Synopsis

Full wave simulations are known for their high accuracy, but simulation optimization is not feasible with FDTD and FEM for vast numbers of MRI coil applications. Optimization strategies do have feasible runtimes for quasi-static solutions, but the system being simulated must be small compared to the electromagnetic wavelength since they do not account for boundary conditions. This work uses multiple single loop coils of different diameters and three phantoms with a simple geometry to compare the accuracy and usefulness of full wave and quasi-static solutions of RF coils at 3T. Full wave simulations proved to be significantly more accurate.

Purpose:

Methods:

Three cylindrically shaped phantoms, Fig 1, were used with solutions of 1.955g CuSO₄ x H₂0 combined with 1.094g NaCl, 3.020g NaCl, and 4.915g NaCl to achieve 0.3, 0.6, and 0.9S/m conductivities (at 20°Celsius), respectively. The phantom height and radius were 10.1 and 13.9cm.

Eight circular 16 AWG copper wire coil loops ranging from 3-10cm in diameter in 1cm increments were constructed for each phantom (24 total). The coils had 1, 2, 3, and 4 tune capacitors for the 3,4cm, 5,6cm, 7,8cm, and 9,10cm diameter loops, respectively. Coils were tuned and matched to the same impedance. The preamplifier socket connected directly to the match circuit, eliminating a cable. The same preamplifier was used for all measurements.

SNR measurements were acquired using 2D axial GRE sequences positioned through the center of each coil with noise calculated as the standard deviation of noise-only image voxels. Images were acquired on a 3T MRI scanner (MAGNETOM Tim Trio, Siemens Healthcare, Erlangen, DE).

Full wave simulations were performed using Computer Simulation Technology Microwave Studio (CST MWS). The FDTD method was used with mesh cell counts ranging from 2-11 million mesh cells, simulation accuracy of -80dB, and an “Enhanced (Preview)” AR-filter with a max error for steady state of 0.001. CST Design Studio (DS) co-simulation was used to tune the coils and calculate the composite magnetic field (B1^-) and total noise (R_t)^2-4. Total noise was calculated by removing the match capacitor and measuring the real part of the Z_1,1 parameter. The active decoupling diode on the match circuit between the signal and ground was included in the CST simulations as a 0.8pF capacitor. Total MWS run times ranged from 24m to 4h22m per coil.

Quasi-static simulations used Biot-Savart for magnetic field calculations and vector potential for noise calculations⁵. Calculations of sample resistance (R_s) and coil resistance (R_c) were done separately and total noise was calculated by R_t = R_s+R_c. Run time was less than 4 seconds per coil.

Total noise bench measurements were made using the same method used for the full wave measurements³.

Preamplifier noise was not included in any of the noise calculations or measurements. Full wave and quasi-static SNR results were scaled (one scaler for each method) to make the SNR calculations of the 3 cm loop on the 0.3S/m phantom match that of the SNR measurement at 8 cm depth from the loop center. We assumed a uniform body coil excitation.

Results:

Discussion:

The full wave simulations correctly represented the signal and noise while the quasi-static simulations did not. Superficial B1^- discrepancies in the full wave simulation were mainly due to flip angles not being 90° in the phantom. Discrepancies in the quasi-static signal and noise are largely due to the assumption that boundary conditions are correctly accounted for at infinity¹. The quasi-static method did not accurately calculate B1^- nor did it account for the increase in noise with coil diameter for the 0.3S/m phantom. This anomalous increase was due to a larger electric field strength for coils larger than 7 cm when compared to that in the 0.6 and 0.9S/m phantoms.

We have demonstrated that the frequency at 3T is high enough for a large system to have destructive wave effects, requiring a full wave simulation for accurate results. Further work would include whether a system that is small compared to the electromagnetic wave could be accurately characterized with a quasi-static solution or if a software package like MARIE using integral equations is necessary and/or practical for all optimizations at 3T⁶.

Acknowledgements

References

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4. Horneff et al. An EM simulation based design flow for custom-build MR coils incorporating signal and noise. IEEE Trans Med Imaging. 2018;37(2):527-535.

5. Roemer et al. The NMR phased array. Magn Reson Med. 1990;16(2):192-225.

6. Villena et al. Fast Electromagnetic Analysis of MRI Transmit RF Coils Based on Accelerated Integral Equation Methods. IEEE Trans Biomed Eng. 2016;63(11):2250-2261.