Carbon-13 MRS is a validated method for the assessment of glucose metabolism in skeletal muscle. It can be used together with an exercise challenge to uncover the dynamics of glycogen stores, or to study glucose/lipid oxidation in different pathologies. However, as many other NMR feasible nuclei, ¹³C NMR suffers from intrinsically low sensitivity, which is further decreased due to the ¹H-¹³C hetero-nuclear J-coupling. To enhance its overall sensitivity, transmission on proton frequency during ¹³C reception can be employed (proton decoupling). Another possibility to gain sensitivity is to move to higher static magnetic field strength, resulting in further increase of RF power deposition posing some limitation to ¹H decoupled ¹³C NMR experiments. Therefore, ¹³C NMR at 7T requires specifically optimized double tuned local RF transceive arrays for high SNR, exhibiting sufficient electrical isolation between the arrays to enable ¹H decoupling and high SAR efficiency as to not invoke SAR limits during proton decoupling. In this work, we present the design for a 7 channel nested ¹H/¹³C RF transceive coil array for ¹³C metabolic studies in the human calf muscle at 7T.

Coil Design: The coil array consists of a 4 channel ¹H array atop of a 3 channel ¹³C configuration. The channels are mounted on an half-cylindrically shaped ABS former with an outer diameter of 15 cm. The distance between the ¹³C and ¹H arrays was chosen to be 1 cm. Previously built ¹³C phased arrays [1,2] often employ so-called LCC traps in order to decouple the concentrically arranged channels, in doing so, incorporating additional loss mechanisms and decreased Q-ratios [3]. By choosing 3 and 4 channels, respectively, we are able to geometrically decouple both arrays, while maintaining a sufficiently large FOV and high SNR. The element sizes are dictated by 3 variables, namely the overall length of the ¹H array, and the optimum overlap between next nearest ¹H and ¹³C channels, respectively. The overall length of the ¹H array was chosen to be 24 cm, which covers almost the whole half cylinder. Depending on the overlap factor for ¹H (ol_H), this yields a ¹H element size of w_1H=24/(1+3*ol_H). In order to remain geometrically decoupled with the ¹H array, the element size of the carbon array is dictated by the choice of the overlap factor (ol_C) and the fact that ol_H*w_1H=ol_C*w_13C. A schematic of this setup can be seen in Fig. 1.

Simulation: The coil design was realized within XFdtd 7.4 (Remcom, State College, PA, USA) using 2 mm thick coil wire, modeled as perfect conductor. It was loaded with a cylindrical phantom filled with tissue-like gel, as well as Ella’s calf (Virtual Family). All capacitor gaps were connected with 50Ω voltage sources to enable RF co-simulation in ADS (Agilent Technologies) [4]. Inductive counter-wound decoupling was realized between all next-nearest neighbors in co-simulation. Realistic loss estimations for inductances, capacitances, and solder joints were modeled as series resistances [5]. The optimal overlap factor was determined beforehand via simulation of 2 channels with varying overlap Static B₁⁺ shimming was achieved using the SimOpTx toolbox (Medical University of Vienna, Austria) for both arrays by maximizing SAR efficiency (B₁⁺/√SAR_{10g, max}) in the region of interest (gastrocnemius muscle, depicted in black in Fig. 3) as a function of the relative channel phases, incremented in 5° steps for ¹³C (5184 phase sets) and 10° steps for ¹H (46656 phase sets).

The optimized overlap factor for the ¹H array was 0.8, yielding an element size of 7.1x12.5 cm², and 0.9 for the carbon array, resulting in an element size of 6.2x10 cm². Decoupling between coil elements was below -14.5 dB and -14.4 dB for the ¹H and ¹³C array, respectively. Cross-coupling was always below -29.4 dB at the proton Larmor frequency (297.2 MHz) and -27.9 dB at the carbon Larmor frequency (74.7 MHz), indicating good geometric decoupling (see Fig. 2). Optimized static B₁⁺ shim could be achieved with a phase set of [120°/40°/-40°/-120°] for ¹H and [50°/0°/-55°] for ¹³C. B₁⁺, SNR and SAR maps can be seen in Fig. 3. The maximum 10g averaged SAR for 1 W input power is 1.5 W/kg for ¹H and 1.3 W/kg for ¹³C.The design and simulation results for a nested 7 channel ¹H/¹³C transceive array, aiming at high SAR efficiency are presented. The shifted setup results in good decoupling between ¹H and ¹³C channels, and therefore seems a promising candidate for a coil enabling proton decoupling to further increase ¹³C SNR in metabolic studies of the human calf at 7T. The physical implementation of the coil is in progress.