Research on Function Family of Large Bending Model Based on Mechanics for Cannula Flexible Needle

Compared to the traditional flexible needles, cannula flexible needle has advantages in terms of the flexibility and the capability of trajectory correction during insertion. In this paper, the cannula flexible needle is treated as a cantilever beam, and the insertion of the needle into the soft tissue is considered as a quasi-static process. And a mechanical bending model for the large bending of the needle is established based on the large bending theory. Then a bending curve is obtained through the discretization in the mechanical bending model. The relationship between the bending curves and the discretization lengths can be defined as a function family. As the bending is directly controlled by the stylet extension length out of the cannula, the relationship between the different stylet extension lengths and the discretization lengths is formulated through the regression according to the experimental data. Hence, the function family of the bending curves with the variable of the stylet extension length is accomplished. In order to validate the proposed function family, the insertion experiments in the phantom tissues were conducted. The results showed that the mean errors were 0.98 mm and 1.02 mm, the maximum errors were 1.43 mm and 1.53 mm, and the root mean square errors were 0.45mm and 0.51mm, respectively for two cases of the stylet extension lengths, fulfilling the required accuracy for the ordinary clinical surgery, which proves the rationality and accuracy of the proposed method.