Finite element analysis of gradient z-coil induced eddy currents in a permanent MRI magnet

Eddy currents analysis methods for an MRI longitudinal gradient coil

PURPOSE

The rapid switching of the gradient fields induces eddy currents in neighboring metallic structures, causing undesirable effects. Numerical computations are thus required to understand eddy-currents effects for designing/implementing mitigation (involving passive shielding) and compensating techniques (using pre-emphasis). Previously, the network-analysis (NA) method was introduced to compute z-gradient eddy currents, although limited to a circularly symmetric and unconnected coil. Multi-layer integral method (MIM) method was recently introduced, modifying the circuit equation involving stream functions. We tailor MIM (TMIM) for a more general eddy-currents analysis in thin structures. Z-gradient eddy currents are analyzed and then compared using three methods (NA, TMIM, and Ansys). The analysis helps to evaluate the efficiency of passive shielding and to compensate eddy currents.

METHODS

NA and TMIM computational frameworks for harmonic and transient eddy-currents analysis were implemented and cross-validated against Ansys Maxwell. A pre-emphasis pulse was modeled for compensating eddy currents.

RESULTS

Eddy-currents analysis of an unconnected z-gradient coil in both the passive shield and cryostat were computed, and results were comparable to the least computationally efficient Ansys simulations. Although NA computations are fast, TMIM is implemented with reasonable efficiency and applied to circularly unsymmetric geometries. TMIM computations were further validated against Ansys using a connected z-gradient. Our computations allowed the effective evaluation of the performance of three various passive-shielding configurations, non-capped, capped, and slitted (for the first time), and an effective pre-emphasis compensation model was computed.

CONCLUSION

Three eddy-currents analysis methods were studied and compared. Computationally efficient TMIM allows both harmonic and transient eddy-currents analysis involving different/complex gradient configurations/situations as well as involved shielding structures. Eddy-currents pre-emphasis compensation was demonstrated.

Transient eddy current analysis for a spiral gradient pulse

Eddy currents are induced in the metallic structures of MRI machines due to the rapid switching of gradient fields generated by gradient coils. Several undesirable effects are associated with the induced eddy currents such as heat, acoustic noise, and MR image distortions. Accurate transient eddy currents numerical computations are required to predict and ameliorate such effects. Spiral gradient waveforms are of importance, particularly for fast MRI acquisition applications. For mathematical convenience, previously published work is mostly concerned with transient eddy currents computations associated with trapezoidal gradient waveforms; where spiral gradient waveforms were not considered. We recently presented preliminary transient eddy currents computations induced by an amplitude-modulated sinusoidal pulse in the scanner's cryostat. In this work, we present a full computational framework for transient eddy currents induced by a spiral gradient waveform. A mathematical model for transient eddy currents involving the spiral pulse was derived and presented in detail using the circuit equation. Computations were implemented using a tailored multilayer integral method (TMIM) and results were compared to Ansys eddy currents analysis for cross-validation. The transient response of resultant fields generated by both an unshielded transverse coil driven by a spiral waveform was computed showing high agreement between Ansys and TMIM; albeit with high computational efficiency concerning time and memory. For further validation, computations for a shielded transverse coil were performed showing how eddy currents effects are reduced.

A Comparative Study for Evaluating Passive Shielding of MRI Longitudinal Gradient Coil

Gradient coils are vital for Magnetic Resonance Imaging (MRI). Their rapid switching generates eddy currents in the surrounding metallic structures of the MRI scanner causing undesirable thermal, acoustic, and field distortion effects. The use of actively shielded gradient coils does not eliminate such undesirable effects totally. Use of passive shielding was proposed lately to particularly help in mitigating eddy currents and loud acoustic noise. Numerical computations are necessary for calculating eddy currents and evaluating the efficacy of passive shielding. Harmonic and temporal eddy current analysis caused by gradient coil(s) using network analysis (NA) can be faster and more flexible than the traditional FDTD and FEM methods. NA was used more than a decade ago but was limited to analyzing eddy currents resulting from z-gradient coils of separated turns. NA with stream function was recently modified resulting in the more general Multilayer Integral Method (MIM) for simulation of eddy currents in thin structures of arbitrary geometries. In this work, we compared the performance of the NA method and an adapted MIM method to analyze eddy current in both the passive shielding and cryostat to the Ansys Maxwell 3D analysis thus evaluating the performance of gradient configurations with and without passive shielding. Both an unconnected and a connected z-gradient coil configuration were used. Our analysis showed high agreement in the profiles of eddy ohmic losses in metallic structures using the three methods. The NA method is the most computationally efficient however, it is limited to specific symmetries unlike the more general MIM and Ansys methods. Our implementation of the adapted MIM method showed computational efficiency relative to Ansys with comparable values. We have developed a computationally efficient eddy current analysis framework that can be used to evaluate more designs for passive shielding using different configurations of MRI gradient coils.

Highly Shielded Gradient Coil Design for a Superconducting Planar MRI System

In a planar, superconducting magnetic resonance imaging (MRI) system, the gradient assembly is placed into the groove of the SC magnet. Conventional gradient coil design method considers the shielding of pole face only, but neglects the surrounding metal structures at the coil side, thus leading to large stray field leakage and resulting in serious eddy current artefact. A novel coil shielding method was proposed in this work by a full consideration of the stray fields on the pole face and also the coil ends. The gradient coil design exemplification of a 0.7T planar superconducting MRI system was presented. In the new design, the maximum stray field at the surface of the ambient structure was reduced more than six times for the transverse coils and around four times for the longitudinal coil. The highly shielded gradient coil also produced linear gradient fields (<5%) over the imaging volume.

An actively shielded gradient coil design for use in planar MRI systems with limited space

In planar magnetic resonance imaging (MRI) systems, gradient coils are usually placed within a very limited space owing to the physical constraints of the small gap size (pole-pole) distance of the permanent magnet. Typically, the unshielded or partially shielded design scheme is adopted to generate required magnetic fields with reduced system costs. However, non-fully shielded coils can induce large eddy currents on the surrounding metal structures, including magnet poles, that significantly impact the imaging performance. This paper elaborates a new design strategy to resolve the limited space problem. Using the peripheral sections of the MRI system, a set of actively shielded gradient coils are purposefully designed. Between the two magnet poles, the actively shielded gradient coils occupy merely four coil layers (six coil layers are usually required), which offers an excellent shielding effect, thus reducing the image distortions. The saved space can be used to integrate a high-efficient cooling system. Moreover, the design scheme does not significantly increase the fabricating complexity.