Tensor-mass Model based real-time simulation of vessel deformation and force feedback for the interventional surgery training system

Mass Spring Model (MSM) and Finite Element Method (FEM) are two basic methods for soft model deformation simulation. However, MSM has a high computation efficiency but low accuracy which is only a coarse approximation of the real biological soft tissue while FEM is inverse on the two sides. To achieve realistic and real-time simulation at the same time, in this paper, we proposed an improved non-linear elastic tensor-mass modelling method, which realizes fast computation of non-linear mechanical deformations, and it is suitable for simulating the hollow biological tissue surface. Based on the tensor-mass concept, we applied the tensors of triangles to the surface vessel model, which is distinguished from the current study of tetrahedral tensors while simulating solid tissue, such as liver. Also, we applied an extension of an efficient implicit numerical analytical method for the simulation. Moreover, we introduced a haptic force feedback device for interactions between the vessel model and the virtual medical instrument which improves the realism of the simulation. A set of experiments, including the interactive deformation of the physical vessel model, and the stress-strain data analyses of different nodes and a single node, were conducted to validate the realism, accuracy, steadiness of the TMM model during the simulation. The simulation results showed high efficiency and real time performance over 91 fps which is about 30% higher than the current realistic simulation method in the training system.