Mathematical Models of 3D Magnetic Field and 3D Positioning System by Magnetic Field

A practical 3D positioning system was developed based on the mathematical models of 3D magnetic field induced by a single loop coil. Mathematical expression of the magnetic intensity in 3D space was derived in detail. 3D positioning using magnetic field provides a new approach to detect the location of a non-visible target inside a non-magnet-shielded object such as human body by taking advantage of penetrative capability of magnetic field through such object. By attaching magnetic sensor to medical instruments, the signals generated by the sensor inside the body response to the magnetic field produced by emitter coils outside body are analyzed to determine the location of sensor as well as the position of the medical instrument. Real-time six-degree freedom measurement for 3D magnetic sensor and five-degree freedom measurement for single magnetic sensor were realized. This system provides a new approach to determine the 3D position and orientation of endoscope inside the patient’s body by harmless magnetic field.