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. Shape-sensing enables physicians to determine the location of needles intraoperatively without requiring radiation of the patient, enabling accurate needle placement. In this article, 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 3-D needle shape during insertion. We evaluate the model's shape sensing capabilities in C- and S-shaped insertions in single-layer isotropic tissue, and C-shaped 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 3-D ground truth needle shape. The results validate a viable 3-D needle shape-sensing model accounting for complex curvatures in flexible needles with mean needle shape-sensing root-mean-square errors (RMSEs) of $0.160 \boldsymbol {\pm } 0.055$ mm over 650 needle insertions.