Design and Characterization of Self-Shielded MRI Gradient Coils With Finite Track Width

Abstract

Gradient coils are essential for the performance of the MR imaging system. Usually, coils are designed assuming thin wire tracks. Here, we design an MR gradient coil set using a more general approach considering the exact track width using the discrete wire approach. The effect of track width on the DC current density distribution and resultant magnetic fields using both loop and Golay coils are first demonstrated. Both, self-shielded X and Z gradient coils of definite width/thickness are designed and optimized. The resistance and inductance of the coils are calculated using the stream functions approach. Track current distribution was used to compute the magnetic fields over the desired volume, and at the cryostat. The linearity of the magnetic field over the volume, the figure of power , and the shielding ratio of the coil are used as parameters in the optimization process. The DC characteristics of the designed coils with definite (small) track width and thickness were compared for verification to that of the corresponding thin wire design where they were found to have approximately similar characteristics. Using our design methodology, the coils' frequency-dependent resistances and inductances were directly/efficiently calculated. The harmonic and transient eddy current interactions between the longitudinal and transverse gradient coils were computed where track slitting was employed to reduce such interactions. This work stresses the importance of considering coil track width in the design process particularly for wide tracks as well as computing the coil's figure of merit, harmonic and transient coil characteristics/interactions.

Eddy currents analysis methods for an MRI longitudinal gradient coil

“…TMIM is a more general approach that we managed to implement at acceptable computational efficiency compared to Ansys. We preliminary applied and validated TMIM using our computational framework for a transverse gradient coil, as shown in Alsharafi et al 55 An agreement is shown in the result of transient analysis for the three methods (see Figure 7B). The distortion of the gradient field waveform is evident and attributed to the induced eddy currents on the cryostat.…”

“…TMIM is a more general approach that we managed to implement at acceptable computational efficiency compared to Ansys. We preliminary applied and validated TMIM using our computational framework for a transverse gradient coil, as shown in Alsharafi et al 55 …”

“…The frequency spectrum of the trapezoidal waveform showed that the frequency components of the waveform are less than 1 kHz, thus justifying the single‐layer model used for the cryostat. For situations in which spectrum components include frequencies making the skin depth smaller than the thickness of the metallic structures, multi‐slicing may be used at the expense of reducing the computational efficiency, or a compensation factor may be used in the circuit equation 55 …”

“…In this work, we used a single layer for both the passive shield and the cryostat operating at frequencies ensuring $$$ t<\delta $$$. Notice that at frequencies making the skin depth smaller the thickness of metallic structures, multi‐slicing, 16,49 or using a compensation factor 55 is important to achieve accurate analysis.…”

“…For situations in which spectrum components include frequencies making the skin depth smaller than the thickness of the metallic structures, multi-slicing may be used at the expense of reducing the computational efficiency, or a compensation factor may be used in the circuit equation. 55 For the NA, the transient eddy currents were computed in the rings using Equation (7). However, they were computed using Equations ( 9) and ( 20) for the TMIM.…”