New Finite Element Algorithm for Surgical Simulation

We propose an efficient numerical algorithm for computing deformations of “very” soft tissues (such as the brain, liver, kidney etc.), with applications to real time surgical simulation. The algorithm is based on the finite element method using the Total Lagrangian formulation, where stresses and strains are measured with respect to the original configuration. This choice allows for pre-computing of most spatial derivatives before the commencement of the time-stepping procedure. We used explicit time integration that eliminated the need for iterative equation solving during the time stepping procedure. The algorithm is capable of handling both geometric and material non-linearities. Stability analysis of the algorithm suggests that due to much lower stiffness of very soft tissues than that of typical engineering materials, integration time steps a few order of magnitude larger than what is typically used in engineering simulations are possible. A numerical example confirms the accuracy and efficiency of the proposed Total Lagrangian Explicit Dynamics (TLED) algorithm. * corresponding author [email protected]