Lie-Group Theoretic Approach to Shape-Sensing Using FBG-Sensorized Needles Including Double-Layer Tissue and S-Shape Insertions.

Flexible bevel-tipped needles are often used for needle insertion in minimally-invasive surgical techniques due to their ability to be steered in cluttered environments. Shapesensing enables physicians to determine the location of needles intra-operatively without requiring radiation of the patient, enabling accurate needle placement. In this paper, we validate a theoretical method for flexible needle shape-sensing that allows for complex curvatures, extending upon a previous sensor-based model. This model combines curvature measurements from fiber Bragg grating (FBG) sensors and the mechanics of an inextensible elastic rod to determine and predict the 3D needle shape during insertion. We evaluate the model's shape sensing capabilities in C- and S-shape insertions in single-layer isotropic tissue, and C-shape insertions in two-layer isotropic tissue. Experiments on a four-active area, FBG-sensorized needle were performed in varying tissue stiffnesses and insertion scenarios under stereo vision to provide the 3D ground truth needle shape. The results validate a viable 3D needle shape-sensing model accounting for complex curvatures in flexible needles with mean needle shape sensing root-mean-square errors of 0.160 ± 0.055 mm over 650 needle insertions.