A Novel FEM-Based Numerical Solver for Interactive Catheter Simulation in Virtual Catheterization

Algorithm 1

The overall algorithm of the proposed numerical solver.

(1) Initialize the positions 𝐱_𝑖(𝑖∈[0,…,𝑛]) of the catheter in an equilibrium state.

(2) Translate each node of the virtual catheter a displacement by the operation from

 the motion sensor of our simulator 𝐱^new_𝑖=𝐱^old_𝑖+𝐝𝐢𝐬𝐩.

(3) Detect the collisions to create the set of colliding nodes and triangular meshes.

(4) Build or update the matrix 𝐴, the matrix 𝐵⁻¹ and the vector 𝐛.

(5) Solve the linear system 𝐀𝐁⁻¹𝐱=𝐛.

(6) Update the positions 𝐱_𝑖 of the virtual catheter to the new equilibrium state.