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An Efficient Nonlinear Mass-Spring Model for Anatomical Virtual Reality

The visuo-haptic surgical simulator providing both visual feedback and haptic interaction is very important for various applications, such as surgical simulation, training, and planning. In this article, we develop a nonlinear mass-spring model (MSM) by introducing the elastica springs that measure the soft tissue deformation based on both spring length and curvature. As a result, our model works well on the triangular surface meshes by producing more realistic simulations with smoother and plumper surfaces. Numerical experiments are conducted on both synthetic sphere and human liver models to demonstrate the superior performance of our method with both position- and force-based interactions. Compared to the traditional and constrained MSMs, our model can well balance accuracy and efficiency, providing simulation results with biomechanical properties, such as nonlinearity and incompressibility. Furthermore, we implement the proposed model as the physical engine for a prototype of anatomical virtual reality, where realistic deformation is rendered at a refresh rate of 33 frames/s on a regular personal computer.