Realistic behavior of deformable objects is essential for many applications such as simulation for surgical training. Existing techniques of deformable modeling for real time simulation have either used approximate methods that are not physically accurate or linear methods that do not produce reasonable global behavior. Nonlinear finite element methods (FEM) are globally accurate, but conventional FEM is not real time. In this paper, we apply nonlinear FEM using mass lumping to produce a diagonal mass matrix that allows real time computation. Adaptive meshing is necessary to provide sufficient detail where required while minimizing unnecessary computation. We propose a scheme for mesh adaptation based on an extension of the progressive mesh concept, which we call dynamic progressive meshes.

The computational burden created by the integration of these complex components often limits the fluidity of real-time interactive simulators. Although haptic interfaces have become increasingly sophisticated, the production of realistic tactile sensory feedback remains a formidable and costly challenge. The rate of future progress may be contingent upon international collaboration between research groups and the establishment of common simulation platforms. Given current limitations, the most potential for growth lies in the innovative design of models that expand the procedural applications of neurosurgery simulation environments.

With the introduction of minimally invasive techniques, surgeons must learn skills and procedures that are radically different from traditional open surgery. Traditional methods of surgical training that were adequate when techniques and instrumentation changed relatively slowly may not be as efficient or effective in training substantially new procedures. Virtual environments are a promising new medium for training. This paper describes a testbed developed at the San Francisco, Berkeley, and Santa Barbara campuses of the University of California for research in understanding, assessing, and training surgical skills. The testbed includes virtual environments for training perceptual motor skills, spatial skills, and critical steps of surgical procedures. Novel technical elements of the testbed include a four-DOF haptic interface, a fast collision detection algorithm for detecting contact between rigid and deformable objects, and parallel processing of physical modeling and rendering. The major technical challenge in surgical simulation to be investigated using the testbed is the development of accurate, real-time methods for modeling deformable tissue behavior. Several simulations have been implemented in the testbed, including environments for assessing performance of basic perceptual motor skills, training the use of an angled laparoscope, and teaching critical steps of the cholecystectomy, a common laparoscopic procedure. The major challenges of extending and integrating these tools for training are discussed.

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In this paper we describe two projects. The first is our novel and superior method of calculating the shape of the cornea of the eye from measuring instuments, called videokeratographs, that typically shine a pattern (usually rings) of light onto the cornea and then capture the reflection pattern on a CCD array using a built-in video camera. Accurate and detailed information about the shape of the cornea is critical for the diagnosis and correction of vision problems. The second project is a virtual environment simulation of the surgical procedure of minimallyinvasive gallbladder removal, which is known as laparoscopic cholecystectomy. Our simulation is designed to enable us to easily experiment with different approaches to addressing the major issues of surgical simulation, and it represents our attempt to leverage a great deal of surgical experience in creating a simulation that focuses on the most important, most error-prone steps in the procedure. Currently we are expanding the simulation code to serve as a general-purpose surgical simulation authoring tool, experimenting with new tissue modeling techniques, and constructing a new haptic interface device.