Suture Thread Modeling Using Control Barrier Functions for Autonomous Surgery

TL;DR

This work addresses the challenge of real-time, accurate suture thread modeling for autonomous surgery. It develops a unified CLF-CBF-QP framework that treats the thread as a line graph of $n$ nodes plus a lead node, enforcing connectivity, obstacle avoidance, stiffness, and damping through dedicated barrier and Lyapunov functions. The approach avoids costly Newtonian dynamics, delivering real-time performance validated on the MagnetoSuture robotic platform and in surgical-task simulations with visual feedback. The results demonstrate safe, realistic thread behavior suitable for autonomous suturing and VR-based training, with potential for extension to more complex tasks and self-collision scenarios.

Abstract

Automating surgical systems enhances precision and safety while reducing human involvement in high-risk environments. A major challenge in automating surgical procedures like suturing is accurately modeling the suture thread, a highly flexible and compliant component. Existing models either lack the accuracy needed for safety critical procedures or are too computationally intensive for real time execution. In this work, we introduce a novel approach for modeling suture thread dynamics using control barrier functions (CBFs), achieving both realism and computational efficiency. Thread like behavior, collision avoidance, stiffness, and damping are all modeled within a unified CBF and control Lyapunov function (CLF) framework. Our approach eliminates the need to calculate complex forces or solve differential equations, significantly reducing computational overhead while maintaining a realistic model suitable for both automation and virtual reality surgical training systems. The framework also allows visual cues to be provided based on the thread's interaction with the environment, enhancing user experience when performing suture or ligation tasks. The proposed model is tested on the MagnetoSuture system, a minimally invasive robotic surgical platform that uses magnetic fields to manipulate suture needles, offering a less invasive solution for surgical procedures.

Figures (9)

• Figure 1: The MagnetoSuture system (left), and closed up look at the workspace that includes the suture needle and thread (right). MagnetoSuture is a magnetic manipulator robot which leverages vision-based feedback to control magnetic tools (e.g., needle) via a coil-generated magnetic field. The workspace used in this setup is a petri dish, 35mm in diameter.
• Figure 2: Conceptual representation of the suture model, moving with needle velocity of $u_0$, and interacting with a circular obstacle. In the figure, $z$ corresponds to the distance between nodes, and $d$ is the shortest distance from a node to the obstacle boundary. The constraints encoded in $h_{obs}$ and $h_{con}$ enforce that the thread does not enter the obstacle and that it does not extends past a maximum length, respectively.
• Figure 3: Smoothing and triangulation of a non-convex shape (left) using the Delaunay method. The polygon vertices and edges are depicted in blue, while the triangulation is highlight by arbitrary colors (right).
• Figure 4: The CLF in \ref{['stiffclf']} acts analogous to a stiff mechanical spring between nodes $i$ and $i+2$. Nodes are represented by gray circles.
• Figure 5: Visual comparison of (a) the experimental behavior of a 19 mm long Polyamide suture thread in the MagnetoSuture system and (b) the behavior of the proposed model for four instances in time (i-iv). For simplicity, the needle is not depicted; instead, its endpoint is represented by a red circle around the lead node.