This paper considers an approach to improving outcomes for neurosurgery patients by enhancing intraoperative navigation and guidance. Currently, intraoperative navigation systems do not accurately account for brain shift or tissue resection. We describe how preoperative images can be incrementally updated to take into account any type of brain tissue deformation that may occur during surgery, and thus to improve the accuracy of image-guided navigation systems. For this purpose, we have developed a non-rigid image registration technique using a biomechanical model, which deforms based on the Finite Element Method (FEM). While the FEM has been used successfully for dealing with deformations such as brain shift, it has difficulty with tissue discontinuities. Here, we describe a novel application of the eXtended Finite Element Method (XFEM) in the field of image-guided surgery in order to model brain deformations that imply tissue discontinuities. In particular, this paper presents a detailed account of the use of XFEM for dealing with retraction and successive resections, and demonstrates the feasibility of the approach by considering 2D examples based on intraoperative MR images. To evaluate our results, we compute the modified Hausdorff distance between Canny edges extracted from images before and after registration. We show that this distance decreases after registration, and thus demonstrate that our approach improves alignment of intraoperative images.