Computational vademecums for real‐time simulation of surgical cutting in haptic environments

Abstract

Summary A new method for the real‐time simulation of surgical cutting in haptic environments is presented. It is based on the intensive use of computational vademecums, that is, a sort of computational parametric meta‐model, which is computed offline and only evaluated online. Therefore, the necessary time savings are obtained, allowing for feedback responses on the order of kilohertz. Such a high‐dimensional, parametric solution of the problem is computed by employing proper generalized decomposition for the offline phase of the method, along with X‐FEM techniques for the incorporation of the discontinuities in the displacement field after cutting, in the online phase. A thorough description of the proposed method, along with examples of its performance in the simulation of corneal surgery, are provided. Copyright © 2016 John Wiley & Sons, Ltd.

A local multiple proper generalized decomposition based on the partition of unity

“…Therefore, extra effort has to be done to set proper interface conditions along the red lines appearing in the same figure. This situation would be equivalent to the method described in the work of Badías et al This is in sharp contrast with the purely additive approach to couple FE and PGD proposed in the work of Ammar et al or in the work of Quesada et al, for instance. In that case, the method resembled the s ‐version of the FEM or the multiscale FEM proposed by Rank and Krause .…”

A review of virtual cutting methods and technology in deformable objects

“…36,47,[92][93][94][95] In addition, it is also an effective method to reduce the cost of calculation by using the model reduction method to reduce the dimension of the model rationally on the basis of ensuring effective precision. [96][97][98][99] In addition, some meshing methods, mesh optimization methods, 12,13,25,[100][101][102] and some meshless methods 103-107 that are not used or applied in fields other than surgical simulation are also of concern.…”

A nonintrusive proper generalized decomposition scheme with application in biomechanics

“…Literature shows that the PGD framework is particularly suitable for many challenging problems in biomechanics such as real‐time simulation and multiparameter identification. In a comprehensive ageing society, osteoporosis is one of the common diseases for the elders.…”

“…It is especially interesting to apply PGD for patient‐specific simulation in biomechanics. For instance, recent works studied the implementation of PGD in real‐time simulation for haptic surgeries. In this work, we present several numerical examples based on linear elasticity model for demonstration of the nonintrusive PGD scheme as well as the new approach of separating the parametric space.…”