Accurate Estimation of Tip Force on Tendon-driven Catheters using Inverse Cosserat Rod Model

Tip force estimation on tendon-driven catheters is of crucial clinical importance for catheter-based surgeries such as radio-frequency ablation (RFA). In this study, a force estimation framework based on Bezier spline shape approximation and inverse Cosserat rod model was proposed and validated. Initially, the necessary condition for a Bezier spline to approximate a constant bending radius catheter was derived. Afterward, the kinematics and balance equations of the catheter were derived based on the proposed shape approximation technique and solved to find the tip force. The proposed method was experimentally tested for accuracy and computation time. The results showed that the estimated forces were in fair agreement with reference with a mean-absolute error of $0.024\pm 0.020\mathrm{N}$ and a computation time of $0.007\pm 0.005\mathrm{s}$ per frame. The exhibited performance was comparable to other studies and was in compliance with the requirements of interventional surgery applications.