A Physically Based Deformable Model with Haptic Feedback for Real-Time Robotic Surgery Simulation

Surgical simulators have been under development for years, formerly intended for surgical training and recently applied for training machine learning models. These systems often employ computationally efficient methods such as mass-spring models or position-based dynamics that prioritize real-time execution over physical accuracy, while the use of the finite element method (FEM) has been limited due its computational cost. In consequence, there has been little improvement in the accuracy of the deformable models and the haptics, relying on hand-tuned stiffness parameters, and empirical solutions to estimate the contact forces. To solve these limitations, we propose to develop a new surgical simulator for laparoscopic cholecystectomy employing the extended position-based dynamics method in conjunction with FEM to compute physically based deformation and obtain accurate contact forces during the collision response. While dense organs like the liver are modeled using tetrahedrons and addressed the element inversion problem in FEM, we propose to simulate the gallbladder as a closed elastic membrane using two-dimensional FEM elements with volume preserving constraints to model the inner incompressible fluid. Because continuous position and contact force measurement on real materials to verify the simulation is challenging, we employ a bilateral robotic system equipped with Fiber Bragg Grating-based force sensors.