Synopsis

Keywords: RF Arrays & Systems, High-Field MRI, Coupling, SCC coils, Faraday's law of induction, SAR reduction

Minimizing coupling between coils constitutes a major challenge in the design of flexible arrays for UHF MRI. Recently, Shielded-coaxial-cable coils (SCC) were shown to be flexible and intrinsically highly decoupled: however, the decoupling mechanism of SCC remains unclear. In this work, we use an high frequency Faraday-equivalent model of the induced voltage to examine coupling between two SCCs in different geometrical configurations. We show that lower coupling in SCC derives from both lower magnitude of electric and magnetic fields as compared to a loop coil, and we discuss the implications in the design of coils for MRI.

Introduction

Especially in the design of flexible arrays, a major challenge is minimizing coupling between coils. Shielded-Coaxial-Cables (SCC) provide flexibility, intrinsic decoupling characteristics, and straight-forward fabrication^1,2, but their decoupling mechanism is still unclear. Understanding coupling of SCCs could enable the design of novel and more efficient coil elements. In this work, we derived an high frequency Faraday-equivalent model of the induced voltage and examined coupling between two SCCs in different configurations.

Methods

Using the reciprocity theorem³ , the reaction concept⁴ , and the full set of Maxwell equations, we derived an expression for the coupled voltage of two coils:
$$ (1) \; \; \; V_{21} = \oint_S ( \textbf{E}_{2}\times \textbf{H}_{1} ) \cdot d\textbf{S} + j\omega \left( \int_V \varepsilon \textbf{E}_2 \cdot \textbf{E}_1 dV + \int_V \mu \textbf{H}_2 \cdot \textbf{H}_1 dV \right) $$
where $$$V_{21}$$$ is the open-circuit voltage induced at the port of coil 2 when coil 1 is active–i.e. the coupled voltage - $$$\textbf{E}_{1}$$$ ($$$\textbf{H}_{1}$$$) is the electric (magnetic) field radiated by coil 1, when coil 1 is excited with 1A of current and coil 2 is open-circuited–and vice versa for $$$\textbf{E}_{2}$$$ and $$$\textbf{H}_{2}$$$-$$$V$$$ is a volume containing at least source 2, and the surface integral is extended over the contour of $$$V$$$, $$$S$$$.
Expression (1) generalizes Faraday’s law of induction, as it represents the voltage induced at the ports of a coil at any desired frequency and for any configuration. Faraday’s law of induction has been extensively used in MRI literature to model coupling in the low-frequency approximation^5,6.
In expression (1), it is possible to recognize similar terms of electric coupling and magnetic coupling as defined in Hong^7,8 , or Awai^9-11 . The additional term accounts for electric and magnetic coupling contributions outside $$$V$$$. Note that the theory of Hong was used to explain the rationale in the design of Self-Decoupled-Coils¹², and that electric coupling in Hong is defined the same as in Roemer⁵ .
We apply expression (1) to the case of two-coil arrays, one of of SCCs and the other of loops, in different configurations, at 300MHz. As input, we used the EM fields simulated by full-wave simulation software (CST MWS, Darmstradt, Germany), and numerical Monte-Carlo integration. Coils were simulated at 12mm distance from a square phantom ε_r=78, σ=0.6[S/m] (figure 1) using the frequency domain solver with adaptive tetrahedral mesh. SCCs simulations were validated earlier by experiments¹³ , and we use the same settings for the loop coil simulations. Coils were excited at the ports by 1A. To perform integrals, we used a spherical volume radius=400mm encompassing both sources and phantom. We use point lists to export the $$$\textbf{E}_{2}\times \textbf{H}_{1}$$$ , $$$\textbf{E}_2 \cdot \textbf{E}_1$$$, $$$\textbf{H}_2 \cdot \textbf{H}_1$$$ fields at defined locations from CST into MATLAB, in which they were integrated, and compared to the voltage $$$V_{21}$$$ by CST.

Results

Figure 2 shows that in each configuration the induced voltage was negligible for the SCCs as compared to the loops. The average relative difference between expression (1) and $$$V_{21}$$$ by CST was -1.8% for the real part and 2.7% for the imaginary part.
Figure 3 shows that the value of the term $$$\oint_S ( \textbf{E}_{2}\times \textbf{H}_{1} ) \cdot d\textbf{S}$$$ was negligible as compared to the electric and magnetic coupling terms. The SCCs showed much less electric and magnetic coupling contributions compared to the loops.
Figure 4 shows that the magnitude of the E and H fields were significantly lower in the SCC case, with comparable value of the magnitude of B₁⁺/√W
Figure 5 shows the magnitude of the E, H, B₁⁺/√W field in a central cross section, in the case of a single capacitive-segmented loop, and in the SCC case. Plots were generated using 1A of current at the ports. The magnitude of the E and H fields was still lower in the SCC case, with comparable magnitude of B₁⁺/√W.

Discussion

Both electric and magnetic coupling were lower in SCCs. From expression (1) we deduce that lower electric (magnetic) coupling can be either related to orthogonality between two radiation profiles, or lower average amplitude of the fields E₁(H₁) and/or E₂(H₂).
To discriminate between these two effects, we examined the plot of the E and H fields in a central cross-section of the phantom. We note that in every configuration the E and H fields -which determine SAR in the tissue- were lower in the SCC case, with comparable magnitude of the B₁⁺/√W field -which determine SNR in the image.
It is well known that capacitors block the radiation of the E field. Therefore, we compared the E, H and B₁⁺/√W fields of a SCC with the E, H and B₁⁺/√W field of a capacitive-segmented loop. To make the two plots comparable, we considered the fields radiated for 1A of current at the ports. We note that the E and H field were lower in the SCC case.

Conclusions

In this work, we discuss coupling in SCCs and further implications in the design of MRI coils. We demonstrate that lower coupling in SCCs derives from lower magnitude of the E and H fields in the calculation volume, with comparable magnitude of the B₁⁺/√W field. Further, we show that a shield is more effective than using capacitors to block the propagation of the E and H fields.

Acknowledgements

No acknowledgement found.