# Three-Line Microstrip Array for Whole-Body MRI System at 7 T
## 2 Methods  
In this study, we investigated a new design for a microstrip array for the whole body using a 7 T MRI system and compared it with existing whole-body RF transmitters. The t-MTL consists of a ground plate, a dielectric material, and a conventional conductor line to which the voltage source is connected. However, in our design, we included additional lines next to the main TL. The adjacent lines are highly coupled to the main line, and the proposed design is expected to increase field propagation uniformity. One of the adjacent lines is terminated with a short circuit to increase the field strength. The two adjacent lines are not connected to the source voltage. The use of a t-MTL array has been previously proposed and analyzed as line couplers for microwave applications [18; 19]. The solution to the TL equations is obtained from the above study using a 3 \(\times\) 3 matrix. The voltage [\(V\)] and current [\(I\)] equation is given by  
\[\frac{d[V]}{dx}=-[z][I] \tag{1}\]  
where [\(z\)] represent the 3 \(\times\) 3 matrix of the impedance of the line, and the solution to this equation is found in [20]. Here, we modified the matrix structure to indicate that the center line is the one carrying the current, as depicted in Figure 1, with the tag L1. \[z=\left[ \begin{array}{ccc}z11&z12&z12\\ z12&z22&z23\\ z12&z23&z22\end{array} \right] \tag{2}\]  
The solution is given as  
\[\gamma_{1}=z22-z23 \tag{3}\]  
\[\gamma_{2}=\left[\frac{z11}{2}+\frac{z22}{2}+\frac{z23}{2}-\frac{1}{2}\sqrt{ z11^{2}-2z11z22-2z11z23+8z12^{2}+z222^{2}+2z22z23+z23^{2}}\right] \tag{4}\]  
Figure 1: The geometry of triple-line microstrip-transmission line with the respective dimensions. \[\gamma_{3}=\left[\frac{z11}{2}+\frac{z22}{2}+\frac{z23}{2}+\frac{1}{2}\sqrt{z11^{2} -2z11z22-2z11z23+8z12^{2}+z222^{2}+2z22z23+z23^{2}}\right] \tag{5}\]  
An analysis of the coupling of the t-MTL array can be found in [21; 22]. In the case of antennas and couplers, the use of t-MTLs was found to be useful for combining two signals into one without any interaction with the signal source. However, by reciprocity, the radiated field can reach a larger area in a constructive manner in the present application for MRI. The \(\mid\)B\({}_{1}\)\({}^{+}\)\(\mid\)-field required for transmission in MRI is given by the x- and y-components of the magnetic field as follows:  
\[B_{1}\)\({}^{+}=B_{x}+jB_{y} \tag{6}\]  
Figure 1 shows a single t-MTL with the corresponding geometry. It should be noted that only the center line is connected to the voltage source, and the adjacent lines are narrower by approximately 15%. The separation between the lines was included to improve coupling between the lines based on the theory in [18]. To determine the best configuration of the t-MTL that can deliver a more uniform \(\mid\)B\({}_{1}\)\({}^{+}\)\(\mid\)-field, we tested four different configurations to justify the use of a triple-line. The first configuration is a simple microstrip with a width of 32 mm and a length of 384 mm. Teflon was used as the dielectric material (height = 10 mm, relative permittivity (\(\varepsilon_{\mathrm{r}}\)) = 2.08); this configuration ensured resonance at 300 MHz. The second configuration is a triple-line with a center line of 32 mm and adjacent lines of 5 mm. The lengths of the lines are 384 mm. The dielectric material is also Teflon with a height of 10 mm; in this case, all the lines were terminated with an open circuit. The third configuration consisted of terminating one of the adjacent lines with a short circuit with the same geometry as the microstrip. We performed electromagnetic simulations to compute the \(\mid\)B\({}_{1}\)\({}^{+}\)\(\mid\)-field in a target area of a 400 \(\times\) 300 \(\times\) 100 mm block with conductivity (\(\sigma\)) and \(\varepsilon_{\mathrm{r}}\) of 0.0764 S/m and 11.745, respectively; these values correspond to the electrical properties of fat at 300 MHz. Figure 2 shows the \(\mid\)B\({}_{1}\)\({}^{+}\)\(\mid\)-field for each of the cases described.