Improving realism of a surgery simulator: linear anisotropic elasticity, complex interactions and force extrapolation

In this article, 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 to perform laparoscopic procedures. Therefore, its main functionality is to simulate the action of virtual laparoscopic surgical instruments for deforming and cutting tridimensional anatomical models. Throughout this paper, we present the general features of this simulator including the implementation of several biomechanical models and the integration of two force-feedback devices in the simulation platform. More precisely, we describe three new important developments that improve the overall realism of our simulator. First, we have developed biomechanical models, based on linear elasticity and finite element theory, that include the notion of anisotropic deformation. Indeed, we have generalized the linear elastic behaviour of anatomical models to 'transversally isotropic' materials, i.e. materials having a different behaviour in a given direction. We have also added to the volumetric model an external elastic membrane representing the 'liver capsule', a rather stiff skin surrounding the liver, which creates a kind of 'surface anisotropy'. Second, we have developed new contact models between surgical instruments and soft tissue models. For instance, after detecting a contact with an instrument, we define specific boundary constraints on deformable models to represent various forms of interactions with a surgical tool, such as sliding, gripping, cutting or burning. In addition, we compute the reaction forces that should be felt by the user manipulating the force-feedback devices. The last 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 behaviour. 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. Copyright (C) 2002 John Wiley Sons, Ltd.