Event-Triggered 3D Needle Control Using a Reduced-Order Computationally Efficient Bicycle Model in a Constrained Optimization Framework

Abstract

Long flexible needles used in percutaneous procedures such as biopsy and brachytherapy deflect during insertion, thus reducing needle tip placement accuracy. This paper presents a surgeon-in-the-loop system to automatically steer the needle during manual insertion and compensate for needle deflection using an event-triggered controller. A reduced-order kinematic bicycle model incorporating needle tip measurement data from ultrasound images is used to determine steering actions required to minimize needle deflection. To this end, an analytic solution to the reduced-order bicycle model, which is shown to be more computationally efficient than a discrete-step implementation of the same model, is derived and utilized for needle tip trajectory prediction. These needle tip trajectory predictions are used online to optimize the insertion depths (event-trigger points) for steering actions such that needle deflection is minimized. The use of the analytic model and the event-triggered controller also allows for limiting the number and extent of needle rotations (to reduce tissue trauma) in a constrained optimization framework. The system was tested experimentally in three different ex-vivo tissue phantoms with a surgeon-in-the-loop needle insertion device. The proposed needle steering controller was shown to keep the average needle deflection within 0.47 [Formula: see text] 0.21[Formula: see text]mm at the final insertion depth of 120[Formula: see text]mm.