Kalman-Filter-Based, Dynamic 3-D Shape Reconstruction for Steerable Needles With Fiber Bragg Gratings in Multicore Fibers

Steerable needles are a promising technology to provide safe deployment of tools through complex anatomy in minimally invasive surgery, including tumor-related diagnoses and therapies. For the 3-D localization of these instruments in soft tissue, fiber Bragg gratings (FBGs) based reconstruction methods have gained in popularity because of the inherent advantages of optical fibers in a clinical setting, such as flexibility, immunity to electromagnetic interference, nontoxicity, and the absence of line-of-sight issues. However, methods proposed thus far focus on shape reconstruction of the steerable needle itself, where accuracy is susceptible to errors in interpolation and curve fitting methods used to estimate the curvature vectors along the needle. In this study, we propose reconstructing the shape of the path created by the steerable needle tip based on the follow-the-leader nature of many of its variants. By assuming that the path made by the tip is equivalent to the shape of the needle, this novel approach paves the way for shape reconstruction through a single set of FBGs at the needle tip, which provides curvature information about every section of the path during navigation. We propose a Kalman-filter-based sensor fusion method to update the curvature information about the sections as they are continually estimated during the insertion process. The proposed method is validated through simulation, in vitro and ex vivo experiments employing a programmable bevel-tip steerable needle (PBN). The results show clinically acceptable accuracy, with 2.87-mm mean PBN tip position error, and a standard deviation of 1.63 mm for a 120-mm 3-D insertion.