Fusion of electromagnetic trackers to improve needle deflection estimation: simulation study

We present a needle deflection estimation method to anticipate needle bending during insertion into deformable tissue. Using limited additional sensory information, our approach reduces the estimation error caused by uncertainties inherent in the conventional needle deflection estimation methods. We use Kalman filters to combine a kinematic needle deflection model with the position measurements of the base and the tip of the needle taken by electromagnetic (EM) trackers. One EM tracker is installed on the needle base and estimates the needle tip position indirectly using the kinematic needle deflection model. Another EM tracker is installed on the needle tip and estimates the needle tip position through direct, but noisy measurements. Kalman filters are then employed to fuse these two estimates in real time and provide a reliable estimate of the needle tip position, with reduced variance in the estimation error. We implemented this method to compensate for needle deflection during simulated needle insertions and performed sensitivity analysis for various conditions. At an insertion depth of 150 mm, we observed needle tip estimation error reductions in the range of 28% (from 1.8 to 1.3 mm) to 74% (from 4.8 to 1.2 mm), which demonstrates the effectiveness of our method, offering a clinically practical solution.