Simulation of Surgical Cutting of Soft Tissue using the X-FEM

Abstract

Modeling and simulation of the behaviour of elastic bodies is an important tool for medical engineering. Most physics-based simulations use the finite element method (FEM) for simulating the behaviour of deformable soft tissue under the effect of external forces. However, especially the task of surgical cutting still remains an open challenge. Current methods which, e.g., require the adjustment of the mesh topology in order to align elements with the cut, still suffer from performance and stability issues. Opposed to this, the extended finite element method (X-FEM) provides a novel approach for modeling discontinuities without creating new mesh elements, and thus minimizes the impact on the performance.
We present the development of a 3D model for the simulation of cutting in soft tissue. The incorporation of a corotation-based formulation into a dynamic FEM simulation enables realistic material behaviour even under larger deformations, and guarantees stability as well as computationally efficient data structures and algorithms which allow for near-to-real-time frame rates.
On the basis of our elasticity simulation, we develop an extended model which allows for the simulation of surgical cutting in soft tissue using the X-FEM. As a distinguishing feature our implementation combines the corotational formulation and the implicit Newmark time integration method, which not only allows for the realistic simulation of large cutting-induced deformations but also results in very stable simulations of arbitrary cuts. For the X-FEM, too, the underlying data structures of our implementation yield a great potential for outsourcing computationally expensive calculations from the actual time-stepping scheme into a pre-computing part, and hence enhance the utility of this simulation for real-time applications.
The evaluation of our methods uses commercial FEM software for comparison and shows the convergence of our simulation results. The X-FEM even exhibits comparable accuracy in terms of DOFs with respect to perfectly remeshed standard FEM. Along with good performance and stability properties, this proves the applicability of the X-FEM-based cutting simulation, e.g., in surgery simulators.