  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.
