Deformable Body Simulation with adaptive subdivision and cuttings

Abstract

We propose a deformable body model in order to simulate the dynamic behaviour of human organs during surgical operations. It is aimed at simulating organs in training surgical simulators, cur- rently developed in our team. However, since this model is general, it can be used in simulation or ani- mation of other deformable objects. In order to be sufficiently realistic, the model must behave dynamically, that is obey to the physical laws of motion. Moreover, it must be possible to interact with it. This requires impacts and contacts to be detected, and an accurate processing of extreme interac- tions such as cuttings and tears to be implemented. The model we present is intended to respond in an optimal manner to these constraints in realtime. It is based on a spring surface mesh, fitted with a vir- tual rigid component which does not interact with the environment and provides the structure with a rigid behaviour. In order to get both contacts precision and realtime, an adaptive subdivision of the sur- face mesh is used: a small number of nodes are defined at the beginning of the simulation, and more nodes are added dynamically to the mesh in the contact zones. 1. Introduction We plan to design a number of training surgical simulators, in areas such as ophthalmology (MKCD95), ultrasound endoscopy (VC95) or gynaecologic laparoscopy. Our goal is simple: we want to build the tools to enable the surgeons to learn how to operate not on actual patients but on virtual ones. Nevertheless, in the medical field, a simulator requires not only to generate highly realistic images but also to reproduce the mechanical interactions between the surgeons and the operated organs. The complete system consists therefore in all the means to measure the motion of the tools manipulated by the surgeons, to compute the behaviour of the manipulated organs and to reproduce their modifications both in a visual and tactile manner. Realtime simulation of the dynamic behaviour of deformable or rigid bodies is a new challenge in computer graphics today. The simulated organs can be quite different, so that the model we plan to design must be general. This generality makes it usable in other areas requiring deformable body animation, providing that the same preliminary hypotheses are chosen. To build such a model, three main problems are to be solved: First, the motion of the objects has to look realistic. This means that the model must be based on the physical laws governing the cinematic and dynamic behaviour of the rigid or deformable bodies. Those equations usually result in second order differential equations, which require a correct integration method. Kinematics is essential for the reproduction of motion, while dynamics is necessary to compute the forces returned to the user. These forces are also called force feedback. Second, the object must interact with its environment. For instance, the surgeon, by means of a tool, can manipulate the organs, come into contact with them, move (push/pull) them and/or deform them. Hence, these interations can produce both local or global deformations and rigid motions (translations, rotations). Finally, the interactions can be drastic and result in structure modifications: cuttings and tears for example. In this paper, we first analyse the previous works in the field of organ modelling. Then, the purposes and constraints of the design of our model are exposed, as well as the necessary preliminary hypotheses to simplify the problem. Our model is then presented. This model includes a refinement process, which enables precise contacts handling without compromising realtime simulation.