## 4 Discussion  
In this study, we evaluated the performance of the proposed CPSCs by comparing the results of FDTD EM simulations and MR experiments. By using the CPSCs, the performance of the 16-leg PFT \({}^{13}\)C birdcage RF coil was verified through MR experiments and hyperpolarized \({}^{13}\)C MRS/MRSI experiments. Through the bench test measurement, the Q-factor ratios (\(\frac{\text{Unloaded Q}}{\text{Loaded Q}}\)) of the 16-leg PFT \({}^{13}\)C birdcage RF coil with CPSCs and the 16-leg \({}^{13}\)C birdcage RF coil without the CPSCs were 9.330 and 10.11, respectively. This Q-factor ratio difference implies that the \({}^{13}\)C signals can be acquired using the PFT \({}^{13}\)C birdcage RF coil without the effects of CPSCs when comparing with the \({}^{13}\)C birdcage RF coil without CPSCs. FDTD EM simulations and phantom MR experiments for \({}^{1}\)H nucleus were performed to verify the performance of the CPSC. The uniformity reduction in the B\({}_{1}^{+}\) field maps of the uniform fat phantom in FDTD EM simulations and the signal intensity maps of ACR phantom in MR experiments with the \({}^{13}\)C birdcage RF coil with and without the CPSCs was evaluated via PIU calculations using the ACR method and observed as negligible and acceptable based on the recommended action criteria of phantom test guidance of ACR [30]. When the fat phantom was surrounded by the 16-leg \({}^{13}\)C birdcage RF coil without CPSCs, the uniformity and intensity reductions in the B\({}_{1}^{+}\) map of the uniform fat phantom were 9.60% higher and 64.1% lower in the FDTD EM simulation, respectively, compared with those of the PFT \({}^{13}\)C birdcage RF coil. Additionally, when the ACR phantom was surrounded by a 16-leg \({}^{13}\)C birdcage RF coil, the ACR phantom could not be imaged due to power transmission errors in the MRI system, indicating excitation failure of the \({}^{1}\)H nucleus. When compared with case 2, the fatal uniformity reduction and power transmission error observed in case 3 were generated because the 16-leg \({}^{13}\)C birdcage RF coil was not transparent to the electromagnetic field at the \({}^{1}\)H resonance frequency, and thus, it began to behave as an RF shield. There was also a fatal uniformity reduction at \({}^{1}\)H T\({}_{2}\)-weighted reference images of corn-oil phantom when surrounded by the 16-leg \({}^{13}\)C birdcage RF coil that did not contain CPSCs than that of the 16-leg PFT \({}^{13}\)C birdcage RF coil. This implies that the results of \({}^{1}\)H FDTD EM simulations and \({}^{1}\)H MR imaging experiments coincide; moreover, the proposed CPSCs were appropriately constructed such that they can be transparent to an electromagnetic field at an \({}^{1}\)H resonance frequency. The 2D CSI data of the corn-oil phantom indicated that there was a slight difference of SNR with and without the CPSCs. This implies that the proposed CPSCs performed appropriately at the resonant frequency of \({}^{13}\)C and the signal loss generated by the noise of  
Figure 8: Three-dimensional \({}^{13}\)C MRSI results in the swine cardiac. (**a**) Signal map of [1-\({}^{13}\)C] pyruvate with 4 \(\times\) 4 \({}^{13}\)C spectral grid; (**b**) corresponding \({}^{13}\)C spectra of [1-\({}^{13}\)C] pyruvate at 4 \(\times\) 4 \({}^{13}\)C spectral grid in (**a**); (**c**) signal map of [1-\({}^{13}\)C] lactate over heart and blood vessels. Color bar numbers are a.u. CPSCs can be negligible and acceptable. The hyperpolarized slab dynamic \({}^{13}\)C MR spectra indicated that the [1-\({}^{13}\)C] pyruvate was decomposed into the [1-\({}^{13}\)C] lactate by lactate dehydrogenase (LDH) and the [1-\({}^{13}\)C] bicarbonate by pyruvate dehydrogenase (PDH), which are the products of enzymatic exchanges [4, 37, 38]. Furthermore, the pyruvate hydrate was visualized, which is a product of non-enzymatic exchange of the [1-\({}^{13}\)C] pyruvate [35].