Emission from human skin in the sub THz frequency band

Recently published Radiometric measurements of human subjects in the frequency range 480–700 GHz, demonstrate the emission of blackbody radiation from the body core, rather than the skin surface. We present a detailed electromagnetic simulation of the dermis and epidermis, taking into account the presence of the sweat duct. This complex structure can be considered as an electromagnetic bio-metamaterial, whereby the layered structure, along with the topology of the sweat duct, reveals a complex interference pattern in the skin. The model is capable of accurately representing the skin greyness factor as a function of frequency and this is confirmed by radiometry of living human skin.


Scientific Reports
| (2022) 12:4720 | https://doi.org/10.1038/s41598-022-08432-5 www.nature.com/scientificreports/ we provide a brief scientific background of the structure of human skin. The human skin model is described and finally the simulation results, discussion and conclusions are presented.

Scientific background
Human skin anatomy. Human skin consists of three main layers: epidermis, dermis; and subcutaneous fatty layer. The outermost two layers, Epidermis and Dermis, are illustrated in Fig. 1, for the relatively thick skin of the hand. Our skin contains 2-5 million eccrine sweat gland ducts 16 . Each of which consist of three main parts: the secretory department, the dermal duct outlet and the upper-coiled outlet duct (see Fig. 2). The eccrine sweat glands are located at the bottom of the dermis, and are deployed throughout the skin. Optical Coherence Tomography (OCT) imaging of the human palm has revealed that the sweat duct in human skin is coiled in the epidermis layer, with a mean diameter of about 90 μm 17 and a mean thickness of the epidermis of 270 μm 17 (measured on a sample size of 32 subject).
The epidermis can be divided into sublayers. This depends on different areas of the skin, but is usually between 4 to 5 in number 18 . For the palm, 5 sublayers are considered. In general these layers consist of of sheets of keratinocytes, which constitute 90% of the cells found in skin, and these are nourished by the diffusion of intercellular fluids, from the dermal vasculature 19 . Keratinocytes undergo 'keratinocytes migration', in which they migrate apically from the deep-most sublayer, the basal layer, and through the granular layers 20 . An accumulation of keratin cells ensues, which then undergoes terminal differentiation to generate the surface layer of cells, the Stratum Corneum (SC). Thus, the live keratinocytes cells' concentration decreases as we move progressively   www.nature.com/scientificreports/ towards the skin surface, leading to a water gradient throughout the epidermis layer. Figure 3 shows the epidermis water concentration profile as a function of the palm skin's depth, measured in the palms of the hand of 15 subjects. The measurements were made in vivo, here Raman spectra were obtained at different depths below the skin surface using a confocal Raman Spectrometer. The average depth of the epidermis was 173 μm with a standard deviation of 37 μm. Reproduced from Egawa et al. 21 ; Copyright 2007, Advanced in Dermatology and Venereology). It was shown that the helical structure of human eccrine sweat ducts, together with the dielectric properties of the human skin, has electromagnetic-properties that resemble to those of passive low Q-factor helical antennas [6][7][8][9]22,23 . The resonance frequency of such kind of antenna can be estimated using Eq. (1) 6 .
where c 0 is the velocity of light in free space, R is the radius of the coiled duct, and ε eff is the effective dielectric permittivity of the dermis, calculated using a mixture formula as follows 22 : where ε bm is the dielectric permittivity of the dry biological structural components, and is estimated to be approximately 2.2 24 , ε w is the dielectric permittivity of water and φ is the volume fraction of the water component 22,24 . The details of the mixture formula application are specified in 6 . In Ref. 14 the natural distribution in both individual coil diameter and water content was shown to lead to an uncertainty of 10% in the value of Eq. (1).
Human skin black body radiation in sub-mm range. The thermal signature of a human being is a familiar image today 25 . Indeed, the human skin temperature of approximately 32 °C leads to an equivalent blackbody spectra in the Infrared 26 . The brightness temperature (or T B ) is the temperature of a blackbody in thermal equilibrium with its surroundings, in order to duplicate the observed intensity of a grey body object at a frequency f 26 This concept is used in radio astronomy, planetary science and materials science 27 . The spectral radiance of a blackbody at temperature T and frequency f, according to Planck's law, is given by: where h = 6.626 × 10 −34 [Js] is the Planck constant, c = 3 × 10 8 [m/s] is the speed of light and k B = 1.38 × 10 −23 [J/K] is the Boltzmann constant, and it is measured in terms of the power emitted per unit area of the body, per unit solid angle, per unit frequency. Although radiating in all frequencies, the main frequency of emission is defined by the temperature of the body and shifts as the temperature increases. At room temperature most of the emission is in the infra-red region of the EM spectrum (30 THz-450 THz). Actual blackbodies do not exist in nature, and real materials emit radiation only at a fraction of an ideal blackbody's radiation. This fraction is described by a parameter called emissivity, which is equal to 1.0 for a perfect blackbody at a constant temperature, and lower than 1 for an actual physical body. A source with lower emissivity regardless of frequency, such as the human body at 37 °C, is referred to as a gray body 28,29 . As the human sweat duct can be considered as an EM entity, one could expect an influence of it on the emission of a blackbody (or a gray body) signal in the mentioned www.nature.com/scientificreports/ frequency band, because they are buried in the dermis and in contact with capillary blood system at 37 °C. In previous works, we have shown that the ac conductivity of the duct's aqueous interior plays a major role in the value of the reflection coefficient [12][13][14] . Therefore, the question begs; Does the ac conductivity in the duct play a similar role in the emissivity? However, at the characteristic frequency of the duct, predicted by its geometry (see right hand side of Fig. 4), there would be a heighten absorption of the blackbody signal. This dependence on the spiral geometry of the duct is reminiscent of the absorption characteristic of a helical antenna, almost like a low-Q resonance, narrow band notch filter, as was shown by our group in [6][7][8][9][10][11]22,23 . In our recent study, we present results that demonstrate that human blackbody is having also a marked contribution in the sub-mm region, previously not noticed. Furthermore, this contribution is sensitive to the physiological state of the subject, opening a possible remote diagnostic channel 5 .

Methods
Human skin model. EM simulations. The EM human skin model is a 3-dimentional stratified structure of the main two layers: dermis and epidermis, where the last is further divided into three sub-layers. In total, the skin model is consist of four layers of different tissues. It is also includes two out of three parts of the sweat duct: the dermal duct and the upper-coiled duct. The skin model configurations are shown in Fig. 4 and the dielectric properties applied to the human skin model are presented in Table 1. The monotonically increasing water content in the epidermis, evident in Fig. 3, leads to a continual change in the effective dielectric permittivity, as defined by Eq. (2). To simplify the simulation and reduce computational load, this layer was approximated by dividing it into two sublayers, based on the average of the water content. In detail, the skin model layers, according to our internal notations, are:  The CST STUDIO SUITE software with the MW MODULE 30 was used (Release Version 2021.05-Jun 28, 2021) for the development of the current model. The Frequency-Domain solver was preferred over the Time-Domain solver for a number of reasons; especially its ability to solve high order elements in a curved mesh, its improved topology change and its detection of mesh move. The model was divided into over 200,000 tetrahedral mesh cells, in an adaptive manner. It means that the coiled portion of the sweat duct was meshed in a finer manner, due to its curvature, as well as the surfaces of the model. Figure 5 demonstrates the adaptive mesh method implemented to our model. Table 1. Dielectric properties applied to the human skin model. The values of permittivity were taken from Ref. 6 . The ac conductivity range of the sweat duct was taken from Ref. 14   Here, as well, a finer mesh division is taking place to overcome the sharp edges of this surface. This figure was generated using CST STUDIO SUITE v2021 30 , https:// www. 3ds. com/ produ cts-servi ces/ simul ia/ produ cts/ cst-studio-suite/. www.nature.com/scientificreports/ Computational method. The accuracy of any simulation greatly depends on the boundary conditions as well as on the computational power available. In order to reduce the computational effort and remove boundary effects, a unit cell boundary condition was applied to the model, so allowing the application of Floquet theorem, which imitate a realistic EM source when being used with a large number of modes. Therefore, for a realistic signal input to the duct was, the first 18 modes of Floquet were applied to the model from its inner side. Namely, Z min port plane. The two fundamental Floquet mode TE(0,0), which is a linearly polarized plane wave, was selected to serve as the perpendicular excitation (see Fig. 6). The emphasis of this research was on the electrical field and current density distributions throughout the model. These distributions reveal the EM behavior of human skin in the sub-mm wave range, and gives a novel insight on the EM mechanism of human skin irradiation in this range. In our previous work, we developed a method which demonstrate the link between the ac conductivity of the coiled sweat duct and the modulated EM skin response of the subjects to an external stimuli that would trigger perspiration14,11.

Results and discussion
Using EM simulations, the electrical field was simulated for nine different frequencies in the range of 500 GHz up to 700 GHz with a constant frequency interval of 25 GHz (500, 525, 550, 575, 600, 625, 650, 675 and 700 GHz). For each frequency, the field distribution was recorded for the same arbitrary fixed phase value of 145°. Figure 7 demonstrate the results of three of the nine frequencies which were simulated (500, 600 and 700 GHz) for an absolute distribution (The following results are shown for all nine frequencies in the figure S1 of the  The simulated electric field shows the dermal duct and the bottom area of the dermis to be the skin components in which the field is mostly concentrated, even to the top of the duct. The simulation of the electric field reveals that is structured inside the layers, in particular, there is an interference pattern of standing waves. In Fig. 7 the red areas indicate field strengths above 0.07 V/m (the maximum field strength is 0.45 V/m at the duct bottom). The decay of the field envelop is exponential, as expected, and can be clearly seen in Fig. 10. In Fig. 7 the dependence on frequency of the standing wave structure, a clear etalon effect is clearly seen. In Fig. 8, the simulation is for a single frequency-550 GHz-but with different initial phases, representing the passage of the plain wave through the strata (The following results are shown for all nine phases, which were simulated, in the Fig. S2 of the supplementary). Figure 9a shows the electric field averaged in the xy-plane, as function of z-axis, i.e., along the skin depth for the nine frequencies (500, 525, 550, 575, 600, 625, 650, 675 and 700 GHz). 0 μm is the bottom of the dermis layer, 1,125 μm is the location at which the dermal duct ends and the coiled section of the duct begins. At around 1,440 μm the skin interfaces with the outer surrounding. In the simulation this is air. In Fig. 9b the E-Field distribution, along with the averaged amplitude along the z-axis, is shown for f = 550 GHz.
As stated above and illustrated in Fig. 10 the decay of the field in the dermis is exponential and follows Beer's law 31 , with an interference pattern superimposed upon it. Although greatly attenuated, this general picture is continued into the epidermis. The boundary between the skin and the air leads to a modification of the wave structure (see inset of Fig. 9a), as the wave propagates outward. Figure 10 shows an enhanced image of the simulation whereby red indicates field strengths above 0.00382 V/m. The image reveals the fine structure of the field in the epidermis. One notes the effect of multiple reflections is to 'compress' the effective field envelope. Although the wavelength in the epidermis is approximately 320 microns, the thickness of the epidermis varies from 300 to 500 microns, depending on the position of the papillae. This leads to a more complex field profile and multiple interference peaks.
To investigate the role of the sweat duct in EM field structure, we have simulated the electrical field in two versions of the model; one that includes the sweat duct and one without the sweat duct. Figure 11 shows the electric field strength for two different frequencies, 550 and 700 GHz. It is clear the presence of the duct leads to a signal modulation by the absorption of energy in the epidermis (starting at approximately 1,125 microns and finishing at 1,440 microns) and deepens the interference pattern in the dermis.
Finally, we have compared the simulation results to the thermal radiation power measured from the human skin at 9 frequencies in the frequency range 500-700 GHz with a step of 25 GHz 5 . As described in the introduction, the brightness temperature has been measured for 3 subjects at these frequency points. Each subject was measured at each point 3 times 5 . The measurements were taken from the palm and so the skin can be considered as thick. The full description of these measurements and their results can be found in Ref. 5. In order to compare to the simulation results one first cast them in terms of an effective brightness temperature.
where α f is the grayness factor (emissivity) and T is the physical temperature of the emitting object.
The grayness factor can be determined through the field energy losses in the skin during the waves propagation from the port (Z = 0 μm) to the surface (Z = 1,440 μm) by considering the intensity of the E-field at the skin surface, normalized by the input port field intensity , where the field value, E L, f , is taken just above www.nature.com/scientificreports/ the skin surface at L = 1,537 μm. The value of the input field, E o , can be estimated inside the skin from the definition of the simulation as E o ∼ = 1.3×10 −3 V/m for a port power P = 5 nW, once the impedance mismatch at the port is taken into account. As a result, the intensity I skin f of the field in the skin is However, in the real radiometric experiment, the reflected wave passes into the region Z < 0 of body, and we have to assume that it would decay rapidly at the penetration depth. Thus, when comparing with experiment, we must assume that the energy of the field accumulated in the skin layer is completely absorbed and therefore Eq. (5) can be equated to the greyness factor, α f = I skin f .
Note that in simulations of wave propagation through the skin layer, its temperature T was accounted for, while the measured brightness temperature in the radiometric experiment in vivo is proportional to the skin temperature T . Consequently, we compare the qualitative nature of both by their normalized values. Such comparison Figure 9. (a) The electrical field as function of distance in Z direction, i.e., throughout the skin model, for a fixed phase 145° and 9 different frequencies. (b) The electric field as function of the z-axis next to the 3D human skin model, for a perspective. This figure was generated using CST STUDIO SUITE v2021 30 , https:// www. 3ds. com/ produ cts-servi ces/ simul ia/ produ cts/ cst-studio-suite/. www.nature.com/scientificreports/ is shown in Fig. 12. The black solid spheres are the measurement, the red solid spheres are the simulation results. The qualitive behavior of the simulation result follows closely to that of the radiometric measurements.

Conclusions
In this work, we have presented an EM model of the human skin, which takes into account the skin multi-layered structure and the sweat duct. For the first time, the dermal portion of the duct was considered. We conducted EM simulations in the frequency range of 500 GHz up to 700 GHz. The model reveals a complex interference structure of the E-field intensity in the skin. In the dermis, this pattern is overlain on a typical Beer's law absorption.
In the epidermis, multiple reflections from the skin surface and dermis/epidermis boundary lead to constructive interference. Furthermore, we trace the origin of the field the core blackbody radiation of the subject. As would be expected, the simulated greyness factor, as seen from the skin surface, replicates the measured radiometry intensities of our subjects 5 , we conclude that our simulation model is verified by experiment, lending confidence to the obtained interference patterns.  and by in vivo radiometric measurements of the skin thermal radiation (Black) 5 . The measurements accuracy is ± 1.7 degree. It can be seen that qualitatively the simulation and experiment results are having the same nature and follow the same trend.