Interactive surgery simulations have conflicting requirements of speed and accuracy. In this paper we show how to combine a relatively accurate deformation model---the Finite Element (FE) method---and interactive cutting without requiring expensive matrix updates or precomputation. Our approach uses an iterative algorithm for an interactive linear FE deformation simulation. The iterative process requires no global precomputation, so runtime changes of the mesh, i.e. cuts, can be simulated efficiently. Cuts are performed along faces of the mesh; this prevents growth of the mesh. We present a provably correct method for changing the mesh topology, and a satisfactory heuristic for determining along which faces to perform cuts. The incision surface will be jagged; this problem is a subject of current research.
keywords: finite elements, tissue deformation, simplicial complex, virtual surgery, tetrahedral mesh, cutting.