Path Planning for Cannula Flexible Needle Based on Function Family of the Mechanical Bending Model

As a kind of the flexible needle, a cannula flexible needle consists of a flexible cannula and a flexible stylet, which can achieve variable-curvature paths through changing the stylet extension lengths out of the cannula, and has the advantages in the path correction and the insertion flexibility compared to the traditional flexible needles. The current path planning is mainly based on the over-idealized wheel-based kinematic models. However, these kinematic models cannot accurately express the bending of the flexible needle and cause the major insertion errors. In this article, a bending model was proposed for predicting the large bending of the cannula flexible needle based on the large bending theory. The relationship between the different stylet extension lengths and the discretization lengths of the mechanical bending model was formulated through the experimental data, and then a function family was established to depict the needle bending relative to the stylet extension length. Based on these, a path planning algorithm for the cannula flexible needle was proposed based on the improved Rapidly-exploring Random Trees in the environments with obstacles. The comparisons between the proposed algorithm and the path planning algorithm based on the wheel-based model were conducted by simulations. The simulation results showed that the proposed path planning algorithm was overall superior to the others not only in terms of the searching speed but also the total insertion length. Then, a series of insertion experiments and the error analysis were performed for the two planned paths. The results were with the mean errors of 0.77 and 0.91 mm, the root mean square errors of 0.85 and 1.13 mm, and the maximum errors of 1.2 and 1.5 mm, for the path-1 and the path-2, respectively. The experimental results met the clinical requirements for the ordinary surgery which proved the effectiveness and the accuracy of the proposed path planning algorithm.