Real-time visio-haptic interaction with static soft tissue models having geometric and material nonlinearity

Abstract

Realistic soft tissue models running in real-time are required for the development of computer-based surgical training systems. To construct a realistic soft tissue model, finite element (FE) modeling techniques are preferred over the particle-based techniques since the material properties can be integrated directly into the FE model to provide more accurate visual and haptic feedback to a user during the simulations. However, running even a static (time-independent) nonlinear FE model in real-time is a highly challenging task because the resulting stiffness matrix (K) is not constant and varies with the depth of penetration into the model. We propose a new computational approach allowing visio-haptic interaction with an FE model of a human liver having both nonlinear geometric and material properties. Our computational approach consists of two main steps: a pre-computation of the configuration space of all deformation configurations of the model, followed by the interpolation of the precomputed data for the calculation of the nodal displacements and reaction forces that are displayed to the user during the real-time interactions through a visual display and a haptic device, respectively. For the implementation of the proposed approach, no a priori assumptions or modeling simplifications about the mathematical complexity of the underlying soft tissue model, size and irregularity of the FE mesh are necessary. Moreover, it turns out that the deformation and force responses of the liver in the simulations are heavily influenced by the selected simulation parameters, such as the material model, boundary conditions and loading path, but the stability of the visual and haptic rendering in our approach does not depend on these parameters. In addition to showing the stability of our approach, the length of the precomputations as well as the accuracy of the interpolation scheme are evaluated for different interpolation functions and configuration space densities.