Improving B1 homogeneity in abdominal imaging at 3 T with light and compact metasurface
Vsevolod Vorobyev, Alena Shchelokova, Alexander Efimtcev, Juan D. Baena, Redha Abdeddaim, Pavel Belov, Irina Melchakova, Stanislav Glybovski
aa r X i v : . [ phy s i c s . m e d - ph ] F e b FULL PAPERSubmitted to Magnetic Resonance in Medicine
Improving B homogeneity in abdominal imagingat 3 T with light and compact metasurface Vsevolod Vorobyev | Alena Shchelokova |Alexander Efimtcev | Juan D. Baena |Redha Abdeddaim | Pavel Belov | Irina Melchakova | Stanislav Glybovski Department of Physics and Engineering,ITMO University, Saint Petersburg, 197101,Russian Federation Department of Radiology, FederalAlmazov North-West Medical ResearchCenter, Saint Petersburg, 197341, RussianFederation Department of Physics, UniversidadNacional de Colombia, Bogota, 111321,Colombia Aix Marseille University, CNRS, CentraleMarseille, Institut Fresnel, F-13013,Marseille, France
Correspondence
Alena Shchelokova, Department of Physicsand Engineering, ITMO University, SaintPetersburg, 197101, RussiaEmail: [email protected]
Funding information
Purpose : Radiofrequency field inhomogeneity is a significant issue in imag-ing large fields of view in high- and ultrahigh-field MRI. Passive shimmingwith coupled coils or dielectric pads is the most common approach at 3 T.We introduce and test light and compact metasurface, providing the samehomogeneity improvement in clinical abdominal imaging at 3 T as a con-ventional dielectric pad.
Methods : The metasurface comprising a periodic structure of copper stripsand parallel-plate capacitive elements printed on a flexible polyimide sub-strate supports propagation of slow electromagnetic waves similar to ahigh-permittivity slab. We compare the metasurface operating inside atransmit body birdcage coil to the state-of-the-art pad by numerical sim-ulations and in vivo study on healthy volunteers.
Results : Numerical simulations with different body models show that thelocal minimum of B +1 causing a dark void in the abdominal domain is re-moved by the metasurface with comparable resulting homogeneity as forthe pad without noticeable SAR change. In vivo results confirm similar ho-mogeneity improvement and demonstrate the stability to body mass index.
Conclusion : The light, flexible, and cheap metasurface can replace a rela-tively heavy and expensive pad based on the aqueous suspension of bariumtitanate in abdominal imaging at 3 T.
KEYWORDS abdominal imaging, 3 T, B inhomogeneity, dielectric pad,metasurface, image shading, passive shimming | INTRODUCTION
Radiofrequency (RF) field inhomogeneity is a significant concern in high-field and ultrahigh-field imaging of a largeField Of View (FOV). It starts to appear at 3 T in abdominal imaging and becomes even more pronounced at higherfields (e.g., body and brain imaging at 7 T). At 3 T, the RF wavelength measures ≈ cm in the air while gettingshortened to ≈ cm when measured inside the body tissues. In this case, such wave effects as phase delay andreflection occur in the abdominal domain causing local constructive or destructive interference of B +1 field excited byany volume coil. This leads to corresponding brighter or darker areas of the image signal, i.e., the artifact referred toas the dielectric resonance, standing wave, or RF interference. At 3 T, the transverse FOV dimensions in most bodyimaging studies, such as abdominal and spinal imaging, and imaging of large water volume (e.g., pregnancy, ascites),are comparable to the wavelength. Therefore, the dielectric resonance effect highly deteriorates the imaging quality[1]. Clinical studies of the abdominal organs are associated with many nuances, the combination of which can playagainst obtaining high-quality diagnostic information. So, for individuals with large Body Mass Indices (BMIs), theartifact causes a decrease, or even loss of signal, in the area of the right and/or left lobe of the liver, the abdomenmiddle floor, and the pancreas [2]. The resulting signal minimum is pronounced when using fast spin-echo (FSE) andtrue fast imaging with steady-state precession (trueFISP) pulse sequences, which are the most important in assessingpathological changes in any localization. The radiologist relies on them to describe and clarify the nature of changesin images with different contrast. The decision to use additional protocols or contrast enhancement is often madeduring the scan, based on the T2-weighted images (T2WI). For example, small pancreatic neoplasms are sometimesasymptomatic and are found by accident. Therefore, in the presence of a pathological process in the artifact zone,the pathology may be missed, and the patient will not receive the necessary treatment. Tuning the parameters ofthese pulse sequences helps to avoid signal loss in the affected zone to a certain extent. The desired effect may beachieved by increasing the gap between slices or using spin-echo (SE) pulse sequences. However, in the first case,this will negatively affect the detection of small pathological changes. In the second one, it is inapplicable in the studyof the abdomen since breath-hold is required. Moreover, the above artifact is of particular relevance in the study ofthe fetus or placenta when the data obtained cannot be adequately interpreted, and the information content of thestudy drops significantly [3]. Definitely, in the above-described cases, additional measures to remove the artifact andimprove the homogeneity of B +1 at the hardware level become unavoidable.Various methods have been developed to homogenize the B +1 level across the Region Of Interest (ROI), includingthe parallel transmit (pTx) and passive shimming by coupled coils or dielectric pads (DPs). The pTx approach [4, 5, 6] car-ries out RF shimming by using multi-element transmit coils, elements of which are individually driven simultaneouslywith custom RF pulses sharing a standard gradient waveform. While the pTx approach has become useful for biomed-ical research, its application in clinics is limited by the hardware complexity and difficulties in ensuring a patient’s RFsafety during RF excitation with different shimming scenarios. The first passive shimming method uses surface RFcoils [7, 8], passively coupled to a driven volume transmit coil. The coupled coil typically has ≈ % higher resonantfrequency than the transmit coil. Therefore, the transmit coil induces conduction current in the coupled coil with aproper phase so that the corresponding secondary B +1 field adds constructively to the primary transmit field in theartifact region. However, the coupled coil has a considerable weight decreasing the patient’s comfort, and its presencebetween the human body and a local receive coil may decrease the latter’s sensitivity. Recently, an arrangement offour resonant wires has been proposed as a coupled element which possesses symmetric (electric) and anti-symmetric(magnetic) type of the induced current oscillations which facilitates the field pattern improvement without undesirablefeedback to the transmit coil [9]. The second widely known passive shimming approach is based on the application of sevolod Vorobyev et al. 3 high-permittivity dielectrics. Many examples of DPs locally modifying B +1 field of a standard transmit body birdcagecoil (BC) have been shown in the literature for cardiac [10, 11, 12], abdominal [13], and fetal [14] imaging at 3 T. Incontrast to the passive coils, in this method, the secondary field required for homogeneity improvement is createddue to induced displacement currents. Thus, by placing a DP over the ROI, the overall B +1 level is equalized [15]. Thethinner the pad, the higher its relative permittivity is required to remove the artifact [16]. Pads should be speciallydesigned for different ROIs and vary in dimensions, thickness, and permittivity of the filling material, usually based onmixtures of liquids and ceramic powders. Despite being a widely-accepted and simple technique, composite ceramicpads have several common drawbacks. Their material parameters can change with time, some materials they maycontain are bioincompatible, and they are heavy (typically weight several kilograms) [17].One of the proposed ways of solving DPs’ problems is replacing the composite ceramic-based mixture with anartificial dielectric metamaterial. The previous study [18] has reported that for brain imaging at 7 T, a DP can bereplaced by an artificial dielectric slab made of stacked Printed Circuit Boards (PCBs) carrying periodically arrangedcopper patches. The signal homogeneity was shown to improve similarly for the pad and slab when their dimensionsare the same, and the effective permittivity of the artificial dielectric is equal to the pad ones. The proposed slabconsisted of low-cost boards, its properties were stable in time, and it was much lighter in weight than the DP. However,the proposed slab was rigid and operated in only one position to the head (parallel to the axial plane). Therefore, itallowed homogenizing B +1 field only in the parietal lobes, whereas temporal lobes imaging is more important in clinicalstudies. Therefore, for brain imaging at 7 T, a PCB structure is needed to replace the DP in a position parallel tothe sagittal plane. Moreover, it is rather important to replace DPs at 3 T, where the dedicated DPs for cardiac andabdominal studies, typically placed in parallel to the coronal plane, are especially heavy.In this paper, we introduce a better alternative to the DPs. An ultra-thin and light periodic structure called themetasurface (MS) is proposed for removing the B +1 inhomogeneity artifact in abdominal imaging at 3 T, providing thesame effect as a dedicated DP.MSs are thin two-dimensional periodic structures with periodicity and thickness both much smaller than thewavelength, which can modify the applied electromagnetic field in a desirable way [19]. When excited by the externalfield, each unit cell of an MS produces a secondary RF field. The secondary field collectively created by all periodicallyarranged unit cells of the MS is similar to the field of a uniform sheet with electric and/or magnetic surface currents.By engineering the unit cells, it is possible to control the RF field’s characteristics, such as magnitude, phase, andpolarization, at least at distances larger than one period from the MS. MSs were first introduced in MRI in [20], wherea periodic rectangular structure of thin parallel wires immersed in water was used as a resonator passively coupledto a BC. This MS almost entirely concentrated the whole energy of B +1 field of the coil in the wires’ vicinity due toresonant excitation of one of the resonant surface modes. This effect locally increased the transmit efficiency andSignal-to-Noise Ratio (SNR) of the BC. The water-filled wire MS was followed by several modifications proposed forthe same type of resonant focusing operation [21, 22, 23, 24, 25, 26, 27, 28], and some alternative MS-based coupledresonators were proposed (e.g., [29, 30]).Here, we design an ultimately thin MS providing the same non-resonant electromagnetic response to an externalBC and making the same effect to B +1 in the artifact region as a given DP optimized for abdominal imaging at 3 T. Theunit cells of the proposed MS should create the same secondary B +1 field as same-sized fractions of the pad. Sincenon-resonant and small dielectric bodies support displacement currents (capacitive response), the same MS unit cellsshould do. With this aim, we introduced an MS comprised of a two-dimensional periodic structure of parallel-platecapacitors printed on two sides of a thin and flexible polyimide substrate and interconnected with thin copper strips.This capacitively-loaded grid was initially proposed for frequency-selective transmission of incident plane waves [31].We show that with an adjusted capacitance of the parallel-plate elements, this structure slows down an external Vsevolod Vorobyev et al. (A (B) ( (cid:1) ) С С СС ll LL W
ССС С С С С СССС СССССС ССС С С С l С С С С С С xz W L (D)
Dielectric WaveguideWaveguide port l xyz С Top-side metallizationBottom-side metallizationSubstrateCopper stripsParallel- platecapacitors
120 122 124 126 1281015202530
Frequency, MHz R e l a t i v e s l o w f a c t o r , % (F)(E) WaveguideWaveguide port
Metasurface unit cells
FIGURE 1 Metasurface (MS) modeling and comparison to a dielectric pad (DP): (A) schematic representation of theMS based on a capacitively-loaded grid (inset shows the topology of the strips loaded with capacitors); (B) one rowof MS’ unit cells placed in a parallel-plate waveguide; (C) schematic representation of the DP; (D) fraction of adielectric layer inside a parallel-plate waveguide; (E) Practical realization of the MS based on a dual-sided printedcircuit board (four unit cells are shown); (F) Numerically calculated wave deceleration ratio (in percents) as a functionof frequency.electromagnetic wave similar to a slab of ceramics with permittivity of 300 (optimal for abdominal imaging). Numericalsimulations and in vivo experiments confirm an equivalence between the effects of the pad and MS. | METHODS2.1 | Metasurface design and optimization
The proposed MS constitutes a square grid of copper strips of width w = 0 . cm with periodicity l = 2 cm printedon a thin dielectric substrate. Each strip is split in its center, and a capacitor with capacitance C is connected to thesplit. Therefore a capacitively-loaded grid is formed [31]. The MS is schematically depicted in Fig. 1(A) with an insetshowing the topology of the strips loaded with capacitors.To behave similarly to a DP of the given permittivity, the unit cells of the MS should possess the same displacementcurrents as induced in the same-sized fractions of the dielectric later of the pad. For certainty, we considered a DPhaving the permittivity of approximately 300 found to be optimal for abdominal imaging with dimensions L × L = sevolod Vorobyev et al. 5 × cm and thickness W = 1 . cm, previously optimized for fetal imaging of 7-months pregnant woman [14]. Theoptimization goal for the proposed MS was to obtain the same displacement current in each unit cell as in the portionof the pad with the same in-plane dimensions l × l = 2 × cm . This condition should be met for an electromagneticwave propagating along the MS. It is assumed that in the MS, all the displacement current is localized in the capacitors,which is valid for small cells in comparison to the wavelength.The value of the displacement current in the unit cell is controlled by capacitance C , which was determined fromthe numerical comparison of two models shown in Fig. 1(B,D). The first one is a single row of n =14 unit cells of the MSarranged in the z direction and placed in a parallel-plate waveguide as shown in Fig. 1(B). The waveguide is composedof two metal plates placed parallel to x z at a distance l from each other. Since the y -directed strips in each unit cellare split and connected to the metal plates, two series-connected capacitors with double capacitance 2 C are modeledinstead of one capacitor with capacitance C as depicted in the inset of Fig. 1(B). Note that the dielectric substrate’spresence has a negligible effect on the MS’s properties and was omitted in the model of Fig. 1(B). The second modelis a fraction of the pad with the same overall dimensions L × l = 28 × cm as the MS row and thickness W = 1 . cm,placed into the same parallel-plate waveguide (see Fig. 1(D)). The equivalence between both models implies that theircapacitance per unit length in z -direction is the same, which can be observed in the numerical simulation as the samephase delay of a slow electromagnetic wave [32] propagating between two waveguide ports. The above comparisonshows the equivalence only to a wave propagating along the waveguide in z -direction with y -polarized electric fieldand x -polarized magnetic field. This scenario corresponds to the RF field characteristics at a pad’s position at theperiphery of a transmit BC when it is positioned parallel to the sagittal or coronal plane.Simulations of both models shown in Fig. 1(B,D) were made using CST Microwave Studio commercial software(Frequency Domain Solver). The phase delay was determined as ϕ = arg ( S ) , i.e., the phase of the complex transmis-sion coefficient between the ports at the Larmor frequency of protons at 3 T ( f = 123 MHz). From the last quantity, aneffective phase velocity υ phase = ( πf · nl )/ ϕ of the wave propagating along the MS and DP can be estimated, whichis much smaller as for free-space propagation in both cases. To compare the MS to the pad, we introduce the wavedeceleration ratio (WDR) equal to WDR = ( ϕ dielectric − ϕ metasurface )/ ϕ dielectric . The best correspondence between theMS and DP is achieved at WDR of 0.We have chosen the MS period of 2 cm based on the reasons explained in the discussion section. For l = 2 cmand w = 0 . cm, we found the capacitance C = 40 pF for equivalence to the pad. In the practical realization of theMS, the capacitors were implemented as paired square parallel copper plates with dimensions of d × d = 5 . × . cm printed on the opposite sides of a substrate with thickness t = 25 µ m with relative permittivity ε s = 3 . and dielectricloss tangent of 0.002. The capacitance was estimated using the formula of a parallel-plate capacitor: C = ε s ε d / t with ε = 8 . pF/m. In the MS layout, the closest strips are also located at different sides of the substrate for properlyconnecting the adjacent capacitors, as shown in Fig. 1(E). The resulting WDR as a function of frequency is shown inFig. 1(F), showing that the optimized MS provides the same phase delay as the pad with the accuracy of 13.5% at 123MHz. | RF simulations
The optimized pad was numerically characterized when placed into the RF field of a two-port high-pass BC tunedto 123 MHz in the presence of several voxel models of the human body. The B +1 field and local SAR patterns insidethe body were calculated using CST Microwave Studio commercial software (Time Domain Solver). The transmit coilhad a diameter of 70 cm, a length of 49 cm, and a shield diameter of 76 cm. These dimensions correspond to theBC on a standard-bore 3 T system. A set of three voxel body models from the CST Voxel Family was used in the Vsevolod Vorobyev et al. simulations, including Emma (26-years-old female with BMI of 28.0 kg/m ), Gustav (38-years-old old male with BMIof 22.3 kg/m ), and Hugo (38-years-old male with BMI of 31.8 kg/m ).A high-permittivity DP with dimensions of × × . cm , relative permittivity of 300, and conductivity of 0.4S/m was used. This permittivity value was previously found to be optimal for abdominal imaging, and the dimensionswere previously selected for fetal imaging of a 7-months pregnant woman [14]. Simultaneously, the conductivity wasfound to have a minor effect on the pad’s performance inside a BC.The MS was designed to have the same in-plane dimensions as the DP and was located in simulations at the samedistance of 0.5 cm from the abdomen surface. The MS had the same shape of unit cells as described in the previoussubsection for the practical realization with optimized square parallel-plate printed elements.The B +1 field and local Specific Absorption Rate (SAR) were calculated assuming 1 W of accepted power and twoperfectly matched BC’ ports driven in quadrature. SAR was averaged over 10 g of body tissues. To analyze the effectof the pad or MS on B +1 inside the human body models, the coefficient of variation Cv was used. Cv (measured inpercents) was calculated as the standard deviation of the B +1 magnitude divided by its mean value calculated acrossthe given ROI in the abdominal region and multiplied by 100. This coefficient was chosen as B +1 field homogeneityfigure of merit as proposed in [13]. | Experimental study
The manufactured high-permittivity DP shown in Fig. 2(A) had the same dimensions and properties as in the simula-tions. It was based on a polyethylene package filled with a powder of BaTiO ceramics mixed with heavy water. Theweight of this pad was 3290 g.The MS shown in Fig. 2(A,B,C) was manufactured as a flexible PCB with dual-layer copper metallization and aprotective mask. The MS corresponds to the simulation model except for four rectangular cuts made on the edges. Thecuts were made to avoid undesirable Fabry-Perot-type resonances at 123 MHz, as further discussed. The substratematerial was DuPont Pyralyx AP8515R with a polyimide thickness of 25 µ m, and a copper thickness of 18 µ m, whichmade the MS easily flexible (Fig. 2(B)), as well as ultralight (the weight of the MS is equal to tens of grams). A close-uplook at the MS’s inner structure can be seen in Fig. 2(C). The semi-transparent substrate allows one to see copperstrips printed on both sides: light-brown strips are on the top, and dark-brown ones are on the substrate’s bottom.Each pair of neighboring strips from different sides is connected through a capacitance of two square plates printedone against the other. In vivo scanning was performed using Siemens Magnetom Trio A Tim 3 T whole-body MRI scanner (Siemens,Germany) with a bore diameter of 60 cm at the Almazov National Medical Research Center. An MRI sequence usedfor imaging was a T2-weighted HASTE sequence with acquisition parameters: FA= ◦ , TR/TE= / ms, acquisitionmatrix= × , FOV= × mm . The receive coil used for the acquisition was either a Body Matrix Coil (localparallel receive coil with six channels) combined with two channels of Spine Matrix Coil or a BC (the same coil as intransmit). During in vivo comparison of the pad and MS, three volunteers with different BMIs were tested: Volunteer , Volunteer , Volunteer . Thescans were obtained under authorization by the local ethics committee (decision document dated July 20, 2020), andinformed consent was obtained from each volunteer before the study. sevolod Vorobyev et al. 7 ( A ) L = c m L=
28 cm L = c m L =28 cm ( B ) ( С ) Copper strips Parallel-plate capacitors
FIGURE 2 To the experimental comparison: (A) manufactured dielectric pad (on the left) and the metasurface (onthe right) used in in vivo tests. (B) Demonstration of the metasurface flexibility. (C) A close-up look at themetasurface showing its periodic copper pattern elements compared to a coin ( ≈ | RESULTS3.1 | RF simulations
Fig. 3 shows simulated B +1 maps for the three different voxel models (Emma, Gustav, Hugo) in three cases: (A,B,C)reference case with the BC without any DP or MS; (D,E,F) with the DP or (G,H,I) with the MS attached on the top ofthe abdomen. The figure of merit was calculated as described in Methods and is denoted as Cv in each calculated B +1 map. The ROI used to calculate Cv for each case is shown by a dashed line.As can be seen, all three voxel models have inhomogeneous B +1 field created by the coil with a pronouncedinterference minimum in the central part of the ROI. In the reference case, the inhomogeneity defined by Cv is similaracross all three models. However, the minimum is more visible and is characterized by a lower field level for biggerBMI values. For two voxel models (Emma and Gustav), the DP and MS decrease Cv and improve homogeneity. Notethat the lowest Cv with the best homogeneity is achieved for Emma. For the Hugo voxel model, the MS increases the B +1 field in the nearby area but decreases the overall homogeneity Cv in the ROI. At the same time, the DP offers onlya minor homogeneity improvement.Fig. 4 shows numerically calculated local SAR corresponding to the same three cases and three voxel models. Thepatterns are shown in the same cross-sections as B +1 in Fig. 3. The peak SAR value increases for all three voxel modelswhen the DP or MS is inserted, while the maximum location does not change. | Experimental study
Experimentally obtained MR images in the transverse plane of the abdominal cavity of three healthy volunteers withdifferent BMI are shown in Fig. 5 and Fig. 6. For the images shown in Fig. 5, the BC was used for transmitting, and a
Vsevolod Vorobyev et al.
Emma Gustav Hugo
Cv=25.8%Cv=9.8%Cv=11.8% (A) ( С )(D) (E) (F) (G) (H) (I) Cv=21.4% Cv=23.6% D i e l e c t r i c p a d c a s e M e t a s u r f a c e c a s e R e f e r e n c e c a s e (B) Cv=14.7% Cv=22.7%Cv=15.8% Cv=31.1% + |B | (uT) FIGURE 3 The numerically calculated magnitude of B +1 for three voxel models for the cases: (A,B,C) reference casewith voxel model only; (D,E,F) with the dielectric pad attached to the top of the abdomen; (G,H,I) with themetasurface attached to the top of the abdomen.local Body Matrix Coil was used for receive. For the results presented in Fig. 6, we used the BC for both transmit andreceive. In both experiments, we compared three cases: reference case with no DP or MS used; DP case, where theDP was attached on the top of an abdomen; MS case, where the MS was attached on the top of an abdomen. Duringthe scans, the DP was placed directly on each volunteer’s body without any spacers. When a local receive coil wasused (see photographs in Fig. 5), the pad was placed between the coil and the body. The MS was covered from bothsides with a 0.5-cm-thick foam spacer to avoid imaging artifacts caused by the periodicity of the secondary local RFfield created by the MS unit cells. The bottom-side spacer was placed directly to the body. When a local receive coilwas used, the coil was placed over the top-side spacer of the MS.In Fig. 5(A,B,C), a dark region with a low signal (marked by the red dashed line) can be seen in the top area of theabdomen for all three volunteers, being most prevalent for Volunteer sevolod Vorobyev et al. 9 Hugo S AR (W/kg) D i e l e c t r i c p a d c a s e M e t a s u r f a c e c a s e R e f e r e n c e c a s e Emma Gustav maxSAR =0.06W/kg
ROI maxSAR =0.06W/kg
ROI maxSAR =0.08W/kg
ROI maxSAR =0.07W/kg
ROI maxSAR =0.07W/kg
ROI maxSAR =0.10W/kg
ROI maxSAR =0.09W/kg
ROI maxSAR =0.08W/kg
ROI maxSAR =0.09W/kg
ROI (A) ( (cid:0) )(D) (E) (F)(G) (I)(B)(H)
FIGURE 4 Local SAR averaged over 10 g of tissue of three voxel models for three cases: (A,B,C) reference casewith voxel model only; (D,E,F) with the dielectric pad was attached on the top of the abdomen; (G,H,I) withmetasurface attached on the top of the abdomen.Fig. S1 in the supplementary data shows three different transverse slices of Volunteer | DISCUSSION AND CONCLUSION
The proposed MS was designed to have the same effect on the BC’s transmit field as a DP, i.e., a flat dielectric layermade of a high-permittivity dielectric. It means that when excited by the transmit coil, each unit cell of the MSshould support the same displacement current and create the same secondary B +1 field as the pad’s fraction of thesame dimensions. As was previously shown, the pad can create a sufficient secondary B +1 field level to remove theinterference medium inside the human body’s abdominal region when having the permittivity of about 300 and athickness of 1.5 cm. Such a DP can only be constructed using quite expensive ceramic materials making the slabheavy. Indeed, a DP with several kilograms is uncomfortable for the patient to wear on the stomach during the scan.On the other hand, the same induced displacement current per unit length of the pad can also be effectivelyinduced in ultra-thin and flexible MS periodic unit cells. With this aim, we realized the unit cells as printed copper Volunteer D i e l e c t r i c p a d c a s e M e t a s u r f a c e c a s e R e f e r e n c e c a s e E x p e r i m e n t p h o t o s (A) (С)( )D ( )E ( )F( )G ( )B( )H ( )I FIGURE 5 MR images of three healthy volunteers obtained with Body Matrix Coil used as a receive coil. Threecases were considered: (A,B,C) reference case with voxel model only; (D,E,F) with the dielectric pad was attached onthe top of the abdomen; (G,H,I) with the metasurface attached on the top of the abdomen. sevolod Vorobyev et al. 11 V o(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8) (cid:9)(cid:10) V (cid:11)(cid:12)(cid:13)(cid:14)(cid:15)(cid:16)(cid:17)(cid:18) (cid:19) V (cid:20)(cid:21)(cid:22)(cid:23)(cid:24)(cid:25)(cid:26)(cid:27) D i e l e c t r i c p a d c a s e M e t a s u r f a c e c a s e R e f e r e n c e c a s e (A) ( С )(D) (E) (F)(G) (B)(H) (I) FIGURE 6 MR images of three healthy volunteers obtained with volumetric body coil used as a receive coil, forthree cases: (A,B,C) reference case with voxel model only; (D,E,F) with the dielectric pad was attached on the top ofthe abdomen; (G,H,I) with the metasurface attached on the top of the abdomen.strips split and connected via parallel-plate printed capacitors. As all the metal parts are printed on two sides of a 25- µ m-thick dielectric substrate, the entire MS is cheap to manufacture, flexible, and very light (less than 100 g togetherwith a foam spacer). This miniaturization requires compact capacitors in each unit cell instead of a distributed ceramicmaterial of the pad. The sufficiently high level of the unit-cell capacitance was achieved thanks to a small separationbetween printed parallel plates equal to the substrate thickness.The parallel-plate capacitors’ capacitance was optimized to have the same properties as the DP for abdominalimaging at 3 T with permittivity of 300. To adjust the capacitance, making the MS equivalent to the pad, we proposeda parallel-plate waveguide model analyzed numerically. In this model, the wave propagating along one row of MS unitcells or a break fraction of the pad with the same in-plane dimensions having an electric field polarized in parallel theMS/pad should experience the same phase delay. In other words, both systems behave as slow-wave transmissionlines [32, 33, 34] with the same phase velocity at the Larmor frequency. The MS and DP excitation inside the waveg-uide is similar to real characteristics of the BC transmit field at its periphery. Indeed, the wave propagation directionand polarization correspond to a wave traveling around a BC’s circumference when forming a fundamental CP mode.Advantageously, the proposed waveguide model is much simpler to optimize numerically than a full MS inside the coil. Once the MS cell’s capacitance is optimized in the waveguide, the full-sized two-dimensional MS behaves similarly tothe DP of the same in-plane dimensions.Despite the collective effect of the MS unit cells on B +1 field was the same, which was confirmed by full-wavenumerical simulations (Fig. 3, Fig. 4) and imaging tests (Fig. 5, Fig. 6), there are some fundamental differences betweena continuous ceramic slab and a periodic slow-wave structure that need to be considered when designing any new MS.The first significant limitation is that the secondary B +1 field of the MS compares to one of the DP only at distancesfrom its plane larger than 1/4-1/2 of the period. Otherwise, the discreteness of the secondary B +1 may affect theimage (the case illustrated in Fig. S3 with a spatially-periodic signal modulation in the vicinity of the MS). Thus, theMS with a 2-cm-period should be separated from the body by at least 0.5 cm-thick foam spacer, while the DP canbe placed onto the body without any gap. The second limitation consists in the limited slow-wave behavior. DPsreported in the literature usually have a relative permittivity in the range from 100 to 300. The lower the Larmorfrequency and the static field B , the larger the required pad permittivity. However, a periodic MS can provide phasedelays only smaller than ◦ per one period due to Bragg’s frequency limit [32]. For the chosen period of 2 cm, themaximum achievable phase delay corresponds to the effective permittivity limit of 3600. Generally, to reach slowerwave propagation and approximate larger permittivity values and larger thicknesses of the pad, it is reasonable tokeep the period as small as possible. On the other hand, as the period decreases, the unit cell’s required capacitancebecomes hard to implement using parallel plates printed on a substrate. In our case, 2 cm allowed us to accommodateparallel-plate capacitors with the required capacitance inside the unit cells using only one PCB layer. If a pad withhigher permittivity and/or thickness is approximated, the capacitance should be increased while keeping the sameperiod. With this aim, lumped surface-mount-device capacitors or multi-layer PCBs could be used.Another critical issue of the proposed MS is the possible excitation of surface resonant modes (standing waves)inside the periodic structure, which needs to be avoided. As follows from the comparison with the waveguide model,both the high-permittivity slab and MS can guide slow-waves, which can, in principle, experience multiple reflectionsfrom the structure’s edges and produce standing-wave mode resonances. While this edge effect in DPs is suppresseddue to high losses, standing waves’ excitation in the low-loss MS may result in high deviation from the expectedeffect on B +1 . Similar edge effects were previously studied in arrays of capacitively coupled strips in [35]. In thepractical MS, all standing-wave resonances’ spectral positions strongly depend on the unit cells’ total amount. Aftermanufacturing the PCB, the standing-wave resonances were controlled by measurements and made different fromthe Larmor frequency by slightly modifying the structure. We have cut from an initially square pattern two unit cellsfrom each edge as shown in Fig. 2(A) to ensure that no narrow-band resonance is observable around 123 MHz. Thisfact was detected by estimating a surface-loop probe’s reflection response placed horizontally over the MS center.The scheme of the setup and example curves of the frequency response before and after modification are shown insupplementary Fig. S4. When working accidentally at the frequency of one of the standing-wave resonances, the MSturns to a focusing resonant surface coil and does not operate as a non-resonant pad.In the previous study [18], we have shown the feasibility of replacing a DP for brain imaging at 7 T with an artificialdielectric slab, limited to improving field homogeneity in the area that was not clinically valuable. In this work, we havesuccessfully replaced a DP in its proper position against the body with an even thinner, two-dimensional, and flexibleperiodic structure, i.e., an MS. We designed the MS to operate similarly to a state-of-the-art DP for abdominal imagingat 3 T. Pads used in this application are especially heavy during large thicknesses and high density of ceramic powders.We have demonstrated in simulations and experimentally that the MS can remove the B +1 inhomogeneity artifact inthe abdomen similar to the pad. Moreover, the proposed MS has shown the same stability of the field homogenizationeffect to a variation of BMI of the patient as the pad. No additional SAR hot-spot has been observed in the simulations.The materials (polyimide films) required for manufacturing are widely available on the market and cheap. The man- sevolod Vorobyev et al. 13 ufacturing process itself, which comes down to printing a layout on a PCB, is a service that is also very widespread andinexpensive for mass production. The manufacturing cost of the considered prototype was around 100 USD. UnlikeDPs, the MS weights incomparably less than one kilogram, and it will last longer in working order. The proposed topol-ogy and the explained design procedure can be adopted for replacing DPs with different thickness and permittivityvalues used in other imaging tasks at different static fields. We believe the proposed MS will become a reasonablealternative to DPs in clinical and research MRI. Conflict of interest
Authors declare no conflict of interests. references [1] Christianson KL, Mangrum W. Duke Review of MRI Principles: Case Review Series. In: Mosby; 1st edition; 2012. p. 304pages.[2] Yang RK, Roth CG, Ward RJ, deJesus JO, Mitchell DG. Optimizing abdominal MR imaging: approaches to commonproblems. Radiographics 2010;30(1):185–199.[3] Semenova ES, Mashchenko I, Trufanov GE, Fokin V, Efimtsev AY, Lepekhina AS, et al. Magnetic resonance imaging duringpregnancy: Current safety issues. Russian Electronic Journal of Radiology 2020 01;10:216–231.[4] Grissom W, Yip Cy, Zhang Z, Stenger VA, Fessler JA, Noll DC. Spatial domain method for the design of RF pulses inmulticoil parallel excitation. Magnetic Resonance in Medicine 2006;56(3):620–629.[5] Grissom WA, Sacolick L, Vogel MW. Improving high-field MRI using parallel excitation. Imaging in Medicine2010;2(6):675–693.[6] Raaijmakers AJE, Ipek O, Klomp DWJ, Possanzini C, Harvey PR, Lagendijk JJW, et al. Design of a radiative surface coilarray element at 7 T: The single-side adapted dipole antenna. Magnetic Resonance in Medicine 2011;66(5):1488–1497.[7] Schmitt M, Feiweier T, Voellmecke E, Lazar R, Krueger G, Reykowski A. B1-Homogenization in abdominal imaging at 3Tby means of coupling coils. In: Proc Intl Soc Mag reson Med, vol. 13; 2005. .[8] Wang S, Murphy-Boesch J, Merkle H, Koretsky AP, Duyn JH. B1 homogenization in MRI by multilayer coupled coils.IEEE Trans Med Imaging 2009;28(4):551–554.[9] Dubois M, Leroi L, Raolison Z, Abdeddaim R, Antonakakis T, de Rosny J, et al. Kerker Effect in Ultrahigh-Field MagneticResonance Imaging. Phys Rev X 2018 Sep;8:031083.[10] Brink WM, Webb AG. High permittivity pads reduce specific absorption rate, improve B1 homogeneity, and increasecontrast-to-noise ratio for functional cardiac MRI at 3 T. Magnetic resonance in medicine 2014;71(4):1632–1640.[11] de Heer P, Bizino MB, Versluis MJ, Webb AG, Lamb HJ. Improved cardiac proton magnetic resonance spectroscopy at3 T using high permittivity pads. Investigative radiology 2016;51(2):134–138.[12] Brink WM, van den Brink JS, Webb AG. The effect of high-permittivity pads on specific absorption rate in radiofrequency-shimmed dual-transmit cardiovascular magnetic resonance at 3T. Journal of Cardiovascular Magnetic Resonance2015;17(1):82.[13] De Heer P, Brink W, Kooij B, Webb A. Increasing signal homogeneity and image quality in abdominal imaging at 3 T withvery high permittivity materials. Magnetic resonance in medicine 2012;68(4):1317–1324. [14] van Gemert J, Brink W, Remis R, Webb A. A simulation study on the effect of optimized high permittivity materials onfetal imaging at 3T. Magnetic resonance in medicine 2019;82(5):1822–1831.[15] Webb AG. Dielectric materials in magnetic resonance. Concepts in Magnetic Resonance Part A 2011;38A(4):148–184.[16] Teeuwisse WM, Brink WM, Haines KN, Webb AG. Simulations of high permittivity materials for 7 T neuroimaging andevaluation of a new barium titanate-based dielectric. Magnetic Resonance in Medicine 2012;67(4):912–918.[17] Neves AL, Leroi L, Raolison Z, Cochinaire N, Letertre T, Abdeddaïm R, et al. Compressed perovskite aqueous mixturesnear their phase transitions show very high permittivities: New prospects for high-field MRI dielectric shimming. Mag-netic resonance in medicine 2018 06;79:1753.[18] Vorobyev V, Shchelokova A, Zivkovic I, Slobozhanyuk A, Baena JD, Del Risco JP, et al. An artificial dielectric slab for ultrahigh-field MRI: Proof of concept. Journal of Magnetic Resonance 2020;320:106835.[19] Glybovski SB, Tretyakov SA, Belov PA, Kivshar YS, Simovski CR. Metasurfaces: From microwaves to visible. PhysicsReports 2016;634:1 – 72. Metasurfaces: From microwaves to visible.[20] Slobozhanyuk AP, Poddubny AN, Raaijmakers AJE, van den Berg CAT, Kozachenko AV, Dubrovina IA, et al. Enhancementof Magnetic Resonance Imaging with Metasurfaces. Advanced Materials 2016;28(9):1832–1838.[21] Glybovski SB, Shchelokova AV, Kozachenko AV, Slobozhanyuk AP, Melchakova IV, Belov PA, et al. Capacitively-loadedmetasurfaces and their application in magnetic resonance imaging. In: 2015 Radio and Antenna Days of the IndianOcean (RADIO); 2015. p. 1–2.[22] Schmidt R, Slobozhanyuk A, Belov P, Webb A. Flexible and compact hybrid metasurfaces for enhanced ultra high fieldin vivo magnetic resonance imaging. Scientific Reports 2017 May;7(1):1678.[23] Shchelokova AV, Slobozhanyuk AP, Melchakova IV, Glybovski SB, Webb AG, Kivshar YS, et al. Locally Enhanced ImageQuality with Tunable Hybrid Metasurfaces. Phys Rev Applied 2018 Jan;9:014020.[24] Shchelokova AV, Slobozhanyuk AP, de Bruin P, Zivkovic I, Kallos E, Belov PA, et al. Experimental investigation of ametasurface resonator for in vivo imaging at 1.5 T. Journal of Magnetic Resonance 2018;286:78–81.[25] Shchelokova AV, van den Berg CAT, Dobrykh DA, Glybovski SB, Zubkov MA, Brui EA, et al. Volumetric wirelesscoil based on periodically coupled split-loop resonators for clinical wrist imaging. Magnetic Resonance in Medicine2018;80(4):1726–1737.[26] Brui EA, Shchelokova AV, Zubkov M, Melchakova IV, Glybovski SB, Slobozhanyuk AP. Adjustable SubwavelengthMetasurface-Inspired Resonator for Magnetic Resonance Imaging. Physica Status Solidi (a) 2018;215(5):1870012.[27] Kretov EI, Shchelokova AV, Slobozhanyuk AP. Control of the magnetic near-field pattern inside MRI machine withtunable metasurface. Applied Physics Letters 2019;115(6):061604.[28] Saha S, Pricci R, Koutsoupidou M, Cano-Garcia H, Katana D, Rana S, et al. A smart switching system to enable automatictuning and detuning of metamaterial resonators in MRI scans. Scientific Reports 2020 Jun;10(1):10042.[29] Yang T, Ford KL, Rao M, Wild J. A Single Unit Cell Metasurface for Magnetic Resonance Imaging Applications. In: 201812th International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials); 2018. p. 131–133.[30] Issa I, Ford KL, Rao M, Wild JM. A Magnetic Resonance Imaging Surface Coil Transceiver Employing a Metasurface for1.5T Applications. IEEE Transactions on Medical Imaging 2020;39(4):1085–1093.[31] Anderson I. On the theory of self-resonant grids. The Bell System Technical Journal 1975;54(10):1725–1731.[32] Elachi C. Waves in active and passive periodic structures: A review. Proceedings of the IEEE 1976;64(12):1666–1698. sevolod Vorobyev et al. 15 [33] Gorur A. A novel coplanar slow-wave structure. IEEE microwave and guided wave letters 1994;4(3):86–88.[34] Yang FR, Qian Y, Coccioli R, Itoh T. A novel low-loss slow-wave microstrip structure. IEEE Microwave and Guided WaveLetters 1998;8(11):372–374.[35] Cavallo D, Syed WH, Neto A. Equivalent Transmission Line Models for the Analysis of Edge Effects in Finite Connectedand Tightly Coupled Arrays. IEEE Transactions on Antennas and Propagation 2017;65(4):1788–1796.
Supplementary Material
Improving B1 homogeneity in abdominal imaging at 3 T with light and compact metasurfaceV. Vorobyev et al.The Supplementary Information includes 4 Supplementary Figures. V (cid:29)(cid:30)(cid:31)!"$%& S’()* +, -./01 23 R e f e r e n c e c a s e D i e l e c t r i c p a d c a s e M e t a s u r f a c e c a s e FIGURE S1 Experimentally measured MR scans of volunteer sevolod Vorobyev et al. 17 V <=>?@ AB CDEFG HI R e f e r e n c e c a s e D i e l e c t r i c p a d c a s e M e t a s u r f a c e c a s e FIGURE S2 Experimentally measured MR scans of volunteer M e t a s u r f a c e c a s e Dist ance between the metasurface and the body:0.5 cm 1 cm