A preliminary study on mathematic modeling of annular magnets in magnetic tracking systems

In the minimally invasive surgery and diagnoses such as wireless capsule endoscopy (WCE) or natural orifice transluminal endoscopic surgery (NOTES), accurate position and orientation information of the instrument is very important when it moves inside human body. Usually, magnetic tracking method is used to locate the target, in which a small magnet is enclosed. With the signals from the magnetic sensors, the position and orientation information of the magnet can be estimated based on an appropriate magnetic field model and optimization algorithm. Magnetic dipole model is the mostly used model in magnetic tracking, which can provide three dimensional position (3D) and two dimensional orientation (2D) information. The rotation information about the magnetic moment cannot be estimated. In order to utilize the six dimensional (6D) information, a specific mathematic model of magnetic field is needed rather than the magnetic dipole model. In this paper, we proposed a mathematic model for the annular magnet. This model can provide 3D position and 3D rotation information for tracking. The proposed mathematic model is based on the superposition principle and the Biot-Savart law. Finite element software is used to verify this model. Simulation result shows that the model is better than magnetic dipole model.