Flexible multi-turn multi-gap coaxial RF coils: enabling a large range of coil sizes
Raphaela Czerny1, Lena Nohava1,2, Roberta Frass-Kriegl1, Jacques Felblinger3, Jean-Christophe Ginefri2, and Elmar Laistler1

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


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 1H RF coaxial coils for most common B0 field strengths.


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 design4. In this work, as recently introduced5, 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 1H MTMG-CCs at commonly used B0 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.


Numerical simulations of the achievable MTMG-CC diameter d0 for common B0 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 nt-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 2ng 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 f0 was evaluated. A higher number of gaps, thicker cables, or a higher characteristic cable impedance increase f0, while more turns, a higher dielectric permittivity, and larger coil diameters decrease f0. For a targeted coil diameter, the remaining parameters (ng, d1, Z0, nt, εr) 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 d1 and εr 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).


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.


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


1. Kriegl R, et al. Novel inductive decoupling technique for flexible transceiver arrays of monolithic transmission line resonators. Magn 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.


Figure 1: Sketch of a single-turn, 2-gap coaxial coil depicting the main design parameters: coil diameter d0, number of gaps ng, number of turns nt (not shown), cable diameter d1, relative permittivity εr and characteristic impedance Z0 (not shown).

Figure 2: Achievable range of coil diameters for MTMG-CCs (blue) and for the single-turn, single-gap coaxial coil (red), sorted by common B0 field strengths.

Table 1: Parameter space considered in the calculations.

Table 2: Design parameters (ng and nt) leading to minimum and maximum coil diameter ranges using MTMG-CCs (blue) and corresponding single-turn, single-gap coaxial coil (red) at different field strengths.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)