A reduced order finite element algorithm for surgical simulation

We present a reduced order finite element (FE) algorithm suitable for real-time nonlinear simulation of soft tissues. A dynamic FE formulation with explicit time integration is employed. We demonstrate significant computation acceleration by performing the time integration in a low-dimensional generalised basis, generated from a set of a priori training simulations. The key mechanism for the acceleration is the large increase in integration time step afforded by this means. Furthermore, we present a simple procedure for imposing inhomogeneous essential boundary conditions, thus overcoming one of the principal deficiencies of such approaches. The algorithm is described and demonstrated using an example neurosurgical simulation. The computation acceleration and errors introduced are examined.