Evaluation of Fiber Optic Shape Sensing Models for Minimally Invasive Prostate Needle Procedures Using OFDR Data

Abstract

This paper presents a systematic evaluation of fiber optic shape sensing models for prostate needle interventions using a single needle embedded with a three-fiber optical frequency domain reflectometry (OFDR) sensor. Two reconstruction algorithms were evaluated: (1) Linear Interpolation Models (LIM), a geometric method that directly estimates local curvature and orientation from distributed strain measurements, and (2) the Lie-Group Theoretic Model (LGTM), a physics-informed elastic-rod model that globally fits curvature profiles while accounting for tissue-needle interaction. Using software-defined strain-point selection, both sparse and quasi-distributed sensing configurations were emulated from the same OFDR data. Experiments were conducted in homogeneous and two-layer gel phantoms, ex vivo tissue, and a whole-body cadaveric pig model. While the repeated-measures ANOVA did not detect any significant differences, the Friedman test analysis revealed statistically significant differences in RMSEs between LIM and LGTM (p < 0.05), with LIM outperforming LGTM in the ex vivo tissue scenario. LIM also achieved over 50-fold faster computation (< 1 ms vs. > 40 ms per shape), enabling real-time use. These findings highlight the trade-offs between model complexity, sensing density, computational load, and tissue variability, providing guidance for selecting shape-sensing strategies in clinical and robotic needle interventions.

Keywords: Fiber optic shape sensing; Lie group methods; linear interpolation; minimally invasive surgery; needle guidance systems; optical frequency domain reflectometry (OFDR); prostate needle interventions; shape reconstruction algorithms.

Fig. 1:

(a) Sparse sensor arrangement with unevenly spaced active areas (AA). (b) Quasi-distributed sensor arrangement with evenly spaced sensing points every 5 mm. (c) Cross-section of the sensorized needle. (d) Cross-section of the sensor,where the three optical fibers are coated in a polymer (light blue). Each fiber is at radial distance $r$ from the neutral axis and at a specific angular offset $\varphi$.

Fig. 2:

(a) Trigonometric triangulation linear shape interpolation method (LIM-TTI). (b) Linear shape interpolation in SO(3) method (LIM-SO(3)).

Fig. 3:

(a) Calibration setup illustration. (b) Strain measured by the three fibers in a single active area during the LIM calibration process. Refer to Section II-B.1 for symbol and variable definitions. (c) Experimental setup for insertions in phantom tissues under stereo visualization, taken from [37]. (d) Experimental setup for insertions in ex vivo tissue under CBCT visualization, taken from [37]. (e) and (f) show the experimental setup for the insertions in the deceased pig model under CBCT visualization.

Fig. 4:

Shape reconstruction results across all algorithms for both calibration and validation datasets.

Fig. 5:

Shape reconstruction results across all algorithms for all experimental scenarios. The exact numerical values for each model and scenario are reported in Table III for improved clarity.