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An FBG-based Stiffness Estimation Sensor for In-vivo Diagnostics

Behnam Moradkhani, Pejman Kheradmand, Harshith Jella, Kent K. Yamamoto, Alireza Tofangchi, Patrick J. Codd, Yash Chitalia

TL;DR

The paper presents an FBG-based stiffness estimation sensor that uses a buckling beam to infer tissue elasticity during shallow indentation, enabling in vivo palpation within constrained spaces. A coupled mechanical model and FE validation link beam buckling and FBG-derived curvature to tissue modulus, with bench-top experiments on tissue phantoms confirming the approach (mean RMSE ~$4.14\times 10^2$ kPa). The authors demonstrate feasibility by integrating the sensor into a mock concentric-tube robot for in-vivo-like indentation, showing separation between soft and hard tissues and outlining practical limitations and possible improvements for contact-point estimation. Overall, the work offers a compact, steerable palpation modality that leverages FBG shape sensing to perform real-time stiffness mapping in minimally invasive settings, with potential impact on IPF diagnostics and tumor identification in tight anatomical spaces.

Abstract

In-vivo tissue stiffness identification can be useful in pulmonary fibrosis diagnostics and minimally invasive tumor identification, among many other applications. In this work, we propose a palpation-based method for tissue stiffness estimation that uses a sensorized beam buckled onto the surface of a tissue. Fiber Bragg Gratings (FBGs) are used in our sensor as a shape-estimation modality to get real-time beam shape, even while the device is not visually monitored. A mechanical model is developed to predict the behavior of a buckling beam and is validated using finite element analysis and bench-top testing with phantom tissue samples (made of PDMS and PA-Gel). Bench-top estimations were conducted and the results were compared with the actual stiffness values. Mean RMSE and standard deviation (from the actual stiffnesses) values of 413.86 KPa and 313.82 KPa were obtained. Estimations for softer samples were relatively closer to the actual values. Ultimately, we used the stiffness sensor within a mock concentric tube robot as a demonstration of \textit{in-vivo} sensor feasibility. Bench-top trials with and without the robot demonstrate the effectiveness of this unique sensing modality in \textit{in-vivo} applications.

An FBG-based Stiffness Estimation Sensor for In-vivo Diagnostics

TL;DR

The paper presents an FBG-based stiffness estimation sensor that uses a buckling beam to infer tissue elasticity during shallow indentation, enabling in vivo palpation within constrained spaces. A coupled mechanical model and FE validation link beam buckling and FBG-derived curvature to tissue modulus, with bench-top experiments on tissue phantoms confirming the approach (mean RMSE ~ kPa). The authors demonstrate feasibility by integrating the sensor into a mock concentric-tube robot for in-vivo-like indentation, showing separation between soft and hard tissues and outlining practical limitations and possible improvements for contact-point estimation. Overall, the work offers a compact, steerable palpation modality that leverages FBG shape sensing to perform real-time stiffness mapping in minimally invasive settings, with potential impact on IPF diagnostics and tumor identification in tight anatomical spaces.

Abstract

In-vivo tissue stiffness identification can be useful in pulmonary fibrosis diagnostics and minimally invasive tumor identification, among many other applications. In this work, we propose a palpation-based method for tissue stiffness estimation that uses a sensorized beam buckled onto the surface of a tissue. Fiber Bragg Gratings (FBGs) are used in our sensor as a shape-estimation modality to get real-time beam shape, even while the device is not visually monitored. A mechanical model is developed to predict the behavior of a buckling beam and is validated using finite element analysis and bench-top testing with phantom tissue samples (made of PDMS and PA-Gel). Bench-top estimations were conducted and the results were compared with the actual stiffness values. Mean RMSE and standard deviation (from the actual stiffnesses) values of 413.86 KPa and 313.82 KPa were obtained. Estimations for softer samples were relatively closer to the actual values. Ultimately, we used the stiffness sensor within a mock concentric tube robot as a demonstration of \textit{in-vivo} sensor feasibility. Bench-top trials with and without the robot demonstrate the effectiveness of this unique sensing modality in \textit{in-vivo} applications.
Paper Structure (13 sections, 13 equations, 5 figures, 2 tables)

This paper contains 13 sections, 13 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Materials and Methods
  3. Design and Fabrication
  4. Strain-Curvature Relation
  5. Mechanical Model
  6. Buckling and Post-Buckling Model
  7. Finite Element Simulation
  8. Experimental Validation
  9. Experiments and Results
  10. Bench-top Stiffness Estimation
  11. Stiffness Estimation with a Robot
  12. Failure Cases
  13. Conclusions

Figures (5)

  • Figure 1: (a) Sensor assembly undergoing vertical force application $P$, exhibiting fixed-pinned buckling deformation with key elements, including the reaction force $R$, optical fiber grating regions/peaks, and global coordinates being shown, (b) Cross-section of the sensor assembly used for computing the combined neutral axis, (c) Beam moment balance for a differential section with the length $ds$ of the sensing assembly, (d) validation data for the modified FBG coefficient due to gluing (fitted by a line with the slope of $0.424~\text{pm}/{\mu\epsilon}$).
  • Figure 2: (a) Ansys model of stiffness sensor assembly buckling at 5 mm displacement, (a-1) cross-section of the model used to conduct FEA, (b) Comparison between Ansys simulation (dotted) and theoretical model (solid lines) of the axial strain along the gratings/peaks of the FBG fiber.
  • Figure 3: (a) Vertical indentation experimental setup used for validating the proposed mechanical model and conducting bench-top tissue sample stiffness estimations, (b) Comparison between post-buckling experimental vertical forces and the corresponding predicted values by the theoretical model for multiple length values, (c) Comparison between the average axial strain of the FBG fiber over the gratings/peaks and the predicted corresponding values by the theoretical model with the length of the sensor being 42mm.
  • Figure 4: Bench-top experimental estimation results and ground truth values. (inset) Close-up schematics of the sensor spherical tip indented into the tissue surface.
  • Figure 5: (a) Robotic setup consisting of the dual roller gear mechanism and multiple 3D-printed mock concentric tube robots with tip angles of 0, 15, 30, and 50 degrees pointing in two (downwards and upwards) directions, (b) Outer and inner roller gears situated external to the actuation mechanism assembly, (c) Stiffness estimation results for soft and hard tissue compared with their corresponding actual values.