Simulation of tissue cutting and bleeding for laparoscopic surgery using auxiliary surfaces

Realistic simulation of tissue cutting and bleeding is important components of a surgical simulator that are addressed in this study. Surgeons use a number of instruments to perform incision and dissection of tissues during minimally invasive surgery. For example, a coagulating hook is used to tear and spread the tissue that surrounds organs and scissors are used to dissect the cystic duct during laparoscopic cholecystectomy. During the execution of these procedures, bleeding may occur and blood flows over the tissue surfaces. We have developed computationally fast algorithms to display (1) tissue cutting and (2) bleeding in virtual environments with applications to laparoscopic surgery. Cutting through soft tissue generates an infinitesimally thin slit until the sides of the surface are separated from each other. Simulation of an incision through tissue surface is modeled in three steps: first, the collisions between the instrument and the tissue surface are detected as the simulated cutting tool passes through. Then, the vertices along the cutting path are duplicated. Finally, a simple elastic tissue model is used to separate the vertices from each other to reveal the cut. Accurate simulation of bleeding is a challenging problem because of the complexities of the circulatory system and the physics of viscous fluid flow. There are several fluid flow models described in the literature, but most of them are computationally slow and do not specifically address the problem of blood flowing over soft tissues. We have reviewed the existing models, and have adapted them to our specific task. The key characteristics of our blood flow model are a visually realistic display and real-time computational performance. To display bleeding in virtual environments, we developed a surface flow algorithm. This method is based on a simplified form of the Navier-Stokes equations governing viscous fluid flow. The simplification of these partial differential equations results in a wave equation that can be solved efficiently, in real-time, with finite difference techniques. The solution describes the flow of blood over the polyhedral surfaces representing the anatomical structures and is displayed as a continuous polyhedral surface drawn over the anatomy.