A Simple Head-sized Phantom for Realistic Static and Radiofrequency Characterization at High Fields

Purpose : To demonstrate a simple head-sized phantom for realistic static and radiofrequency field characterization in high field systems. Methods : The head-sized phantom was composed of an ellipsoidal compartment and a spherical cavity to mimic the nasal cavity. The phantom was filled with an aqueous solution of polyvinylpyrrolidone (PVP), to mimic the average dielectric properties of brain tissue. The static and radiofrequency (RF) field distributions were characterized on a 7T MRI system and compared to in vivo measurements and simulations. MR thermometry was performed and the results were compared to thermal simulations for RF validation purposes. Results : Accurate reproduction of both static and RF fields patterns observed in vivo was confirmed experimentally, and was shown to be strongly affected by the inclusion of the spherical cavity. MR thermometry and transmit efficiency ( B 1+ ) measurements were obtained in close agreement with simulations (peak values agreeing within 0.3 °C and 0.02 μ T/ √ W) as well as fiber optic thermal probes (RMSE < 0.18 °C). Conclusions : A simple head-sized phantom has been presented which produces B 0 and B 1+ nonuniformities similar to those encountered in the human head, and allows for accurate MR thermometry measurements, making this a suitable reference phantom for RF validation and methodological development in high field MRI.


Introduction
Tissue-mimicking magnetic resonance (MR) phantoms are instrumental for various MR applications including sequence development as well as system characterization and quality assurance. Tissue properties that are often mimicked include MR relaxation times such as T1 and T2 (1,2), magnetic susceptibility (3), diffusive properties (4), flow (5) and dielectric properties (6). Dosimetric phantoms are also commonly used as reference standards for radiofrequency (RF) safety assessment of implants at 1.5 and 3 Tesla (T) (7).
As MR systems continue to increase in static field strength, with whole body systems reaching 10.5T (8), the associated increases in RF frequency lead to a much stronger load-dependence of the RF fields involved (9,10). Inhomogeneities in the transmit RF (B1 + ) field are generally governed by the bulk dielectric properties of the sample, leading to a shortening of the RF wavelength, as well as being sensitive to the geometry and positioning of the sample (6,11). In the head at 7T, these B1 + field patterns involve pronounced areas of low transmit efficiency in the temporal lobes, which can be attributed to the elliptical shape of the head (11). Additionally, local dielectric heterogeneities in the sample can lead to local B1 + perturbations (12), but more importantly, can confine the local RF power deposition and corresponding specific absorption rate (SAR) (13)(14)(15). RF safety analyses therefore generally involve heterogeneous body models with many different tissue types to capture such mechanisms and determine safe power limits at which MR systems can be operated.
An important step in such RF safety assessments is to validate the simulated coil model via RF field mapping and MR thermometry techniques, guided by a well-defined reference phantom (16). The increased load-dependence at high field strengths underlines the importance of performing such a validation under realistic loading conditions, so that the validation corresponds well with the in vivo situation. This aspect will become more relevant as MR systems are moving from single channel transmission using a volume coil towards parallel transmission using transmit arrays composed of surface elements (17), which are more dependent on inter-element coupling and generally more complex to model. A phantom which produces realistic B1 + non-uniformities would also be valuable in the development of MR methods for RF inhomogeneity correction such as multidimensional RF pulses, dielectric shimming or parallel transmission (17)(18)(19).
Given such considerations, there is a growing interest in head-mimicking phantoms with increasing complexity to reproduce these sensitivities in a realistic manner (20)(21)(22)(23). Several materials such as aqueous solutions of polyethylene powder (21,24), sugar (22,25) or ethanol (23) are known to allow for appropriate tuning of their dielectric properties to reach values similar to those of human tissues.
These phantom recipes typically incorporate salt as an additive to control electrical conductivity and also gelling agents to reduce thermal convection (26). Advanced 3D-printed anthropomorphic phantoms with multiple compartments have also been proposed to better reproduce the dielectric heterogeneity of the human head (21,23). Despite these efforts, the correspondence of the RF fields obtained in these advanced phantom designs with those obtained in vivo is still rather weak.
In the current work, we present a very simple head-sized phantom composed of a single ellipsoidal compartment and a spherical air cavity to mimic the nasal cavity. It is filled with an aqueous solution of polyvinylpyrrolidone (PVP), which has recently been shown to feature advantageous properties such as a high signal-to-noise ratio (SNR) and low spectral contamination with respect to conventional phantom materials (27). Experiments performed at 7T show that the phantom produces both static (B0) and RF transmit (B1 + ) field interactions corresponding very closely to those produced in the head in vivo. The phantom was also tested in terms of the measured temperature rise when using a high permittivity dielectric pad and compared to thermal simulations and fiber optic probe readings.

Phantom design
The head-sized phantom was designed by means of electromagnetic simulations (XFdtd 7.5, Remcom inc., State College, USA). The geometry of the phantom was designed to approximate the head contours of the heterogeneous body model 'Duke' of the Virtual Family (28), which resulted in an ellipsoidal structure of 18×22×27 cm in size as shown in Figure 1. The dielectric properties of the phantom were then optimized in steps of 5 in relative permittivity (εr ) and in steps of 0.05 S/m in electrical conductivity (σ) in order to reproduce the B1 + field patterns produced in the heterogeneous head model when positioned in a numerical model of the birdcage transmit coil. This resulted in a relative permittivity of εr = 50 and electrical conductivity of σ = 0.6 S/m, which is very similar to the average dielectric properties of brain tissue (estimated by averaging the properties of grey and white matter) yielding εr = 52 and σ = 0.55 S/m (29). Finally, a 7-cm diameter spherical cavity was incorporated at an offset of 6 cm from the phantom center in the anterior-posterior direction to account for both the static (B0) and the RF transmit (B1 + ) field perturbations induced by the nasal cavity (30).
The ellipsoidal phantom shell (Simulacrum Capitis, VDL Wientjes-Roden B.V., Roden, The Netherlands) was constructed from polymethylmethacrylate (PMMA). Two hemispherical shells were constructed using a vacuum-forming technique, and connected to an elliptical ring which was created by means of computer numerical controlled milling. The spherical cavity was implemented using a hollow PMMA sphere, supported by a thin PMMA bar running in the anterior-posterior direction within the central ring. The shell was filled using an aqueous solution of 76g polyvinylpyrrolidone (PVP10, Sigma Aldrich, The Netherlands) with 1.78g Sodium Chloride (NaCl) per 100g of demineralized water, in order to reach the desired dielectric properties (27). We note that the recipe of this solution differs from the recipe reported in (27) due to the difference in polymer chain length of the polyvinylpyrrolidone compound (31). The solution was finally gelled using 1.5% (w/w) agarose (A9539, Sigma Aldrich, The Netherlands) to reduce thermal convection.
The dielectric properties of the phantom material were characterized using a dielectric probe kit

MR System and RF Coil
All experiments were performed on a whole body 7T MR system operating at an RF frequency of 298 MHz (Achieva, Philips Healthcare, Best, the Netherlands). B0 and B1 + field characterization in the phantom and comparisons with that obtained in vivo were performed using a commercial quadrature birdcage transceive coil with 32-channel receive array (Nova Medical, Wilmington, MA).
MR thermometry was performed using a custom-built quadrature birdcage RF coil so that all circuit elements could be modeled exactly (some features of the commercial coil are restricted in their description by the manufacturer). The custom birdcage had an inner diameter of 30 cm, 16 rungs with a length of 17 cm and a shield with a diameter of 36 cm. The birdcage structure was of a highpass design and was tuned to resonate in the homogeneous mode using fixed end-ring capacitances of 7.1 pF. The two orthogonal ports of the coil were connected between the end ring and the shield to improve coil balance (33). The in vivo study protocol was approved by the local institutional review board and informed consent was obtained.

Static and RF Field Mapping
B0 and B1 + field maps obtained in the phantom were compared with in vivo data obtained in a male volunteer using the commercial RF coil setup, and with B1 + simulations when using the custom-built birdcage coil. B1 + maps were acquired using a multi-slice DREAM sequence (2.5 mm 2 in-plane resolution, 5 mm slice thickness, TR/TE = 3.2/1.1 ms, STEAM/imaging tip angle = 50°/10°), and normalized with respect to the input power accepted by the coil. B0 maps were acquired using a dual-echo gradient echo sequence (3.75 mm 3 isotropic resolution, 240 mm 3 field-of-view, TR/TE/TE Temperature difference maps were reconstructed from the phase difference with respect to the first dynamic, according to Δ = Δ 0 in which Δ is the temperature difference, Δ is the phase difference and the gyromagnetic ratio. The PRF coefficient (α) relating temperature to phase change was determined to be the same as that of water (α = -0.01 ppm/°C) in a separate cooling experiment (data not shown). Temporal phase unwrapping was performed for each voxel. Mineral oil phantoms were included in the setup to perform bias field correction up to first order (i.e. both constant and spatial gradient terms) by means of a least squares fitting procedure (35). Two fiber optic temperature probes (OTG-MPK5 series, Opsens, Quebec City, CA) were inserted into the phantom to validate the reconstructed temperature maps. A separate 3D gradient echo acquisition at 1.5 mm 3 isotropic resolution was used to locate the probe tips.
The transmitted RF power was measured at the coil plugs to be 51.1 W using a calibrated RF power meter (PSM 5320, Tektronix Inc., Beaverton, OR). The input reflection coefficients of the loaded birdcage coil (S11 and S22) were measured at -11.9 dB and -11.2 dB via a network analyzer (TR1300/1, Copper Mountain Technologies, Indianapolis, IN), which resulted in a total of 47.5 W of RF power entering the coil. Thermal simulations were performed in XFdtd (XFdtd 7.5, Remcom inc., State Collega, PA) using these parameters to model the corresponding temperature increase.
Additionally, the RF heating experiment was repeated using a high permittivity dielectric pad positioned laterally on the phantom to validate simulations thereof. The dielectric pad was constructed using a deuterated suspension of barium titanate resulting in a relative permittivity of 286 and an electrical conductivity of 0.44 S/m, and measured 14 × 14 cm in size and 1 cm in thickness (37).

Phantom design
The importance of including a spherical air cavity within the otherwise homogeneous phantom is illustrated in Figure 2  MR thermometry Figure 5 compares the simulated and measured temperature difference maps obtained after 30 minutes of heating in the custom-built birdcage, which were validated using two fiber optic probes.
The simulated data show a good agreement with measured data, with a peak temperature increase of 8.6 °C simulated compared to a 8.4 °C measured (both without dielectric pads). The root-meansquare errors between the fiber optic probe readings and MR thermometric data, calculated over the entire 30 minutes measurement period, were 0.13 °C and 0.18 °C for probetips #1 and #2, respectively.

Discussion
A simple head-sized phantom has been presented which allows realistic static and radiofrequency system characterization and provides a useful tool for methodological development of neuroimaging at high fields. The phantom produces realistic B0 and B1 + nonuniformities similar to those encountered in the human head, and allows for accurate MR thermometry measurements for RF validation purposes. The simplicity and symmetry of the design, as opposed to taking an irregular head shaped shell, not only allows for easy and economical production, but also allows for easy interpretation of physical mechanisms to better direct modeling efforts. This makes the phantom a strong candidate as a reference phantom for high field MRI, where RF safety evaluation is becoming more important and methodological development more demanding.
A spherical air cavity was introduced in the phantom as this was found to be an important contributor to the B1 + asymmetries observed in vivo (30). These asymmetric features were also observed in other studies at our institute, and required an asymmetric and gender-specific B1 + correction method to (38) to take into account the typically larger nasal cavity in men (38). Although this was not the goal of the current phantom design, future developments towards a gender-specific phantom may consider this aspect.
In addition to yielding more realistic RF field distributions, the spherical cavity also reproduces the local B0 inhomogeneities typically encountered in the frontal lobes. The joint-correspondence of these field nonuniformities can be of great interest in the area of spatiotemporal RF pulse design where both B1 + variations as well as off-resonance behavior have to be accounted for. Some smaller B0 inhomogeneities measured around the ear canals in vivo were not reproduced in the phantom, as can be observed from Fig. 2a, as these anatomical features were not included in the design, but can be incorporated without much modification.
Advantages of the demonstrated RF validation procedure compared to other approaches such as using near field probes (39,40) include the simplicity of the experiment as well as the realistic experimental conditions to which the RF coil is exposed. Methods using near-field probes typically require a mechanical positioning system to scan the interior of the phantom, which is difficult to realize within the MR scanner and in ellipsoidal phantom designs. Performing the RF validation via MR thermometry allows for arbitrary phantom geometries and ensures that the RF coil will be exposed to similar RF coupling mechanisms as those of the corresponding in vivo scenario.
The current study focused on evaluating the phantom in a neuroimaging setup at a field strength of 7T, but the approach can essentially be transferred to any field strength. Although the 7T birdcage head coil was used to guide the phantom design, additional studies confirmed that the phantom also produces realistic B1 + fields in a 16-channel transmit array for 9.4T ( (41); data provided as supplementary material). We do note that, as the phantom does not incorporate a torso section, the RF field response within a body-sized RF transmit coil with larger longitudinal field-of-view may be substantially different from the in vivo situation.
Residual minor differences between RF modeling and experimental characterization may arise from various sources, such as residual cable coupling effects, manufacturing tolerances on capacitor values, errors in phantom positioning within the RF coil, or the presence of the plexiglas support structure and oil phantoms which were not taken into account in the simulations. Another source of experimental error is the limited dynamic range of the B1 + mapping sequence, especially in areas of lower transmit efficiency, which can be improved by employing B1 + mapping sequences with a higher dynamic range (42).
A limitation of the simplified two-compartment phantom design is that the impact of tissue heterogeneities on local RF heating cannot be captured. For this purpose, multi-compartment designs would be desirable, however these are difficult to implement (23). Finally we note that, although the phantom has been shown to be suitable for guiding the validation of simulated RF coils, the measured temperature increases should not be taken as a surrogate measure for in vivo tissue heating, which requires heterogeneous body models as well as the incorporation of thermoregulatory response mechanisms (15).