Three-Dimensional Needle Shape Reconstruction using an Array of Firber Bragg Grating Sensors

We present a prototype of a flexible nitinol needle ($phi$ 1.0 mm and length 172 mm) integrated with an array of 12 Fiber Bragg Grating (FBG) sensors. These sensors measure the axial strain, which enables the computation of the needle curvature. We reconstruct the three-dimensional (3-D) needle shape from the curvature. Experiments are performed where the needle is deflected in free space. The maximum errors between the experiments and beam theory-based model are 0.20 mm (in-plane deflection with single bend), 0.51 mm (in-plane deflection with double bend), and 1.66 mm (out-of-plane). We also describe kinematics-based and mechanics-based models for predicting the 3-D needle shape during insertion into soft tissue. We perform experiments where the needle is inserted into a soft-tissue simulant, and the 3-D needle shape is reconstructed using the FBG sensors. We compare the reconstructed needle shape to deflection obtained from camera images and our models. The maximum error between the experiments and the camera images is 0.74 mm. The maximum errors between the kinematics-based and mechanics-based models and the camera images are 3.77 mm and 2.20 mm, respectively. This study demonstrates that deflection models and needles integrated with FBG sensors have the potential to be used in combination with clinical imaging modalities in order to enable accurate needle steering.