On Extended Finite Element Method (XFEM) for Modelling of Organ Deformations Associated with Surgical Cuts

The Extended Finite Element Method (XFEM) is a technique used in fracture mechanics to predict how objects deform as cracks form and propagate through them. Here, we propose the use of XFEM to model the deformations resulting from cutting through organ tissues. We show that XFEM has the potential for being the technique of choice for modelling tissue retraction and resection during surgery. Candidates applications are surgical simulators and image-guided surgery. A key feature of XFEM is that material discontinuities through FEM meshes can be handled without mesh adaptation or remeshing, as would be required in regular FEM. As a preliminary illustration, we show the result of XFEM calculation for a simple 2D shape in which a linear cut was made.