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On the Relationship Between Field Strength and Permittivity for Desired Effects of High-Permittivity Materials in MRI1Radiology, New York University, New York, NY, United States, 2Radiology, University of Minnesota, Minneapolis, MN, United States
Synopsis
Experience and general understanding dictate that greater relative permittivity is required to produce a similar effect at lower B0 field strengths and B1 frequencies. Here we use some fundamental explanations and preliminary numerical results for improving receive array performance at different field strengths to propose, more specifically, that permittivity should increase approximately with the inverse of the square of the field strength for an expected effect.
Introduction
Materials with a high electric permittivity have been used to improve efficiency of transmitted RF magnetic fields (B1+) and thus improve SNR in regions of otherwise low B1+ 1-5. The ability of HPMs to improve sensitivity of receive arrays in the entire imaging volume, where each coil is relatively small compared to the HPM, has also recently shown impressive first results in simulations for 7T6-8. Experience and general understanding dictate that greater relative permittivity is required to produce a similar effect at lower B0 field strengths and B1 frequencies. Here we use some fundamental explanations and preliminary numerical results for improving receive array performance at different field strengths to propose that permittivity should, more specifically, increase approximately with the inverse of the square of the field strength for an expected effect for similar arrangements at different B0 field strengths.Theory
In Maxwell’s modified Ampere equation, Δ×B=μ(J+ jωεE), J is the conduction current and is presumably strongest in the coil, while jωεE is the displacement current, and presumably strongest in a high-permittivity material (HPM) very near the coil where electric fields E are strong. Here, E can be seen as having two sources, the conservative electric field resulting from charge density associated with voltages along the wires of the coil needed to produce J, and the magnetically-induced electric field associated with the changing magnetic field via Faraday’s Law, Δ×E=-jωB. Both Faraday’s Law and Ohm’s Law for conductive segments of a coil (V=IjωL) indicate that |E| will increase proportionally to frequency ω for a given magnetic field B, at least in the quasi-static regime.
If we then assume that for a certain desired effect of an HPM in a similar configuration of coil, HPM, and sample we would like for the displacement current in the HPM and conduction current in the coil to have similar relative contributions (i.e., |J|/|jωεE| remains nearly constant with changing frequency), we find that ε should be proportional to 1/ω2.
Simulation Methods and Results
To determine an optimal permittivity of a thin HPM helmet-shaped shell at 7T, simulations including a numerical model of the human body (Virtual Family’s “Duke”) in a 16-element stripline array were performed at 300 MHz4, 5. Later simulations of a similar helmet with an 8-channel receive array both without6 and with7 tuning and matching of the individual elements showed improvements in SNR of about 40% on average throughout the whole brain. Further simulations with a more densely-packed array of 28 elements showed similar improvements with the HPM helmet at 7T (Figure 1, middle row)8. In all this work, an optimal εr of about 110 was found.
To determine an optimal permittivity of a similar helmet-shaped shell at 3T, simulations including the same body model in a body-sized birdcage coil were performed9. An optimal er of about 600 was found. Using this permittivity, SNR in the head for the 28-channel receive array were seen to have significant improvements compared to the array alone (Figure 1, top row).
Noting that between 3T and 7T the optimal permittivity followed roughly a ε proportional to 1/ω2 relationship and considering the theoretical arguments above, a relative permittivity of 50 was recommended for an ongoing coil design for head imaging at 10.5T. With no optimization it was seen that the addition of the same helmet for a very different coil design resulted in significant improvements in SNR even though addition of the helmet required moving the coil further from the head (Figure 1, bottom row).
Discussion
At 3T, 7T, and 10.5T, use of a thin, helmet-shaped HPM can dramatically improve SNR of a close-fitting, densely-packed receive array throughout brain, including significant improvements near the center of brain, which is not expected from further increasing the number of array elements. While first results at 3T and 10.5T have some regions of slight decrease in SNR, we anticipate that, as at 7T, further optimizations will see improvements in SNR there as well. A relationship where ε is proportional to 1/ω2 seems to be reasonable in first estimates of what εr to use in getting similar results for similar arrangements at different frequencies. Future work will include further optimization of permittivities and coil geometries before implementation at all three field strengths.Acknowledgements
This work has benefitted from discussions with researchers at HyQRS, LLC (especially Qing X. Yang and Sebastian Rupprecht) and from funding by the National Institutes of Health through R01 EB0021277, P41 EB017183 (CAI2R), R01 EB024536, and U01 EB025144.References
1. Alsop et al., Magn Reson Med 1998;40:49-54
2. Yang et al., J Magn Reson Imag 2006;24:197-202
3. Haines et al., J Magn Reson 2010;203:323-327
4. Collins et al., Proc. 2013 ISMRM, p. 2797
5. Collins et al., Proc. 2014 ISMRM, p. 1340
6. Collins et al., Proc. 2014 ISMRM, p. 404
7. Haemer et al., Proc. 2017 ISMRM p. 4283
8. Carluccio et al., Proc. 2018 ISMRM p. 4405
9. Yu et al., Magn Reson Med 2017;78:383-386
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