Multi-contact Model for FEM-based Surgical Simulation

This paper presents a novel method to simulate multiple contacts of deformable objects modeled by the finite-element method. There have been two main approaches for contact models in the literature. The penalty method fails to guarantee the non-penetration condition. In the constraint method, imposition of multiple position constraints on arbitrary points of the surface, caused by the multiple contacts, can be non-deterministic depending on the contact configurations. Infinite number of solutions exists in most cases. The proposed method uses a deformable membrane of mass and spring to determine the initial position constraints to obtain a unified solution regardless of the contact configurations. The membrane is locally generated at the contact region, and is identical to the local triangular surface meshes of the finite-element model. The membrane is then deformed by the contacts caused by rigid objects such as surgical tools. Displacements of the mass points of the deformed membrane at the equilibrium state are, then, applied to the finite-element model as the position constraints. Simulation results show satisfactory realism in the real-time simulation of the deformation. The proposed method prevents penetration of the rigid object into the deformable object. The method can be applied to interactions between tools and organs of arbitrary shapes.