Detection and modelling of contacts in explicit finite-element simulation of soft tissue biomechanics

Realistic modelling of soft-tissue biomechanics and mechanical interactions between tissues is an important part of surgical simulation, and may become a valuable asset in surgical image-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 the scenarios typically encountered in image-guidance. The responses are computed with an evolution of the Lagrange-multiplier method first used by Taylor and Flanagan in PRONTO 3D with spatio-temporal smoothing heuristics for improved stability with coarser meshes and larger time steps. For contact search, a bounding-volume hierarchy (BVH) capable of identifying self collisions, and which is optimised for the small time steps by reducing the number of bounding-volume refittings between iterations through identification of geometry areas with mostly rigid motion and negligible deformation, is introduced. Further optimisation is achieved by integrating the self-collision criterion in the BVH creation and updating algorithms. The effectiveness of the algorithm is demonstrated on a number of artificial test cases and meshes derived from medical image data.