A survey on puncture models and path planning algorithms of bevel-tipped flexible needles.

Percutaneous needle insertion is a minimally invasive surgery with broad medical application prospects, such as biopsy and brachytherapy. However, the currently adopted rigid needles have limitations, as they cannot bypass obstacles or correct puncture deviations and can only travel along a straight path. Bevel-tip flexible needles are increasingly being adopted to address these issues, owing to their needle body's ease of deformation and bending. Successful puncture of flexible needles relies on accurate models and path planning, ensuring the needle reaches the target while avoiding vital tissues. This review investigates puncture models and path-planning algorithms by reviewing recent literature, focusing on the path-planning part. According to the literature, puncture models can be divided into three types: mechanical, finite element method (FEM), and kinematic models, while path-planning algorithms are categorized and discussed following the division used for mobile robots, which differs from the conventional approach for flexible needles-an innovation in this review. This review systematically summarizes the following categories: graph theory search, sampling-based, intelligent search, local obstacle avoidance, and other algorithms, including their implementation, advantages, and disadvantages, to further explore the potential to overcome obstacles in path planning for minimally invasive puncture needles. Finally, this study proposes future development trends in path-planning algorithms, providing possible directions for subsequent research for bevel-tipped flexible needles. This research aims to provide a resource for researchers to quickly learn about common path-planning algorithms, their backgrounds, and puncture models.