Real-Time Haptic-Interactive Deformable Model Simulation for Biomedical Engineering Using Mass-Spring System

A number of studies and researches have been conducted on Virtual Surgery Planning. More specifically, topics on interactive virtual surgery using haptic device have been discussed in [1][2] and so on. Due to the nature of high demand in physical accuracy, many researchers adapted Finite Element Method(FEM) for the simulation. In this paper, I propose simplified massspring model for the interactive biomedical application which performs well on modern(even older) computers. Figure 3. SimpleDeformableSurface of the Haptic-Toolkit. The mass-spring system in the “SimpleDeformableSurface” provides following physical properties. A. Initial length of each spring B. Spring constant C. Damping coefficient D. Mass of every particle E. Nail Constraints In this project I used A,B,C and D to construct following conceptual mass-spring model over the model. 1) Neighborhood Springs Figure 4. Every vertex is connected to neighboring vertices with spring that have a length of Euclidian distance between two vertices. Every vertex is connected to its neighboring vertices with spring that have a rest-length equal to Euclidian distance between vertices. The force exerted on one vertices is a sum of forces of its neighboring vertices as following equation : where k is damping coefficient, k is spring constant, , are velocity and acceleration and is the position of a vertex. This can be easily implemented since I maintain a connectivity information – corner table. 2) Return Spring In [4], they introduced return-springs to give every vertex a tendency to go back to the original position. Figure 5. Return Springs. Figure from [4]. The return spring is simply a spring that connects a vertex with its original position with length 0. In this way if a vertex has any discrepancy it will go back to the original position. I have implemented return-springs by 1) duplicate every vertex and 2) connecting original and duplicated vertices with springs whose rest-length is 0.