Real-time simulation of surgical cutting in haptic environments using computational vademecums

Congress on Numerical Methods in Engineering Lisboa, June 29 to July 02, 2015 © APMTAC, Portugal, 2015 cmn2015 | Congresso de Métodos Numéricos em Engenharia Edited: José Miranda Guedes, Nuno Silvestre, Miguel Tavares da Silva, Jesús María Blanco, Irene Arias, Manuel Tur Valiente RESUMO N° 181 REAL-TIME SIMULATION OF SURGICAL CUTTING IN HAPTIC ENVIRONMENTS USING COMPUTATIONAL VADEMECUMS Carlos Quesada, [email protected] Universidad de Zaragoza, Mechanical Engineering, Spain David González, [email protected] Universidad de Zaragoza, Mechanical Engineering, Spain Icíar Alfaro, [email protected] Universidad de Zaragoza, Mechanical Engineering, Spain Elías Cueto, [email protected] Universidad de Zaragoza, Mechanical Engineering, Spain Francisco Chinesta, [email protected] Ecole Centrale de Nantes, EADS Corporate International Chair, France Keywords: Computational Vademecum, PGD, X-FEM, Real-Time Simulation, Surgical Simulation, Haptic Environment Realistic simulation of surgical cutting in soft tissues is a specially challenging problem in real-time modelling, since it involves very complex physics. Remarkably, topological changes in the geometry of the organs and their associated meshes must be accomplished avoiding the penalization of the computation time. This work introduces a new method for real-time simulation of surgical cutting in haptic environments. It is based on the intensive use of computational vademecums, i.e., parametric high-dimensional meta-models that, in the style of the ancient reference handbooks consulted by engineers, provide a quick solution for any possible situation. The computation of these meta-models is implemented off-line and only once, whereas its evaluation is performed on-line, interactively, as many times as needed. Thereby, impressive time savings are achieved, reaching feedback rates of the order of 1 kHz, compatible with the response needs of the haptic peripherals. The method here proposed is based on an a priori model order reduction technique known as Proper Generalized Decomposition (PGD). Recent advances in the field employ PGD methods to construct the computational vademecums. Essentially, PGD determines the best basis for the simulation of the system (although results are often not optimal, since it uses a greedy algorithm) to efficiently solve high-dimensional problems. In this approach, a vademecum is computed for all the possible responses of the organ to any load applied on its surface by the surgical tool. As a novelty, this work combines the concept of computational vademecum and X-FEM techniques, which significantly simplify the generation and management of the discontinuities. To accurately describe a cut, the model of the organ is modified on the fly by the incorporation into the displacement field of the required degrees of freedom. Examples of the performance of the technique will be provided.