Cardiac catheterism is important because it offers many advantages in comparison to open surgery, for example, fewer injuries, lower risk of infections, and shorter recovery times. Simulators play a fundamental role in training packages, and virtual learning environments are less stressful. Moreover, they can also be used in certification boards and in performance assessments. A realistic and interactive simulator must be fast. In this work, the physical model of the guidewire used in catheter simulations has been improved. In particular, we determined a simple analytic expression to calculate the direction of a guidewire segment, which minimizes the total energy. The surface energy resulting from the guidewire--artery interaction and the bending energy of the guidewire is approximated up to the second order, which gives rise to interactions between segments. Furthermore, the multiple segment relaxations are introduced, enhancing the convergence especially at the beginning of the relaxation cycle. The formulas are written in matrix form of dimension 4M×4M⁠, where M represents the number of segments varied in the update step. The method results in a more stable static solution.