Raphaela Czerny^{1}, Lena Nohava^{1,2}, Roberta Frass-Kriegl^{1}, Jacques Felblinger^{3}, Jean-Christophe Ginefri^{2}, and Elmar Laistler^{1}

^{1}Division MR Physics, Center for Medical Physics and Biomedical Engineering, Medical University of Vienna, Vienna, Austria, ^{2}IR4M (Imagerie par Résonance Magnétique et Multi-Modalités), Université Paris-Sud, CNRS, Université Paris-Saclay, Orsay, France, ^{3}Université de Lorraine, Inserm, IADI, Nancy, France

### Synopsis

Flexible single-turn coaxial RF coils with
one gap in the outer and one gap in the inner conductor are restricted to a
specific geometry, determined by the target resonance frequency and the specifications
of the cable used. In this work we demonstrate by numerical simulations that, by
combining the concept of coaxial coils with that of multiple turns and gaps transmission
line resonators (MTMG TLRs) and the additional degree of freedom offered by varying
the cable parameters, a large diameter range can be achieved to design ^{1}H
RF coaxial coils for most common *B*_{0}
field strengths.

### Introduction

Auto-resonant coils, such as transmission
line resonators (TLRs)^{1,2} and single-turn, single-gap coaxial coils,
as introduced by Zhang et al.^{3}, demonstrate high flexibility in RF
coil array applications. As discussed in the supplementary material of Ref. 3
for the single-turn single-gap coaxial coil, the possible coil diameter range can
be varied slightly using different dielectrics and cable diameters. For co-planar
transmission line resonators it has been shown that multiple turns and gaps considerably
increase the degrees of freedom in coil design^{4}. In this work, as
recently introduced^{5}, we applied the concept of multi-turn multi-gap
resonators to coaxial TLRs (multi-turn multi-gap coaxial coils, MTMG-CCs). The
purpose of this work is to investigate the achievable coil diameters for ^{1}H
MTMG-CCs at commonly used *B*_{0} field strengths from 1.5 to 10.5 T by
varying the number of gaps and turns, as well as cable parameters in a realistic
range of values of commercially available flexible coaxial cables. ### Methods

Numerical simulations of
the achievable MTMG-CC diameter *d*_{0}
for common *B*_{0} field
strengths were performed accounting for realistic limitations for each coil/cable
parameter. The parameter space and the reasoning for the values used in
simulations are presented in Table 1.
The diameter range of
each MTMG-CC configuration yielding a desired resonance frequency was numerically
simulated using MATLAB 2017b (The Mathworks, Inc., Natick, USA). All calculations
are based on the resonance condition for MTMG-CCs, which corresponds to the
cancellation of the total reactance of the coil, consisting of the inductive reactance
created by an *n*_{t}-turn loop $$$X_L(\omega_0)=n_t^2\omega_0\mu_0\frac{d_0}{2}\left[ln\left(\frac{8d_0}{d_1}\right)-2\right]$$$ and 2*n*_{g} times the capacitive reactance of a coaxial stub of
length between an inner and an outer gap (see Figure 1) $$$X_C(\omega_0)=-Z_0cot\left(\frac{\omega_0l\sqrt{\epsilon_r}}{c_0}\right)$$$. ### Results and Discussion

The influence of the
design parameters on the simulated resonance frequency *f*_{0} was evaluated. A higher number of gaps, thicker
cables, or a higher characteristic cable impedance increase *f*_{0}, while more turns, a higher
dielectric permittivity, and larger coil diameters decrease *f*_{0}. For a targeted coil diameter, the remaining
parameters (*n*_{g}, *d*_{1}, *Z*_{0}, *n*_{t},
*ε*_{r}) have to be adjusted to tune the coil to the desired resonance
frequency.
The achievable diameters
for a coaxial coil with 1 gap and 1 turn are depicted in red in Figure 2 and show
that with increasing frequency the coil size decreases. For ultra-high field
strength (≥ 7 T) the maximum coil diameter would be too small (3 to 6 cm) for most
MR applications. On the other hand, at lower field strength the design of single-gap
single-turn coils is rather limited by the smallest possible size (13.8 cm at
1.5 T, 7.4 cm at 3 T).
By allowing for a variable
number of turns and/or gaps, the possible coil diameter range, represented by
the blue areas in Figure 2, starts
at approximately 3 cm for all field strengths and almost continuously covers a
range up to 60/60/49/38/35 cm in diameter for 1.5/3/7/9.4/10.5 T, respectively.
The range of accessible coil diameters appears continuous since *d*_{1} and *ε*_{r} were varied continuously within the identified realistic
parameter space. In reality, commercially available coaxial cables have a
limited and discrete set of parameter values, leading to discrete values of achievable
coil diameters. However, these will be sufficiently close resulting in free
choice of the coil size in practice.
To illustrate the
diameter range extension achieved by the MTMG-CC design together with the
variation of cable properties, lower and upper bounds of the accessible coil
diameters are given in Table 2 (blue
cells) alongside the single-turn single-gap coil (red cells).### Conclusion

We demonstrated that the restriction of the
accessible coil diameter range encountered with single-turn single-gap coaxial
coils can be overcome by introducing multiple turns and gaps. The gained additional
degrees of freedom enable adaptation of the coil diameter to a given biomedical
application, thus optimizing SNR and FOV, especially in an array configuration.
The presented approach combines optimized element size with the high
flexibility of coaxial coils and therefore makes the construction of tight
form-fitting coil arrays possible. This will benefit clinical applications,
especially where anatomical inter-subject variability is strong. A validation of the presented
findings by bench tests and MR measurements is the subject of an ongoing study.### Acknowledgements

This project was funded by the
Austrian/French FWF/ANR grant, Nr. I-3618, “BRACOIL“, and Austrian/French
OeaD WTZ grant FR 03/2018.### References

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Novel inductive decoupling technique for flexible transceiver arrays of
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Reson Med. 2015;73(4):1669-1681.

2. Gonord P, et al. Multigap parallel-plate bracelet resonator
frequency determination and applications. Rev Sci Instrum. 1994;65:3363–3366.

3. Zhang B, Sodickson D K,
Cloos M A. A high-impedance detector-array glove for magnetic resonance
imaging of the hand. Nat Biomed Eng.
2018;2(8):570-577.

4. Frass-Kriegl R, et
al. Multi-turn multi-gap transmission line resonators - Concept, design
and first implementation at 4.7T and 7T. J
Magn Reson. 2016;273:65-72.

5. Laistler E, Moser E. Handy magnetic resonance coils. Nat Biomed Eng. 2018;2:557-558.