Real-time finite element (FE) analysis can be used to represent complex deformable geometries in virtual environments. The need for accurate surgical simulation has spurred the development of many of the new real-time FE methodologies that enable haptic support and real-time deformation. These techniques are computationally intensive and it has proved to be a challenge to achieve the high modeling resolutions required to accurately represent complex anatomies. The authors present a new real-time methodology based on linear FE analysis that is appropriate for a wide range of surgical simulation applications. A methodology is proposed that is characterized by high model resolution, low preprocessing time, unrestricted multipoint surface contact, and adjustable boundary conditions. These features make the method ideal for modeling suturing, which is an element common to almost every surgical procedure. This paper describes constraints in the context of a Suturing Simulator currently being developed by the authors.

Realistic deformation of computer-simulated anatomical structures is computationally intensive. As a result, simple methodologies not based in continuum mechanics have been employed for achieving real-time deformation of virtual anatomy. Since the graphical interpolations and simple spring models commonly used in these simulations am not based on the biomechanical properties of tissue structures, these "quick and dirty" methods typically do not represent accurately the complex deformations and force-feedback interactions that can take place during surgery. Finite Element (FE) analysis is widely regarded as the most appropriate alternative to these methods. Extensive research has been directed toward applying this method to modelling a wide range of biological structures, and a few simple FE models have been incorporated into surgical simulations. However, because of the highly computational nature of the FE method, its direct application to real-time force-feedback and visualisation of tissue deformation has not been practical for most simulations. This limitation is due primarily to the overabundance of information provided by the standard FE approaches. If the mathematics are optimised through preprocessing to yield only the information essential to the simulation task, run-time computation requirements can be reduced drastically. We are currently developing such methodologies, and have created computer demonstrations that support real-time interaction with soft tissue. To illustrate the efficacy and utility of these fast "banded matrix" FE methods, we present results from a skin suturing simulator which we are developing on a PC-based platform.

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