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A self-supervised learning and error compensation method for needle deflection prediction and control during

Chengsi Xing¹, Zhiyong Yang¹, Zeyang Zhou¹

¹School of Mechanical Engineering, Tianjin University, Tianjin, People's Republic of China.

Physics in Medicine and Biology

|June 5, 2026

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This study introduces a novel method combining physics-based models and data-driven techniques to accurately predict flexible needle deflection during tissue insertion. The approach enhances targeting accuracy and control for medical procedures.

Area of Science:

Robotics
Medical Device Engineering
Computational Mechanics

Background:

Flexible needles are prone to deflection during soft tissue insertion, impacting targeting accuracy and control.
Existing physics-based models lack generalization, while data-driven methods lack interpretability.

Purpose of the Study:

To develop a flexible needle tip deflection prediction method combining physical modeling and data-driven correction.
To improve prediction accuracy, robustness, and generalization performance for flexible needles.

Main Methods:

A mechanics-guided framework integrating self-supervised consistency learning and supervised residual correction.
Utilized the Rayleigh-Ritz method for a physically informed needle bending model.
Incorporated self-supervised consistency and supervised residual branches for error compensation.

Keywords:

closed-loop control flexible needle insertion mechanics model needle tip deflection prediction residual correction self-supervised learning

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Main Results:

Achieved a mean absolute error of 0.36 mm and root mean square error of 0.51 mm under optimal configuration.
Demonstrated stable performance across network scales and favorable generalization beyond training depth.
Attained average errors of 0.95±0.16 mm in static puncture and 0.28±0.22 mm in trajectory tracking.

Conclusions:

The proposed method enhances flexible needle tip deflection prediction accuracy and maintains physical interpretability.
Provides stable and reliable prior information for autonomous closed-loop control.
Offers an effective approach for high-accuracy and robust needle insertion in soft tissue.