Simulation of Complex Cuts in Soft Tissue with the Extended Finite Element Method (X-FEM)

  • Christoph Paulus (Author)
    Project-team Simulation in Healthcare using Computer Research Advances (SHACRA) – INRIA Lille – North Europe Research Center
  • Stefan Suwelack (Author)
    Institute for Anthropomatics, Karlsruhe Institute of Technology (KIT)
  • Nicolai Schoch (Author)
    Engineering Mathematics and Computing Lab (EMCL), Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University
  • Stefanie Speidel (Author)
    Institute for Anthropomatics, Karlsruhe Institute of Technology (KIT)
  • Rüdiger Dillmann (Author)
    Institute for Anthropomatics, Karlsruhe Institute of Technology (KIT)
  • Vincent Heuveline (Author)
    Engineering Mathematics and Computing Lab (EMCL), Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University

Abstract

In this paper we present an approach to model discontinuities in the solution of the elasticity problem without changing the initial grid topology. In the context of surgery simulation or real-time intraoperative registration this method allows for adapting a finite element model during the operation in the presence of cutting or resection.

We outline a formulation of the eXtended finite element method (X-FEM) for elastic solids and present an approach for modeling arbitrary cuts by means of finite elements on tetrahedral grids. For this purpose, completely cut elements are enriched with the shifted Heaviside function and partially cut elements are enriched with so-called asymptotic crack tip functions. In this context we show how to handle the geometry of partial cuts and how the necessary local coordinate system based on polar coordinates is constructed. Finally, we present a flexible implementation of the approach.

A numerical validation shows that the approach can handle complex cuts through low resolution geometries. Furthermore, a convergence analysis reveals that the approach is superior to standard remeshing techniques in terms of accuracy per degrees of freedom. The source code of the presented method is available under an open-source license.

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Published
2014-12-14
Language
en
Academic discipline and sub-disciplines
Applied Mathematics; Numerics; Medical Engineering
Contributor or sponsoring agency
This work was carried out with the support of the German Research Foundation (DFG) within the projects A01 and I03 of the SFB/TRR 125 ’Cognition-Guided Surgery’.
Keywords
Applied Mathematics; Numerics; Medical Engineering; Cutting Simulation; X-FEM