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

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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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