To study inductive interactions between gradient coils and to find the optimal track widths in the design of gradient coils for a conventional MRI configuration.An MRI system comprises three sets of spatial encoding gradient coils to produce a magnetic field along x, y and z directions [1]. Due to the switching of gradient coils, eddy currents are induced in the surrounding coil tracks especially when wide tracks are used for the purpose of heating reduction [2]. Here, we will study the eddy currents induced in the surrounding coils with respect to different coil track widths in a conventional MRI system. A series of gradient coils with different track widths were designed [3]. The maximum track widths of transverse coils varied from 10 to 40 mm with a step of 2 mm and the z-coil had a fixed track width of 6 mm. All the coils were designed with a cold shield made of aluminum to produce a maximum gradient strength G0 = 30 mT/m in a 50×50×40 cm region of interest (ROI). The maximum field error was ±5% for all the coils. A minimum gap between tracks of 1mm was used. Table 1 lists the properties of the coils and cryostat, and Fig.1a presents the configuration of the gradient coils. The electromagnetic analysis was based on a multilayer integral method [4]. A set of simulations were defined by changing the track width of transverse coils (Fig.2b shows the mesh of a passive y-coil). In this work, the x-coil was driven by a current at a frequency 1 kHz, the y and z coils were un-energized (passive coils). Performance figures were compared between the active coil (energized coil) with surrounding coils and the isolated coil. It was assumed that an isolated coil was not surrounded by the neighboring coils. This allows us to study the impacts the surrounding coils have on the active coil’s performance.

Fig.2a and b describe the induced current density distribution in the passive y-coil and cold shield. The transverse coils have a maximum track width of 40 mm. The current density distribution in the passive y-coil is much higher than that of the cold shield, and mainly accumulates in the right middle of the passive y-coil. Fig.2c compares the real part of the magnetic field along the x-axis across the ROI induced by the eddy currents in the passive coils and cold shield. We can see that the field produced by the passive coils is higher and more nonlinear than that of cold shield.

Fig.3 presents a significant difference of the coil performance between the isolated x-coil and the active x-coil with surrounding y and z-coils. The difference increases rapidly with the track width in a range of 10 to 20 mm and keeps relatively stable for track widths from 20 to 40 mm. The total power loss dissipated by x, y and z coils reaches a local minimum value of 20.9 kW at track widths of 14 and 16 mm. The resistance reaches a minimum at a track width of 14 mm. The inductance and coil efficiency decrease with the track width. The figure of merit (FoM, defined as η²/L, where η is coil efficiency and L is inductance) and η²/R have peak values at the track width of 14 mm. η²/R of the coil with a track width of 14 mm is 10.1% larger than the case of 10 mm and 4% larger than the case of 20 mm.

The magnetic field shown in Fig.2c demonstrates that the surrounding passive coils dissipate more eddy currents than those of the cold wall. The eddy currents mainly concentrate in the part overlapping with the “eye” of the active x-coil because of the higher local current density in this region [5]. Despite the fact inductance has been slightly reduced, the eddy currents in the passive coils leads to more power loss, lower efficiency, lower FoM and η²/R as well as a larger secondary field, effects which should be mitigated as much as possible. From this study, we found that the total power loss, coil resistance, FoM and η²/R reach a local minimum value at a track width of 14 mm, meanwhile the coil with a track width of 14 mm has a relative high efficiency. Therefore, the track widths around 14 mm are recommended to use in the design of a conventional transverse coil. It is hoped that this intra-gradient coil interactions study will be useful for future gradient coil design and analysis.