Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
A model for efficient and accurate interaction with elastic objects in haptic virtual environments
Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Real-Time Elastic Deformations of Soft Tissues for Surgery Simulation
IEEE Transactions on Visualization and Computer Graphics
Non-linear anisotropic elasticity for real-time surgery simulation
Graphical Models - Special issue on SMI 2002
Haptically Driven Travelling through Conformational Space
WHC '05 Proceedings of the First Joint Eurohaptics Conference and Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems
Real-Time subspace integration for St. Venant-Kirchhoff deformable models
ACM SIGGRAPH 2005 Papers
Physically realistic virtual surgery using the point-associated finite field (PAFF) approach
Presence: Teleoperators and Virtual Environments - Special issue: Virtual heritage
IEEE Computer Graphics and Applications
VR-Based Simulators for Training in Minimally Invasive Surgery
IEEE Computer Graphics and Applications
Force Feedback is Noticeably Different for Linear versus Nonlinear Elastic Tissue Models
WHC '07 Proceedings of the Second Joint EuroHaptics Conference and Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems
Six-DoF Haptic Rendering of Contact Between Geometrically Complex Reduced Deformable Models
IEEE Transactions on Haptics
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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.