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, non-toxicity, 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.