Learning to Track Permanent Magnets by Example

Minimally invasive surgeries require navigation modalities without the requirement for a free line-of-sight. The current gold standard for minimally invasive endovascular interventions is fluoroscopic guidance, which provides visual feedback to the interventional radiologist. To minimize radiation exposure, previous work proposes to complement fluoroscopy by Electromagnetic Tracking (EMT) as a second navigation modality. However, EMT systems require tethered sensors, which are expensive and difficult in the handling. This thesis investigates Permanent Magnet Tracking (PMT) as a potential wireless and inexpensive alternative to EMT for intra-operative navigation. Instead of locating a tethered sensor inside of the patient, a strong permanent magnet is attached to a surgical instrument and tracked by external sensors. These wired sensors on the exterior sense the magnet inside the patient, enabling wireless navigation at a low cost. The major challenge of this approach is the localization of the permanent magnet, merely based on a few simultaneous sensor readings. In this thesis, an inexpensive and reproducible PMT setup is proposed. This setup uses four magneto resistive sensors to track a cylindrical Neodymium magnet in up to six degrees of freedom. Unlike most of its predecessors, this tracker uses a data-driven approach to localize the permanent magnet. In particular, neural networks are employed as general function approximators, which are trained to deduce magnet positions from sensor readings. Hand-collected data are fed to the neural networks to learn a mapping from magnetic field measurements to positions in 3D space, together with orientation around the x-, y- and z-axes. In an experimental phase, different optimizations for the data driven approach are proposed. These experimental results suggest that incorporating temperature data, captured by the sensors, increases prediction accuracy. Similarly, converting input points to spherical coordinates increases accuracy. However, augmenting the data by either simulated or interpolated data does not yield satisfying results.