Estimation of flexible needle deflection in layered soft tissues with different elastic moduli

The estimation of needle deflection when the needle interacts with biological tissue is challenging in needle steering. Most previous studies have used homogeneous tissue models to estimate the deflection of a needle. However, biological tissue typically has a layered structure with variable mechanical properties and geometric features. In this study, we propose a needle deflection model with a double-layered elastic medium. Each layer possesses distinct mechanical properties, which result in inconsistent degrees of friction force on the needle surface, needle-cutting force, and forces caused by the stiffness of the elastic medium. The model uses the Rayleigh-Ritz method to analytically estimate the needle deflection. To validate the model, needle steering experiments were performed using double-layered tissue phantoms and porcine tissues. The experimental results revealed that changes in reaction force at the needle base occurred when the needle passed through the boundary between the two layers. The mean absolute error between the estimated and measured needle tip trajectory was 0.88 ± 0.30 mm for the double-layered tissue phantom and 1.85 ± 0.73 mm for the porcine tissue. These results are comparable with previous studies of homogeneous tissue. The proposed model could improve needle steering in biological tissues, which consist of multiple layers.