Abstract: A simulator simulates interaction between a surgical tool and biological tissue, providing real time visual and/or haptic feedback. The simulator receives tool input device information representative of a user's movement of a physical tool. The simulator simulates, based on the tool input device information, an interaction between the simulated tool and simulated biological tissue. The simulator uses multiple computational threads, some of which provide their calculations to interrelated threads for use. The simulator displays a visual representation of the simulated interaction between the simulated tool and the simulated biological tissue and provides haptic feedback to the user. The threads may operate asynchronously and have different spatial and/or temporal resolutions. Threads may be selectively activated and deactivated. Threads may move their spatial coverage.