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Analysis of ICNIRP 2020 Basic Restrictions for Localized Radiofrequency Exposure in the Frequency Range Above 6 GHz

Lemay, Eric; Gajda, Gregory B; McGarr, Gregory W.; Zhuk, Mykola; Paradis, Jonathan1

Author Information
Health Physics: May 21, 2022 - Volume - Issue - 10.1097/HP.0000000000001581
doi: 10.1097/HP.0000000000001581
  • Open
  • PAP



Modern handheld or body-worn radiocommunication technologies operating at frequencies above 6 GHz have led to the development of new basic restrictions (BRs) for localized exposures, namely the absorbed power density (APD or Sab) and absorbed energy density (AED or Uab) within the tissues (ICNIRP 2020), also referred to as epithelial power density (IEEE 2019). Absorbed power and energy density BRs have been reasonably established as the proper exposure metrics for devices operating at frequencies above 6 GHz because they offer a better correlation with skin surface temperature rise (Foster et al. 2016; Funahashi et al. 2018). The need for power and energy density BRs for localized exposures was made apparent in several studies; as the penetration depth of RF energy becomes increasingly shallow with increasing frequency (Funahashi et al. 2018; Morimoto et al. 2017), the use of a volumetric exposure metric such as specific absorption rate (SAR) leads to progressively disproportionate relations with temperature rise.

ICNIRP (2020) specifies a new spatial averaging area of 4 cm2 for localized exposures above 6 GHz and an additional spatial averaging area of 1 cm2 for frequencies above 30 GHz to account for smaller beam diameters that can be produced at higher frequencies. The IEEE C95.1-2019 standard’s epithelial power density for evaluation against dosimetric reference levels (akin to basic restrictions) specifies the same spatial averaging scheme as ICNIRP (2020) and the same localized exposure limits for continuous exposures. However, IEEE differs from ICNIRP in that it specifies requirements for pulsed RF exposures in the form of a peak power density limit for a reference window of 100 ms and a fluence limit (energy density limit per pulse) that is applicable above 30 GHz. The latter appears to be overly restrictive and does not behave according to the accepted heat exchange model proposed initially in Pennes (1948). Therefore, the detailed analysis in this study focuses on the ICNIRP (2020) guidelines.

For their guidelines, ICNIRP has set an operational adverse health effect threshold (OAHET) of 5 oC temperature rise above an assumed Type 1 (skin or cornea) normothermal temperature of 36 oC. In addition, safety factors of one-half and one-tenth are imposed for occupational and general public exposures respectively, resulting in target temperature rises of 2.5 and 0.5 oC, respectively, for the two tiers of local APD and AED limits. Furthermore, the target temperature rises are independent of duration, implying that the ICNIRP limits intend to restrict steady-state (indefinite) and short term transient temperature rise equally.

Exposure to millimeter-wave radiofrequency electromagnetic fields (RF-EMF) of sufficient intensity can result in a heat-pain sensation if the absolute tissue temperature reaches or exceeds a threshold of ~42–43 oC (Defrin et al. 2006; Walters et al. 2000). This may be especially concerning for brief, high intensity pulses where a painful stimulation may occur before a behavioral response to avoid the stimulus can be initiated. Thermal tissue damage of the skin or cornea (classified as Type 1 tissues in ICNIRP 2020) may also occur when absolute tissue temperatures exceed the ~42–43 oC threshold for a sufficient duration (Dewhirst et al. 2003). The cumulative equivalent minutes at 43 oC (CEM43; Sapareto and Dewey 1984) is a well-established method for quantifying tissue thermal exposures by determining the number of cumulative minutes at 43 oC required to cause an equivalent effect. This standardized approach allows for the direct comparison of thermal sensitivities between different tissues and/or exposure scenarios, each of which may occur with different time-temperature histories, thus permitting the comparison of specific effects using a single common unit. For human skin, a CEM43 threshold of >20 minutes exists for minor damage to the skin (i.e., erythema), while a CEM43 > 288 minutes is necessary for complete necrosis to develop (Yarmolenko et al. 2011). Clearly, a temperature rise at the Type 1 OAHET for a fraction of the averaging time (360 s), as would be produced by a short duration pulse, has a lesser impact on tissue function and viability than a steady-state one produced by a continuous exposure (> > 360 s).

Study objective

Our objective was to assess the degree to which the assumed temperature rise safety factors (i.e., one-half and one-tenth of the OAHET) are maintained for localized exposures at the recommended BRs specified in ICNIRP (2020) above 6 GHz (repeated in Table 1). This amounted to estimating the APD or AED necessary to produce the target temperature-rise and comparing with the corresponding BR limit. A ratio of the requisite APD or AED to the BR greater than unity suggests that the safety factor is exceeded, while a ratio less than unity implies that the safety factor is not maintained.

Table 1 - Summary of occupational ICNIRP basic restrictions (Sab,BR and Uab,BR) for localized exposures between 6 GHz and 300 GHz. Exposure duration td is in s and power density exposures are to be averaged over 360 s. General public BRs may be obtained by dividing the occupational BRs by 5.
Exposure duration, s Frequency range, GHz Averaging area, cm 2 Basic restriction limits for U ab (kJ m −2 ) or S ab (W m −2 )
td < 360 6 to 300 4 Uab,BR = 36[0.05 + 0.95(td /360)0.5]
30 to 300 1 Uab,BR = 72[0.025 + 0.975(td /360)0.5]
td > 360 6 to 300 4 Sab,BR = 100
30 to 300 1 Sab,BR = 200

Numerical modeling was employed using an approximate tissue model to estimate the absorbed EMF as a function of depth and solving the Pennes Bio Heat Transfer Equation (PBHTE) in all tissue layers by considering the effect of heat diffusion, heat transport by blood perfusion, and convective heat loss at the air-skin boundary. As a representation of human superficial tissues, a 3-layer model composed of skin, subcutaneous adipose tissue (SAT), and muscle was considered for frequencies from 6 GHz to 60 GHz and a 4-layer model composed of epidermis, dermis, SAT, and muscle was considered for frequencies from 60 GHz up to 200 GHz (Fig. 1). The numerical model allowed an evaluation of the impact of time and spatial-averaging for both continuous and pulsed exposures.

Fig. 1:
Representation of the 3-tissue and 4-tissue models used in the evaluation.

Study limitations

The validity of theoretical analyses presented in this paper may be limited by two fundamental circumstances: (a) the classical Pennes’ model of bioheat transfer is empirical in nature and is absent of conclusive validation from experimental evidence (Crezee and Lagendijk 1990); and (b) the data on biophysical properties of tissues, obtained from widely used databases found from experimental studies, may not be representative or accurate due to inherent uncertainties in the measurement methodology (e.g., excised human or animal tissues isolated from their surrounding tissues). In particular, the tissue blood perfusion rate is known to vary widely across individuals, body sites, and external environmental conditions.

Despite alternatives to the PBHTE (Charny 1992; Huang and Horng 2015; Shrivastava 2018), an extensive critical survey by Foster et al. (2016) of available experimental data on microwave heating of tissues supports the use of the PBHTE to aid in the development and evaluation of RF safety limits at frequencies above 3 GHz and for millimeter waves.

Our analysis is confined to a restricted range of temperatures so that the coefficients and the source terms in the PBHTE are temperature-independent. For long exposures, a more accurate model would take into account changes in the local blood perfusion with respect to its baseline value due to tissue temperature elevation (Sekins et al. 1984). This effect comes about as a result of thermally induced vasodilation of the local blood vessels. In addition, the available permittivity data for tissues have been obtained from experimental studies where the blood flow was absent. This can be countered by extending the homogenization approach for a mixture of substances (e.g., ceramic and polymer) in Lakhtakia (1996) and Sihvola (2000) for the purpose of theoretical evaluations of the effective permittivity of a tissue. Lastly, parametric mathematical functions can be employed in lieu of the common Cole-Cole dispersion model to better approximate the frequency and temperature dependence of dielectric properties, namely the bivariate Chebyshev series method of Zhuk and Paradis (2021).

The most important limitation of this study is the employment of tissue models having fixed thicknesses. Though computationally intensive, a Monte Carlo approach for varying tissue thickness (Anderson et al. 2010, Sasaki et al. 2017) can be employed, thereby allowing an assessment of the temperature rises at any desired percentile level.


The assessment of the ICNIRP (2020) occupational basic restrictions above 6 GHz consisted of computing the AED or absorbed power density APD necessary to produce 2.5 oC peak temperature-rise (both spatially and temporally) in Type 1 human tissues and comparing them against the BRs in Table 1. Table 2 explains symbols, units, and quanitities. The penetration depth for frequencies above 6 GHz is shallow enough (mainly absorbed in the skin) to exclude Type 2 tissues (e.g., brain and all other tissue not classed as Type 1) from the analysis. If those values are greater than their corresponding BR, then the assumed safety factor is maintained, at least for the range of exposure conditions (i.e., frequencies and beam diameters or spot sizes) used in this assessment. Similar conclusions can be made of general public BRs due to the linearity of the governing relationship between temperature rise and exposure and also due to the assumed absence of localized or whole-body thermoregulatory effects (e.g., vasodilation).

Table 2 - Symbols, units and quantities.
Symbol Units Quantity
Uab kJ m−2 Absorbed energy density within the tissues
Sab W m−2 Absorbed power density within the tissues
Uab,BR kJ m−2 Absorbed energy density BR
Sab,BR W m−2 Absorbed power density BR
Sinc W m−2 Plane-wave power density incident normally on the tissue surface
HPBD m Span over which the projected power density falls to one-half the maximum value
SAR(r, z) W kg−1 Circularly symmetric spatial SAR distribution
SAR(z) W kg−1 Axial SAR distribution due to a plane wave
FWHM m Span over which the transverse SAR distribution falls to one-half the peak intensity
td s Exposure duration
g m Gaussian width parameter of the radial SAR distribution (= 0.601 FWHM)
gs m Gaussian width parameter of the radial HPBD distribution (= 0.601 HPBD)
mb m3 kg−1 s−1 Blood perfusion rate specific to each tissue
ρ kg m−3 Mass density specific to each tissue
C J kg−1 oC −1 Specific heat capacity of each tissue
k W m−1 oC −1 Heat conductivity specific to each tissue
h W m−2 oC −1 Surface convection heat transfer coefficient
α m2 s−1 Thermal diffusivity
Tair oC Ambient temperature of air on the surface of the tissue
T(r,z) oC Spatial distribution of temperature in the tissue with respect to radial and axial coordinates
Tb oC Temperature of blood—fixed at 37oC
Tnull (z) oC Equilibrium temperature distribution in the tissues in the absence of exposure
ΔT oC Maximum skin surface temperature rise

Heat transfer model

The heat transfer model pertains to an external, circularly symmetric beam of RF power density that gives rise to a cylindrically symmetric SAR distribution given by SAR(t,r,z). This and the power generated per unit mass by metabolic processes, Q(r,z), are the energy rate terms in the PBHTE in cylindrical coordinates given by:


where T(t,r,z) is the local tissue temperature, and Tb is the blood temperature. For layered tissues, the z-dependent (along the depth of tissues) thermal/physical parameters are mb, the blood perfusion (volumetric) rate in units m3 kg−1 s−1; ρ, the mass density of the tissue layer in units of kg m−3; C, the specific heat capacity of the tissue in units of J kg−1 oC−1; and k, the tissue heat conductivity in units of W m−1 oC−1. The parameters Cb, the specific heat capacity of blood, and ρb, the mass density of blood, are uniform throughout all layers. Since the primary focus of this analysis was on temperature rise, the metabolic parameter, Q(r,z), can be ignored.

For the implicit finite difference method used in the solution of eqn (1), the spatial differentials are converted to coupled difference equations that are solved using sparse matrix methods. Theoretically, the axial (z) and radial (r) dimensions extend to infinity; however, for the finite difference solution, they are truncated in both directions, and appropriate boundary conditions are assigned to ensure proper behavior of the solution. The time derivative is also represented as a finite difference, and the temperature evolution is computed in a series of time steps, referred to as a “time-stepping” process. This means that the solution at a given time depends on the one calculated at the previous time step. The implicit time-stepping scheme provides stable solutions at any length of time step.

Eqn (1) is solved subject to the convective boundary condition on the surface:


where Tair is the ambient air temperature, and h is the convective heat transfer coefficient in units of W m−2 oC−1.

Two additional boundary conditions and an initial condition are used to solve eqn (1). The local temperature is made equal to the blood temperature at the axial truncation boundary. At the radial truncation boundary, the local temperature approaches the equilibrium distribution of temperature in the tissues in the absence of exposure, Tnull(z), which is the steady state solution of the 1D PBHTE (i.e., with only z dependence) with SAR(t,r,z) = 0. The initial condition, T(0,r,z) = Tnull(z), ensures that all starting temperatures within the computation domain are again equal to the equilibrium distribution of temperature in the tissues in the absence of exposure. Thus, the net temperature rise at any point in time in the computation domain is given by ∆T(t,r,z) = T(t,r,z) − Tnull(z), where T(t,r,z) is the time-stepped solution of eqn (1). For all temperature-rise computations, a convective surface with a heat loss coefficient of h = 10 W m−2 oC−1 was adopted. This value or ones close to it were used in a number of studies (Anderson et al. 2010; Sasaki et al. 2017; Morimoto et al. 2017).

RF exposure model

Details of the circularly-symmetric Gaussian beam exposure model used for this assessment can be found in Gajda et al. (2019). It makes use of normal incidence as this represents the worst case for maximizing absorbed power in tissues for a given incident power density.

It is assumed that the beam gives rise to a 3-dimensional SAR distribution of the form:


where H(t) is the unit step function in time; exp{−r2/g2} is an assumed Gaussian transverse distribution, where g is a distribution width parameter (related to the beam diameter); and SAR(z) represents the distribution of SAR along the depth due to propagation of a plane wave in the layered tissues (Drossos et al. 2000). It is found by considering an incident, transverse electric and magnetic plane wave (impedance of 377 Ω) with power density Sinc illuminating a planar, multi-layer tissue at normal incidence. The internal fields in the layers are computed by enforcing the electromagnetic boundary conditions at every interface, from which the axial SAR distribution, SAR(z), is found. Through this process, the strength of the axial SAR distribution is linearly related to the external, unperturbed power density, Sinc. Also, the transmission of power across the air/tissue interface is calculated, allowing the absorbed power and energy density to be computed.

The transverse or radial distribution of SAR is characterized by its half-power diameter, defined as the Full Width at Half Maximum (FWHM) and termed the “spot size.” As a result, the Gaussian width parameter is g = 0.601 FWHM. The unperturbed external beam that would be projected on the planar tissue is characterized by its half-power diameter (i.e., in terms of power density) defined as the Half Power Beam Diameter (HPBD). The parameters FWHM and HPBD are related for a specific antenna type with the corresponding HPBD equal to or larger than the FWHM (the FWHM is closely correlated to the normal component of the Poynting vector; Nakae et al. 2020). The HPBD determines the spatial average of the external power density, while the FWHM is a determining factor for temperature rise over relatively long timescales. A fixed relationship or ratio FWHM/HPBD = 0.80 is used in this assessment, which was estimated for resonant dipoles in close proximity to a planar tissue model (see Appendix for more details).

Spatial averaging

In the aforementioned exposure model, the APD is equal to the product of the unperturbed incident power density and the transmission coefficient across the air/tissue interface. It is assumed to be circularly symmetric with Gaussian intensity distribution with respect to the radial distance, r given by:


where Sab,o is the spatial peak APD (in the centre of the beam).

Over a square area of X cm2 with side length √X, the spatially averaged APD is given by:


where Sab,4cm corresponds to a 4 cm2 spatially averaged APD, and Sab,1cm corresponds to a 1 cm2 spatially averaged APD.

For example, a spot size of FWHM = 0.5 cm, corresponding to an assumed beam diameter of HPBD = 0.625 cm, gives spatially averaged APDs of Sab,4cm = 0.111 Sab,o and Sab,1cm = 0.392 Sab,o. The coefficients of Sab,o can be termed “averaging factors” and illustrate the level of reduction in spatially-averaged APD from the spatial peak for such a small beam diameter.

Wide beams versus narrow beams

For sufficiently wide beam diameters and resulting spot sizes, the maximum tissue temperature can be found by solving the 1-dimensional PBHTE, obtained by dropping the radial dependence of both temperature and SAR terms in eqn (1) and eqn (3). This is approximately valid for FWHM greater than 10 times the effective “diffusion length” (a parameter that governs the rate of temperature-rise decay with distance in the tissue after reaching steady state; Gajda et al. 2019). Thus, results from solution of the 1D PBHTE will be given to represent the associated temperature rise from “wide-beams” that satisfy the previously stated condition.

The effective diffusion lengths of the two tissue models used in this study are nominally 9-10 mm. Therefore, spot sizes satisfying the wide-beam criterion would have FWHM greater than approximately 9 cm to 10 cm, with associated HPBDs being commensurately larger. Thus, wide beam (1D) evaluations in the Results section will be quoted as pertaining to FWHM 0.1 m, since this value can be considered the boundary between narrow and wide-beams.

The minimum SAR spot size for frequencies below 30 GHz was selected as FWHM = 0.010 m, while for frequencies equal to and greater than 30 GHz, it was chosen as FWHM = 0.005 m (based on computation results presented in the Appendix). Since the minimum spot size is related to wavelength, spot sizes smaller than FWHM = 0.005 m are theoretically possible at frequencies of 30 GHz and beyond.

Tissue models

Two tissue models and thermal/dielectric parameter databases were used depending on the frequency range. The tissue thickness selection shown in Table 3a (6–60 GHz frequency range) was based on a configuration that produced a relatively high temperature-rise per unit absorbed incident power density, while retaining realistic thicknesses of skin and SAT that occur in the human population. At the higher range of frequencies, 60–200 GHz, a 4-tissue configuration consisting of separate layers of skin (epidermis and dermis) was employed (Table 3b), which used the dielectric data in Sasaki et al. (2014) and thermal parameters in Sasaki et al. (2017).

Table 3a - Thermal parameters (from Hasgall et al. 2018) for the 3-tissue model in the 6–60 GHz frequency range (skin layer consists of combined epidermis and dermis). The values outside of brackets are those given in the database as means and used in our analysis, while those inside the brackets are the minimum to maximum values found in the database (shown here to illustrate the level of variation in the tissue model parameters).
Tissue layer Tissue thickness (mm) Density (kg m 3) Heat capacity (Jkg 1 °C 1) Thermal conductivity (W m 1 °C 1) Blood perfusion rate
(m3 kg 1 s 1) x 10 6
Skin 0.6 1109 (1100 – 1125) 3391 (3150 – 3662) 0.37 (0.32 – 0.50) 1.80 (0.83 – 3.0)
SAT 6.0 911 (812 – 961) 2348 (1806 – 2973) 0.21 (0.18 – 0.24) 0.56 (0.33 – 1.07)
Muscle 43.4 1090 (1041 – 1178) 3421 (2624 – 3799) 0.49 (0.42 – 0.56) 0.36 (0.31 – 1.60)
Blood N/A 1050 (1025 – 1060) 3930 (3300 – 3900) N/A N/A

Table 3b - Thermal parameters and tissue thicknesses for 4-tissue model in the 60–200 GHz frequency range. Layer thicknesses are described as being the mean thickness values found in the abdominal region (Sasaki et al. 2017).
Tissue layer Tissue thickness (mm) Density
(kg m 3)
Heat capacity
(Jkg 1 °C 1)
Thermal conductivity
(W m 1 °C 1)
Blood perfusion rate
(m3 kg 1 s 1) x 10 6
Epidermis 0.08 1109 3391 0.42 0
Dermis 1.25 1109 3391 0.42 1.99
SAT 14.3 911 2348 0.25 0.45
Muscle 34.37 1090 3421 0.50 0.60

The choice of a 3- or 4-layer model and the parameter database depending on frequency was predicated on several factors. At 60 GHz and above, a 4-tissue model was used (i.e., the skin was split into epidermis and dermis) due to the smaller in-tissue wavelengths and consequent greater interactions with the thinner layers. The dielectric data in Hasgall et al. (2018) is from a Cole-Cole dispersion model used for fitting measured data (to approximately 20 GHz; Gabriel et al. 1996) and extrapolated beyond. This is in contrast to the Sasaki et al. (2014) dielectric data that was obtained from measurements to at least 100 GHz, with some to 1,000 GHz, along with extrapolation for some tissues based on data from Pickwell et al. (2004).

Evaluation metrics

For the given time-dependence of exposure, computed temperature rises are normalized to the AED or APD that produced them to generate the ratios: ΔT/Uab,Xcm, and ΔT/Sab,Xcm (the subscript “X” can take on the symbols “4” or “1” to denote whether the spatial average is performed over 4 cm2 or 1 cm2, respectively).

The AED or the APD that produces 2.5 oC surface temperature rise are calculated using:


These quantities can be compared directly to the corresponding BRs in Table 1; alternatively, ratios of Uab,Xcm,2.5 and Sab,Xcm,2.5 to their respective BR can be formed. If the ratio is greater than unity, then a level of APD or AED greater than the BR is necessary to produce the 2.5 oC target temperature rise, and the BR can be considered conservative with respect to the specific exposure conditions (e.g., frequency, exposure duration, beam diameter, tissue model, etc.) under consideration. Additionally, the ratio gives a quantitative measure of the degree to which the safety factor is maintained; e.g., a ratio of 2 means that the safety factor is doubled, while a ratio of 0.5 means that the safety factor is halved.


Evaluations were performed for single, non-recurring exposures of duration td and for continuous pulse trains having a single pulse of width td every 360 s. It was found (and supported by Neufeld and Kuster 2018 and Foster et al. 2020) that pulse trains produced higher temporal-peak temperature rise in the steady state than was produced by a single, non-recurring exposure for the same absorbed energy density per pulse. This can be observed in the example results shown in Fig. 2 for both the wide beam and narrow beam cases.

Fig. 2:
Spatial maximum skin surface temperature-rise versus time for wide beams and narrow beams (FWHM = 0.010 m and HPBD = 0.0125 m), both at the 4 cm2 spatially-averaged AED BR in Table 1. Responses are for the application of 5 pulses of 50 s pulse width and 360 s period to the 3-tissue model at 30 GHz.

In Fig. 2, the absorbed power densities for both wide-beam and narrow-beam cases were set to levels at the maximum allowable AEDs in Table 1 for a 4 cm2 spatial average (291 W m−2 and 742 W m−2, respectively, when converted to spatial-peak APDs). The smaller beam delivers the same amount of energy but to a much smaller tissue area, thus causing a much higher temperature rise.

For a step application of the pulse train, the temperature-rise peaks gradually increase with each succeeding pulse until a steady state is reached. The length of time to reach the steady state becomes greater as the spot size increases; five pulses were necessary for the wide-beam peak temperature rise to plateau (i.e., when the variation between consecutive pulses is less than 2%). It should be noted that pulse trains with more than one pulse per 360 s produced lower temporal-peak temperature rise than for a single pulse per 360 s when their respective pulse widths and 360-s time averages were equal. Thus, a single pulse per 360 s forms the most sensitive exposure condition for testing AED BRs. Additionally, continuous pulse trains with a single pulse per 360 s can also be quantified in terms of their APD averaged over 360 s. However, the pulse height is determined by the AED BR, which is more restrictive than the APD BR in this case.

It was found that for the narrowest beams tested below 30 GHz (FWHM = 0.010 m), the difference between the temperature rise after the fifth pulse and the first pulse was less than 10% for the full range of td used. Above 30 GHz, where the minimum beam size is FWHM = 0.005 m, the difference dropped to 3%. This is due to the short times needed to reach steady state for narrow beams. For wide beams, the fifth-to-first pulse temperature rise difference ranged from approximately 2% for the shortest duration pulse (td = 0.05 s) to 35% for td = 200 s.

The use of steady-state data for the 5-pulse train shown in Fig. 2 for testing AED BRs might be considered overly restrictive due to the inevitable movement of the beam relative to the skin. However, the effect of beam movement may not arise for exposures to a single short pulse from a narrow beam, where all of the incident energy and subsequent transient temperature rise is manifested over a small distance and time scale. For this reason, reporting of AED results will be done for a single isolated pulse or after the first pulse in the pulse train.

For exposure durations of td ≥ 360 s, the evaluation of the APD safety factors was carried out using a step application of continuous wave (CW) for durations ranging from 360 s to 5,000 s (the latter being more than sufficient to reach steady state).

Ratios of the computed metrics to their corresponding BRs (eqn 6) are tabled in Figs. 3 to 10. Within each figure, the tables are color-coded in accordance with the color scheme in Table 4. Ratios greater than unity signify that the occupational BRs are conservative with respect to the specific exposure conditions (e.g., frequency, exposure duration, spot size, tissue model, etc.) that gave rise to the evaluation metric. Though evaluations were carried out at 6 GHz, these results are not shown due to their overwhelming conservativeness. Similarly, intermediate results between 120 GHz and 200 GHz are not shown since they differ only slightly from the results at these two frequencies.

Fig. 3:
Tables of U ab,4cm,2.5/ U ab,BR where U ab,BR = 36[0.05 + 0.95(t d/360)0.5] (i.e., for occupational, 4 cm2 spatial average) for the 3-tissue model (Hasgall database) exposed to a single pulse at carrier frequencies from 10–60 GHz versus pulse width, t d, and FWHM.
Fig. 4:
Tables of U ab,4cm,2.5/ U ab,BR where U ab,BR = 36[0.05 + 0.95(t d/360)0.5] (i.e., for occupational, 4 cm2 spatial average) for the 4-tissue model (Sasaki database) exposed to a single pulse at carrier frequencies from 60–200 GHz versus pulse width, t d, and FWHM.
Fig. 5:
Tables of U ab,1cm,2.5/ U ab,BR where U ab,BR = 72[0.025 + 0.975(t d/360)0.5] (i.e., for occupational, 1 cm2 spatial average) for the 3-tissue model (Hasgall database) exposed to a single pulse at carrier frequencies for 30 and 60 GHz versus pulse width, t d, and FWHM.
Fig. 6:
Tables of U ab,1cm,2.5/ U ab,BR where U ab,BR = 72[0.025 + 0.975(t d/360)0.5] (i.e., for occupational, 1 cm2 spatial average) for the 4-tissue model (Sasaki database) exposed to a single pulse at carrier frequencies from 60–200 GHz versus pulse width, t d, and FWHM.
Fig. 7:
Tables of S ab,4cm,2.5/ S ab,BR where S ab,BR = 100 Wm−2 (i.e., for occupational, 4 cm2 spatial average) for the 3-tissue model (Hasgall database) for CW exposure at carrier frequencies from 10–60 GHz versus exposure duration, t d, and FWHM.
Fig. 8:
Tables of S ab,4cm,2.5/ S ab,BR where S ab,BR = 100 Wm−2 (i.e., for occupational, 4 cm2 spatial average) for the 4-tissue model (Sasaki database) for CW exposure at carrier frequencies from 60–200 GHz versus exposure duration, t d, and FWHM.
Fig. 9:
Tables of S ab,1cm,2.5/ S ab,BR where S ab,BR = 200 Wm−2 (i.e., for occupational, 1 cm2 spatial average) for the 3-tissue model (Hasgall database) for CW exposure at carrier frequencies of 30 and 60 GHz versus exposure duration, t d, and FWHM.
Fig. 10:
Tables of S ab,1cm,2.5/ S ab,BR where S ab,BR = 200 Wm−2 (i.e., for occupational, 1 cm2 spatial average) for the 4-tissue model (Sasaki database) for CW exposure at carrier frequencies from 60–200 GHz versus exposure duration, t d, and FWHM.
Table 4 - Color code for evaluation table entries.
Range of ratio:
U ab,Xcm,2.5 / BR
or S ab,Xcm,2.5 / BR
Color Temperature-rise for an exposure at the occupational BR Temperature-rise for an exposure at the general public BR
ratio ≥ 1.0 blue ΔT ≤ 2.5 oC ΔT ≤ 0.5 oC
0.50 ≤ ratio < 1.0 green 2.5 oC < ΔT ≤ 5 oC 0.5 oC < ΔT ≤ 1.0 oC
0.25 ≤ ratio < 0.50 yellow 5 oC < ΔT ≤ 10 oC 1.0 oC < ΔT ≤ 2.0 oC
ratio < 0.25 red 10 oC < ΔT 2.0 oC < ΔT

It should be noted that the two decimal place precision of the ratios given in Figs. 3 to 10 are kept to highlight the differences between each case studied and do not imply a level of accuracy that is not present.

Influence of perfusion rate variation

A full analysis of the influence of variations in thermal parameters on the estimation of temperature rise is beyond the scope of this work and would be more appropriate for a separate paper. For a chosen tissue configuration and the electromagnetic/PBHTE model, the principal sources of temperature rise uncertainty are the dielectric and thermal properties of the biological tissue (Hirata et al. 2021). The effect of blood perfusion rate is of special interest due to its high variability. Insight into its effect on temperature rise estimates can be gained by looking at approximate solutions of the PBHTE for the case of homogeneous tissue under adiabatic surface conditions (i.e., h = 0).

After a step application of SAR to the tissue, the initial rate of temperature rise scales as C−1. This can be seen by dropping the diffusion, perfusion, and metabolic terms in eqn (1). Thus, the perfusion rate (mb) and the thermal diffusivity (α), given by α = k ρ−1C−1, play no role for very short pulses. At longer durations (the first hundred seconds or so), where there is still insufficient time for blood to carry away heat, the approximate solution for the 1D PBHTE scales primarily with an inverse power (<1) of the diffusivity (Foster et al. 2017) and is still relatively insensitive to perfusion rate.

At much longer durations and in the steady state, the solution to the 1D PBHTE scales roughly as mb−1/2 (Hirata et al. 2021), implying that for wide beams, the variability of perfusion will have a significant effect on the temperature rise estimate. A doubling or halving of the perfusion rate should result in changes of the order of 0.7 to 1.4 times the baseline value, respectively. Narrowing the beam reduces the sensitivity to the perfusion rate due to the concentration of the energy into a narrow spot, which can be verified using a high-frequency asymptotic steady-state solution for normalized temperature rise under adiabatic boundary conditions, as given in Foster et al. (2016):


where erfc{X} is the complementary error function of X, and where R1 (diffusion length in units of m) is given by: R1α1/2ρ−1/2mb−1/2.

Using eqn (7) and the tissue parameters for dermis in Table 3b and a spot size of FWHM = 0.005 m, a doubling and halving of the perfusion rate results in deviations from the baseline steady-state temperature rise of −8.6% and 6.9%, respectively. This was tested in the numerical model at 200 GHz using the 4-tissue configuration for the smallest spot size (FWHM = 0.005 m) and wide beams (FWHM ≥ 0.10 m) vs. the exposure duration of a single pulse (Fig. 11).

Fig. 11:
Deviation in % from the baseline temperature rise versus single pulse exposure duration (t d) for a doubling and halving of the perfusion rate for either all 4 tissues in the model, or for only the dermis. Calculations were made for the narrowest beam (FWHM = 0.005 m) and wide beams (FWHM ≥ 0.10 m) at 200 GHz using the 4-tissue model (baseline material parameters in Table 3b).


The significance of our results with respect to their applicability to the general public (as would be encountered from the use of consumer devices) is a reduction of RF-EMF exposures, leading to the ratios in Figs. 3 to 10 (based on the maximal allowable occupational BRs) by a factor of 5 (e.g., general public BRs: Sab,1cm = 200/5 = 40 W m−2, or Sab,4cm = 100/5 = 20 W m−2).

As part of this study, the smallest theoretically achievable spot sizes from half-wave resonant dipoles were assessed as a function of frequency (see Appendix). This was done since pulsed exposures with small spot sizes at intensities that are allowed by the spatially-averaged BR result in a high peak temperature rise on the skin surface (as evidenced in Fig. 2). At 30 GHz, the smallest SAR spot size that is likely realizable is of the order FWHM ≈ 0.005 m, with smaller spot sizes possible as the frequency increases. In addition, from consideration of the power density beam diameters that produced the SAR spots, a fixed ratio of FWHM/HPBD = 0.8 appears to be a reasonable average for a wide range of offsets between the source antenna (half-wave dipole) and tissue surface. As a result, this ratio was used for all calculations involving spatial averaging. The ratio FWHM/HPBD would likely increase for electrically larger antennae since the SAR distribution width is correlated to the normal component of the Poynting vector (Nakae et al. 2020), and such antenna would produce beams with more parallel rays.

Tissue model comparison

Examination of the CW results at the overlapping frequency of 60 GHz in Figs. 7 and 8 indicates that ratios pertaining to the 3-tissue model are lower overall, suggesting that the 3-tissue model is more conservative. The largest difference between the two is on the order of 30%.

Pulsed exposures and AED BRs

For the 4 cm2-averaged pulsed data below 30 GHz (Fig. 3), safety factors are largely maintained or exceeded, as seen by most ratios exceeding unity. At 30 GHz and beyond (Figs. 3 and 4), there is a substantial decrease in the ratios as the pulse duration and spot size diminish. This is due to the spatial averaging of beams whose diameter becomes much smaller than the averaging area, allowing more intense exposures and higher subsequent temperature rises in the center of the beam. For the 1 cm2 averaged pulsed data (Figs. 5 and 6), this is mitigated somewhat, with generally higher ratios for the smallest spot sizes and shortest pulse durations as compared with the 4 cm2 results. In addition, there is a slow drop in the ratios for a given spot size and pulse duration with increases in frequency due to the increasingly superficial deposition of RF power.

CW exposures and APD BRs

The 4 cm2-averaged data for the CW exposures for td > 360 s (Figs. 7 and 8) show a similar tendency with their AED counterpart (that is, decreasing ratios as the spot size decreases) but with an overall greater maintenance of the safety factors. By contrast, the 1 cm2-averaged APD data (Figs. 9 and 10) show a decrease in the ratio with increasing spot size (except for the smallest spot size FWHM = 0.005 m). This is due to the 1 cm2 average being essentially equivalent to the spatial peak of the beam, with larger beams producing higher temperature rises at the same CW duration. Again, there is an overall greater maintenance of safety factors as compared with the 1 cm2-averaged AED data, with ratios staying above 0.5.

Filtering action of the two spatial averaging tiers

The two spatial averaging tiers should act like a filter such that the smaller of the resulting spatial peak power densities form the BR when the averaging factor is considered. This is most easily seen for the case of CW exposures (td > 360 s) where the spatial peak power density limit (based on the occupational APD BR) is plotted vs. FWHM for an assumed ratio of FWHM/HPBD = 0.8 in Fig. 12. It is seen that the two curves cross over at approximately FWHM = 0.010. Below this spot size, 200 Wm−2 averaged over 1 cm2 forms the BR, while above the BR is 100 Wm−2 averaged over 4 cm2.

Fig. 12:
Maximum allowable spatial peak APD versus FWHM for the 4 cm2 and 1 cm2-averaged, occupational BRs of 100 Wm−2 and 200 Wm−2, respectively.

The situation becomes slightly more complicated for the AED BRs (i.e., td < 360 s), since they serve to limit the applied power density over the duration of the pulse. To find the maximum allowable pulse intensity, the energy density must be converted to a power density for each value of td. This was carried out for selected td of 0.1, 1.0, and 100 s (using an assumed ratio FWHM/HPBD = 0.8). The results are shown in Fig. 13 and reveal that the crossover spot-size depends on the pulse duration. At the lowest pulse duration of td = 0.1 s, the crossover is FWHM = 0.020 m, while it approaches FWHM = 0.010 m (the same as for APD BRs) for longer durations.

Fig. 13:
Maximum allowable (during the pulse) spatial peak absorbed power density versus FWHM for the 4 cm2 and 1 cm2-averaged, occupational AED BRs for t d values of 0.1 s, 1.0 s, and 100 s.

For pulsed exposures, the low safety factors occurring for the smallest spot sizes and short durations seen in the 4 cm2-averaged data would not normally apply due to the filtering action of the two tiers of spatial averaging. The low ratios in the 1 cm2-averaged data are reconcilable in view of the fact that for narrow beams and short durations, the illuminated spot on the skin would likely experience a transient temperature rise that is much briefer than the CEM43 necessary to induce damage to the skin. For example, the worst case ratios applicable to the 1 cm2-averaged data are in Fig. 6 and pertain to FWHM = 0.005 at 200 GHz. The worst-case temperature rise is 8.9 oC, and a worst-case CEM43 of 1.3 min (corresponding to td = 50 s) is estimated, assuming that the 8.9 oC is held for 50 s (when in reality, as per Fig. 2, this occurs for only an instant). This calculation assumed a very worst-case pre-exposure skin surface temperature of 38 oC. This CEM43 is well below the figure of 21 min given in Yarmolenko et al. (2011) as the threshold for minor damage to the skin. In addition to this, the size of the “hot-spot” or diameter of the 50% isotherm on the skin surface after 50 s is estimated to be 7 mm, while the 90% isotherm diameter is under 1.5 mm for a spot size of FWHM = 0.005 m

For the CW (td > 360 s) data, filtering results in the ratios for 1-cm2 averages applying only for FWHM = 0.005 m, while the 4-cm2-averaged ratios apply to all remaining data. Thus, the worst-case ratios correspond to those found in Fig. 9 at 60 GHz for the spot size FWHM = 0.005 m. The ratios range from 0.75 for td = 360 s to 0.73 for td = 5,000 s. The resulting worst-case skin temperature is 41.4 and results in a CEM43 of 6.4 min for a 60-min exposure (assuming a very worst-case pre-exposure skin temperature of 38 oC). Assuming that it were possible to hold such a small beam stationary on the skin for that length of time, this value of CEM43 is still well below the threshold for minor damage. For the CW case, the somewhat higher safety factors and consequent lower temperature rise are offset by the longer exposure times, resulting in a higher worst-case CEM43.

Mitigation of the low safety factors for narrow beams/short pulses

If the low safety factors found in the 1-cm2-averaged pulsed data are undesirable, mitigation can be effected simply by replacing the 1-cm2 average with the spatial peak in the AED BRs. The effect of this can be seen in the resulting temperature rises for the worst-case AED BR safety factors that occurred at 200 GHz (Figs. 4 and 6). Like the maximum allowable APDs in Figs. 12 and 13, temperature rises for the two spatial averaging tiers at the AED BRs display a crossover behavior when plotted vs. FWHM. For the 4-tissue model at 200 GHz, the resulting temperature rises for a single pulse of td = 0.1 s are plotted vs. FWHM (assuming a ratio FWHM/HPBD = 0.8) for the two averaging tiers.

From Fig. 14, it is seen that the two temperature rise responses for the 4-cm2 and 1-cm2-averaged AED BRs cross over at FWHM = 0.020 m (at the same spot size as for the maximum allowable spatial peak absorbed power density in Fig. 13). Below this spot size, the 1-cm2-averaged AED BR would normally apply, resulting in temperature rise responses exceeding the occupational target by a considerable amount (with corresponding low safety factors). If the same AED limit (i.e., 72[0.025 + 0.975(td/360)0.5]) is applied to the spatial peak, the resulting temperature rise response still crosses over at approximately FWHM = 0.020; however, with temperature rises below the crossover that are closer to the temperature rise target (about 3.5 oC for this example), the result is an improved safety factor.

Fig. 14:
Temperature rises at the 4 cm2 and 1 cm2-averaged AED BRs versus FWHM (FWHM/ HPBD = 0.8) for a 0.1 s pulse at 200 GHz. Also shown is the temperature rise for the spatial peak U ab given by U ab = (72[0.025 + 0.975(t d/360)0.5]).

If the smaller of the two spatial averaging tiers in Table 1 (for both td < 360 s and td > 360 s) is replaced with the spatial peak instead of 1 cm2, the low safety factors found in the ratios in Figs. 5, 6, 9, and 10, are improved. Amongst all of the results in those figures, the highest temperature rise resulting from changing the 1 cm2 averaging area to 0 cm2 is an approximate temperature rise of 3.5 oC as compared to a worst-case temperature rise of 8.9 oC obtained using ICNIRP’s original recommended averaging area of 1 cm2.

Effect of perfusion rate variation

As seen in the sample results of Fig. 11, the temperature rise estimate at 200 GHz is relatively unaffected by variations in perfusion rates for pulse durations less than approximately 100 s. This is in agreement with the observation that perfusion requires a relatively long time to transport heat away from the source. The large deviations for long exposures and wide beams is consistent with the scaling of mb−1 found in the steady-state solution of the 1D homogeneous PBHTE. Nevertheless, for the narrowest spot size even at long durations, the sensitivity of the temperature rise to variations in perfusion rate remains low, which is consistent with the approximate, steady state solution in eqn (7). Since the worst of the reduction in safety factors in Figs. 3-9 occur for the narrowest beams, it is somewhat reassuring that these data are least affected by variations in the perfusion rates.


Numerical computations of the SAR distribution and resulting temperature rise in models of superficial tissue at levels allowed by the ICNIRP (2020) BRs for frequencies above 6 GHz were carried out to investigate the safety factors from the assumed OAHET thermal thresholds inherent in the BRs.

The results showed that for a range of beam sizes, pulse durations, and carrier frequencies, the safety factors are reduced from their assumed values of 2 times below an OAHET temperature rise of 5 oC for the occupationally exposed. The lowest safety factors (the worst case was 0.56, resulting in a temperature rise of 1.8 times the OAHET) occurred for single pulses with the smallest assumed spot size of FWHM = 0.005 m (or an assumed unperturbed power density beam diameter of 0.0063 m) for short durations (td < 1 s) at 200 GHz.

Examinations of SAR distributions from half-wave resonant dipoles (Appendix) led to the decision to set a lower value of FWHM = 0.005 m for frequencies of 30 GHz and beyond. While it may be argued that current mobile applications may not deliver such small SAR distributions, there exists the theoretical possibility that even smaller spots sizes can be generated at the higher millimeter-wave frequencies covered in the ICNIRP (2020) guideline.

Safety factors for CW exposures (td > 360 s) were generally higher than for a single pulse, with the worst-case (a safety factor of 1.46 as opposed to the assumed value of 2) again occurring for the smallest spot size.

Despite the low worst-case safety factors and high resulting temperature rises, CEM43 calculations suggest that even minor damage to the skin is unlikely at the current BR levels in ICNIRP (2020). The small beam diameters at which the lowest safety factors occur would suggest that maintaining the beam on the skin for a length of time necessary to induce even minor damage would be practically impossible, especially given that under such conditions, exposed individuals would likely remove the affected tissue away from the RF heat source in response to the sensation of warmth and/or heat pain before tissue damage could occur.

Mitigation of the low safety factors that occurred for the smallest beam diameters can be accomplished by changing the 1 cm2 spatial averaging 0 cm2 (essentially the spatial peak of the beam). If this modification to the local BRs is applied, the associated maximum (worst-case) tissue temperature rise is ≈ 3.5 oC for exposures at the occupational BR (≈ 0.7 oC for general public BR). This modification to the BR rules is easy to implement and would allow use of the ICNIRP (2020) AED formulae and APD limits for localized exposures above 6 GHz to 300 GHz to remain unchanged.


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This appendix investigates SAR spot sizes (FWHM) that are attainable in the near and far field of a half-wave dipole at different offsets from the tissue and their relationship to the unperturbed power density beam diameter (HPBD). The latter is important for computing the spatial averages of beams that produce a given spot size, while knowledge of the smallest possible spot size for a given frequency is necessary for fully evaluating the spatially-averaged BRs.

Computations of SAR spot sizes (FWHM) were performed with WIPL-D (WIPL-D d.o.o., 7 Gandijeva, Belgrade, Serbia) and Ansys HFSS (Ansys HFSS 2021R1, Ansys Canada Ltd., Waterloo, ON, CA) for a dipole illuminating a homogeneous tissue block with dielectric parameters of skin (Hasgall et al. 2018) up to 20 GHz. Dipole lengths were one-half the free space wavelength and had diameters of 2 mm except at 30 GHz, which had a diameter of 1 mm. The tissue block was made sufficiently large as to appear as an infinite half-space. The height and width were nominally four free-space wavelengths, and the thicknesses were approximately a single free-space wavelength.

The SAR distribution was computed along two principal axes (defined here as the E- and H-axes as in Fig. A1) at a depth of 0.1 mm inside the tissue for all frequencies. The front surface of the tissue block is fixed at z = 0 mm, and the dipole is moved in the negative z direction to achieve different offset distances between the antenna and the surface. (The offset is defined as the distance between the skin surface and the dipole axis.)

Fig. A1:
Half-wavelength dipole illuminating a tissue block with dielectric parameters of skin.

The FWHM versus offset is plotted in Figs. A2(a) and A3(a) for 20 GHz and 30 GHz, respectively. Results for the lower frequencies are not shown but display similar behavior except that they produce larger FWHMs for the same dipole offsets. From these figures and the data for the lower frequencies, it is seen that the average spot size for a fixed offset generally decreases with frequency. Small average spot sizes of the order of 4–5 mm were obtained at 20 and 30 GHz for the closest offsets (2 mm). However, it is assumed that a somewhat larger offset between the antenna and the tissue is more likely in an actual device. Thus, the smallest FWHM for 30 GHz and above was taken to be 5 mm, while for frequencies less than this, it was assumed to be 10 mm. Although these are somewhat arbitrary distinctions, they are conservative and allowed for easy implementation in the temperature-rise solver.

Fig. A2:
(a) FWHM of SAR distributions along H and E axes versus dipole offset for 20 GHz and (b) ratio FWHM/HPBD versus dipole offset, also at 20 GHz.

To determine corresponding beam diameters (HPBD) at the different offsets, the same dipole/coordinate system as indicated in Fig. A1 was used except with the tissue block removed. This creates an “unperturbed” beam whose dimensions can be measured on the surface of the imaginary tissue (the plane defined by z = 0 mm).

Rather than plotting the resulting HPBDs directly, the ratio FWHM/HPBD for the same offset and axis (E or H) are plotted in Figs. A2(b) and A3(b). Also plotted in these figures is the line for which FWHM/HPBD = 0.8. This is the assumed value used in the evaluation of the BRs over the full range of FWHMs. For small offsets and resulting FWHMs, it is seen that the average FWHM/HPBD ratio is somewhat below 0.8. However, at the larger offsets that produce the larger spot sizes, the average ratio trends closer to the 0.8 value.

Fig. A3:
(a) FWHM of SAR distributions along H and E axes versus dipole offset for 30 GHz and (b) ratio FWHM/HPBD versus dipole offset, also at 30 GHz.

electromagnetic fields; exposure, radiofrequency; safety standards; modeling, dose assessment

Copyright © 2022 The Author(s). Published by Wolters Kluwer Health, Inc. on behalf of the Health Physics Society.