Anisotropic Elasticity and Forces Extrapolation to Improve Realism ofSurgery

In this paper, we describe the latest developments of the hepatic surgery simulator prototype developed at INRIA. The goal of this simulator is to provide a realistic training testbed for performing laparoscopic procedures. Therefore, its main functionality is to allow to cut and deform tridimensional anatomical models with the help of two virtual laparoscopic surgical instruments. Thoughout this paper, we present the general features of the simulator including the creation of anatomical models from medical imaging, the implementation of diierent biomechanical models based on linear elasticity and nite element theory and the integration of two force-feedback devices in the simulation platform. More precisely, we describe two new important developments that improve the overall realism of the simulator. First, we can create biome-chanical models that include the notion of anisotropic deformation. Indeed, we have generalized the linear elastic behavior of anatomical models to "transver-sally isotropic" materials, i.e. materials having one privileged direction of deformation. The second improvement is related to the problem of haptic rendering. Currently, we are able to achieve a simulation frequency of 25Hz (visual real-time) with anatomical models of complex geometry and behavior. But to achieve a good haptic sensation requires a frequency update of the applied forces typically above 300Hz (haptic real-time). Thus, we propose an extrapolation algorithm of the forces computed by the deformable model in order to reach haptic real-time.