Small catheters undergo significant torsional deflections during endovascular interventions. A key challenge in enabling robot control of these catheters is the estimation of their bending planes. This paper considers approaches for estimating these bending planes based on bi-plane image feedback. The proposed approaches attempt to minimize error between either the direct (position-based) or instantaneous (velocity-based) kinematics with the reconstructed kinematics from bi-plane image feedback. A comparison between these methods is carried out on a setup using two cameras in lieu of a bi-plane fluoroscopy setup. The results show that the position-based approach is less susceptible to segmentation noise and works best when the segment is in a non-straight configuration. These results suggest that estimation of the bending planes can be accompanied with errors under 30 degrees. Considering that the torsional buildup of these catheters can be more than 180 degrees, we believe that this method can be used for catheter control with improved safety due to the reduction of this uncertainty.

翻译：小型导管在血管内介入手术中会经历显著的扭转变形。实现这类导管机器人控制的关键挑战在于估计其弯曲平面。本文研究了基于双平面图像反馈估计弯曲平面的方法。所提出的方法旨在最小化直接（基于位置）或瞬时（基于速度）运动学与双平面图像反馈重建的运动学之间的误差。在一套利用两台相机替代双平面荧光透视系统的实验装置上，对这些方法进行了比较。结果表明，基于位置的方法对分割噪声的敏感性较低，且在导管段处于非直线构型时效果最佳。这些结果表明，弯曲平面估计的误差可控制在30度以内。鉴于这些导管的扭转累积可能超过180度，我们认为该方法通过降低不确定性，可用于更安全的导管控制。