Computational and experimental evaluation of the Tic-Tac-Toe RF coil for 7 Tesla MRI

A variety of 7 Tesla RF coil systems have been proposed to produce spin excitation (B1+ field) and MR image acquisition. Different groups have attempted to mitigate the challenges at high and ultra-high field MRI by proposing novel hardware and software solutions to obtain uniformly high spin excitation at acceptable RF absorption levels. In this study, we extensively compare the designs of two distributed-circuit based RF coils: the Tic-Tac-Toe (TTT) head coil and TEM head coil on multiple anatomically detailed head models and in-vivo. Bench measurements of s-parameters and experimental B1+ field distribution were obtained in volunteers and compared with numerical simulations. RF absorption, quantified by both average and peak SAR, and B1+ field intensity and homogeneity, calculated/measured in terms of maximum over minimum and coefficient of variation (CV) in the region of interest (ROI), are presented for both coils. A study of the RF consistency of both coils across multiple head models for different RF excitation strategies is also presented.

At UHF frequencies, the human head size becomes comparable to the RF wavelength (at 7T, the wavelength is approximately 13cm in the brain tissues). As a result, the electromagnetic interactions between the human body/head and the RF coil become increasingly sensitive to variations in the size/shape of the sample [14]. Such interactions can lead to significant variations in the distribution/intensity of the circularly polarized component responsible for a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 excitation (B 1 + ) field as well as specific absorption rate (SAR) across different subjects. This issue in addition to the inherent electromagnetic field inhomogeneity and elevated RF power deposition associated with UHF human imaging can have detrimental effects on the quality and safety in high field MRI. Moreover, it is important to assure that the RF excitation does not result in localized SAR across different subjects [15]. While many electromagnetic simulation tools are currently used to calculate estimates of SAR for RF shimming purposes [16,17], B 1 + fields are typically experimentally measured/mapped in an experimental setting.
The adoption of multichannel RF coil designs for UHF MRI allows for multiple degrees of freedom in manipulating the RF fields [18]. As a result, several designs of RF transmit arrays have been proposed to improve RF coil performance, mainly evaluated in its capability to produce homogenous B 1 + field distributions at acceptable levels of RF tissue absorption [19][20][21].
It is worth noting however, that several MR sequences and pulse designs can also improve the homogeneity of the spin excitation (as opposed to B 1 + field distribution), such as adiabatic pulses [22,23], tailored pulses [24,25], and transmit SENSE [26,27] or interleaved excitation of the modes with TIAMO [28,29]. Many studies have been done to evaluate coil performance and safety assurance at 7T. Wolf et.al. 2013 carried out a comprehensive study of different human body models at 7T using a 16-element band-pass Birdcage coil, to assess how much detail is needed to accurately predict local SAR. In addition to looking at current distributions and SAR in different models, the paper compared local SAR hotspots in Duke (male) and Ella (female) virtual family models. Wang et.al. [30] compared B 1 + homogeneity and SAR in a sphere at 7T for a 16-element birdcage, transverse electromagnetic resonator (TEM) and microstrip coils. The results showed that the B 1 + homogeneity in the central axial plane of the sphere in the TEM coil was most homogeneous, with marginal difference in B 1 + inhomogeneity between the microstrip and birdcage coils.
In this work, we study RF characteristics due to different human heads and compare different coils that are used at 7T. Specifically, the transverse electromagnetic resonator (TEM) coil [31] and 5-sided Tic-Tac-Toe (TTT) coil [32,33] are evaluated via RF simulations using different anatomically detailed human head models and measurements utilizing a network analyzer and in-vivo 7T B 1 + mapping on different human heads. We chose the 16-element TEM and TTT designs due to the availability of both coils as well as FDTD coil models in our facility and because they are based on distributed-circuit approach and have shown to produce the homogenous B 1 + field distributions at 7T [34,35]. The detailed analysis is performed through comparing finite-difference time-domain (FDTD) calculated and measured coil impedance, B 1 + field (homogeneity and intensity) and SAR (average and local) across different heads for both coils.

Materials and methods
Coils TTT coil design. Fig 1(A) shows the prototyped cuboid coil. The coil is made out of five sides of a TTT square-shaped array as described in [36][37][38][39]. The 7T TTT head coil is a bigger version (228x228 mm 2 ) of the breast coil; detailed description of the coil design and construction can be found in [37]. One side of a tic tac toe shaped array has four transmit (Tx) channels/elements (Fig 1(D)). The assembly of 5 tic tac toe shaped arrays (surrounding the human head except for the neck side) allows for up to 20 Tx channels/elements. Only 16 Tx channels are used since the top tic tac toe side is not utilized. Each channel of the coil is tuned to 297.2 MHz by adjusting the inner rod length pushed inside the outer strut for all the coil elements. The excitation channels of each coil are combined using Wilkinson power dividers (2-, 4-, and 8-ways), with phase cables to implement particular RF shim phases (more on that in the "Excitation Strategy" section).

RF modeling
Anatomically detailed human head models. Five anatomically detailed head models varying in shape/volume and weight were used to analyze the transmit coil characteristics of the TEM and TTT transmit coils at 7T using FDTD simulations. The anatomically detailed head models H1-5 were created from Duke male model of the Virtual family head models [41] (age: 34, height: 1.74 m, weight: 70 kg, body mass index (BMI): 23.1 kg/m 2 ). The 22 tissue volumes, identified by its constitutive properties-conductivity and dielectric constant (σ, ε r )-of the different head models are shown in Table 1. The head models were created by morphing the base model (H2) to produce models (H1-5) that varied in shape/eccentricity and volume and weights.
The maximum variation in the mass was 14% and changes in shape was quantified by eccentricity of the head. The eccentricity measure is defined as the ratio of major to minor axis at the eye brow level and was obtained from the cross-sectional area and perimeter estimate at the same location. This was achieved using the DIP library [42] where the method1 by Proffitt et.al. [43] used different weights for inclined boundary lines, and the method2 by Vossepoel et. al. [44] used corner correction to obtain the perimeter of odd shapes. Eccentricity of heads Table 1. Anatomically detailed head models. The 22 tissue volumes (inside each head model), identified by their constitutive properties (conductivity and dielectric constants) (σ, ε r ) of the different head models H1-5, are shown. The anatomically detailed head models H1-5 were created by morphing the Duke male model (H2) of the Virtual family head models (34). Models are arranged in increasing volume/mass. varied from circular (eccentricity~1) to elliptical (eccentricity~1.4). Fig 1(C) shows the contours of the different head models (axial, coronal and sagittal boundary of brains and heads) used in the FDTD simulations. The relative permittivity map is also shown in Fig 1(B). The perimeter of the models and their eccentricity when compared with those measured on the 4 volunteers indicate the shape and volume of heads used in the RF simulations represent a comprehensive sample of an adult population who might undergo an MRI [45].

Epsilon
Software. FDTD models of the TTT and TEM head coils i.e. the coil geometry: including the coaxial transmission lines, RF shielding, anatomically detailed head models and the terminating (perfectly matched layers) PML [46] are shown in Fig 1(A). The 3-dimensional computational domains with isotropic resolution of~1.6mm was constructed by setting the constitutive properties to that of the RF coil (comprising of Rexolite or, Teflon, or Copper) or to the different tissues of the anatomically detailed head models. The coil model has a true transmission line model for the excitation elements with accurate modeling capability of the coil's input impedance and coupling [36,[47][48][49].
The numerical models of the coils were tuned to Larmor frequency of 7T (297 MHz) using head model (H2) by adjusting the gap between the inner coaxial elements of the TTT and TEM elements and the modeling of the excitation source(s) while observing the scattering (S) matrix of the true transmission line model. The same tuning configuration applied on H2 is utilized for all other head models without re-tuning/matching for each individual head model.
Note that the full wave 3D FDTD models of the TTT and the TEM coils and the generic framework of validating experiment with simulation studies of the transmit field, input impedance and coupling between coil elements have been performed and validated in earlier studies [36,48,49].
Excitation strategy. The fields (electric and B 1 + ) associated with the individual ports of each coil are combined using: 1) quadrature (TEM) and pseudo-quadrature (TTT) excitation, and 2) RF shimming (optimized excitation using phase-only or amplitude-and-phase excitation) for both the TEM and TTT coils. The RF shimming aims at achieving the lowest combination of the coefficient of variation (CV) and maximum to minimum (max/min) inside the region of interest (ROI) for all 5 head models. The ROI is the volume encapsulating the whole head above and including the temporal lobes and cerebellum while excluding the ears and the nasal cavity. The minimization of the CV and max/min inside the ROI is achieved by constraining the mean transmit B 1 + field intensity to 11.74 μT, which results in 180 o flip angle with 1 ms square pulse, using ã 4.4 kW RF amplifier capacity (45% power loss from a standard 8 kW RF amplifier to the coil ports). Note that the phase-only shim cases (quadrature and phase-only arrangements) can be readily implemented in the combined mode of the MRI system without the need for parallel transmission mode.
RF absorption in the whole head quantified by SAR (W/Kg) averaged over any 10g of tissue was obtained for a continuous wave with mean transmit B 1 + field intensity of 2μT in the ROI.

Experimental measurements
Network analyzer measurements. This study was approved by the University of Pittsburgh's Institutional Review Board (IRB PRO17030036) and involved four volunteers with approved written consent. The individuals have given a written informed consent to publish the details in this manuscript. Bench measurements were performed using a calibrated network analyzer (E5062A and 87050E multiport test set; Agilent Technologies Inc., CA, USA) together with an 85032B S-parameter test set. The Smith Chart measurements of different excitation ports of the TTT and TEM coils were recorded for the four volunteers (without re-tuning/re-matching of the excitation ports between different heads). Thus, both measurements in-vivo on the four volunteers, and with the five head models (H1-5) in FDTD simulations, were obtained without re-tuning/re-matching of the excitation ports.
In-vivo B 1 + field measurements. To achieve the desired phase shifts, the quadrature (for TEM) and pseudo-quadrature (for TTT) cases were implemented by adjusting the lengths of the coaxial cables feeding the coils. Imaging was performed on two volunteers using a 7T scanner (Siemens Medical Solutions, Germany). B 1 + maps were acquired with a turbo FLASH sequence with the following parameters: number of flip angles = 6, TR = 2.2 sec, TE = 1.4 msec, FOV = 220 mm, Matrix = 64x64, slice thickness = 3.2 mm and bandwidth = 510 Hz/ pixel. The images from the six measurements of the B 1 + map sequence was summed and used to create a brain mask. FSL's brain extraction tool (BET) [50] was used to create a brain mask (bet -m -f 0.4 options were used). The created brain masks were visually inspected and corrected manually using ITK SNAP tool [51] in the regions where automatic segmentation of the brain failed. The numerical (across five different head models) and experimental (across four volunteers) results show that the reflection coefficient (Sxx) and input impedance values of both the TTT and TEM coils did not change appreciably. In terms of the input impedance, the maximum variation (between the five different head models) was 3.5% for the TEM coil (twenty cases represented by four excitation channels and five different head models) and 2.3% for TTT coil (eighty cases represented by sixteen excitation channels and five different head models.) The maximum variation measured with the network analyzer was 5%.

Numerical and In-vivo B 1 + field distributions and intensities
Transmit B 1 + field distributions across the five head models are shown for different excitation strategies (Figs 3-6 and Table 2). We compared three different excitation sets including quadrature, and variable amplitude-and-phase, and phase-only cases for the two coils. Due to the consistent tuning, and matching for both coils across different subjects, the coils were not retuned/matched in the simulations (five head models). B 1 + field homogeneity. Homogeneity of the B 1 + field distribution was calculated in terms of maximum over minimum B 1 + (max/min) and coefficient of variation (CV) which is defined as the standard deviation over mean (σ/μ) in the ROI. Figs 4-6 show multiple axial, one coronal, and one sagittal slices of B 1 + field distribution. Sagittal conductivity maps of the different head models are also plotted with a line indicating the end of cerebellum in each of the five head models. The ROI, where stats were obtained in the five head models (Fig 3 and Table 2), includes the whole head above and including the cerebellum and excluding the nasal cavities and ears. The ROI volume of the different head models are different as indicated by the different axial slice number # which determines the end of cerebellum for each head model. Simulations and network analyzer measurements. In A), reflection (Sxx) of a representative port of the TTT coil with the 5 different head models (H1-5) using full wave FDTD simulations. The maximum variation (between different head models) in input impedance amongst all the ports using the five different head models (80 cases) was 2.3%; In B), reflection of a representative port of the TEM coil with the 5 different head models using FDTD simulations. The maximum variation (between different head models) in input impedance amongst all the ports using the five different head models (20 cases) is 3.5%. There was no re-tuning or re-matching for any of the ports in both coils; the coils were tuned/matched to H2 and used in the same configuration for the other head models; In C), experimental impedance measurements (Smith Chart) for 2 representative ports for the TTT & TEM coils. Both coils showed consistent (< 5% variation) input impedance among all four volunteers. In terms of CV, the TTT design provides 40%/35%/41% average (across H1-H5) percentage improvement over the TEM design for quadrature/phase-only/amplitude-and-phase-excitation strategies. In terms of max/min, the TTT design provides 597%/99%/116% average (across H1-H5) percentage improvement over the TEM design for quadrature/phase-only/amplitudeand-phase excitation strategies. B 1 + field vs. input power and B 1 + field vs. SAR. We evaluated B 1 + field efficiency based on SAR as well as input power.   Table 2 are shown. B 1 + field homogeneity is quantified in terms of max/min, and CV in the region of interest (ROI). The ROI is defined as the whole head above and including the cerebellum and excluding the nasal cavities for all head models. The SAR performance is presented in terms of relationships between peak local SAR, average SAR, and B 1 + field. Each line in each subfigure represents the mean value.  TTT/TEM Coils. Therefore, the TTT design has~44% lower average B 1 + intensity for 1W input power and~18% higher average B 1 + for 1 W/kg average SAR for this case. In terms of phase-only   Fig 7 for the quadrature (TEM) and high flip angle pseudo-quadrature (TTT) excitation cases. The calculated CV for the TTT/TEM coils are~21%/26% and~20%/25% respectively for the two subjects (note that the utilized phases/cable lengths were the same for both subjects). Lack of sufficient B 1 + field intensity in parts of the temporal lobe and cerebellum by the TEM coil makes measurement and use of max/min criterion inaccurate, and therefore it was not measured.

Numerical SAR distributions and intensities
SAR distributions across the five head models are shown for the three different excitation strategies (Fig 8).
Average SAR. We evaluated SAR efficiency based on calculating average SAR (across the whole head volume) for 2μT mean B 1 + field intensity in ROI.  Evaluation of the Tic-Tac-Toe RF coil for 7 Tesla MRI compared to the TEM design for quadrature/phase-only/amplitude-and-phase excitation strategies. Local SAR. We evaluated SAR distribution based on calculating local SAR (W/Kg for 10 g) to average SAR (W/Kg for 10 g) ratio. Table 2 and Fig 3 provide details of the following stats. In terms of quadrature (TEM) and pseudo-quadrature (TTT) excitation, the mean (across H1-5) local to average SAR ratio are 3.2/4.3 respectively for the TTT/TEM coils. In terms of phase-only RF shimming, the mean (across H1-5) local to average SAR ratio are 3.2/ 4.6 respectively for the TTT/TEM Coils. In terms of amplitude-and-phase RF shimming, the mean (across H1-5 local to average SAR ratio are 2.9/4.4 respectively for the TTT/TEM Coils. In terms of local SAR to average SAR ratio, the TTT design provides 25%/30%/34% lower average (across H1-H5) values when compared to the TEM design for quadrature/phase-only/ amplitude-and-phase excitation strategies.

Consistency of the RF field distributions
We evaluated the consistency of B 1 + field based on the four-abovementioned criteria namely: CV, max/min, mean B 1 + field intensity for 1 W input power and mean B 1 + field intensity for 1 W average SAR. B 1 + field consistency was based on calculating the maximum variation change among the five head models, i.e. for any criteria, maximum variation is defined as [maximum value-minimum value] over [minimum value]. In terms of CV, the maximum variation change is 12/7%, 10/7.5%, and 8.2/6.3% respectively for the TTT/TEM coils and for quadrature, phase-only, and amplitude-and-phase excitation strategies, respectively. For max/min, the maximum variation change is 9.3/217%, 10/44%, and 6.1/38% respectively for the TTT/TEM coils and for the three excitation strategies. For mean B 1 + field intensity for 1 W input power, the maximum variation change is 3/9.4%, 3/9.8%, and 2.9/9.9% respectively for the TTT/TEM coils and for the three excitation strategies. For mean B 1 + field intensity for 1 W average SAR, the maximum variation change is 1.6/5.1%, 2.2/5%, and 3.0/5% respectively for the TTT/TEM coils and for the three excitation strategies. SAR. We evaluated the consistency of SAR based on the two-abovementioned criteria namely average SAR (in whole head volume) for 2μT mean B 1 + field intensity in ROI and local Evaluation of the Tic-Tac-Toe RF coil for 7 Tesla MRI to average SAR ration. In terms of SAR (in whole head volume) for 2μT mean B 1 + field intensity in ROI, the maximum variation change is 3.1/10%, 4.5/10%, and 4.5/10% respectively for the TTT/TEM coils for quadrature, phase-only, and phase-and-amplitude excitation strategies. For local to average SAR ratio, the maximum variation change is 4.9/12%, 6.3/14%, and 6/14% respectively for the TTT/TEM coils for the three excitation strategies.

B 1 + field distribution
The overall results show that transmit B 1 + field homogeneity measured by CV as well as max/ min (maximum B 1 + over minimum B 1 + in the ROI) are substantially improved with the TTT coil when compared to the TEM coil. The TTT coil is well suited for exciting cerebellum and brain stem [32] at 7T. That being said, the TEM coil design with its arrangement of multiple transmission lines aims at providing increased excitation in the middle of the brain [31] as opposed to extended coverage in the peripheries. Based on our simulations, the central positioning in conjunction with the same back-ofhead positioning in XY plane for different head models within the coils is optimal for in-vivo MRI acquisitions for the TEM coil. Prior simulations [52] showed that a slightly shifted  Table 2 for the conditions under which the SAR distributions are plotted. position in the XY plane provides moderate better coil performance for the TTT coil. To keep consistency between both coils, this shifted case (with the TTT coil) was not considered in this study.

B 1 + field vs. input power
The load insensitive nature of the TTT coil comes from having strongly coupled elements [53], which decreases the load to coil interactions. Although this comes at a price as its transmit efficiency evaluated as B 1 + / p forward power is substantially lower when compared to the TEM coil. That being said, the implementation of the TTT coil has been shown to provide adequate B 1 + for inversion (180 o flip angle at 1 ms pulse width), and turbo spin echo and other clinical scans requiring inversion with a standard 8 kW RF amplifier [52,[54][55][56].

SAR distribution and intensity
Despite lower ratio of B 1 + field vs. input power for the TTT design, it provides~22%-30% lower average (across H1-H5) SAR values (for 2μT mean B 1 + field intensity in ROI) when compared to the TEM design for quadrature and RF shimming excitation strategies. In terms of local SAR to average SAR ratio which can be the limiting factor in determining the allowed amount of tissue absorption, the TTT design also provides~25%-34% lower average (across H1-H5) ratios when compared to the TEM for quadrature and RF shimming excitation strategies.

Consistency of the B 1 + field and SAR distributions and intensities
Strategies to overcome patient specific electromagnetic interactions at UHF include; building systems/sequences that are invariant across subjects and using a safety factor in SAR monitoring [57]. B 1 + inhomogeneity can potentially be alleviated using a combination of multi-port transmission and/or by adiabatic/hyperbolic or composite pulse sequences that produce constant flip angle independent of transmit field [58]. However, to achieve optimal performance (image quality as well as safe RF levels), one must know how the RF fields produced by coils/ arrays behave in every imaged subject prior to an MR experiment. The process of measuring and/or simulating the RF fields and implementing a targeted excitation profile is time consuming and often cannot be performed in real-time with the subject in the scanner. Additionally, the measurements may be inaccurate when signal voids exist in the images and cannot be generalized across subjects when the RF field produced by coil/array is widely varying across different subjects. Therefore, the coil performance across different subjects presented in this study becomes relevant for effective and safe coil use at UHF MRI. This work shows that both the TEM and TTT coils showed consistent tuning and matching across different subjects/head models. Across 5 head models with brain volumes changing between 1330 and 1740 cc and eccentricity changing between 1.04 and 1.48. That being said, the variation in transmit B 1 + field and SAR distributions/intensities (across different head models) for the TTT coil was substantially lower than the TEM coil. Hot-spot changes are predicted to changes in boundary conditions due to significant changes in constitutive properties (σ, ε) and varying resistance to induced currents, in the different heads. These should result in different local SAR for the different heads. Thus, SAR accumulation or hot-spots at eye/nose sinuses, bone-CSF interface, among other regions, are anticipated for different head/(model)s as the boundary regions differ for each of them. For local to average SAR ratio, the maximum variation change is~5.7%/13% respectively for the TTT/TEM coils.

Conclusion
We studied the B 1 + field produced in the ROI that encapsulates the whole head above and including the temporal lobes and cerebellum and excludes the nasal cavity, and SAR in the whole head volume. Statistics of the simulated B 1 + field (efficiency, homogeneity, and consistency), and SAR (intensity and consistency of average and local values) across the 5 head models are tabulated in Table 2, shown in Fig 3, and further elaborated in the Results Section. A direct comparison between the TTT and TEM coils for the phase-only shim case (directly implementable in the single transmit mode of the 7T scanner) shows the following observations. 1) Both coils present negligible variance of input impedance among different head models/ subjects (<5%) in the simulated/measured data.
2) The TTT design shows substantial improvement in the B 1 + homogeneity and consistency demonstrated in the max/min values of the TTT design (mean max/min = 3.97, maximum variation = 10% between different heads) when compared with that achieved with the TEM design (mean max/min = 7.94, maximum variation = 44%), which represents a significant a) excitation drop in the cerebellum and temporal lobes and b) variation between subjects.
3) The TTT design presents substantial improvement in the B 1 + homogeneity, as demonstrated in the values of the CV (TTT = 0.20 mean, 10% maximum variation between different heads; TEM = 0.27 mean, 7.5% maximum variation). This is critical for achieving fidelity of the B 1 + field distribution across the human head. The TTT design has a significant lower B 1 + / power efficiency, with mean B 1 + = 0.25μT for 1W input power (with 3.0% maximum variation) against 0.45μT (with 10% maximum variation) for the TEM design; however, both coils present enough B 1 + intensity to have spin inversion with 1ms square pulse and 8kW RF power amplifier including power losses. This could be critical when high peak B 1 + intensity is needed with limited RF power amplifier capacity. 4) The TTT design has better SAR efficiency, with 1.44 μT/ p (W/kg) (maximum variation = 2.2% between different heads) against 1.27 μT/ p (W/kg) (maximum variation = 5.1%) for the TEM design. This is critical for high SAR acquisitions (turbo spin echo, FLAIR, DTI, etc . . .).
5) The TTT design has lower peak over average SAR ratio (3.24) with maximum variation = 6.3% between different heads against 4.58 (which is~41% higher than the TTT value) and maximum variation =~14% for the TEM design. This is critical for high SAR acquisitions as well as meeting the regulatory limits for local and average SAR. Note that with the FDAapproved single transmit mode 7T systems, the scanner's online SAR calculations do not significantly change between different human heads.
For the TTT coil, the lack of significant variation in terms of B 1 + distribution/intensity and local/average SAR in different subjects translates to ease in set up (no B 1 + maps and RF shimming for every subject are necessary). This is very important in a clinical environment when the time to scan a subject is very limited and any retuning or extra acquisition is costly. Moreover, the subject-insensitivity RF performance associated with the TTT design provides greater RF safety assurance measured by consistency in the local and average SAR with different subjects. With narrow tolerance parameters associated with TTT coil, the results also show that numerical simulations can be potentially performed on a representative head model without the need for 1) subject-specific transmit B 1 + maps measured in-vivo or 2) subject-specific SAR calculations. Finally, the TTT and TEM RF coils can be used in either parallel transmit or in single transmit systems.