XFEM Framework for Cutting Soft Tissue - Including Topological Changes in a Surgery Simulation

Currently, there are many approaches in computer graphics (CG) that deal with topological changes; some of these are non-interactive animations, unstable or not precise enough to medical applications. It has been found that the Extended Finite Element Method (XFEM) is stable, accurate, with excellent performance and suitable for virtual surgery in real time; nevertheless, to maintain the provided advantages, the selection and creation of a set of CG methods is required that fulfill the requirements of the XFEM. We propose an embedded mapping method that enables the relation of the XFEM elements, with the visual and collision meshes, making the user interaction more dynamic. Furthermore, based on this new mapping method an interactive cutting algorithm is suggested considering a geometric analysis. The XFEM, as a core of our framework, efficiently simulates the topological changes consequently, making the interaction in real time possible, which will allow the creation of more complex simulations of higher impact in the medical area.