Real-time finite element based virtual tissue cutting

Tool-tissue interaction is most accurately modeled as an imposed dispalcement constraint, thus augmenting the traditional finite element equation, Ku = f, to a 2 × 2 block system. This augmentation does two things: it enlarges the system, and it introduces the Schur complement(S) during the solution. This research has focused on efficient methods to update the Schur complement and it's inverse during displacement constraint removal and addition to allow for soft-tissue cutting to occur in real-time. By taking advantage of how the constraints impact the Schur complement, removal and addition of these constraints are handled by either performing a rank- 2 or rank-1 update on S^-1, respectively. This greatly reduces the computational load on the CPU; and through use of timing tests shows that the update frequencies are well within an acceptable range for tactile feedback. To further solidify this method as being highly useful, a prototypical simulator has been developed that allows users to haptically perform bi-manual soft-tissue cutting.