FBG-Based Estimation of External Forces Along Flexible Instrument Bodies

Abstract

A variety of medical treatment and diagnostic procedures rely on flexible instruments such as catheters and endoscopes to navigate through tortuous and soft anatomies like the vasculature. Knowledge of the interaction forces between these flexible instruments and patient anatomy is extremely valuable. This can aid interventionalists in having improved awareness and decision-making abilities, efficient navigation, and increased procedural safety. In many applications, force interactions are inherently distributed. While knowledge of their locations and magnitudes is highly important, retrieving this information from instruments with conventional dimensions is far from trivial. Robust and reliable methods have not yet been found for this purpose. In this work, we present two new approaches to estimate the location, magnitude, and number of external point and distributed forces applied to flexible and elastic instrument bodies. Both methods employ the knowledge of the instrument's curvature profile. The former is based on piecewise polynomial-based curvature segmentation, whereas the latter on model-based parameter estimation. The proposed methods make use of Cosserat rod theory to model the instrument and provide force estimates at rates over 30 Hz. Experiments on a Nitinol rod embedded with a multi-core fiber, inscribed with fiber Bragg gratings, illustrate the feasibility of the proposed methods with mean force error reaching 7.3% of the maximum applied force, for the point load case. Furthermore, simulations of a rod subjected to two distributed loads with varying magnitudes and locations show a mean force estimation error of 1.6% of the maximum applied force.

Keywords: cosserat rod; external force estimation; fiber bragg gratings; flexible instruments; multi-core fibers.

FIGURE 1

(A) cross-sectional view of a four core MCF where ${\lambda }_i$ represents the wavelength in the ith core, r is the distance between the center of the ith core and the fiber’s central axis, and ${\theta }_b$ is the angle of the bending plane with respect to the x-axis which intersects the second core, (B) isometric view of a segment with four cores and two FBG sets, i.e. four FBGs at a given cross-section, separated by a center-to-center distance $l_z$.

FIGURE 2

A deformed elastic rod parametrized by arc length s subjected to a set of point forces $F_1$ and $F_2$, and distributed forces $f_1$ and $f_2$.

FIGURE 3

Example plot illustrating the differences between the theoretical, measured, and estimated curvature profiles.

FIGURE 4

Force estimation experimental setup comprising: ① electromagnetic (EM) field generator, ② electromagnetic tracking (EM) sensors, ③ ATI Nano17 six DoF force sensor, ④ tensioned cable to transmit a force to the Nitinol rod, ⑤ weights suspended by gravity, ⑥ Nitinol rod with an MCF embedded internally, ⑦ optical fanout and interrogator systems, ⑧ monitor to display wavelength spectra. Forces $F_1$ and $F_3$ are applied by suspending known weights, and force $F_2$ is applied along an adjustable direction by pulling on the ATI Nano17 six DoF force sensor which is attached to a cable that encircles the Nitinol rod.

FIGURE 5

Example result for the case where three external point forces are applied onto the rod. (A) profile of the x-component of the curvature, (B) profile of the y-component of the curvature, (C) deformed rod showing a comparison between the ground truth and estimated shape and applied forces.

FIGURE 6

UKF simulation with two distributed forces applied onto a rod. The magnitudes and locations are varying sinusoidally over time (gt = ground truth, est = estimated).