A framework for open surgery simulation

In this thesis we present a framework for the simulation of surgery procedures, like they occur during operations in open surgery. While various algorithms for simulating the deformation oforgans have been developed in the past, few tried to modify the underlying geometry. The geometric modification, however, is a very important component in every type of surgical simulation, since it is the modification in the tissue structures that constitutes the success of a surgical operation. This thesis focuses on an accurate simulation of tissue intersections ofarbitrary trajectories, as they are performed by a surgical scalpel. To provide a realistic simulation environment, further components, like physically-based tissue deformation and realistic haptic feedback are also integrated in our framework, as well as some surgical hooks that allow to open the resulting incisions. The representation ofour models by tetrahedral meshes allows to simulate volumetric effects, while still providing the basis for an efficient calculation of the tissue's deformation. The algorithm that ensures the consisteney of the tetrahedral mesh during cutring is based on a state machine which describes the topological cut pattern of each tetrahedron. This state machine concept enables an incremental construction of the tetrahedral subdivisions by applying state transitions, efficiently represented by preprocessed lookup table entries, A recursive continuation of this state machine makes it possible to even track very complex scalpel trajectories by a local refinement of the mesh structures. For the efficient registration of collisions berween surgical tools and the tissue structures, a collision detection algorithm determines possible intersections between the involved objects. Hierarchical and local recursive algorithms have been developed that keep the computational burden of the collision detection low and guarantee a consistent detection of all mesh inrersections even within heavily moving tissue. Two models represent the physical behavior of the tissue. An explicit finite .element method correctly simulates incornpressibiliry, whereas a simpler but faster damped mass spring systern handles large deformations more realistically. Both models are solved with implicit numerical methods bya parallelized solver that allows adaptive time steps for each individual node. Realistic haptic feedback ofour surgical tools is achieved by building a hierarchy ofsfmulation loops running at different update rates, and by physically modeling the various occurring friction forces. We demonstrated several surgical tasks with the resulting surgery simulation framework. The simulation shows very realistic seenarios and reacrs interactively for substantial mesh sizes while supporting real-time frame rates. In particular, the cut algorithm captivates with its geometrical accuraey, and its flexibility concerning topological modifications.