Limits and Opportunities for Miniaturizing Ultrasonic Surgical Devices Based on a Langevin Transducer

Minimally invasive surgery offers opportunities for reduced morbidities, faster postoperative recovery, and reduced costs, and is a major focus of surgical device innovation. For ultrasonic surgical devices, which offer benefits of high precision, low force, and tissue selectivity in surgical procedures, there exist laparoscopic ultrasonic shears for minimally invasive surgeries that combine tissue cutting with vessel hemostasis and sealing functions. Another approach to laparoscopy that could enable new procedures, and increase the sites of surgeries that could be reached by an ultrasonic device, involves integrating a miniature ultrasonic tool with a flexible surgical robot. However, miniaturization presents challenges in delivering the ultrasonic vibrational energy required to cut hard and soft tissues, partly due to the concomitant small volume of piezoelectric material. This article aims to provide insights into the trade-offs between transducer size, volume of piezoceramic material, resonance frequency, and the achievable displacement amplitude of devices that, consistent with current ultrasonic surgical tools, are based on a bolted Langevin transducer (BLT) and tip. Different configurations of BLTs are studied, including a cascaded version, simple bar versions, and BLTs with different front mass geometries. Results show that a BLT with a larger number of piezoceramic rings exhibits a higher coupling coefficient k_eff but with the compromise of a lower mechanical Q and stronger nonlinear response at increasing excitation levels. Displacement amplitude is reduced considerably when a BLT is excited at a higher harmonic, where the PZT rings are maintained at a nodal plane, and the resonance frequency shift at increasing excitation levels increases significantly. The electromechanical and dynamic characteristics of a cascaded transducer excited in its third longitudinal mode (L3) are almost equivalent to a much shorter version of a BLT driven at the same frequency but in its first longitudinal mode (L1), showing that a cascaded BLT can be a realistic proxy for studying the dynamics of small BLT devices. A new figure of merit is proposed that is the product of Q, k_eff², and gain, which accounts for the gain of cylindrical BLTs which is shown not to be unity. It also proves effective as it incorporates the key factors affecting the achievable displacement amplitude of a BLT, including for BLTs with gain profiles in the front mass. The order of highest to lowest amplitude of a series of six gain-profile BLTs matches the order estimated by the figure of merit. It is shown that a BLT with a stepped profile front mass can achieve displacement that has the potential to cut hard or soft tissue and exhibits the smallest shifts in resonance frequency at increasing excitation levels.