Modelling and simulation of guide-wire interaction with vasculature using constrained multibody dynamics

In this paper, we describe the mathematical modeling of guide wire dynamics for an intravascular surgical procedure as a problem of constrained multibody dynamics involving surface to surface interactions. The goal of this project is to develop a physics based real time simulator with haptics for the above procedure. The guide-wire is segmented into a finite number of massless and inextensible rods attached with spheres on either sides thus reducing the problem to that of the dynamics of rolling motion of spheres on the re-parameterized surface of vasculature under the action of unilateral constraints with associated Lagrange multipliers. The constrained problem is solved as LCP using Lemke's method and stabilized using Baumgarte constrain stabilization. The parameters for the constrained violation stabilization are learned real-time using a method based on adaptive control theory. Simulations were performed on geometries representing different sections of vasculature. The results show that this method can be implemented on a full-scale three dimensional vasculature with a hardware interface for haptic feedback.