Explicit contact modeling for surgical computer guidance and simulation

Realistic modelling of mechanical interactions between tissues is an important part of surgical simulation, and may become a valuable asset in surgical computer guidance. Unfortunately, it is also computationally very demanding. Explicit matrix-free FEM solvers have been shown to be a good choice for fast tissue simulation, however little work has been done on contact algorithms for such FEM solvers. This work introduces such an algorithm that is capable of handling both deformable-deformable (soft-tissue interacting with soft-tissue) and deformable-rigid (e.g. soft-tissue interacting with surgical instruments) contacts. The proposed algorithm employs responses computed with a fully matrix-free, virtual node-based version of the model first used by Taylor and Flanagan in PRONTO3D. For contact detection, a bounding-volume hierarchy (BVH) capable of identifying self collisions is introduced. The proposed BVH generation and update strategies comprise novel heuristics to minimise the number of bounding volumes visited in hierarchy update and collision detection. Aside from speed, stability was a major objective in the development of the algorithm, hence a novel method for computation of response forces from C0-continuous normals, and a gradual application of response forces from rate constraints has been devised and incorporated in the scheme. The continuity of the surface normals has advantages particularly in applications such as sliding over irregular surfaces, which occurs, e. g., in simulated breathing. The effectiveness of the scheme is demonstrated on a number of meshes derived from medical image data and artificial test cases.