The research work presented for the habilitation thesis aim to provide new simulation tools for medical and surgical interventions.These tools have many applications including training of physicians, planning of interventions (for rehearsal and for the validation of a therapy) or providing assistance during a real intervention. However, to obtain a realistic or even predictive simulation of the procedure, we must take into account the deformation of anatomical structures and the mechanical interactions between devices and tissues. At the same time, the simulation must be interactive and computed in real-time to keep the gesture of the physician in the loop of the simulation. The major challenge of our work is to guarantee a certain level of accuracy in the simulation while keeping a very short computation time, consistent with the real-time. First, we present an optimized formulation of the finite element method (FEM) for the deformable models and new numerical tools (preconditionner, coupling between models...) dedicated to real-time FEM computation. This approach is used to compute the biomechanics of anatomical soft-tissues, as well as flexible instruments. The second key point is the boundary conditions: the mechanical interactions between organs and/or with surgical devices are often difficult to account for. Yet, a bad modeling of these interaction can lead to a large source of errors. Our approach builds on non-smooth mechanics for modeling contact and friction between solids but also extends to other models of interaction (like needle insertion for instance). In this context, we also address the difficult problem of computing the compliance of deformable structures in real-time. Third, during some procedures, the visual feedback is far from perfect and the physician uses haptic feedback for guidance. In such case it is important to provide haptic rendering using dedicated haptic devices and simulation algorithms. In this domain, we provide a new asynchronous approach that is centered on the mechanical interactions between devices and human tissues. The method addresses the problem of high-refresh rates (1kHz) needed in the haptic loop. Finally, we present some research results on concrete application examples that we are currently developing. We present the remaining challenges to allow a large diffusion of the simulation as a clinical tool, used by physicians in the future.
Real-time haptic simulation of medical procedures involving deformations and device-tissue interactions