In needle-based medical procedures, beveled-tip flexible needles are steered inside soft tissue with the aim of reaching pre-defined target locations. The efficiency of needle-based interventions depends on accurate control of the needle tip. This paper presents a comprehensive mechanics-based model for simulation of planar needle insertion in soft tissue. The proposed model for needle deflection is based on beam theory, works in real-time, and accepts the insertion velocity as an input that can later be used as a control command for needle steering. The model takes into account the effects of tissue deformation, needle-tissue friction, tissue cutting force, and needle bevel angle on needle deflection. Using a robot that inserts a flexible needle into a phantom tissue, various experiments are conducted to separately identify different subsets of the model parameters. The validity of the proposed model is verified by comparing the simulation results to the empirical data. The results demonstrate the accuracy of the proposed model in predicting the needle tip deflection for different insertion velocities.

This paper represents an extension to the kinematic bicycle model for beveled-tip needle motion in soft tissue, which accounts for non-constant curvature paths for the needle tip. For a tissue that is not stiff relative to the needle, the tissue deformation caused by needle insertion deviates the needle tip position from a constant curvature path. The proposed model is obtained by replacing the bicycle wheels with omnidirectional wheels that move in two orthogonal directions independently. Such wheels can move sideways, providing a means for modeling the deviations of the needle tip from a constant curvature path by incorporating new parameters in the model. Using an experimental setup, the needle is inserted into soft phantom tissue at different constant velocities and model parameters are fitted to experimental data. The model is verified by comparing the results from the model to empirical data.