Calculated Epithelial/Absorbed Power Density for Exposure From Antennas at 10–90 GHz: Intercomparison Study Using a Planar Skin Model

International organizations have collaborated to revise standards and guidelines for human protection from exposure to electromagnetic fields. In the frequency range of 6–300 GHz, the permissible spatially averaged epithelial/absorbed power density, which is primarily derived from thermal modeling, is considered as the basic restriction. However, for the averaging methods of the epithelial/absorbed power density inside human tissues, only a few groups have presented calculated results obtained using different exposure conditions and numerical methods. Because experimental validation is extremely difficult in this frequency range, this paper presents the first intercomparison study of the calculated epithelial/absorbed power density inside a human body model exposed to different frequency sources ranging from 10–90 GHz. This intercomparison aims to clarify the difference in the calculated results caused by different numerical electromagnetic methods in dosimetry analysis from 11 research groups using planar skin models. To reduce the comparison variances caused by various key parameters, computational conditions (e.g., the antenna type, dimensions, and dielectric properties of the skin models) were unified. The results indicate that the maximum relative standard deviation (RSD) of the peak spatially averaged epithelial/absorbed power densities for one- and three-layer skin models are less than 17.49% and 17.39%, respectively, when using a dipole antenna as the exposure source. For the dipole array antenna, the corresponding maximum RSD increases to 32.49% and 42.55%, respectively. Under the considered exposure scenarios, the RSD in the spatially averaged epithelial/absorbed power densities decrease from 42.55% to 16.7% when the frequency is increased from 10–90 GHz. Furthermore, the deviation from the two equations recommended by the exposure guidelines


I. INTRODUCTION
Owing to the development of various wireless systems, research on the protection of humans exposed to electromagnetic fields (EMFs) has attracted considerable attention [1], [2], [3], [4]. In 2019 and 2020, the IEEE International Committee on Electromagnetic Safety (ICES) Technical Committee (TC) 95 and the International Commission on Non-Ionizing Radiation Protection (ICNIRP) revised the exposure standards and guidelines, respectively, to prescribe the exposure limits for people in restricted environments/occupational exposure and for unrestricted environments/general public exposure conditions [5], [6].
In the revised standard/guidelines, the two-tier approach is used, similar to the previous versions. The epithelial/absorbed power density (hereafter referred as APD) is used as a new internal physical quantity to set the dosimetric reference limit (DRL) or basic restriction (BR), which is derived from the operational threshold of adverse health effects, considering the safety or reduction factor in the frequencies from 6-300 GHz. These DRL or BR were derived based on thermal modeling [7], [8], [9], [10], [11], [12], which provides a high degree of protection against dominant adverse health effects of exposure, that is, localized temperature elevation on the surface of human skin tissue. To correlate well with the local maximum temperature increase, it is suggested that the APD be averaged over an area of 4 cm 2 from 6-300 GHz. Above 30 GHz, a smaller spatial averaging area of 1 cm 2 should also be considered to account for possible narrowbeam exposure scenarios. For this averaging area, the limit was relaxed by a factor of 2. Conversely, the permissible external exposure reference level (ERL) [5] or reference level (RL) [6], that is, the incident power density (IPD) in free space, which is derived from the APD, has been prescribed conservatively. Based on the exposure guidelines/standards, the IPD should be averaged over an area of 4 cm 2 for frequencies ranging from 6-300 GHz. For frequencies higher than 30 GHz, additional criteria of the IPD averaged over 1 cm 2 are given with a relaxation of ERL/RL by a factor of two for local beam-like exposures, similar to those of the spatial average of the APD.
Under Subcommittee 6 of the IEEE ICES TC95, a new working group (WG) was established, which aims to study and quantify the effects of different schemes on the spatial average of the APD above 6 GHz. The cause of the variances of the numerical calculations in the dosimetry analyses will be evaluated through an objective comparison of the computation results from participating organizations using their proper assessment methods and average schemes with various body and antenna models. This intercomparison of the specific absorption rate (SAR) has been conducted for standardization in frequency bands of a few GHz [48]. This is because the measurement of the field strength in biological bodies is difficult; thus, a computational approach is often conducted. Additionally, for exposure at higher frequencies (particularly above 6 GHz, where the penetration depth is below approximately 1 cm), precise measurement in the depth direction becomes extremely difficult.
The WG task for the average scheme and assessment method of the spatially averaged APD is divided into three phases: • intercomparison of spatially averaged APD using conventional planar models • appropriate average schemes using non-planar shaped models (e.g., cylinder or sphere) • ultimate challenge of the complex irregular voxel model of realistic human tissue, including thermal analysis To evaluate the deviation of the spatially averaged APD caused by the numerical calculation method of each research VOLUME 11, 2023  organization, a traditional planar skin model with unified computational conditions was utilized for the first step of the intercomparison, as mentioned above. This study computed the spatially averaged IPD and APD at the skin surface from 10-90 GHz using computational approaches with unified body and antenna models. An intercomparison of the numerical calculation variances from different research organizations using their simulation codes and commercial electromagnetic (EM) solvers was performed.  Table 1 presents an overview of the scenarios evaluated numerically by participating organizations. As presented in the table, a separation distance between the antenna and skin surface ranging within 5-15 mm was considered for frequencies of 10 and 30 GHz. At 90 GHz, the separation distances were set from 2-10 mm for the extreme near-field exposure conditions of interest at higher frequencies. Nonetheless, in most wireless device application scenarios, the antenna was not located close to the body to such a separation distance. All the conditions presented in this study clarify the variances in spatially averaged APD computed by different research organizations.

II. ANALYTICAL MODEL AND METHOD
The antenna and planar skin models for the numerical simulations used by different organizations are shown in Fig. 1. As suggested in the discussion of the WG under Subcommittee 6 of the IEEE ICES TC95, a single half-wavelength dipole antenna and a 4 × 4 dipole antenna array were used in this intercomparison study. The half-wavelength dipole was modeled as a perfect electric conductor. Dipoles were designed at 10, 30, and 90 GHz by each research organization. For most research organizations, the antenna was resonated with an adjusted length to obtain the maximum radiation power emitted from the antenna to the extent possible. Table 2 summarizes the dipole lengths used by each organization. For the 4 × 4 dipole antenna arrays, almost the same length ( Table 2) was used by the corresponding organization  of the dipole element in the array. The separation distance between the feeding points of any two adjacent dipole elements is λ/2, where λ is the free-space wavelength. For both dipole and dipole arrays, the total antenna input power was normalized to 10 mW representing a typical power level of mobile devices in the considered frequency range, as in the previous WG [40], [41].
On the other hand, a one-layer skin model and stratified models composed of skin, fat, and muscle layers were employed in this study for dosimetry analysis (Fig. 1). The dimensions of the skin models were L × L × T (mm 3 ; Table 3). The dielectric properties of the tissues obtained by a four-Cole-Cole dispersion model [49], [50], [51] were employed. The electrical parameters for each tissue layer in the skin model are summarized in Table 4. Table 5 summarizes the numerical techniques used to evaluate the IPD in free space and the APD inside the simplified human tissue models. The spatial resolutions used in each organization were also summarized. The finite-difference time-domain (FDTD) [51] method was adopted by six organizations that used their own developed in-house codes. In   addition to the FDTD methods, the Galerkin-Bubnov indirect boundary element method (GB-IBEM) [53], finite integration technique (FIT) [54], finite element method (FEM) [55], and transmission line method (TLM) [56] have been used separately by other research organizations. It should be noted that the FIT, FEM, and TLM methods used by O4, O8, and O10, respectively, are the three different EM-solvers from commercial simulation software. The other group (O11) that used the FEM method was performed using different types of commercial software. Therefore, this study first covered almost all the commonly used methods of EM simulation for dosimetry analysis without the duplication of commercial software and code. This enables the provision of very neutral and representative intercomparison results to determine the deviation of the calculated APD caused by different numerical methods.
First, the IPDs in free space were calculated without the presence of the body to clarify the influence of the different algorithms on the EM calculations of the antenna near-field. Similar to the previous WG, two definitions of the spatial-average incident power density (sIPD), i.e., the normal (sIPD n ) and norm (sIPD tot ) component of the time-averaged power density for the EMF, were examined in the absence of the human body (Eqs. (6) and (7) in [41]). The spatial-average APD (sAPD) in the tissue was calculated for the modeling scenario using the simplified human block model. As recommended in the ICNIRP-2020 exposure guidelines [6], two general equations for deriving the sAPD were employed by each organization, which are expressed by the following formulae: where E and H indicates the effective values of the complex electric and magnetic fields inside the body surface, respectively; * denotes the complex conjugate; z max is the depth where the EMF is negligibly small in respect to that at the skin surface; r denotes the position vector; and ds is the integral variable vector whose direction is normal to the integral area A on the body surface (x-y plane at z = 0). Because only the planar skin model was considered in this paper, the averaging areas in Eqs. (1) and (2) were averaged over a cubic volume and square area of the flat body surface, respectively, corresponding to the average area of the sIPDs.

III. INTERCOMPARISON RESULTS
The intercomparison results in terms of the peak spatialaverage IPD and APD (psIPD and psAPD) using different antennas are presented in this section. The psIPD n , psIPD tot , and psAPD were averaged over an area of A = 4 cm 2 and A = 1 cm 2 at 10-90 GHz. Figures 2 and 3 show the results of psIPD as a function of the antenna-to-skin separation distance d exposed to the single half-wavelength dipole or 4 × 4 dipole array antenna for the exposure scenarios in Table 1  In the case of the dipole antenna ( Fig. 2), both psIPD n and psIPD tot decrease monotonically with an increase in the separation distance d. psIPD tot is greater than psIPD n in the 5-10 mm range at 10-30 GHz and the 2-5 mm range at 90 GHz. At d > 10 mm, all the results do not show any significant differences between the two definitions of the sIPD. The maximum absolute differences of the psIPD among all the research groups are within 0.62, 0.45, and 0.43 dB respectively, at 10, 30, and 90 GHz when d > 5 mm. For the 4 × 4 dipole array (Fig. 3), the profiles of both psIPD n and psIPD tot exhibit different trends compared to those of the dipole antennas owing to the dispersion of multiple near-field peaks generated by the wave source of the antenna array. Moreover, the difference between the psIPD n and psIPD tot was reduced.

A. COMPARISON OF PEAK SPATIAL-AVERAGE INCIDENT POWER DENSITY
The maximum absolute differences of psIPD among all the organizations for the 4 × 4 dipole array are within 5.09, 0.77, and 0.6 dB respectively, at 10, 30, and 90 GHz when d is greater than 5 mm. The above results indicate that, at a separation distance d > 5 mm, there is no obvious discrepancy between the different EM-simulation and spatial average methods for the calculation of psIPD n and psIPD tot for either the dipole or dipole antenna arrays.
Tables 6 and 7 summarize the mean value and standard deviation of computed psIPD n and psIPD tot for the dipole and dipole array, respectively. The separation distances from the antenna for the cases of d = 5, 10, and 15 mm for 10-30 GHz and d = 2, 5, and 10 mm for 90 GHz were compared. The relative standard deviation (RSD), which is defined as the ratio of the standard deviation to the mean value, was analyzed as a metric for the intercomparison of different research groups.
For the dipole source, as presented in Table 6, the maximum RSD values of psIPD were 4.05% (d = 5 mm), 2.58% (d = 15 mm), and 4.84% (d = 2 mm), respectively, at a frequency of 10-90 GHz. Conversely, for the case of the 4 × 4 dipole array, as presented in Table 7, the maximum RSD was approximately 23.55% (d = 5 mm), 5.0% (d = 5 mm), and 5.26% (d = 2 mm) at a frequency of 10-90 GHz. The above results agree well with the outcomes of previous WG activities (see Tables 6 and 7 in [41]). This shows that the impact on the calculation of the antenna near-field distribution in free space caused by the different numerical methods used by each organization is very small, demonstrating the effectiveness of EM-simulation methods for the antennas themselves.  tance d exposed to the dipole when the averaging area A is 1 and 4 cm 2 , respectively. In Figs. 4 and 5, the solid lines with circular markers indicate the results obtained using the onelayer model, whereas the dashed lines with square markers denote those obtained using the three-layer model.
As shown in Figs. 4 and 5, for both the one-and threelayer skin models exposed to a dipole antenna, the profiles of psAPD decrease gradually as d increases. At 10 GHz, relatively large deviations are observed in the different organizations. The maximum absolute differences of psAPD are 3.24 and 3.0 dB at d = 5 mm, respectively, for the one-and three-layer models when A = 1 cm 2 . When A increases to 4 cm 2 , the corresponding differences are reduced to 3.62 and 2.89 dB, respectively.
However, at frequencies ranging from 30-90 GHz, the deviations caused by the EM simulation methods are very small for both the one-and three-layer models. As shown in Figs. 4 (b) and (c) and Figs. 5 (b) and (c), the maximum absolute differences of psAPD are within 1.07 and 2.46 dB, respectively, at 30 and 90 GHz when A = 1 cm 2 . This difference is further reduced to 1.21 and 2.49 dB, respectively, for A = 4 cm 2 . Figures 6 and 7 show the intercomparison results of the psAPD as a function of the antenna-to-skin separation distance d exposed to the radiation sources of the 4 × 4 dipole array when the average area A is 1 and 4 cm 2 , respectively. Unlike the dipoles illustrated in Figs. 4 and 5, the deviation of psAPDs at 10 GHz is nonexistent at d = 5 mm, but at d = 15 mm. The maximum absolute differences of psAPD at 10 GHz are 9.84 and 10.15 dB at d = 15 mm when A is 1 and 4 cm 2 , respectively.    Tables 8 and 9 list the statistical mean values and standard deviations of psAPD for cases of the dipole and dipole array, respectively. For the dipole source (Table 8), the maximum RSD of the one-layer models were 20.0%, 8.03%, and 13.33%, which occurred at frequencies of 10 GHz when d = 5 mm, 30 GHz when d = 10 mm, and 90 GHz when d = 10 mm.
When using the three-layer skin models, the corresponding maximum RSD were 17.39%, 5.77%, and 7.02%, which occurred at 10 GHz when d = 5 mm, 30 GHz when d = 5 mm, and 90 GHz when d = 2 mm. 7426 VOLUME 11, 2023 For the dipole array, as presented in Table 9, the maximum RSD of the one-layer models were 33.13%, 32.49%, and 12.07% at 10 GHz when d = 15 mm, 30 GHz when d = 5 mm, and 90 GHz when d = 10 mm, respectively. When using the three-layer skin models, the corresponding maximum RSDs were within 42.55%, 29.55%, and 16.7%, respectively, at 10 GHz when d = 15 mm, 30 GHz when d = 5 mm, and 90 GHz when d = 5 mm.
The above results indicate no evident difference exists between the psAPD values in the different organizations when using dipole antennas at 30 GHz and 90 GHz; however, some deviations occur at 10 GHz when d = 5 mm. The difference in the psAPD from 11 organizations when using the 4 × 4 dipole array was relatively greater than that of the dipole at 30 and 90 GHz. Additionally, a significant difference is observed at 10 GHz when d = 15 mm.
These facts indicate that a difference in the numerical analysis of the spatial-average APD among various organizations may exist depending on the different antenna types at specific frequency ranges as well as antenna-to-skin separation distances, whereas the difference caused by the skin models is relatively marginal. Particularly, when using a dipole VOLUME 11, 2023   array at 30 GHz, relatively large deviations were observed, regardless of the skin models. To determine the skewness and tail weights of the data batches, statistical analysis of the significant differences in the calculated sPDs is conducted hereafter.

C. STATISTICAL ANALYSIS OF THE SIGNIFICANT DIFFERENCE
The variations in the psAPD values between the different groups in the previous sections suggest that they may be affected by the antennas types. In this section, the variability in psAPD caused by antenna models is evaluated. Figures 8 and 9 show the box plots of the calculated psIPD and psAPD, respectively, as a function of the frequency from 10 to 90 GHz. The results are shown in Figs. 8 (a-b) and 9(a-b), respectively, when using a half-wavelength dipole and 4 × 4 dipole array. In Figs. 8 and 9, the height of the rectangular box indicates the interquartile range (IQR), which is the range between the 75th and 25th percentiles. The horizontal line in the middle of the box denotes the statistical median value of psPD from different groups. The error bars show the range of maximum to minimum values, where the 7428 VOLUME 11, 2023 plus sign indicates the outliers. Notably, for each box with error bars, three sets of antenna-to-skin separation distances (5, 10, and 15 mm or 2, 5, and 10 mm) and two types of skin models (one-and three-layer; or two definitions for sIPD, namely, sIPD n and sIPD tot ) were included. Therefore, the 11 research groups provided a maximum of 66 sets of data in each frequency band and averaging area, which was sufficient for statistical analysis.
In Fig. 8 (a), for the sIPD values obtained using a dipole antenna, only one outlier was observed at 90 GHz when A = 4 cm 2 . When using a dipole array, as can be seen in Fig. 8 (b), four outliers appear at 10 GHz. However, the IQRs of the sIPD values for the dipole array cases are much smaller than those of the dipole antennas. For the psAPD values obtained using the dipole antennas, as illustrated in Fig. 9 (a), two outliers occurred at 10 GHz when A = 4 cm 2 . When the dipole array was used, there were no outliers. Conversely, the IQRs of the psAPD values for the dipole arrays at 30 and 90 GHz are comparable or even larger than those of the dipole antennas, particularly when A = 1 cm 2 . However, the deviation caused by the numerical calculation error is not evident for both the psIPD and psAPD values.

D. VARIABILITY OF APD FOR THE DIPOLE ARRAY AT 30 GHz
As shown in Figs. 6 (b) and 7 (b), relatively large variations in the psAPD values occurred when using the 4 × 4 dipole array antennas at 30 GHz. In this section, the variability in the psAPD caused by the number of dipole antenna elements is evaluated. Figures 10 and 11 show the calculated psIPD and psAPD values, respectively, as a function of the antenna-to-skin separation distance d at 30 GHz, which were provided by O1. For simplicity, only the results for sIPD tot are shown in Fig. 10. Figs. 10 (a-b) and 11 (a-b) denote the average areas of 1 and 4 cm 2 , respectively. To evaluate the impact of the number of antenna arrays, three different antenna typeshalf-wavelength single dipole, 2 × 2, and 4 × 4 dipole arrays-were compared.
As shown in Fig. 10 (a), all the results of psIPD smoothly change with an increase in the antenna-to-skin separation d. VOLUME 11, 2023  For the single dipole and 2 × 2 dipole arrays, the trends are close to monotonically decreasing as d increases. For the case of the 4 × 4 dipole array, the curve first exhibits an upward trend and then slowly declines as d increases. This may be due to the increased number of antenna arrays or dimensions, which changes the boundary conditions of the near field. However, when A = 4 cm 2 , the above changes become less observable, as illustrated in Fig. 10 (b).
However, in Fig. 11 (a), the curves of psAPD when using the dipole arrays show evident periodic fluctuations as d increases. Particularly, at integer multiples of half wavelength, that is, 10 mm at 30 GHz, some bursts can be observed. This phenomenon did not change as the average area increased from 1 to 4 cm 2 , as shown in Fig. 11 (b).
From the above results, it is deduced that, unlike the results of psAPD when using a single dipole, an increase in the number of dipole arrays may significantly change the mutual interaction between the antennas and skin models. This eventually results in a calculation error of psAPD at 5, 10, or 15 mm at 30 GHz, which corresponds well with the relatively large deviation shown in Figs. 6 (b) and 7 (b).

E. VARIABILITY OF APD DEFINITION
In this intercomparison study, the formula for deriving the sAPD was not unified among all research groups. Therefore, it is necessary to discuss the difference in the calculated sAPD caused by the two definitions in (1) and (2), that is, the volumetric integral for the entire skin model and surface integral of the normal component of the Poynting vector perpendicular to the skin model, respectively, as recommended by the ICNIRP exposure guidelines [6].
Tables 10 and 11 list the results of the maximum absolute difference in psAPD ( psAPD) due to different definitions using dipole and dipole array antennas evaluated by O6 and O8, which employed the numerical methods of the FDTD and FEM, respectively. The same separation-distance conditions and skin models were used.
In Table 10, for the FDTD method, the maximum psAPD caused by the use of different equations are within 0.2 dB for the dipole and dipole array at frequencies within 10−90 GHz when one-layer skin models are employed. When using the three-layer models, the corresponding difference did not exceed 0.51 dB. When using the FEM method, as shown in Table 11, the maximum psAPD slightly increases to within 0.49 and 0.51 dB, respectively, for cases of the dipole and dipole array at 10−90 GHz when the one-layer skin models are used. The corresponding difference is up to 0.69 and 1.3 dB, respectively, when using the three-layer skin models.

IV. DISCUSSION AND CONCLUSION
Compared with the intercomparison study of previous WG [40], [41], this study unified simulation conditions to the extent possible, such as the antenna type for the radiation source, planar skin model, and dielectric constants of body tissues, to minimize the number of variables that may affect the fairness of the intercomparison results. Moreover, the number of research groups as well as the EM-simulation algorithm have increased from the last 6 to 11. We believe that the established exposure scenarios considered in this study are more accurate and rigorous for clarifying the validity of the APD averaging method, which will be very informative for the next intercomparison of dosimetry analysis using more realistic body models.
In the first step of the intercomparison of the peak value of spatially averaged incident power densities, that is, psIPD n and psIPD tot , all the results provided by the eleven groups showed good agreement with each other. For the cases using dipole antennas, the maximum RSDs among the different organizations were 4.04%, 2.58%, and 4.84% at frequencies of 10, 30, and 90 GHz, respectively. For the dipole array, the maximum RSDs did not exceed 23.55%, 5.0%, and 5.26% at frequencies of 10, 30, and 90 GHz, respectively. Relatively large deviations of up to 23.55% were observed for the dipole arrays at 10 GHz when d = 5 mm. For a large dimension of an array with 16 dipole elements, this distance can be regarded as an extreme near-field at 10 GHz. In this case, it is understandable that the difference in the electromagnetic field distribution obtained by different simulation methods increases owing to different approaches for solving Maxwell equations with different boundary conditions and resolutions. Additionally, the maximum RSDs of all the results did not exceed 5.26%. The above results are in agreement with the outcomes from a previous study (Tables 6 and 7 in [41]), demonstrating the effectiveness of all the employed methods for the EM simulation of the antenna near-field distribution.
As the second step of intercomparison for the peak value of spatially averaged epithelial/absorbed power densities, that is, psAPD, an excellent agreement for the considered exposure scenarios using a dipole antenna can still be observed. At frequencies of 10, 30, and 90 GHz, the maximum RSDs among different organizations were 18.83%, 8.03%, and 13.33%, respectively, for both the one-and three-layer skin models. When using dipole arrays as the radiation source, relatively obvious deviations in the calculated psAPD are shown in several scenarios (e.g., 10 GHz at d = 15 mm, 30 GHz when d is from 5 to 15 mm, and 90 GHz at d = 10 mm). Despite this, the maximum RSDs for the cases using the dipole arrays did not exceed 42.55%, 29.55%, and 16.7%, respectively, at frequencies of 10, 30, and 90 GHz, regardless of the skin model. Based on the statistical significance analysis, the number of outliers is very small compared to the overall sample of the calculated data, including all the parameters of the antenna types, skin models, and separation distance. Furthermore, it is confirmed that the maximum difference caused by the equations of deriving the sAPD recommended by the ICNIRP exposure guidelines, i.e., the volumetric integral for the entire skin model and surface integral of the normal component of the Poynting vector perpendicular to the skin model, is generally approximately 0.5 to 1 dB or even less. The difference depends on the calculation condition, e.g., field segmentation; here, we found that the difference can be suppressed to approximately 0.2 dB or lower in almost all exposure scenarios.
This study represents the first intercomparison of the calculated sAPD in a simplified body model for exposure from different antennas ranging from 10 GHz to 90 GHz. The main causes of variance in the numerical calculations in the dosimetry analysis of psAPD were evaluated using an objective comparison of the analysis results from different research groups. The fair agreement among the intercomparison results demonstrated that deviations caused by the numerical method, definition, and spatial average of the calculated psAPD using planar skin models are marginal. However, with the increasing number of antenna arrays, the dependence on the antenna types that are used as the radiation sources for the dosimetry analysis of sAPD may be slightly increased. In 2016, she joined the Department of Electrical and Mechanical Engineering, Nagoya Institute of Technology, where she is currently an Associate Professor. Her current research interests include electromagnetic and thermal dosimetry modeling in humans for radio frequency and ambient heat exposures. Dr