Manouchehr Takrimi1 and Ergin Atalar2
1National Magnetic Resonance Research Center, Bilkent University, Ankara, Turkey, 2Department of Electrical and Electronics Engineering, Bilkent University, Ankara, Turkey
Synopsis
A z-gradient array coil equipped with a tunable shield array is proposed to achieve multiple imaging volumes that can be shifted along the coil axis. This is achieved by a set of independently tunable power amplifiers that feed the array elements. The proposed array dynamically provides a proper shield for the main array in which its magnetic profile can be adjusted on the fly. Five multiple-region magnetic profiles are simulated to demonstrate the flexibility of the proposed array: (a) a double-gradient profile; (b) shifted version of (a); (c) highly linear double-gradient profile without shielding; (d) triple-gradient profile; (e) quintuple-gradient profile.
Purpose
A set of independently tunable arrays can replace the conventional gradient coils and their active shields. It makes the gradient system highly customizable and offers a broader range of features in addition to the currently available traditional functionalities.Method
Gradient arrays have been used for different applications such as shimming1-2, field profiling without shielding3-6, self-shielded7-8 field profiling, and multiple volume imaging9-11. As a proof of concept, we recently proposed a 24-element active-shield z-gradient array12-13 fed by digitally tunable independent power amplifiers14. Based on a combinational scenario of analytical and numerical optimizations, a proper set of feeding waveforms of 100A maximum is calculated to achieve a programmable magnetic field profile within the imaging volume(s). It is possible to vary different performance parameters, including the gradient intensity, size and position of the ROI(s), linearity error, shielding effectiveness, and the slew rate. The optimization toolbox for MapleTM 2018 software is deployed to carry out the optimizations.Results
Figure 1(a) shows the cross-section view of the proposed z-gradient array consisting of 12 pairs of wire bundles, each with ten copper wires. Physical dimensions are given in the caption. A 10mm thick aluminum cylindrical shell of 90cm diameter and 80cm height has been inserted in the simulations to include the effect of induced eddy currents within the warm cryostat. All feeding waveforms are trapezoidal with 100μs rise, fall, and plateau times. For shielding effectiveness assessment, we define “residual eddy current” (REC) as the $$$\it{B_Z}$$$ field ratio 20μs after to 20μs before the fall-time in an appropriate point within the ROI(s). Additionally, the linearity error is calculated by the maximum field deviation about the ideal field normalized to the maximum ideal field within the ROI(s). The numerical simulations are based on Ansys Maxwell 2019.R1.
Starting with double ROI, Fig. 2(a) shows a half cross-section view of the logarithmic magnitude plot of the $$$\overline{B}$$$ field for the proposed array at t=100μs (at the end of the plateau). The cryostat, both ROIs at $$$\pm7$$$cm, the primary and shield arrays, and the surrounding fields are visible. Fig. 2(b) shows another half-plot simulation where the same ROIs are shifted by 2cm along the coil axis. To see more details clearly, Fig. 3(a) and (b) show the corresponding magnified $$$\it{B_Z}$$$ field map around the arrays and within the ROIs. The maximum RMS current for all array elements are 42.0A and 78.6A, and the maximum induced voltages across the elements are 38.2V and 42.3V, respectively. The ROI diameter, average linearity error, average gradient strength, and REC are 100mm, 24.5%, 62.7mT/m, and less than $$$2.4\times10^{-4}$$$%, respectively.
By sacrificing the shielding effectiveness and 16% of the gradient, six times higher linearity is achieved. Figure 4(a) shows the modified double gradient profile with 100mm, 4.0%, 50mT/m, and $$$1.5\times10^{-2}$$$% as the relevant parameters. The maximum RMS current and induced voltages are 82.7A and 52.4V, respectively. Since the field interaction with the cryostat is increased, the REC is about 100 times higher, as shown by the $$$\overline{B}$$$ field’s logarithmic magnitude plot for the half gradient in Fig. 4(b).
Figure 5(a) shows the $$$\it{B_Z}$$$ field map of the fourth configuration consisting of three 60mm diameter ROIs along the coil axis. The linearity error is less than 25.7% and the average gradient strengths at the center of three ROIs are $$$\pm60$$$mT/m at $$$z=0,z=\pm8$$$cm, respectively. The REC is about $$$1.0\times10^{-4}$$$%, while the maximum RMS current and induced voltages are 81.2A and 48.5V, respectively.
Figure 5(b) shows five ROIs with 7cm intervals. The average gradient strengths are $$$\pm22.4$$$mT/m at $$$z=0,\pm7$$$cm and 20.0mT/m at $$$z=\pm14$$$cm. The diameter and linearity error for five ROIs are 50 mm and less than 27%, respectively. The REC is about $$$8.8\times10^{-4}$$$%, which is 4 to 8 times higher than the previous shielded cases. The maximum RMS current and induced voltages are 87.6A and 43.7V, respectively.Discussion
In conventional gradient coil design, the wire positions are optimized to satisfy linearity, efficiency, gradient strength, shielding, and other performance constraints. Also, the whole coil is fed by an expensive yet powerful amplifier to supply enough power for both coils connected in series. After construction, only the feeding waveform can be adjusted to fine-tune the gradient assembly. In the proposed tunable array-based design, less expensive but independent power amplifiers supply an optimized set of 24 feeding waveforms to satisfy the constraints. Five case studies are simulated to show its flexibility in changing the magnetic field profile on the fly. In addition to different capabilities12-13 discussed earlier, it is possible to generate multiple imaging volumes for parallel imaging in MRI. Conclusion
The benefit of deploying the array configuration designing gradient coils is fourfold: (a) It is highly flexible and fully customizable, even for nonlinear profiles; (b) It speeds up the imaging process since the impedance of the individual array elements is less than the conventional coils; (c) Unprecedented magnetic field profiling is possible for a broader range of MRI applications; (d) If shielding is not concerned, both arrays may be used to achieve more sophisticated field profiles; (e) It can be used to generate nonlinear field profiles. We expect these proof-of-concept simulations to be verified by field measurements using the implemented coils.Acknowledgements
No acknowledgement found.References
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