Interactive Cuts through 3‐Dimensional Soft Tissue

Abstract

We describe a physically based framework for interactive modeling and cutting of 3‐dimensional soft tissue that can be used for surgery simulation. Unlike existing approaches which are mostly designed for tensorproduct grids our methods operate on tetrahedral decompositions giving more topological and geometric flexibility for the efficient modeling of complex anatomical structures. We start from an initial tetrahedralization such as being provided by any conventional meshing method. In order to track topological changes tetrahedra intersected by the virtual scalpel are split into substructures whose connectivity follows the trajectory of the cut, which can be arbitrary. For the efficient computation of collisions between the scalpel and individual tetrahedra we devised a local collision detection algorithm. The underlying physics is approximated through masses and springs attached to each tetrahedral vertex and edge. A hierarchical Runge‐Kutta iteration computes the relaxation of the system by traversing the designed data structures in a breadth‐first order. The framework includes a force‐feedback interface and uses real‐time texture mapping to enhance the visual realism.