## 4 Conclusions  
In this paper, a novel passive dual-tuned magnetic metasurface for 1.5T MRI \({}^{1}\)H and \({}^{23}\)Na imaging has been proposed. In particular, the dual-tuned metasurface is able to enhance the magnetic field strength both in transmission and receiving phases and for both the required Larmor frequencies simultaneously. The final metasurface design consists of a 5 \(\times\) 5 passive capacitively loaded array, in which each unit-cell is composed, in turn, of two concentric spirals. The two concentric spirals are responsible for the dual-frequency metasurface response, since they are made resonant at the two Larmor frequencies, i.e., 17 and 64 MHz. Due to the metasurface finiteness and consequent truncation effects, an appropriate compensation loading procedure was carried out through an analytical model. This correction led to homogenization of the unit-cells current distribution, thus avoiding the metasurface response degradation while also enhancing the magnetic field strength.  
To validate the proposed solution, we conceived a numerical test-case, comprising a RF loop and a metasurface placed 5 mm above it. Next, we performed full-wave simulations with and without the presence of the metasurface, when the radiative system is loaded with a representative biological load. The performance of the metasurface with respect to the single RF loop was evaluated in terms of transmission efficiency \(T_{x}\). A significant \(T_{x}\) improvement of factor 3.5 at 17 MHz and of 5 at 64 MHz was observed in the presence of the biological phantom. Finally, we also fabricated PCB prototypes, achieving excellent agreement with the simulations in terms of \(S_{11}\) parameters, proving the overall design procedure effectiveness.  
To conclude, this solution can be potentially helpful in the MRI multi-nuclei diagnostic technique, allowing for better image quality by using the same hardware configuration, thus reducing the scanning time, the invasiveness on the patient and the final overall costs.  
Figure 11: RF loops with metasurface with and without biological phantom: comparison between simulated and measured \(|S_{11}|\) parameters at the two desired frequencies, showing a general good agreement.  
Clearly, several aspects must be addressed before the solution can be adopted in actual MRI clinical imaging, as evaluating its robustness for different human districts and size scalability. Therefore, future works will be directed to apply and refine the solution in a real clinical scenario, addressing the aforementioned issues.  
[PERSON], [PERSON] and [PERSON] were the main contributors to this work and were responsible for developing and implementing the methods, conducting measurements, and analysis; [PERSON] was responsible for investigation, supervision and writing; [PERSON] and [PERSON] critically analyzed the results, suggested modifications and reviewed the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
Work partially supported by the Italian Ministry of Research (MUR) in the framework of the FoReLab and CrossLab projects (Departments of Excellence).  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
AWG  
American Wire Gauge  
CAD  
Computer Aided Design  
DT  
Dual Tuned  
MRI  
Magnetic Resonance Imaging  
PCB  
Printed Circuit Board  
RF  
Radio-Frequency  
SMA  
Sub-Miniature version A  
SNR  
Signal-to-noise-Ratio  
VNA  
Vector Network Analyzer