Anisotropic elasticity and force extrapolation to improve realism of surgery simulation

We describe the latest developments of the minimally invasive hepatic surgery simulator prototype developed at INRIA. The goal of this simulator is to provide a realistic training test-bed for performing laparoscopic procedures. Therefore, its main functionality is to simulate the deformation and cutting of tri-dimensional anatomical models with the help of two virtual laparoscopic surgical instruments. Throughout the paper, we present the general features of the simulator including the implementation of different bio-mechanical models based on linear elasticity and finite element theory and the integration of two force-feedback devices in the simulation platform. More precisely, we describe two important developments that improve the overall realism of the simulator. First, we can create bio-mechanical models that include the notion of anisotropic deformation. Indeed, we have generalized the linear elastic behavior of anatomical models to "transversally 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 25 Hz (visual real-time) with anatomical models of complex geometry and behavior. But to achieve a good haptic feedback requires a frequency update of applied forces typically above 300 Hz (haptic real-time). Thus, we propose a force extrapolation algorithm in order to reach haptic real-time.