Modélisation mécanique de fils pour la simulation chirurgicale

Minimally Invasive Surgery (MIS) represents one of the major progresses in surgery in the last decade. In general, it is based on the application of small body-cuts through which instruments are inserted into the patient's body allowing the surgeon to carry out their job. The advantages are numerous, mainly related to the patient's health, and economic advantages. The rather small size of the necessary cuts means a decreased risk of trauma and a faster recovery. It follows that hospitalization time and costs are reduced significantly. The conditions in which such surgery takes place are considerably different from traditional surgery. First of all, the extent to which the surgical instruments may be moved freely is reduced, as they have to pass through a fixed point. Then, visualisation of the surgery site takes place on a computer screen. In laparoscopy, the screen is connected to a micro-camera whereas in interventional radiology, an image created by x-rays is displayed on the screen. As more new surgical techniques are continuously invented, it is expected that these techniques can be practiced by the surgeons and, more importantly, preferred by patients. Amongst these surgical techniques, the suturing during laparoscopic surgery requires a certain skill in instrument handling to realize the required knots. In interventional radiology, during an angiography, the manipulation of the catheter requires a highly trained hand as the catheter has to pass through a complex, 3-dimensional network of blood vessels. The catheter is only visible when a radio-opaque marker is injected while the patient is under the emission of x-rays. Furthermore, such pictures are 2D. To help the surgeons to improve their abilities, we propose a haptic simulator to learn how to realize the knots for the suturing and a virtual environment for the angiography. For both training modules, we developed a model of filament based on the Cosserat theory applied to one-dimensional structures, which can describe the behaviour of a string as well as the behaviour of a rigid and flexible rod (catheter). This model starts from the energetic formulation of the filament considering the Hook laws of continuum mechanics. The Lagrange equations provide us with the equations of motion which describe the model deformation. This model takes collisions and auto-collisions into account and it is revealed to be very efficient for interactive applications. The training module dedicated to angiography permits to carry out the most usual gesture: beside the catheter navigation, a marker can be injected to visualize the vessels, to drive the balloon angioplasty towards the pathology and to set stents. Moreover, the visual rendering is very realistic and the heart beatings as well as breathing are also simulated.