Stiffness matrix representation of hyper-elasticity for surgical simulation and navigation

Nowadays, physics-based simulation plays an important role in industries and clinical fields thanks to the outstanding progress of computer technologies and numerical simulation. One of the demands for the applied technology of physics-based simulation, is the surgical simulation of organ tissue not only for surgical training but also for intra-operative navigation. Although linear Finite Element Method (FEM) is capable of real-time simulation, the conventional FEM analysis does not satisfy the accuracy of non-linear response and interactivity at the same time. The aim of this study is to establish the surgical simulation and navigation to consider hyper-elasticity (HE), which represents the organ´s non-linear response material better than the conventional linear material. In this paper, we propose a novel method to decompose the stress-strain relationship of HE, and construct the stiffness matrix for real-time and interactive simulation by extending the linear FEM, which is capable of efficient simulation. The experimental results showed that the proposed method is able to simulate non-linear FEM deformation accurately almost equivalent to the existing non-linear FEM analysis by shorter calculation time. In addition, the deformation with the kidney model was demonstrated.