## 2 Materials and Methods  
### PFT \({}^{13}\)C Birdcage RF Coil with CPSCs  
Each CPSC was designed and fabricated in a PFT \({}^{13}\)C birdcage RF coil consisting of two capacitors (C\({}_{1}\) and C\({}_{2}\)) and one inductor (L), which is shown in Figure 1. The CPSCs act as short and open circuits at the resonant frequency corresponding to \({}^{13}\)C (32.13 MHzat 3.0 T) and \({}^{1}\)H (127.74 MHz at 3.0 T), respectively [23]. The impedance of the CPSCs can be described as parallel and series resonant circuits as follows:  
\[Z_{\text{parallel}}(\omega)=\bar{\jmath}\text{L}_{\text{eq}}\omega=\bar{\jmath }\text{L}\omega\left(1-\frac{\omega}{\omega_{\text{off}}}\right)^{-1} \tag{1}\]  
\[Z_{\text{series}}(\omega)=\bar{\jmath}\text{L}_{\text{eq}}\omega\left(1-\frac {\omega_{\text{on}}^{2}}{\omega}\right) \tag{2}\]  
\[\omega_{\text{off}}=\frac{1}{\sqrt{\text{LC}_{1}}} \tag{3}\]  
\[\omega_{\text{on}}=\frac{1}{\sqrt{\text{L}_{\text{eq}}\text{C}_{2}}} \tag{4}\]  
where the \(\omega_{\text{off}}\) and \(\omega_{\text{on}}\) are the resonant frequency of \({}^{1}\)H and \({}^{13}\)C, respectively. The CPSC minimizes the effect of undermining the image quality throughout the acquisition of \({}^{1}\)H MR images and maximizes the efficiency when obtaining \({}^{13}\)C MR signals. A total of 40 CPSCs were fabricated and installed in the PFT \({}^{13}\)C birdcage RF coil by creating gaps in four locations on each end-ring and between every leg. The low-pass PFT \({}^{13}\)C birdcage RF coil was constructed with 16 legs by considering the drive port connection, power deposition, and electromagnetic balance [24; 25]. In this study, the design of the PFT \({}^{13}\)C birdcage RF coil was decided to accommodate a 20\(-\)40 kg swine. According to the [PERSON] et al. [26], the dimension of the 40 kg swine with semi-recumbent position is approximately 270 mm in diameter and 1013 mm in length. Considering the size of the swine, the design of the PFT \({}^{13}\)C birdcage RF coil was decided  
Figure 1: Circuit diagram of the 16-leg PFT \({}^{13}\)C low-pass birdcage RF coil containing 40 carbon-proton switching circuits (CPSCs). Trimmer capacitors with high Q-factors are connected to ports 1 and 2 and used for fine-tuning of PFT \({}^{13}\)C birdcage RF coil. Only half of the coil circuitry is shown in the figure; the other eight legs with 20 CPSCs without RF feeding are omitted for simplicity. to be fabricated on a cylindrical acrylic tube frame with 10 mm thickness, 320 mm outer diameter, and 320 mm length. The acrylic support structures with constant curvature were attached to a cylindrical acrylic tube frame to support and fasten the PFT \({}^{13}\)C birdcage RF coil on a patient table rail system. The PFT \({}^{13}\)C birdcage RF coil was constructed using a copper sheet with 0.2 mm thickness. Rectangular end-rings and legs were used in the setup. The length and width of the legs were 240 mm and 30 mm, respectively; the width of the end-rings was 40 mm; and the gap for tuning the capacitors was 10 mm. The 16 legs were distributed at equal distances to improve RF field homogeneity, and each port was selected with 90\({}^{\circ}\) phase delay for quadrature transmission [27]. The construction of the 16-leg low-pass PFT \({}^{13}\)C birdcage RF coil with the CPSCs involved the use of capacitors with a high quality (Q) factor (Q-factor \(\cong\) 10,000, working voltage = 500-7200 V, non-magnetic, Dalicap, Dalian, China) and trimmer capacitors with high Q-factors (Q-factor \(>\) 3000, capacitance range = 1.0-14.0 pF, working voltage = 125 V, non-magnetic, Voltronics, Denville, NJ, USA) to resonate the PFT \({}^{13}\)C birdcage RF coil at 32.13 MHz in a 3.0 T MRI system. The initial capacitance value of the PFT \({}^{13}\)C birdcage RF coil was determined using the birdcage builder software package [28] and optimized for fine-tuning. Each port of the PFT \({}^{13}\)C birdcage RF coil was tuned to the uniform mode at 32.13 MHz and impedance matched to 50 \(\Omega\) with a \(\pi\)-matching network using a corn-oil phantom [29].