Predicting tip deflection of puncture needle in multi-layer renal soft tissues: Experimental validation of a coupled Eulerian-Lagrangian model

Accurate needle placement is critical to the success of percutaneous nephrolithotomy (PCNL); However, targeting accuracy often deteriorates due to tip deflection during insertion. To capture and predict this behavior, a high-fidelity finite element model based on the Coupled Eulerian-Lagrangian (CEL) approach was constructed to characterize needle-tissue interaction while avoiding mesh distortion. A multi-layer tissue model was built, with material parameters calibrated using mechanical tests to faithfully represent the anatomical complexity of renal soft tissues. Systematic simulations were performed, and the results were validated by physical experiments at an 84 mm insertion depth to quantify tip deflection across different puncture angles. The findings reveal a non-monotonic relationship between insertion angle and tip deflection. Notably, an optimal stability window was observed at 19° for a 17° bevel-tip needle, yielding a minimal experimental deflection of 1.581 mm. Beyond providing a rigorous numerical framework for quantifying puncture errors, this study uncovers the mechanical basis of angle-dependent stability, offering essential guidance for trajectory planning and real-time error compensation in robot-assisted percutaneous renal access systems.