Many tasks in robot-assisted surgery require planning and controlling manipulators' motions that interact with highly deformable objects. This study proposes a realistic, time-bounded simulator based on Position-based Dynamics (PBD) simulation that mocks brain deformations due to catheter insertion for pre-operative path planning and intra-operative guidance in keyhole surgical procedures. It maximizes the probability of success by accounting for uncertainty in deformation models, noisy sensing, and unpredictable actuation. The PBD deformation parameters were initialized on a parallelepiped-shaped simulated phantom to obtain a reasonable starting guess for the brain white matter. They were calibrated by comparing the obtained displacements with deformation data for catheter insertion in a composite hydrogel phantom. Knowing the gray matter brain structures' different behaviors, the parameters were fine-tuned to obtain a generalized human brain model. The brain structures' average displacement was compared with values in the literature. The simulator's numerical model uses a novel approach with respect to the literature, and it has proved to be a close match with real brain deformations through validation using recorded deformation data of in-vivo animal trials with a mean mismatch of 4.73$\pm$2.15%. The stability, accuracy, and real-time performance make this model suitable for creating a dynamic environment for KN path planning, pre-operative path planning, and intra-operative guidance.