In Vivo B₁⁺ Enhancement of Calf MRI at 7T via Optimized Flexible Metasurfaces

Abstract

Purpose:

Ultra-high field (≥7T) magnetic resonance imaging (MRI) is at the cutting edge of medical imaging, enabling enhanced spatial and spectral resolution as well as enhanced susceptibility contrast. However, transmit (B₁⁺) field inhomogeneity due to standing wave effects caused by the shortened radiofrequency (RF) wavelengths at 7T, is still a challenge to overcome. Novel hardware methods such as dielectric pads have been shown to improve the B₁⁺ field inhomogeneity but are currently limited in their corrective effect by the range of high-permittivity materials available and have a fixed shelf life. In this work an optimized metasurface design is presented that demonstrates in vivo enhancement of the B₁⁺ field.

Methods:

A prototype metasurface was optimized by an empirical capacitor sweep and by varying the period size. Phantom temperature experiments were performed to evaluate potential metasurface heating effects during scanning. Finally in vivo Gradient Echo (GRE) images and B₁⁺ maps were acquired on five healthy subjects on a 7T system. Dielectric pads were also used as a comparison throughout the work as a standard comparison.

Results:

The metasurfaces presented here enhanced the average relative SNR of the GRE images by a factor of 2.26 compared to the dielectric pads factor of 1.61. Average B₁⁺ values saw a similar enhancement of 27.6% with the metasurfaces present versus 8.9% with the dielectric pads.

Conclusion:

The results demonstrate that metasurfaces provide superior performance to dielectric padding as shown by B₁⁺ maps reflecting their direct effects and resulting enhancements in image SNR at 7T.

Introduction

Magnetic resonance imaging (MRI) has been used as a standard medical diagnostic tool due to its high soft tissue contrast and lack of ionizing radiation. Due to the dependence of imaging signal-to-noise (SNR) on system field strength, there has been a trend toward moving to higher field strengths to improve image quality. In recent years, ultra-high field MRI systems (≥7T) have gained regulatory approval for human clinical imaging. These systems outperform their lower field strength counterparts by providing an increase in SNR, which can be used to increase spatial resolution, as well as an increase in chemical shift, which improves the spectral resolution^1,2. This allows for an increased metabolic specificity in sequences such as chemical exchange saturation transfer (CEST)^3-5, nuclear Overhauser effect (NOE) techniques⁶, and various spectroscopy techniques¹. This makes 7T an excellent tool for studying metabolic diseases in ways that 1.5T and 3T are unable to.

However, one of the major challenges at 7T is transmit field (B₁⁺) inhomogeneity which stems from the shortened radiofrequency (RF) wavelengths used that are approximately the same size as the human head dimensions. This results in a “standing wave” pattern that typically produces constructive interference near the center of the tissue region and destructive interference at approximately λ/4 distance from the center leading to degraded image quality^7,8. Several active areas of research are aimed at mitigating the issue of transmit field inhomogeneity at 7T.

One such method, parallel transmit (pTx), uses several independently driven transmit RF coils to enable control over waveform amplitude and phase modulation during RF transmission. However, pTx still remains limited in use due to potential increases in RF power absorption in tissue, which is described in the local specific absorption rate (SAR), as well as complex sequences implementation and translation that restricts its widespread application⁹. Specialized post-processing methods have also been developed to correct contrast changes caused by these B₁⁺ inhomogeneities, especially in the case of CEST¹⁰. However, these correction tools are less effective under a certain minimum B₁⁺, leading to potential quantification inaccuracies.

Dielectric padding has also become a standardized tool for increasing the local B₁⁺ field in regions of signal drop off. Dielectric pads utilize high permittivity materials mixed into an aqueous suspension (usually water (H₂O) or deuterium oxide (D₂O)) placed into plastic pouches to generate a secondary B₁⁺ field, via induced displacement currents within the material, that adds constructively with the primary B₁⁺ field of the RF coil¹¹. Dielectric pads have found utility in improving 7T imaging for inner ear imaging¹², spine imaging¹³, knee imaging¹⁴, and neuroimaging^15-18. However, while effective, dielectric pads also have several drawbacks. They are inherently limited in their B₁⁺ corrective effect due to the limited permittivity of materials found in nature, with the most used, calcium titanate and barium titanate, allowing for an upper limit of approximately 110 and 150 in suspension respectively¹⁹. Dielectric pads can also be relatively bulky and difficult to fit into the tight-fitting receive arrays that are typically used, have a limited shelf life, and can be relatively expensive. To avoid the above-mentioned limitations, there have been several efforts made to implement metasurfaces as an alternative approach for correcting B₁⁺ inhomogeneities. A metasurface is described as a 2-dimensional composite material that is made from metallic periodic unit cells, typically manufactured on a printed circuit board (PCB) substrate, leading to effective properties that can mimic homogenous bulk materials that may not be found in nature²⁰. These metasurfaces are typically thin and light weight, have no shelf life, and can be produced at a fraction of the cost of dielectric pads.

Similar to dielectric pads, metasurfaces aim to produce a secondary B₁⁺ field, via induced currents on the structure, that adds constructively to the primary B₁⁺ field. In contrast to dielectric pads, which carry displacement currents that are in phase with the primary B₁⁺ field, the metallic structures of metasurfaces carry conduction currents, seen in Figure 1a, which would in principle be 90° out of phase with the primary B₁⁺ field²¹. This phenomenon stems from the fact that, while the conduction current $({\overrightarrow{J}}_C)$ is in phase with the local electric field $(\overrightarrow{E})$ the displacement current $({\overrightarrow{J}}_D)$ is related to the time derivative of the electric field $(\overrightarrow{E})$ and is therefore 90° out of phase. This is reflected in the modified version of Ampere’s law below, as EQN 1.

Figure 1.

a) An illustration showing the movement of the induced metasurface currents ($i_{MS}$) along path $l$ through an example unit cell with a constant impedance ($Z$) and b) a diagram relating the phase angle of the unit cell to its real and imaginary impedance values where the horizontal axis is resistance, and the vertical axis is (capacitive) reactance.

$$\nabla \times \overrightarrow{H}={\overrightarrow{J}}_C+{\overrightarrow{J}}_D=\sigma \overrightarrow{E}+ϵ\frac{\partial \overrightarrow{E}}{\partial t}$$ (1)

This means that the secondary B₁⁺ field produced by such conduction currents would also be 90° out of phase with the primary B₁⁺ field and may not sum in a constructive manner with the primary B₁⁺ field, but rather sum orthogonally and therefore result in a negligible amount of image enhancement. In previous work a 90° phase delay was therefore introduced in the metasurface structure by adjusting the length of the primary parallel configured wires to approximately λ/4, resulting in field enhancement^22-24. Another approach has been to induce this phase delay by adding capacitive reactance to each unit cell. By tuning the distributed capacitance, the overall impedance of the unit cell $(Z_{MS})$, which is primarily inductive in nature, can be adjusted to obtain the appropriate amount of phase delay, bringing the secondary fields in phase with the primary^20,25. This relationship can be seen in EQN 2 where the phase angle ($\phi$) is dependent on the ratio of the real and imaginary components of the unit cell impedance, as illustrated in Figure 1b.

$$\phi ={\tan }^{-1}\left(\frac{Im(Z_{MS})}{Re(Z_{MS})}\right)$$ [2]

Previous studies have shown several in vivo implementations of this technology including wrist^22,26 and head imaging²⁷ at 1.5T as well as abdominal imaging at 3T²¹. However, the metasurfaces designs described in those previous studies were focused on in vivo applications at field strengths below 7T. Many promising 7T studies have been previously performed based on electromagnetic (EM) simulations or phantom experiments^28,29. Other work has included the use of different hybrid metasurface designs that also integrate high-permittivity materials³⁰, while other more recent work has shown the effectiveness of a similar 7T design for improving brain imaging in vivo³¹.

In the present work, an optimized metasurface design is presented and evaluated both in a phantom study and in vivo demonstrating its effectiveness in correcting for B₁⁺ inhomogeneities present in gradient-recalled echo (GRE) images acquired at 7T. This work primarily covers three areas: the initial design and B₁⁺ enhancement characterization of the metasurface, phantom temperature measurements, and an in vivo imaging demonstration on the calf.

Methods

The metasurface described here is based on a frequency selective surface (FSS), particularly an inductive mesh grid. This type of mesh grid-based design has been used in the past towards different applications, such as communications³². Furthermore, extensive work has been done in characterizing the behavior and creating the corresponding equivalent circuit models³³. Due to these reasons, this basic topology was chosen as the optimization starting point for MR imaging.

Metasurface Capacitance Optimization

A prototype 18 × 18 cm² single-layer flexible PCB was designed (Figure 2a) in a 9 × 9-unit cell arrangement with a unit cell size of 15 mm, trace width of 1 mm, and a polyimide substrate thickness of 83.5 μm. In this design, 220 evenly spaced solderable pads were incorporated into the layout to allow for placement of discrete capacitors at the unit cell trace midpoints, as shown in Figure 2b. An initial optimization sweep was performed by testing a range of 21 discrete capacitor values (0.5 to 75 pF) with the metasurface positioned on a cylindrical saline phantom (20 cm height, 6 cm radius), as shown in Figure 2c and Figure 2d, using a B₁⁺ mapping sequence. Throughout this work, additional comparisons were performed using conventional dielectric pads, composed of calcium titanate (CaTiO₃) suspended in D₂O (Multiwave Imaging, Marseille, France) with an estimated permittivity of 110¹⁷.

Figure 2.

a) The prototype single layer metasurface used for optimization and b) the physical PCB with discrete capacitors soldered on c) fixed to the top of a cylindrical saline phantom for B₁⁺ mapping d) in the 7T MRI. e) Additionally, the temperature testing PAA phantom can be seen with fiber optic probes inserted.

Metasurface Period Size Optimized

To determine the effect of metasurface unit cell size on B₁⁺ enhancement, four separate PCB designs were manufactured using unit cell sizes of 11.25 mm, 15 mm, 18mm, and 21 mm. A capacitance value of 11 pF was chosen to be integrated into these designs as parallel plate capacitors. The size of the printed parallel plate capacitor was calculated as seen in EQN 3, in which $d$ is the capacitor plate side length, t is the thickness of the polyimide substrate (25 μm), ${\epsilon }_s$ is the relative permittivity of the substrate (3.4), ${\epsilon }_0$ is the relative permittivity of free space (8.85 × 10⁻¹² F/m), and $C$ is the desired capacitance (11 pF).

$$d=\sqrt{\left(\frac{tC}{{\epsilon }_s{\epsilon }_0}\right)}$$ [3]

From this expression the value $d$ for patch side length was calculated to be 3.02 mm. In these experiments, both a single and dual configuration was used, in which one metasurface was placed on top or two would surround the saline phantom, respectively. Additionally, S-parameter characterization was performed on each unit cell size configuration with an untuned loop probe (33mm diameter) placed 1 cm away near the center of the unloaded metasurface, using a Network Analyzer (Agilent E5061A).

Phantom Temperature Testing

Four fiber optic temperature probes (Omega Engineering, Swedesboro, NJ, USA) were inserted into an 800 mL cylindrical tissue mimicking polyacrylic acid (PAA) phantom (10 g/L PAA, 1.32 g/L NaCl)³⁴, as depicted in Figure 2e, with each probe separated by an increasing distance from the phantom edge. In this testing configuration the metasurface had a total separation of approximately 1 cm from the closest temperature probe and approximately 2.5 cm from the farthest. The PAA phantom was allowed to cool to the scanner room temperature (~14 °C) before scanning using a high SAR level (>95% on Siemens UI monitor) GRE sequence for 20 minutes to measure the maximum rate of temperature increase. As was done in the period optimization, a single and dual metasurface configuration was implemented in comparison to the reference. For each testing condition three experimental replicates were acquired to account for measurement variability.

MR Image Acquisition

All images and measurements were acquired on a 7T MRI system (MAGNETOM Terra, Siemens Healthcare, Erlangen, Germany), in which initial B₁⁺ maps were acquired using a single channel transmit/32-channel receive phased array proton head coil (Nova Medical, Wilmington, MA, USA). Temperature testing and in vivo image acquisition were performed using a single channel transmit/28-channel receive phased array proton knee coil (Quality Electrodynamics, Mayfield Village, OH, USA). Axial in vivo images were acquired on the distal calf skeletal muscles of five healthy volunteers with written informed consent under an approved institutional regulatory board protocol. B₁⁺ mapping was performed as described by Volz et al.³⁵ under the following scan parameters: three datasets were obtained using nonselective preparation pulses with flip-angles of 20°, 40°, and 80° across a 12-slice slab. The time between preparation was 7400 ms, TR/TE = 3.50/1.46 ms, shots = 5, matrix size = 240 × 204, in-plane resolution = 1 × 1 mm², and slice thickness = 1 mm. Dual-echo GRE images were acquired across a 12-slice slab using a flip angle = 30°, TR = 200 ms, TE₁ = 2.99 ms, TE₂ = 5.79 ms, matrix size = 240 × 210, in-plane resolution = 1 × 1 mm², and a slice thickness = 2 mm. These images were also used to calculate B₀ maps. Three experimental conditions were tested: a reference scan with no corrective measures, a scan with the inclusion of two dielectric pads (one placed on top and bottom of the calf – Figure 3a and Figure 3c), and a scan with the inclusion of two optimized metasurfaces (one placed on top and bottom of the calf – Figure 3b and Figure 3d). A 10 mm thick foam spacer was placed between the subject and the metasurfaces during acquisition. All images were processed, and calculations made in MATLAB (The Mathworks, Natick, MA, USA).

Figure 3.

a) An aqueous calcium titanate dielectric pad produced by Multiwave Imaging and b) the flexible 11.25 mm unit cell metasurface with 11 pF parallel plate capacitors. c) Below are images of the physical configurations of the dual dielectric pad and d) dual metasurface implemented inside the knee coil.

Results

Capacitor Optimization Sweep

B₁⁺ mapping showed that as capacitance was varied from 0.5 to 75 pF, four distinct interaction regimes could be observed, as can be seen in Figure 4a. At extremely low capacitance values (0.5 pF and 1 pF) no substantial amount of enhancement can be seen, due to the negligible degree of phase shift and lack of coupling. For capacitance values between 5.6 pF and 13 pF a clear enhancement in the B₁⁺ field can be seen close to the metasurface, with the 11 pF configuration showing the highest amount of relative B₁⁺ enhancement in the region immediately below it (0.98), relative to similar valued configurations, such as 10 pF (0.95). From 15 pF to 24 pF a transition region exists where the amount of B₁⁺ field enhancement decreases substantially, both directly underneath the metasurface as well as in the center of the phantom. From 27 pF to 75 pF large regions of B₁⁺ field cancellation, or “nulling”, can be seen, with the most significant of these occurring at 27 pF and 30 pF. A comparison of the B₁⁺ field distribution between the metasurface, dielectric pad, and reference can be seen in Figure 4b, showing the metasurface creating a larger amount of enhancement by comparison. Finally, Figure 4c shows the average relative B₁⁺ strength inside of a region of interest (ROI; see figure inset) near the vicinity of the metasurface across all capacitor values tested as well as the dielectric pad, and references cases. In this ROI, the 11 pF configuration had an average relative B₁⁺ strength of 0.98, whereas the dielectric pad, and reference case had values of 0.81 and 0.70 respectively. Overall, metasurface configurations in the 10 pF to 13 pF range were found to produce more local B₁⁺ enhancement than when using the standard calcium titanate dielectric pad, yielding a gain of approximately 40% when compared to the 16% obtained with using the dielectric pad.

Figure 4.

a) B₁⁺ maps for all capacitors tested, showing the 11 pF produced the highest amount of enhancement. b) A comparison showing the enhancement differences between the reference phantom, calcium titanate dielectric pad, and the 11 pF metasurface. c) A graphical representation showing the amount of relative B₁⁺ for each capacitance (11 pF = 0.98), the dielectric pad (0.81), and reference case (0.70) within the red dashed ROI of the inset image.

Comparison of Unit Cell Period Size

Results from unit cell size testing, presented in Figure 5, show that the 11.25 mm size metasurface in the dual configuration produced the highest amount of B₁⁺ enhancement while also the highest amount of local B₁⁺ enhancement over the imaging slice, between metasurfaces tested. Furthermore, the 11.25 mm metasurface size and configuration also outperformed the dielectric padding by producing larger enhancement regions in its vicinity. Comparisons from all four of the unit cell size configurations demonstrate a dependence of higher mean relative B₁⁺ values and lower standard deviations as unit cell size decreased, ranging from 0.74±0.11 at 21mm to 0.82±0.08 at 11.25mm. All quantified B₁⁺ values can be seen in supporting information table S1. S21 and S11 characterization curves can also be seen in Figure S2 showing that the only unit cell size that showed a natural resonance frequency at the Larmor frequency of 300 MHz was the 21 mm variant.

Figure 5.

Relative B₁⁺ maps showing the effect of metasurface unit cell size in the B₁⁺ distribution in a saline phantom. The top row shows the reference case and dielectric padding comparison while the lower four rows show the metasurface data. PCB layouts for each unit cell size configuration can be seen in the first column while the second and third columns show the effect of a single and dual metasurface arrangement.

Phantom Temperature Assessment

Results showed that the highest temperature increases generally occurred in the single metasurface configuration with the largest increase of 1.52±0.08 °C being seen in probe 1 (Figure 6a). The highest temperature increase in the dual metasurface configuration and reference phantom configurations were measured 1.11±0.02 °C and 0.99±0.03 °C, respectively. All other configurations of probe locations produced similar temperature increases of less than 1 °C (Figure 6b, Figure 6c, Figure 6d). Detailed average temperature data for all experimental replicates and fiber optic probes can be seen in supporting information table S3.

Figure 6.

Mean temperature and shaded standard deviation regions can be seen for fiber optic a) probe 1, b) probe 2, c) probe 3, d) and probe 4 for the metasurface configurations tested (reference, single, dual). In this experiment, probe 1 is closest to the metasurface while probe 4 is the farthest.

Image SNR Comparison

GRE images, seen in Figure 7, show that the metasurfaces consistently increase relative SNR values within the calf region in comparison to the increase seen with dielectric padding across all subjects. Specifically, the average relative SNR gain seen across all subjects for the metasurface was 2.26±0.58, whereas the average relative SNR gain with the dielectric padding was 1.61±0.48. This resulted in an average relative SNR increase from the reference case to dielectric pads of 61.8% while the increase from the reference case to metasurface was 126.5%. Image contrast-to-noise ratio (CNR) calculations were also made between two different tissue types in the calf (muscle and tibial bone marrow fat) across subjects and showed a reasonable increase in average relative CNR for the metasurface (2.01±0.81) compared to the dielectric pads (1.76±0.70). Additional subject sagittal GRE images can be viewed in the supporting information section as Figure S4. Additionally, it was found during these in vivo experiments that the amount of inter coil element coupling did not change substantially, while the amplitude of the receiver noise did slightly increase when a larger calf was present versus a smaller one. This can be viewed as noise correlation matrices between subject 2 and 5 as Figure S5 in the supporting information section.

Figure 7.

GRE skeletal muscle images in the axial orientation between the three experimental conditionals for all five subjects. The highest relative SNR was produced by the metasurface, followed by the dielectric padding and reference cases.

Transmit Efficiency Map Comparison

Transmit efficiency maps can be seen in Figure 8a, showing the same corresponding slices as were presented in the GRE images. Qualitatively, the metasurface images show a consistent increase in the average transmit efficiency compared to both the reference case and the dielectric padding across all subjects. The average transmit efficiency across the imaging slice for the metasurface case across all subjects was 0.051±0.024 μT/V, while the reference and dielectric padding cases were 0.040±0.017 μT/V and 0.043±0.019 μT/V respectively. The transmit efficiency increase when using the dielectric pads was 7.5% compared to 27.5% when using the metasurface (Figure 8b). Exact transmit efficiency quantification values for each condition and subject can be viewed in supporting information table S6.

Figure 8.

a) Transmit efficiency maps reflecting the B₁⁺ field distribution shows a substantial and consistent increase in the local transmit field across subjects when the metasurfaces were used. Dielectric pads also produced an increase in transmit efficiency, although to a lesser extent. b) A graphical representation of the image slice transmit efficiency mean and standard deviation can be seen below showing that use of the metasurfaces resulted in a consistent increase in mean transmit efficiency values. It should also be noted that the average and standard deviation measures were calculated across the presented imaging slices.

Discussion

The aim of this work was to design and demonstrate a flexible metasurface for regional B₁⁺ field enhancement for 7T MR images. In phantom studies we found an added capacitance value of 11 pF was optimal in producing the highest amount of B₁⁺ enhancement in a saline phantom relative to the other capacitance values and that using the 11 pF value in combination with a unit cell size of 11.25 mm produced the highest amount of enhancement in the same phantom compared to other sizes tested (15mm, 18mm, and 21mm).

Previous groups have developed metasurfaces with similar designs for use at 3T, such as Vorobyev et al.²¹, and used a capacitance of 40 pF to produce an estimated “effective” permittivity of 300. From this work, it was predicted that for higher field strength systems, less capacitance would be needed to produce the same amount of phase delay and hence the same form of enhancement seen in the 3T study. This finding also reflects the observation seen in dielectric pad design that lower permittivity values are needed as field strength is increased³⁶. Therefore, since the metasurfaces described here have a high amount of enhancement using a lower capacitance, it can be reasonable assumed that their “effective” permittivity is lower than the metasurface with a permittivity of 300 described in the previous study.

It was also found that a relatively small unit cell size produced a more homogenous region of enhancement for both the single and dual metasurface configurations, as seen previously in Figure 5. As the unit cell size was increased the amount of B₁⁺ distortion became more significant to the point where degraded images were produced. This could be due, in part, to the fact that as the unit cell size is increased the characteristic impedance of an individual unit cell changes. The 11 pF capacitance value was optimized for a given unit cell size and as the unit cell size changes, the capacitance values that would produce the optimal amount of enhancement would also be expected to change. Another important factor is that the degree of enhancement is proportional to the number of total unit cells on the metasurface. When the unit cell size is increased relative to a fixed size metasurface, the total number of unit cells decreases which impacts its enhancing ability, as was tested here³⁷.

When designing these metasurfaces, the theoretical framework assumes an idealized infinite planar array of equal-sized unit cells, in which each has the same frequency response and induced current flow. However, when practically constructing these metasurfaces, there will only ever be a relatively small finite number of total unit cells. This means that the unit cells closer to the edges will experience different loading effects from the asymmetrical distribution of surrounding unit cells compared to those in the center of the surface. As a result, the secondary fields produced by the physical metasurfaces may be distorted in comparison to the ideal metasurface model due to current phase differences³⁸. This effect can be seen manifested in some of the calf images when the metasurfaces were present (Subjects 2, 3, and 5) where darker areas can be seen in the medial and lateral regions. Prior work suggests that this effect can be mitigated by decreasing the amount of added capacitance, in unit cells located towards the edges³⁹. In the future, fine-tuning of the capacitor values could be performed to determine the proper decrease applied to the unit cells near the edges of the array.

When introducing a conductive metallic structure into the transmit field, potential RF induced tissue hotspot formation is always a concern. Dielectric pads have thus far been shown not to increase the local specific absorption rate despite functioning in a similar manner to metasurfaces. One possible factor may be that the bulk high-permittivity materials used typically have much higher losses than metasurfaces do. In the case of metasurfaces, lossy materials are not present and the concern for local hotspot formation is more significant due to potential edge reflections that may form within the metallic structure when interacting with an external EM field. In our study, PAA phantom temperature evaluation of the metasurfaces described here, showed that when two are used (one on top and one on bottom) the local maximum temperature increase was only 1.11±0.02 °C in comparison to the 0.99±0.03 °C increase from the reference case that did not have metasurfaces present. These measurements also came from the fiber optic probe that was closest to the metasurface (10 mm separation), while the other three probes showed a negligible difference in temperature increase, which effectively shows that the minor temperature increase seen is in the immediately proximity to the metasurface. The results from these temperature experiments also reflect a “worst-case” safety scenario for in vivo translation in which the PAA phantom used was of relatively small volume and lacked any active heat-diffusive properties that would be present in living tissue. As an added safety measure foam padding was used which acted both as a standardized separator but also as a thermal insulator between the metasurface and calf tissue.

The in vivo calf images shown here reflect a substantial increase in both relative SNR and transmit field magnitude directly resulting from the metasurfaces in comparison to the reference case. While the calcium titanate dielectric pad also performed as intended; increasing the relative SNR by an average 61%, the metasurface consistently outperformed it by increasing the relative SNR by an average of 126%. These results, taken as a whole, show that the metasurface described here is not only safe but also highly effective in increasing the amount of signal with a low flip angle GRE-type sequence. Previous work by Schmidt et al.³⁰ showed a hybrid metasurface design that utilized both a metallic structure and high-permittivity calcium titanate substrate to enhance the transmit field and relative SNR of brain images taken at 7T. They were able to achieve transmit efficiency enhancement ratios of 2.0±0.3 over the local ROI in the occipital lobe immediately adjacent to where the metasurface was placed. The results shown in the present work are comparable to these previous results with the primary difference being lack of a high-permittivity material substrate and the anatomical region being imaged. However, in the context of the broader literature most metasurface development has been focused on image enhancement at 1.5T^22,24,27 and 3T^21,23. Furthermore, there has also been work that has focused on exclusively enhancing the receive field (B₁^-) rather than the transmit field, in contrast to what was done here^26,37. The general optimization procedure described here can also be applied to other field strengths as well as other nuclei of interest. In principle the characteristic impedance of the metasurface will only need to be further adjusted, corresponding to more capacitance for lower Larmor frequencies. This would be especially useful in multinuclear MRS applications where the intrinsic SNR is inherently low (e.g. ³¹P). Unfortunately, due to the tedious nature of the empirical testing described, simultaneous parameter optimization is not possible, but could be aided in the future via integration of EM solvers. One potential limitation of this optimization methodology is the manufacturer tolerance that is present in discrete capacitors. This may result in a slight change of the individual unit cell impedance values, however, the translation from a discrete board to a printed parallel plate design should compensate for this by providing a more consistent and controllable capacitance value across the metasurface.

Lastly, it should also be noted that acquired B₀ maps also showed no major deviations within the calf muscle caused by the metasurfaces being present in comparison to the reference. This is also compared to the dielectric pads which performed similarly to the reference case as well. This implies that no off-resonant effects should be expected from use of the metasurface and that sequences which rely on a homogenous B₀ field for accurate and adequate contrast generation, such as CEST and NOE-based techniques, could potentially benefit from the metasurfaces without major image degradation^40,41. These B₀ maps can be viewed in supporting information as Figure S7. Future work should be geared towards continued metasurface development that would include fine tuning the capacitive network by shifting from a constant valued network to a variable valued network, testing on more SAR-intensive sequences, and moving toward other anatomical regions such as brain via the use of multiple metasurfaces.

Conclusion

In this work, a flexible 7T metasurface is presented in which the design optimization process was characterized via phantom experimentation and subsequently tested for in vivo feasibility. Our results showed that the metasurfaces were able to substantially increase the relative SNR of anatomic GRE images by an average factor of 2.26±0.58 by increasing the local transmit field. Furthermore, these metasurfaces also performed better than the conventional calcium titanate dielectric pads which only improved the relative SNR of the images by an average factor of 1.61±0.48. This work offers an alternative approach towards enhancing the transmit field at 7T and in the future will be further developed and tested for neuroimaging applications.

Supplementary Material

Supinfo

Table S1. Calculated mean and standard deviation values for the relative B₁⁺ strength across the imaging slice for the reference phantom, the calcium titanate dielectric pads, and the various metasurface unit cell sizes. Both single and dual configurations are presented as well.

Figure S2. A plot showing the S21 parameter (left) and the S11 parameter (right) as a function of frequency for the four different unit cell sizes tested. Only the 21 mm unit cell size showed a slight self-resonance at 300 MHz.

Table S3. Maximum temperature increases for each metasurface configuration and fiber optic probe channel across the three experimental replicates. Calculated mean and standard deviation are also presented for the total replicated to illustrate the temperature increase variability.

Figure S4. Complementary GRE images in the sagittal orientation between the three experimental conditions for all five subjects imaged. Metasurfaces and dielectric pads were placed towards the distal end of the coil (top of the image) near the lower region of the calf. It can be observed that metasurfaces increase image SNR more in the case of the metasurface in comparison to the dielectric pad relative to the reference condition. The position of the metasurfaces can be seen visualized by the red dashed lines in the top right panel.

Figure S5. Noise correlation matrices without and with the metasurfaces present for subjects 2 and 5. A third column can be seen as the difference between the two showing only marginal differences, but with the larger effect coming from subject 2, the larger of the two.

Table S6. Transmit efficiency summary table showing the average and standard deviation values for each subject and experimental condition across the imaging slice shown.

Figure S7. Complementary delta B₀ maps from the corresponding axial GRE images showing the deviations from the center frequency for the reference case while in the presence of the dielectric pads and metasurfaces. It can be seen consistently across all subjects imaged that the B₀ maps showed minimal changes for either the dielectric pads or the metasurface case. The only region that can be seen having significant changes were in the marrow of the tibia and fibula.