Learning-Based Modeling of a Magnetically Steerable Soft Suction Device for Endoscopic Endonasal Interventions

This paper introduces a learning-based modeling framework for a magnetically steerable soft suction device designed for endoscopic endonasal brain tumor resection. The device is miniaturized (4 mm outer diameter, 2 mm inner diameter, 40 mm length), 3D printed using biocompatible SIL 30 material, and integrates embedded Fiber Bragg Grating (FBG) sensors for real-time shape feedback. Shape reconstruction is represented using four Bezier control points, providing a compact representation of deformation. A data-driven model was trained on 5,097 experimental samples to learn the mapping from magnetic field parameters (magnitude: 0-14 mT, frequency: 0.2-1.0 Hz, vertical tip distances: 90-100 mm) to Bezier control points defining the robot’s 3D shape. Both Neural Network (NN) and Random Forest (RF) architectures were compared. The RF model outperformed the NN, achieving a mean RMSE of 0.087 mm in control point prediction and 0.064 mm in shape reconstruction error. Feature importance analysis revealed that magnetic field components predominantly influence distal control points, while frequency and distance affect the base configuration. Unlike prior studies applying general machine learning to soft robotic data, this framework introduces a new paradigm linking magnetic actuation inputs directly to geometric Bezier control points, creating an interpretable, low-dimensional deformation representation. This integration of magnetic field characterization, embedded FBG sensing, and Bezier-based learning provides a unified strategy extensible to other magnetically actuated continuum robots. By enabling sub-millimeter shape prediction and real-time inference, this work advances intelligent control of magnetically actuated soft robotic tools in minimally invasive neurosurgery.

💡 Research Summary

This paper presents a data‑driven modeling framework for a magnetically steerable soft suction device intended for endoscopic endonasal brain tumor resection. The device is miniaturized (4 mm outer diameter, 2 mm inner suction channel, 40 mm active length) and fabricated by direct 3‑D printing of a biocompatible silicone elastomer (SIL 30). A hollow cylindrical permanent magnet at the distal tip enables magnetic steering, while a multi‑core Fiber Bragg Grating (FBG) sensor is embedded along the neutral axis to provide real‑time curvature measurements.

To capture the highly nonlinear magneto‑elastic behavior without explicit material characterization, the authors collected 5,097 experimental trials covering magnetic field magnitudes from 0 to 14 mT, rotating frequencies from 0.2 to 1.0 Hz, and tip‑to‑coil distances from 90 to 100 mm. For each trial, the measured curvature profile was fitted with a cubic Bézier curve defined by four control points (12 scalar values), providing a compact, smooth representation of the robot’s 3‑D shape.

Two regression architectures were trained to map the three actuation inputs (field components, frequency, distance) directly to the Bézier control points: a multilayer perceptron neural network (NN) and a Random Forest (RF) ensemble. Cross‑validation showed that the RF model outperformed the NN, achieving a mean root‑mean‑square error (RMSE) of 0.087 mm on the control‑point predictions and an overall shape reconstruction RMSE of 0.064 mm. Feature‑importance analysis revealed that the magnetic field vector primarily influences the distal control points, whereas frequency and distance affect the base configuration, offering intuitive insight for control‑law design.

The use of Bézier control points as a low‑dimensional latent space is a key contribution. It preserves the ability to represent complex, spatially varying deformations while enabling real‑time inference (sub‑millimeter accuracy) suitable for closed‑loop surgical control. Compared with traditional constant‑curvature or Cosserat‑rod models, the learning‑based approach eliminates the need for accurate Young’s modulus, shear modulus, and damping coefficients, which are difficult to obtain for 3‑D‑printed hyperelastic materials and can vary between batches. Moreover, the model inherently captures rate‑dependent viscoelastic effects and the coupled magnetic torque distribution that change with the robot’s configuration.

By integrating embedded FBG sensing with the learned mapping, the framework provides a unified strategy: external magnetic fields can be commanded, the RF model instantly predicts the resulting shape, and the FBG feedback can be used for verification or adaptive correction. This enables precise navigation through the narrow, tortuous pathways of the nasal cavity and sphenoid sinus, reducing the risk of damaging critical neurovascular structures.

The authors argue that the methodology is generalizable to other magnetically actuated continuum robots, such as steerable catheters, micro‑endoscopes, or drug‑delivery platforms. The combination of a compact Bézier parametrization, sensor‑based shape acquisition, and a fast, interpretable machine‑learning model offers a scalable solution for intelligent control of soft surgical tools in minimally invasive neurosurgery.