Frank Tendick, Xunlei Wu, Michael Downes, Tolga Goktekin, M. Cenk
Cavusgolu, David Feygin, and Gunnar Proppe
University of California, San Francisco and
University of California, Berkeley

“Adaptive Nonlinear Finite Elements for Deformable Body Simulation
Using Dynamic Progressive Meshes”

The VESTA (Virtual Environments for Surgical Training and Augmentation) project at U.C. San Francisco, U.C. Berkeley, and U.C. Santa Barbara includes engineers, computer scientists, physicians, and psychologists developing and evaluating simulation systems for surgical training.  Our goals are to develop technologies and algorithms for simulation, improve methods of surgical training
and education, and to elucidate the cognitive basis of surgical skill.

This presentation will focus on our work in accurate real-time deformable tissue modeling.  Past techniques of deformable modeling for real time simulation have either used approximate methods that are not physically accurate or linear methods that do not produce reasonable global behavior.  Nonlinear finite element methods (FEM) are globally accurate, but conventional FEM is not real time.  We apply nonlinear FEM using mass lumping to produce a diagonal mass
matrix, and explicit integration, allowing real time computation scaling as O(n).  A major challenge in nonlinear FEM is to maximize offline computation to reduce the computational demand while the simulation is running.  In addition, accuracy should be maximized in areas where there is fine detail, and computation minimized elsewhere. The approach we have developed to address these issues is called Dynamic Progressive Meshes (DPM).  This is an extension of the
progressive mesh method in the computer graphics literature, and works for either triangular or tetrahedral meshes.  Parameters for the finite element model are pre-computed at a range of mesh resolutions from coarse to fine in a hierarchy.  When the simulation is running, the mesh is refined locally where necessary, such as where instruments are in contact with the tissue.
Mechanical properties have been obtained from a variety of abdominal tissues in the pig using in vivo measurement instrumentation we have developed.  We are developing key extensions to the DPM method, including fast stress propagation with explicit integration using multi-grid techniques; collision detection and  response optimized for DPM; parallelization methods; and modeling fracture (cutting and crack propagation in tissue). Because the DPM model is  hierarchical, cutting can occur with minimal re-computation.

In addition, we have developed methods for haptic interaction with simulation, including a multirate scheme for stable haptic interaction at fast update rates using a local linear approximation.  We are also exploring the role of kinesthetic feedback and haptic guidance in training complex perceptual-motor skills.

Some information on the project and relevant papers may be found at
http://robotics.eecs.berkeley.edu/~tendick/vesta.html.