Constraint-Based Soft Tissue Simulation for Virtual Surgical Training

Most of surgical simulators employ a linear elastic model to simulate soft tissue material properties due to its computational efficiency and the simplicity. However, soft tissues often have elaborate nonlinear material characteristics. Most prominently, soft tissues are soft and compliant to small strains, but after initial deformations they are very resistant to further deformations even under large forces. Such material characteristic is referred as the nonlinear material incompliant which is computationally expensive and numerically difficult to simulate. This paper presents a constraint-based finite-element algorithm to simulate the nonlinear incompliant tissue materials efficiently for interactive simulation applications such as virtual surgery. Firstly, the proposed algorithm models the material stiffness behavior of soft tissues with a set of 3-D strain limit constraints on deformation strain tensors. By enforcing a large number of geometric constraints to achieve the material stiffness, the algorithm reduces the task of solving stiff equations of motion with a general numerical solver to iteratively resolving a set of constraints with a nonlinear Gauss-Seidel iterative process. Secondly, as a Gauss-Seidel method processes constraints individually, in order to speed up the global convergence of the large constrained system, a multiresolution hierarchy structure is also used to accelerate the computation significantly, making interactive simulations possible at a high level of details. Finally, this paper also presents a simple-to-build data acquisition system to validate simulation results with ex vivo tissue measurements. An interactive virtual reality-based simulation system is also demonstrated.