Magnetic tracking for TomoTherapy systems: Gradiometer based methods to filter eddy‐current magnetic fields

Abstract

TomoTherapy systems lack real-time, tumor tracking. A possible solution is to use electromagnetic markers; however, eddy-current magnetic fields generated in response to a magnetic source can be comparable to the signal, thus degrading the localization accuracy. Therefore, the tracking system must be designed to account for the eddy fields created along the inner bore conducting surfaces. The aim of this work is to investigate localization accuracy using magnetic field gradients to determine feasibility toward TomoTherapy applications. Electromagnetic models are used to simulate magnetic fields created by a source and its simultaneous generation of eddy currents within a conducting cylinder. The source position is calculated using a least-squares fit of simulated sensor data using the dipole equation as the model equation. To account for field gradients across the sensor area (≈ 25 cm(2)), an iterative method is used to estimate the magnetic field at the sensor center. Spatial gradients are calculated with two arrays of uniaxial, paired sensors that form a gradiometer array, where the sensors are considered ideal. Experimental measurements of magnetic fields within the TomoTherapy bore are shown to be 1%-10% less than calculated with the electromagnetic model. Localization results using a 5 × 5 array of gradiometers are, in general, 2-4 times more accurate than a planar array of sensors, depending on the solenoid orientation and position. Simulation results show that the localization accuracy using a gradiometer array is within 1.3 mm over a distance of 20 cm from the array plane. In comparison, localization errors using single array are within 5 mm. The results indicate that the gradiometer method merits further studies and work due to the accuracy achieved with ideal sensors. Future studies should include realistic sensor models and extensive numerical studies to estimate the expected magnetic tracking accuracy within a TomoTherapy system before proceeding with prototype development.