Thermal variation in gradient response: measurement and modeling

Purpose Many aspects and imperfections of gradient dynamics in MRI have been successfully captured by linear time-invariant (LTI) models. Changes in gradient behavior due to heating, however, violate time invariance. The goal of this work is to study such changes at the level of transfer functions and model them by thermal extension of the LTI framework. Methods To study the impact of gradient heating on transfer functions, a clinical MR system was heated using a range of high-amplitude DC and AC waveforms, each followed by measuring transfer functions in rapid succession while the system cooled down. Simultaneously, gradient temperature was monitored with an array of temperature sensors positioned according to initial infrared recordings of the gradient tube. The relation between temperatures and transfer functions is cast into local and global linear models. The models are analysed in terms of self-consistency, conditioning, and prediction performance. Results Pronounced thermal effects are observed in the time resolved transfer functions, largely attributable to in-coil eddy currents and mechanical resonances. Thermal modeling is found to capture these effects well. The keys to good model performance are well-placed temperature sensors and suitable training data. Conclusion Heating changes gradient response, violating time invariance. The utility of LTI modeling can nevertheless be recovered by a linear thermal extension, relying on temperature sensing and adequate one-time training.