Shape estimation of the anterior part of a flexible ureteroscope for intraoperative navigation

Purpose Flexible ureteroscopy (FURS) plays an important role in the diagnosis and treatment of urological diseases. However, manipulating a flexible ureteroscope to the target quickly and safely may be challenging because of the tortuous lumen or poor visibility. Thus, information on the shape of the anterior part of a flexible ureteroscope in addition to the real-time pose is needed to perform accurate maneuvering in the lumen with minimal impingement on the inner renal wall and resulting tissue damage in FURS. Methods An adaptive mixed-order Bézier curve fitting algorithm and electromagnetic tracking (EMT) technique were developed for shape estimation utilizing the length of the anterior part, kinematic constraints and the pose information provided by two electromagnetic (EM) sensors mounted at the tip and base of the anterior part. A series of experiments were performed to qualitatively and quantitatively verify the validity of our method. Moreover, algorithm threshold conditions with reference significance under various shape cases were studied. Results The performance of our method was evaluated based on 19 representative planar bending shapes that often appear in FURS and eight non-planar shapes, yielding an average error (AE) of 1.0 mm. Moreover, the experiments proved the feasibility of applying our method in cases in which large bending angles (near 270 degrees) occur. Conclusion Based on data from two EM sensors mounted at the tip and base of the anterior part of a flexible ureteroscope, the proposed algorithm adaptively selects a cubic or quartic Bézier curve to fit the shape of the anterior part. Experimental results prove the feasibility of our shape estimation method over a broad bending range. The proposed method demonstrates significant potential for use in ureteroscopic navigation systems and robot-assisted surgery.