Introduction

The design of radiofrequency (RF) arrays is an ongoing challenge in MRI applications with regarding sensitivity, SAR, and coupling effects between the individual coils^1,2. The recently proposed shielded-coaxial-cable coils (SCC) have a flexible nature while satisfying good decoupling characteristics³ ideal for transceiver arrays. How the low coupling characteristics arise is largely unknown^4,5 and a better understanding of their mode of operation and coupling characteristics is desired for optimal designs.
In this work, we have investigated impedance characteristics, operation modes and coupling characteristics of SCCs designed to work at 298MHz. We present their broadband circuit representation based on the current flow of the coil model. We show that second resonance mode operation is crucial to preserve intrinsic low coupling between elements. Sweeping the distance between two SCCs clearly shows that the coupling performance is directly related to the coil’s resonance mode.

Methods

A circular SCC (HUBER+SUHNER K_02252_D) with a loop radius of 60mm was modeled in free space. The full-wave electromagnetic simulations in frequency domain (10MHz-500MHz) were performed using CST Microwave Studio.
The circuit model was generated by observing the coils current flow and the loop inductance of the outermost surface is
$$L=\mu_0 a \Big(ln\big(\frac{8a}{b}\big)-2\Big)$$
where $$$\mu_0$$$ is free space permeability, $$$a$$$ is the loop radius, and $$$b$$$ is the wire radius⁶ while the cable’s physical dimensions are used for the coaxial cable modeling. The input impedance of the SCC is generated by the circuit model and the electromagnetic simulations.
The coupling behavior were observed by varying the center-to-center distances (0mm, 60mm, 90mm, and 125mm) between two coils.
The input impedance of the single coil is plotted to observe couplings at first and second resonance modes. The coupling coefficient between the adjacent inductors is numerically calculated on the circuit model to have similar frequency split at the first resonance mode with electromagnetic simulations.
The coil performance is compared with a conventional coil of the same loop radius with distributed capacitors.

Results

Figure 1 shows the physical model of an SCC with a capacitive matching network.
Figure 2 shows the current flow on the outer gap, the broadband circuit model, and the input impedance of the SCC.
Figure 3 shows the input impedance of the SCC for various center-to-center distances.
Figure 4 shows the circuit model of two SCCs with coupling of the adjacent inductors and the input impedance of an SCC when another SCC is present and center-to-center distance is 125mm.
Figure 5 shows simulated $$$B_1^+$$$, 10gram averaged SAR $$$SAR_{10g}$$$, and $$$B_1^+/\sqrt{max(SAR_{10g})}$$$ratios of conventional loops and SCCs.

Discussion

SCCs have identical single gaps on the inner and outer conductors, which are located on opposite sides as in Fig. 1. SCCs are excited from the inner gap while the outer gap directs the current flow to the outermost surface and leads to the electromagnetic radiation.
The current inside the coaxial cable obey transmission line equations and the current on the outermost surface acts as a radiator for the SCC also perceived as a loop antenna. The continuous current flow through the outer gap between the inner and outer surfaces of the outer conductor is observed in Fig. 2a. Thus, the circuit representation (Fig. 2b) is constituted with two coaxial cables and two inductors, while each corresponds to the half-length of the coil⁷. The coaxial cables model the inside of the cable while the inductors model the outermost surface. The connections between the elements are made with the consideration of gap locations. The impedance characteristics of the circuit model and the SCC’s electromagnetic simulations are plotted together, showing excellent agreement.
Fig. 3 emphasizes that SCCs couple at the first resonance mode while the second mode stays decoupled. At the first mode, the highest coupling is observed when the center-to-center distance is 0 mm while there is almost no coupling at 90mm (25% overlap) as expected for the coils at their first mode⁸. No change in input impedance observed at the second mode, clearly showing that the coil is well decoupled.
When the center-to-center distance is 125mm, adjacent SCCs transfer energy with adjacent arms. In the circuit model, this corresponds to the coupling of adjacent inductors only (Fig 4a). In Fig 4b, the agreement between the electromagnetic simulations and the circuit model is shown by numerically calculating the coupling coefficient for adjacent inductors (k=0.0525). This highlights that the coupling between SCCs takes places due to the radiation from the outermost surfaces which results in strong coupling at the first resonance mode.
Fig. 5 shows that SCCs have similar radiation characteristics and a good performance compared to conventional loops with distributed capacitors.

Conclusion

We described the mode of operation of SCCs by showing the relationships between the electromagnetics simulations and the circuit model. We also observe that the coupling at the first resonance mode takes place due to the outermost surface acting as inductive elements. At the second mode, the coils do not couple at any distance, and we show good performance compared with conventional loops which makes them outstanding candidate for 7T MRI where advanced multichannel transceiver arrays are desired for optimizing homogeneity.

Acknowledgements

No acknowledgement found.