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We present a computational method for simulating needle insertions interactively in both 2D and 3D models of soft tissue. The approach is based on the Finite Element Method (FEM) and uses quasi-static stick-slip friction for needle/tissue interactions. The FEM equations are solved using an iterative method, and the mesh is refined adaptively near the needle trajectory. The boundary formed by the needle surface is not represented explicitly in the mesh, but its geometry is accounted for in the friction forces. This has the advantage that we can use a simple and therefore fast refinement scheme that is guaranteed to keep the mesh quality at the initial level. This approach can also be applied to the 3D situation as well as to nonlinear geometry and material models. We present results of computational experiments of the 2D simulation, and show promising samples of the 3D implementation.
Nienhuys et al. (Thu,) studied this question.