Introduction

There is a number of studies suggesting the use of metamaterials for enhancing the RF field distribution and tailoring it in MRI ^1,2,3. However, at radio frequencies, such as 297 MHz, the size of metamaterial unit-cells lies in tens-of-centimeter range and thus physically large compared to the available space in an MRI scanner. In this current work, we present a novel metasurface field enhancer based on Hilbert curve that is electrically small and easy to fabricate. The performance of the proposed structure in terms of enhancement of coil sensitivity as a function of Hilbert Curve order and frequency is analyzed and compared based on realistic simulation results. It is found that the proposed structure provides effective enhancement for coil sensitivity in a 7T system.

Methods

Figure 1(a) shows the proposed metasurface which is placed in between a phantom and a loop coil (see for details in the caption). The metasurface consists of one or several unit cells such as the one shown in Figure 1(b). Each unit cell consists of two layers: a dielectric substrate (FR4) and a copper Hilbert curve. Hilbert curve is a continuous fractal that belongs to the category of 'space-filling curves', and can shape an electrically long wire within a compact area. The inset at Figure 1(c) shows unit cells of Hilbert curves of orders two to six. They were analyzed using CST Eigenmode solver ⁴ for identifying the relation between the resonant frequency and the size of the unit cell. The results shown at Figure 1(c) suggest that 1) at a fixed frequency, with the increase of the Hilbert curve order, the unit cell size can be significantly decreased; 2) higher order curves can be used for lower resonance frequencies. CST Microwave Studio⁴ was used to perform a full-wave analysis of the 3D model shown in Figure 1(a). The effect of metasurface on the B₁⁺-field distribution of the coil at 300 MHz is examined.

Results

Figure 2(b) shows the simulation results of the B₁⁺ -field distribution with and without the metasurface at 7T measured along a straight line that goes across the central axial slice of the load, as shown at Figure 1(a). The field strength was normalized to the maximum field strength in the case of a single loop. It is clear that with the increase of the order of the Hilbert curve, the intensity of B₁⁺-field is increasing. It is 70% higher than a single loop in the case of the forth order Hilbert curve. Figure 3 shows the simulation results of B₁⁺-field distribution with and without the metasurface of different orders at 7T on central planes. The top and bottom rows present central sagittal and central axial slices, respectively. The first column shows simulation results for loop without any metasurface, the second, third and forth columns show simulation results for the loop with a metasurface of the second, third and forth order Hilbert curve, respectively. Similar to the data along the line, as the order of the Hilbert curve goes higher, so does the intensity of B₁⁺-field. In the sagittal slice, it is observed that the field distribution is asymmetric for the second and third order. However, this asymmetry can be solved by using a three-layer structure shown in Figure 4(a). It consists of a unit cell Hilbert curve, a substrate and a copy of that unit cell on the other side of the substrate rotated 180°. This anti-parallel third layer compensates the inhomogeneities of a single layer design. The comparison of the resulting B₁⁺-field distribution for the single and double layer structures is shown in Figure (b) and (c). As can be seen, with the third layer, the field strength is further enhanced and the symmetry is obtained.

Conclusions

A novel metasurface field enhancer based on Hilbert curve is presented. Its resonance behavior was studied and the B₁⁺-field enhancement with symmetry is successfully demonstrated at 7T. On a simple loop coil model, it is shown that higher orders of Hilbert curve can form a metasurface that increases the coil sensitivity effectively.

Acknowledgements

No acknowledgement found.

References

1. Wiltshire, M. C. K., et al. "Microstructured magnetic materials for RF flux guides in magnetic resonance imaging." Science 291.5505 (2001): 849-851.\\ 2. Freire, Manuel J., Ricardo Marques, and Lukas Jelinek. "Experimental demonstration of a μ=− 1 metamaterial lens for magnetic resonance imaging." Applied Physics Letters 93.23 (2008): 231108.\\ 3. Slobozhanyuk, Alexey P., et al. "Enhancement of magnetic resonance imaging with metasurfaces." Advanced materials 28.9 (2016): 1832-1838.\\ 4. CST Microwave Studio 2017 (Darmstadt, Germany), www.cst.com.\\