Lorentz force and vibrations in transverse gradient coils in MRI

Acoustic noise during Magnetic Resonance Imaging (MRI), with Sound Pressure Levels (SPL) exceeding 130 dB, is an ongoing issue for health and well-being of patients and operators and causes difficulties in signal acquisition. Understanding the characteristics and generation mechanisms of noise and vibrations is essential for the accurate development of noise control methods to be applied in the design of new devices and imaging sequences. The aim of this work is to present a closed-form analytical model for the spatial distribution of the Lorentz force per unit area that acts on simplified transverse gradient coil wire patterns. The geometrical configuration of the wire patterns has been explicitly modelled, in order to identify relationships between Lorentz forces and design parameters. To the best of our knowledge, this is the first time that a closed-form expression for the Lorentz force on transverse gradient coils has been presented on the basis of the spatial distribution of the wire patterns. Theoretical results for the Lorentz force distribution confirm that the amplitude of the Lorentz force on each elliptical spire constituting the transverse coil is linearly dependant on the static magnetic field strength B0 and the coil driving current I. A modulation along the length of each elliptic spire following a cosine law was identified. The difference of size between the elliptical conductors has been identified for the first time as a key parameter influencing the Lorentz force amplitude along different spires. Numerical simulations for the vibrational response of an insert gradient assembly excited by the proposed force field are carried out. The numerical results for the free and forced vibrations are in good agreement with numerical and experimental results in the open literature.