulerian (grid-based) methods. We developed a novel hybrid Particle Level set method where the level set values are carried by the particles. This approach results in accurate and efficient interface simulations that are not hindered by a CFL condition.

Parallel Computing

We contributed to the new Parallel Particle Mesh (PPM) Library developed in the group of Prof. Koumoutsakos. PPM is a multi-purpose Fortran library for hybrid particle mesh simulations on massively parallel computer architectures. We implemented an rSPH client based on this library that shows a very good scalability up to 128 processors. We can simulate 70 mio. particles on 64 processors in 78 seconds per time step with an efficiency of 95% by using efficient summation techniques combined with look-up tables.