Mechanics-based model for predicting in-plane needle deflection with multiple bends

Bevel-tipped flexible needles naturally bend when inserted into soft tissue. Steering such needles along curved paths allows one to avoid anatomical obstacles and reach locations inside the human body which are unreachable with rigid needles. In this study, a mechanics-based model is presented which predicts needle deflection for a needle undergoing multiple bends during insertion into soft tissue. The model is based on a Rayleigh-Ritz formulation, and inputs to the model are a force at the needle tip and a distributed load which acts along the needle shaft. Experiments are used to evaluate the distributed load, and needle deflection is then predicted using the model. The results of the model are compared with a kinematics-based model. Maximum errors in final tip deflection are found to be 0.5 mm and 0.6 mm for the mechanics-based and kinematics-based model, respectively. Though both models are found to be comparable, the mechanics-based model can account for deflection when the needle radius of curvature is not constant (e.g., biological tissue).