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 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.

Methods

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 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 2n_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 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 (n_g, d₁, Z₀, 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 d₁ 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.