Total Lagrangian explicit dynamics finite element algorithm for computing soft tissue deformation

Abstract

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. The total Lagrangian explicit dynamics (TLED) algorithm using eight-noded hexahedral under-integrated elements requires approximately 35% fewer floating-point operations per element, per time step than the updated Lagrangian explicit algorithm using the same elements. 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 orders of magnitude larger than what is typically used in engineering simulations are possible. Numerical examples confirm the accuracy and efficiency of the proposed TLED algorithm. Copyright © 2006 John Wiley & Sons, Ltd.