Volume Preserved Mass–Spring Model with Novel Constraints for Soft Tissue Deformation

An interactive surgical simulation system needs to meet three main requirements, speed, accuracy, and stability. In this paper, we present a stable and accurate method for animating mass-spring systems in real time. An integration scheme derived from explicit integration is used to obtain interactive realistic animation for a multiobject environment. We explore a predictor- corrector approach by correcting the estimation of the explicit integration in a poststep process. We introduce novel constraints on positions into the mass-spring model (MSM) to model the nonlinearity and preserve volume for the realistic simulation of the incompressibility. We verify the proposed MSM by comparing its deformations with the reference deformations of the nonlinear finite-element method. Moreover, experiments on porcine organs are designed for the evaluation of the multiobject deformation. Using a pair of freshly harvested porcine liver and gallbladder, the real organ deformations are acquired by computed tomography and used as the reference ground truth. Compared to the porcine model, our model achieves a 1.502 mm mean absolute error measured at landmark locations for cases with small deformation (the largest deformation is 49.109 mm) and a 3.639 mm mean absolute error for cases with large deformation (the largest deformation is 83.137 mm). The changes of volume for the two deformations are limited to 0.030% and 0.057%, respectively. Finally, an implementation in a virtual reality environment for laparoscopic cholecystectomy demonstrates that our model is capable to simulate large deformation and preserve volume in real-time calculations.