FBG-Based Estimation of External Forces Along Flexible Instrument Bodies

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.