A Two-Body Rigid/Flexible Model of Needle Steering Dynamics in Soft Tissue

Robotics-assisted needle steering can enhance targeting accuracy in percutaneous interventions. This paper presents a novel dynamical model for robotically controlled needle steering. This is the first model that predicts both needle shape and tip position in soft tissue, and accepts needle insertion velocity, needle 180° axial rotation, and needle base force/torque as inputs. A hybrid formulation of needle steering dynamics in soft tissue is presented, which considers the needle as a two-body rigid/flexible coupled system composed of a moving, discrete, and rigid part attached to a vibrating compliant part that is subject to external excitation forces. The former is the carrier representing the surgeon's hand or the needle inserting robot, while the latter is a beam modeling the continuous deflection of the needle inside tissue. A novel time-delayed tissue model and a fracture mechanics-based model are developed to model the tissue reaction forces and cutting force at the needle tip, respectively. Experiments are performed on synthetic and ex vivo animal tissues to identify the model parameters and validate the needle steering model. The maximum error of the 2-D model in predicting the needle tip position in the insertion plane was 1.59 mm in the case of no axial rotation and 0.74 mm with axial rotation.