A New Approach to Cutting into Finite Element Models

Abstract

Abstract. Virtual reality based surgical simulators offer a very elegant approach to enhancing traditional training in endoscopic surgery. In this context a realistic soft tissue model is of central importance. The most accurate procedures for modeling elastic deformations of tissue use the Finite Element Method to solve the governing mechanical equations. Therapeutic interventions (e.g. cutting) require topological changes of the Finite Element mesh, thus making a non-trivial remeshing step necessary. This paper describes a new approach to cutting in Finite Element models. The central idea is not to introduce new nodes/elements but to displace the existing ones to account for the topological changes introduced by a cut. After the displacement of the nodes/elements the mesh is homogenized to avoid tiny elements which destabilize the explicit time integration necessary for solving the equations of motion.

Simultaneous cutting of coupled tetrahedral and triangulated meshes and its application in orbital reconstruction

“…All models employ physically based finite element methods (FEM) [41][42][43]38], as they allow the specification of material properties, such as Young's modulus and Poisson ratio. The methods vary in terms of accuracy and performance.…”

XFEM FRAMEWORK FOR CUTTING SOFT TISSUE - Including Topological Changes in a Surgery Simulation

“…Nevertheless, subdividing can cause simulation instability because it generates ill-conditioned elements (slivers); moreover, the subdivision increments the degrees of freedom (DOFs) impacting directly on the simulation performance. Another alternative consists of removing the elements in contact with the blade (Forest et al, 2005); despite this method has the advantage that it does not affect the simulation stability, it is physically inaccurate and visually uneven; another option, to avoid the previous methods, is a successive snapping of nodes to the cutting trajectory (Serby et al, 2001); unfortunately, this kind of method leads to degenerated elements. Other approaches merge methods like snapping and subdivision (Steinemann et al, 2006), but only nonprogressive cutting is enabled.…”

A Hybrid Cutting Approach for Hysteroscopy Simulation

“…Some of these problems could be ameliorated with topology adaptation approaches as suggested in [20] and [17]. The central idea is to approximate a cutting path with existing edges or surfaces.…”

“…Including these procedures in our simulator system necessitates updates of the underlying tissue model. Different approaches for handling cutting have been proposed, which can be summarized into three major categories: straight-forward element deletion [2,7,5], mesh subdivision [12,16,8,3,1] and topology adaptation [20,17]. While the first method is not appropriate for a realistic simulator, the latter two have produced reasonable results.…”