A method for predicting needle insertion deflection in soft tissue based on cutting force identification

The deflection modeling during the insertion of bevel-tipped flexible needles into soft tissues is crucial for robot-assisted flexible needle insertion into specific target locations within the human body during percutaneous biopsy surgery. This paper proposes a mechanical model based on cutting force identification to predict the deflection of flexible needles in soft tissues. Unlike other models, this method does not require measuring Young's modulus ($E$) and Poisson's ratio ($\nu$) of tissues, which require complex hardware to obtain. In the model, the needle puncture process is discretized into a series of uniform-depth puncture steps. The needle is simplified as a cantilever beam supported by a series of virtual springs, and the influence of tissue stiffness on needle deformation is represented by the spring stiffness coefficient of the virtual spring. By theoretical modeling and experimental parameter identification of cutting force, the spring stiffness coefficients are obtained, thereby modeling the deflection of the needle. To verify the accuracy of the proposed model, the predicted model results were compared with the deflection of the puncture experiment in polyvinyl alcohol (PVA) gel samples, and the average maximum error range predicted by the model was between 0.606 ± 0.167 mm and 1.005 ± 0.174 mm, which showed that the model can successfully predict the deflection of the needle. This work will contribute to the design of automatic control strategies for needles.