Electrothermal Head Phantom Overview

• Electrothermal head phantoms are engineered models replicating the human head's electromagnetic absorption and thermal diffusion for controlled dosimetry, MRI QA, and therapeutic studies.
• They utilize diverse material systems such as liquids, gels, semi-solids, and solids to emulate tissue dielectric and thermal properties while supporting anatomical realism and multi-layered structures.
• Advanced modeling techniques, including boundary element and lumped-element methods, enable non-invasive SAR estimation and precise validation of thermal responses for safety and efficacy evaluations.

Searching arXiv for relevant papers on electrothermal head phantoms and closely related head phantom methodologies. An electrothermal head phantom is a physical or computational surrogate of the human head designed to reproduce, to a task-dependent extent, both electromagnetic and thermal behavior under externally applied fields, implanted devices, or diagnostic instrumentation. In the supplied literature, the concept appears across several adjacent problem classes: contactless dosimetry and SAR estimation in homogeneous and inhomogeneous head phantoms (Mitharwal et al., 2015), artificial tissue-emulating head phantoms for microwave and hyperthermia studies (Mobashsher et al., 2015), MRI SAR quality-assurance phantoms (Blackwell et al., 2020), skull-specific electrical phantoms for EEG and transcranial electric stimulation (Hunold et al., 2018), anatomically realistic MRI artefact phantoms (Fierens et al., 2023), and explicitly electrothermal validation platforms for microwave hyperthermia in deep brain targets (Rahmani et al., 17 Sep 2025). Taken together, these works define electrothermal head phantoms as measurement and validation platforms in which dielectric properties such as relative permittivity $\varepsilon_r$ and conductivity $\sigma$, together with thermal properties such as specific heat capacity and thermal conductivity, are engineered so that electromagnetic power deposition and the resulting temperature field can be studied under controlled, repeatable conditions.

1. Scope and defining characteristics

The purpose of an electrothermal head phantom is to support controlled assessment of electromagnetic interaction with the head when direct human testing is impractical, ethically constrained, or insufficiently reproducible. The reviewed literature associates these phantoms with safety evaluation, especially SAR, therapeutic heating, device performance, and diagnostic imaging (Mobashsher et al., 2015). In this context, SAR is explicitly written as

$SAR = \frac{\sigma |E|^2}{\rho}$

in the review of artificial human phantoms (Mobashsher et al., 2015), and as

$SAR = C_{phantom} \cdot \frac{ΔT}{Δt}$

for MRI phantom thermometry in short, non-perfused settings (Blackwell et al., 2020). These expressions illustrate the dual electrothermal nature of the subject: one may characterize absorption from internal electric fields, or infer it from measured temperature rise.

The literature distinguishes between homogeneous and inhomogeneous head phantoms. A regularized boundary element formulation was developed for “homogeneous and inhomogeneous head phantoms,” with the inhomogeneous case described as important for “realistic electrothermal analysis” (Mitharwal et al., 2015). More generally, the review of artificial human phantoms notes that early head phantoms were often homogeneous, whereas modern systems for imaging, SAR, and hyperthermia favor multi-layer, heterogeneous structures such as skin, skull, CSF, grey matter, and white matter (Mobashsher et al., 2015).

A recurring design criterion is that the phantom should match not only dielectric behavior over the relevant frequency band but also the thermal response needed for heating or thermometric studies. The review explicitly states that for electrothermal testing, phantoms must mimic “specific heat and thermal conductivity,” while also noting that “few formulations truly mimic both simultaneously” (Mobashsher et al., 2015). This limitation is central to the topic: an electrothermal head phantom is not merely an electrical phantom with optional temperature measurement, but a platform intended to preserve the coupling between absorbed electromagnetic energy and heat diffusion.

2. Material systems and fabrication strategies

The most general material taxonomy in the supplied literature is the classification of artificial tissue-emulating materials into liquid, gel, semi-solid or jelly, and solid (dry) forms (Mobashsher et al., 2015). Each class supports different electrothermal compromises.

Liquid ATE materials are predominantly water with additives such as NaCl and sucrose, sometimes with hydroxyethylcellulose, and are described as simple, inexpensive, and common in “dosimetric (SAR) and hyperthermia (heating) studies” (Mobashsher et al., 2015). Their disadvantages include dehydration, microbial spoilage, the need for containers, and difficulty in constructing layered or heterogeneous structures. Gel materials offer improved homogeneity and stability but still require containers and are susceptible to air bubble entrapment and long set times (Mobashsher et al., 2015). Semi-solid materials are especially relevant to head phantoms because they permit “multi-layered, heterogeneous phantom construction” and realistic anatomical models such as multi-layer heads with distinct bone, CSF, grey matter, white matter, and skin (Mobashsher et al., 2015). Solid materials provide durability and long shelf-life but are harder to tune for high-conductivity tissues and anatomical complexity (Mobashsher et al., 2015).

Several supplied studies instantiate these categories. For MRI global SAR QA, a head phantom was built in a 3-liter round-bottom borosilicate glass flask and filled with an agar-based gel containing agar: 60 g/L, sodium chloride: 10 g/L, and copper sulfate: 1 g/L (Blackwell et al., 2020). Glass was chosen because of its lower specific heat capacity, stated as 80 J/kg·K vs. 1700–1900 J/kg·K for plastics, to improve thermal response (Blackwell et al., 2020). The phantom’s measured specific heat capacity was 4292 J/kg·K (Blackwell et al., 2020).

For deep-brain microwave hyperthermia, an explicitly electrothermal head phantom used distilled water, canola oil, and gelatin powder (Rahmani et al., 17 Sep 2025). Its dielectric design used the Bruggeman mixing formula to achieve $\epsilon_r = 43$, $\sigma = 0.9$ S/m, and $C_p = 3700$ J/kg/K (Rahmani et al., 17 Sep 2025). The paper states that gelatin ensures the phantom holds shape and can embed tumor regions (Rahmani et al., 17 Sep 2025).

The skull compartment is treated as a special case in low-frequency bioelectric phantoms. For EEG and transcranial electric stimulation, fired plastic clay was proposed as a skull material because it is formable, ion-permeable, adjustable in conductivity, reusable, and dimensionally stable after firing (Hunold et al., 2018). After immersion in 0.9% sodium chloride solution, conductivity stabilized between 0.0716 S/m and 0.0224 S/m depending on clay type and firing temperatures in the abstract, while the detailed summary reports a broader observed range of 0.024 S/m to 0.191 S/m across all clays and firings (Hunold et al., 2018). The best skull match reported was type 33 at 950°C, with 0.024 S/m, compared with a commonly used skull conductivity value of 0.022 S/m (Hunold et al., 2018).

This body of work suggests that no single material system defines the electrothermal head phantom. Rather, material selection is application-specific: agar-based gels for MRI thermometric SAR QA (Blackwell et al., 2020), water–oil–gelatin mixtures for microwave electrothermal focusing (Rahmani et al., 17 Sep 2025), and clay barriers for skull-dominated conduction problems (Hunold et al., 2018).

3. Geometric realism and anatomical compartmentalization

Head phantom realism is discussed in both geometric and compartmental terms. The review of artificial human phantoms places anatomical realism, geometrically accurate structure, and spatial tissue distribution among the desirable features of head phantoms (Mobashsher et al., 2015). It also notes that anatomically realistic designs can be achieved with 3D printing, layered molds, and models scanned from MRI/CT (Mobashsher et al., 2015).

One extreme is the simplified but controlled geometry. The microwave hyperthermia electrothermal phantom is described as spherical with diameter 140 mm, approximating the adult human head, and containing a spherical embedded “tumor” with radius 5 mm (Rahmani et al., 17 Sep 2025). The simplicity of this geometry supports comparison with simulation and controlled focusing experiments. Likewise, the 2026 lumped-element electrical model idealizes the head as three concentric spherical layers: brain, skull, scalp, surrounded by air, each represented by frequency-dependent radial and tangential RC pathways (Faccia et al., 28 May 2026). Although this model is computational rather than a physical phantom, it formalizes the compartmental abstractions that many physical phantoms approximate.

At the other extreme are anthropomorphic constructs. The MRI artefact phantom study employed an anatomically correct artificial skull with mandible and C1-C6 vertebrae, eyes modeled as 30 mm diameter 3D-printed hollow spheres filled with silicone, and separately fabricated grey matter, white matter, and CSF compartments based on MRI segmentation (Fierens et al., 2023). Brain compartments were filled with MnCl$_2$ solutions at 0.025 mM for grey matter and 0.044 mM for white matter, while CSF was simulated with a CuSO$_4$ water bath at 1.1 mM (Fierens et al., 2023). This phantom was designed for implant-induced MRI artefact testing rather than heating, but it demonstrates the architectural sophistication available to head phantom design.

A different form of geometric realism appears in the EIT head-imaging framework, where a library of fifty heads was used to construct a principal-component model of human head-shape variation (Candiani et al., 2019). Head shapes were represented by star-shaped parameterizations over the upper hemisphere, and the parametric model

$$S(\hat{x}; \alpha) = \left( \bar{r}(\hat{x}) + \sum_{k=1}^{\tilde{n}} \alpha_k \hat{\rho}_k(\hat{x}) \right)\hat{x}$$

was used with typically $\sigma$0 in examples (Candiani et al., 2019). The paper does not present a physical electrothermal phantom, but it explicitly proposes that the statistical shape space can inform the creation of “standardized” yet varied physical head phantoms (Candiani et al., 2019). A plausible implication is that future electrothermal phantoms may couple thermal property matching with low-dimensional, population-informed geometric variability.

4. Electromagnetic and thermal modeling frameworks

Electrothermal head phantoms are tightly linked to forward and inverse models that determine what properties must be matched and how measurements should be interpreted. For contactless electromagnetic assessment, a Boundary Element Method formulation was introduced for SAR evaluation within homogeneous and inhomogeneous head phantoms (Mitharwal et al., 2015). The method is based on a regularized BEM approach requiring electric measurements only, with regularization obtained by extending Calderon techniques to rectangular systems, yielding well-conditioned problems independent of discretization density (Mitharwal et al., 2015). The scheme is hybridized with surfacic homogeneous and volumetric inhomogeneous forward BEM solvers accelerated with fast matrix-vector multiplication schemes, thereby permitting “rapid and effective dosimetric assessments” and the use of “inhomogeneous and realistic head phantoms” (Mitharwal et al., 2015).

For the low-frequency or electro-quasi-static regime, the lumped-element head model provides a compact circuit abstraction of head electrostatics (Faccia et al., 28 May 2026). Each of the three shells is represented through radial branches and tangential branches, each branch being a parallel RC element, with tissue dispersion expressed through

$\sigma$1

The study states that neglecting dispersion and capacitive pathways can lead to an overestimation of scalp potentials over the considered frequency range (Faccia et al., 28 May 2026). Although not a phantom paper, it is directly relevant because physical phantoms intended for broadband EQS validation would need to reproduce both conductive and capacitive current pathways rather than only static conductivity.

In microwave hyperthermia, the absorbed power density is given in the supplied material as

$\sigma$2

and the thermal evolution is modeled with the Pennes bioheat equation

$\sigma$3

(Rahmani et al., 17 Sep 2025). The associated figure of merit

$\sigma$4

was reported as $\sigma$5, with the stated ideal condition being $\sigma$6 (Rahmani et al., 17 Sep 2025). This formulation makes explicit that electrothermal phantom design for therapy validation requires simultaneous agreement in field penetration, local absorption, and heat transport.

MRI SAR QA employs a thermometric rather than field-reconstruction route. The proton resonance frequency shift method converts measured phase change to temperature change through

$\sigma$7

which is then converted to SAR through the phantom heat capacity (Blackwell et al., 2020). This framework places premium value on thermal homogeneity, known heat capacity, and thermometric stability, rather than high anatomical realism.

5. Measurement modalities and validation protocols

A defining feature of electrothermal head phantoms is that they support quantitative validation. The supplied literature presents several such protocols.

In MRI SAR quality assurance, the phantom was equilibrated overnight in the MRI bore, imaged with a 2D fast gradient echo baseline sequence, heated using a high-duty-cycle 2D FLAIR sequence, then re-imaged with the same GRE sequence (Blackwell et al., 2020). Phase subtraction produced a temperature map via PRF thermometry, and SAR was computed from the bulk temperature rise (Blackwell et al., 2020). The SAR estimates were validated initially against whole-body calorimetry using a FLIR One Pro infrared thermal camera with 70 mK sensitivity and fiber optic temperature sensors (Opsens OTG-M170) placed centrally and peripherally (Blackwell et al., 2020). Scanner output SAR values ranged from 0.42 to 1.52 W/kg, and percentage differences between independently estimated values and scanner-calculated values were 0–2.3% (Blackwell et al., 2020).

The microwave hyperthermia validation study used a semi-enclosure with metallic/PEC walls, a fabricated metasurface transmitarray, and an ETS 3160-03 horn antenna (1.7–2.6 GHz band) placed 50 cm from the metasurface for plane-wave excitation (Rahmani et al., 17 Sep 2025). Measurements were carried out at 1.8 GHz for 20 minutes, and temperature profiling was performed using a Testo 872 thermal camera (Rahmani et al., 17 Sep 2025). Experimentally, the hotspot size was 9.29 mm on the y-axis and 9.53 mm on the z-axis, the tumor region temperature increased by $\sigma$8C to 21.4$\sigma$9C from a $SAR = \frac{\sigma |E|^2}{\rho}$0C laboratory baseline, and surrounding tissue increased by <2$SAR = \frac{\sigma |E|^2}{\rho}$1C (Rahmani et al., 17 Sep 2025). The study notes that simulations predicted a tumor site temperature of $SAR = \frac{\sigma |E|^2}{\rho}$2C from 37$SAR = \frac{\sigma |E|^2}{\rho}$3C body temperature, highlighting the difference between laboratory phantom conditions and physiological starting conditions (Rahmani et al., 17 Sep 2025).

In contactless dosimetry, the BEM formulation enables SAR estimation from external electric measurements without inserting probes into the phantom (Mitharwal et al., 2015). The stated benefit is that the assessment is contactless, hence non-invasive and free of probe-induced perturbation (Mitharwal et al., 2015). This is methodologically important because intrusive thermal or electromagnetic sensors can distort both the field and the local temperature distribution.

The 2026 infrared medical imaging laboratory presents a related but broader thermal-phantom methodology. It used a controlled enclosure, infrared detection, internal thermal reference elements, and a correction pipeline that reduced measurement uncertainty to approximately 25 mK (Frixou et al., 7 Apr 2026). Validation used wax phantoms with elevated-temperature sources of $SAR = \frac{\sigma |E|^2}{\rho}$4 to $SAR = \frac{\sigma |E|^2}{\rho}$5 K, and reconstructed 3D images were in quantitative agreement with thermocouples and $SAR = \frac{\sigma |E|^2}{\rho}$6CT source positions (Frixou et al., 7 Apr 2026). Although the study is not limited to head phantoms, it establishes a high-precision thermal measurement paradigm directly relevant to electrothermal head phantom instrumentation.

6. Application domains

Electrothermal head phantoms serve multiple research and engineering domains, each emphasizing a different subset of properties.

Dosimetry and SAR assessment are the most direct application class. The regularized BEM work targets “contactless SAR evaluations within homogeneous and inhomogeneous head phantoms” (Mitharwal et al., 2015). The artificial human phantom review identifies SAR evaluation and hyperthermia among the primary uses of tissue-emulating phantoms (Mobashsher et al., 2015). MRI QA extends this to scanner-level verification, where a reproducible head phantom and protocol independently verify global SAR output in 1.5 T and 3 T clinical scanners (Blackwell et al., 2020).

Microwave hyperthermia requires explicitly electrothermal phantoms because the endpoint is controlled temperature elevation rather than field measurement alone. In the deep-brain study, the phantom supported the “first experimental demonstration of metasurface-based time-reversal focusing for deep brain hyperthermia,” with localized heating at a tumor-like inclusion while minimizing temperature rise in healthy tissue (Rahmani et al., 17 Sep 2025).

EEG and transcranial electric stimulation use head phantoms to model low-frequency current flow, especially the skull as the “main conductivity barrier” (Hunold et al., 2018). These phantoms are electrical first, but the supplied data place them within the broader family of electrothermal head phantoms because they contribute to the material and compartment design knowledge needed for multi-physics platforms.

MRI device compatibility and artefact testing rely on realistic head phantoms that mimic anatomy and MR relaxation properties (Fierens et al., 2023). The study notes that such phantoms may be “readily adapted” for electrothermal testing, although tissue heating properties were not specifically evaluated there (Fierens et al., 2023). This suggests a convergence between imaging phantoms and electrothermal safety phantoms.

Head imaging and inverse problems provide another adjacent use case. The EIT framework addresses absolute head imaging under uncertainty in head shape and electrode positions, using a regularized Newton-type output least squares reconstruction algorithm with Gaussian priors (Candiani et al., 2019). The paper explicitly proposes that its statistical head-shape model can drive the design and testing of electrothermal phantoms (Candiani et al., 2019).

7. Limitations, trade-offs, and research directions

The literature emphasizes that electrothermal head phantom design is governed by unavoidable trade-offs rather than a single optimum. The review of artificial human phantoms states that while dielectric matching is routinely pursued, truly simultaneous matching of dielectric and thermal properties is rare (Mobashsher et al., 2015). Liquid and gel systems are easy to fabricate and tune but require containers and have stability issues; semi-solid systems allow layered realism but remain susceptible to dehydration and deformation; solid systems are durable but difficult to engineer for broadband, lossy tissues (Mobashsher et al., 2015).

Biological realism is also limited. The deep-brain hyperthermia phantom lacked “dynamic biological effects” such as blood perfusion and metabolism, used a spherical rather than anatomically accurate head, and operated from a $SAR = \frac{\sigma |E|^2}{\rho}$7C baseline rather than physiological 37$SAR = \frac{\sigma |E|^2}{\rho}$8C (Rahmani et al., 17 Sep 2025). The MRI SAR phantom relied on a homogeneous agar-based gel in a glass flask, which is suitable for global QA but not for local heterogeneous heating analysis (Blackwell et al., 2020). The EEG/tES skull phantom isolates conductivity barrier behavior effectively, but it is a compartment-level material study rather than a full electrothermal head (Hunold et al., 2018).

Measurement realism and uncertainty remain active concerns. The infrared tomography laboratory shows that high-precision thermal measurement of weak surface signatures requires environmental stabilization, internal references, and image corrections to reach ~25 mK uncertainty (Frixou et al., 7 Apr 2026). This suggests that phantom sophistication alone is insufficient; the surrounding metrology must be equally controlled.

A plausible implication of the supplied studies is that future electrothermal head phantoms will integrate four elements more tightly than most current systems do: anatomically realistic multi-compartment geometry, dispersive electrical behavior across frequency, thermally faithful bulk and boundary properties, and embedded or contactless metrology that does not perturb the field. The EIT head-shape model based on a library of fifty heads (Candiani et al., 2019), the dispersive RC formulation for three-shell head physics (Faccia et al., 28 May 2026), and the validated electrothermal hyperthermia phantom with known dielectric and thermal targets (Rahmani et al., 17 Sep 2025) together indicate a path toward population-aware, multi-physics, quantitatively validated head phantoms.

In that sense, the electrothermal head phantom is best understood not as a single device category but as a methodological class of head surrogates in which electromagnetic excitation, thermal response, and quantitative validation are co-designed for a specific research objective.