Progressive update approach to real-time cutting of finite element models in surgical simulation

We present an extension of our work on topology modification and deformation for Finite Element Models, in which the inverse stiffness matrix is updated rather than recomputed entirely. Previously we integrated condensation to allow for realistic interaction with larger models. We improve on this by redistributing computational load to increase the system's real-time response. Removing a tetrahedron only requires data associated with the nodes of that tetrahedron, and the surface nodes, to be updated, in order to drive the simulation. However, the update procedure itself needs the entire data structure to be updated. The equations used to update the inverse stiffness matrix are split up such that calculations are only performed for the affected nodes. Data regions corresponding to the surface nodes necessary for deformation calculations are computed immediately, whilst remaining regions can be computed as required, resulting in up to a ten-fold improvement in system response times.