This study aimed to develop a lump-element double-tuned common-mode-differential-mode (CMDM) radiofrequency (RF) surface coil^1-3 with independent frequency tuning capacity for MRS and MRI applications. The presented double-tuned RF surface coil design can be extended to a broad range of heteronuclear MRI applications, including ¹³C, ²³Na, ¹⁵N and ¹²⁹Xe and other hyperpolarized and non-hyperpolarized heteronuclear MR applications, especially for those that require high local sensitivity.

Circuit analysis: The presented design has two modes that operate with different current paths, allowing independent frequency adjustment. According to Kirchhoff’s voltage law for two inner coil loops and one auxiliary capacitor loop (in Figure 1a), the presented coil circuit can be described as $$\begin{cases}-j\omega L_{1}I_{1}+\frac{j}{\omega C_{S}}(I_{1}-I_{3})+\frac{j}{\omega C_{T1}}(I_{1}+I_{2})-j\omega L_{2}(I_{1}+I_{2})=0 \\-j\omega L_{1}I_{2}+\frac{j}{\omega C_{S}}(I_{1}+I_{3})+\frac{j}{\omega C_{T1}}(I_{1}+I_{2})-j\omega L_{2}(I_{1}+I_{2})=0 \\\frac{j}{\omega C_{T2}}I_{3}+\frac{j}{\omega C_{S}}(I_{3}+I_{2})+j\omega C_{S}(I_{3}-I_{1})=0\end{cases}$$Eq. 1

where C_S is the splitting capacitors, C_T1 is the tuning capacitor for differential mode and L₁ and L₂ are the equivalent inductors on the outer loops and the central conductor, as defined in Figure 2a. Assuming the distribution of common mode (CM) current follows the illustration of i₁ in Figure 1d (left), i.e., let I₁ = I₂ in Eq. 1, the resonant frequency is given by $$\omega_{CM}=\sqrt{\frac{\frac{1}{C_{S}}+\frac{2}{C_{T1}}}{L_{1}+2L_{2}}}$$Eq. 2

Utilizing Kirchhoff’s voltage law and assuming the distribution of differential mode (DM) current follow the illustration of i₂ in Figure 1d (right), i.e., let I₁ = -I₂ in Eq. 1, resonant frequency is given by $$\omega_{DM}=\frac{1}{\sqrt{(\frac{C_{S}}{2}+C_{T2})2L_{1}}}$$Eq. 3

where C_T2 is the tuning capacitor for differential mode. The coil prototype was tested on the bench and then examined in phantom and in vivo experiments. Eqs. 2 and 3 clearly show that resonant frequencies of common mode and differential mode can be adjusted independently via C_T1 and C_T2.

Bench test: For the tuning dependency measurement, a network analyzer with full two ports (Agilent, E5071C) was used. The frequency span was set as 100 kHz and the number of points for frequency sweeping was 20000, allowing a nominal resolution of 5 Hz/point. The resonant frequency was detected automatically by searching the minimum value of the magnitude S11 (which identifies the resonant mode) within the span (i.e., 100 kHz), while the impedance at the resonant frequency was measured on the Smith chart.

MRI protocol: All MR experiments were performed on a 7T whole-body MRI scanner (GE Healthcare, Waukesha, WI). The ¹H-¹³C phantom was made using a 21.7-mm-diameter cylinder syringe that was filled with ethylene glycol (HOCH2CH2OH, anhydrous, 99.8%, Sigma-Aldrich, St. Louis, Missouri). For the in vivo experiment, a three-plane and multi-slice GRE ¹H imaging was preformed, lasting 32 s. Non-selective dynamic spectroscopy data (readout bandwidth = 5000 Hz and sampling points = 2048) were acquired following a bolus injection of approximately 3 mL hyperpolarized [1-¹³C]-pyruvate solution (80 mM), produced using SpinLab (GE Healthcare, Niskayuna, New York).

Standard deviations of frequency and impedance fluctuations measured in one resonator, while changing the tuning capacitor of another resonator, were less than 13 kHz and 0.55 Ω. The unloaded S21 was -36 dB and -41 dB, while the unloaded Q factor was 260 and 287, for ¹³C and ¹H, respectively. In vivo hyperpolarized ¹³C MR spectroscopy data demonstrated the feasibility of using the CMDM coil to measure the 3-second/spectrum-dynamics of lactate, alanine, pyruvate and bicarbonate signal in a normal rat head along with fast acquiring ¹H anatomical reference images.In the current study, we have demonstrated the independent frequency tuning capacity of the developed lump-element double-tuned CMDM coil. Using a circuit analysis, we demonstrated that one tuning capacitor could be used to adjust the resonant frequency of one mode without having current flowing in another tuning capacitor for the other mode. The bench test result clearly showed that the two resonant frequencies could be tuned independent of each other, verifying the circuit analysis. Compared with double-tuned quadrature volume coils, the presented double-tuned surface coil provided relatively high local sensitivity for heteronuclear MRI, but involved inhomogeneous B₁ fields.Independent frequency tuning capacity was demonstrated in the presented lump-element double-tuned CMDM coil. This CMDM coil maintained intrinsically decoupled magnetic fields, which provided sufficient isolation between the two resonators. The results from in vivo experiments demonstrated high sensitivity of both the ¹H and ¹³C resonators.