Synchronous simulation for deformation of liver and gallbladder with stretch and compression compensation

One challenge in surgical simulation is to design stable deformable models to simulate the dynamics of organs synchronously. In this paper, we develop a novel mass-spring model on the tetrahedral meshes for soft organs such as the liver and gallbladder, which can stably deform with large time steps. We model the contact forces between the organs as a kind of forces generated by the tensions of repulsive springs connecting in between the organs. The simulation system couples a pair of constraints on the length of springs with an implicit integration method. Based on the novel constraints, our simulator can efficiently preserve the volumes and geometric properties of the liver and gallbladder during the simulation. The numerical examples demonstrate that the proposed simulation system can provide realistic and stable deformable results.