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Modelling millimetre wave propagation and absorption in a high resolution skin model: the
effect of sweat glands
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2011 Phys. Med. Biol. 56 1329
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IOP PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 56 (2011) 1329–1339 doi:10.1088/0031-9155/56/5/007
Modelling millimetre wave propagation and
absorption in a high resolution skin model: the effect
of sweat glands
Gal Shafirstein1and Eduardo G Moros2
1Department of Otolaryngology, College of Medicine, University of Arkansas for Medical
Sciences, 4301 W. Markham, # 543, Little Rock, AR 72205, USA
2Division of Radiation Physics and Informatics, Department of Radiation Oncology, College of
Medicine, University of Arkansas for Medical Sciences, 4301 W. Markham, #771, Little Rock,
AR 72205, USA
E-mail: shafirsteingal@uams.edu
Received 15 September 2010, in final form 6 January 2011
Published 4 February 2011
Online at stacks.iop.org/PMB/56/1329
Abstract
The aim of this work was to investigate the potential effect of sweat gland
ducts (SGD) on specific absorption rate (SAR) and temperature distributions
during mm-wave irradiation. High resolution electromagnetic and bio-heat
transfer models of human skin with SGD were developed using a commercially
available simulation software package (SEMCAD XTM). The skin model
consisted of a 30 μm stratum corneum, 350 μm epidermis and papillary
dermis (EPD) and 1000 μm dermis. Five SGD of 60 μm radius and 300 μm
height were embedded linearly with 370 μm separation. A WR-10 waveguide
positioned 20 μm from the skin surface and delivering 94 GHz electromagnetic
radiation was included in the model. Saline conductivity was assigned inside
SGD. SAR and temperatures were computed with and without SGD. Despite
their small scale, SAR was significantly higher within SGD than in the EPD
without SGD. Without SGD, SAR and temperature maxima were in the dermis
near EPD. With SGD, SAR maximum was inside SGD while temperature
maximum moved to the EPD/stratum-corneum junction. Since the EPD
participates actively in perception, the effect of SGD should be taken into
account in nociceptive studies involving mm-waves. This research represents
a significant step towards higher spatial resolution numerical modelling of the
skin and shows that microstructures can play a significant role in mm-wave
absorption and induced temperature distributions.
0031-9155/11/051329+11$33.00 © 2011 Institute of Physics and Engineering in Medicine Printed in the UK 1329
1330 G Shafirstein and E G Moros
1. Introduction
The last 20 years have witnessed an explosion in human exposure to electromagnetic (EM)
radiation in the millimetre-wave band. When aimed towards humans, radiation in this part
of the EM spectrum is mostly absorbed in the skin (Alekseev et al 2005,2008, Alekseev
and Ziskin 2003,2007, Walters et al 2000). The interaction of millimetre wave (mm-wave)
radiation with the skin depends on the dielectric properties of the various components of the
skin. It is well known that dielectric properties of biological tissues substantially depend
on water content (Alekseev et al 2008, Naito et al 1997). The dielectric properties of the
human skin in vivo in the range of the frequencies of 37–74 GHz under the assumption that
the dielectric constant of the various skin layers is determined by their respective bulk water
content was investigated by Alekseev et al (2008) and Alekseev and Ziskin (2007). They also
assumed that the non-constitutive water contained in the stratum corneum (SC) affects the
interaction of mm-wave with human skin. In their model, the skin structure was described
as two layers: the SC and a combined epidermis and papillary dermis (EPD)/dermis layer.
Analytical and finite differences methods were used to model EM propagation, reflection and
absorption in the skin in the forearm and palm of the hand. The thickness of the SC was
assumed to be 0.015 and 0.4 mm in the forearm and palm, respectively, and the modelling was
verified with experimental results. Their work showed that the thicker the SC (more water)
the more reduced was the reflection of the mm-wave radiation. A thick and moist SC acted as
a matching layer (Alekseev et al 2008).
Recent studies by Feldman et al (2008), (2009) suggested that the human eccrine sweat
ducts or sweat gland ducts (SGD) have a major effect on the reflection and propagation of mm-
waves in the human skin . The eccrine sweat duct system is responsible for thermoregulation
of the body and is under the control of the sympathetic nerve response (Shibasaki et al 2006).
The EPD contains between 2 and 5 million SGD that extend into the dermis. The concentration
of these glands varies from site to site in the human body (Wilke et al 2007). The greatest
density of SGD is on the palms of the hands and soles of the feet, followed by the head, trunk
and limbs. Increased in sweating occurs through the combination of increasing the number
of sweat glands that are activated and increasing the amount of sweat released per gland.
Sweat is primarily water (99%) and therefore it can influence the absorption of mm-waves in
skin. Furthermore, the shape of the sweat glands can also affect the absorption and reflection
of mm-waves by the skin. Feldman et al 2008), (2009) demonstrated that the helical part
of the SGD located in the EPD may act as low Qhelical antennas. They have shown that
for the frequency region of 75–110 GHz (within the W band) the helical glands will affect
the modulus of reflection. They assumed that proton hopping was the primary mechanism
for electrical current transport along the sweat ducts during exposure to mm-wave radiation.
They verified their results with a clinical study. Thus, their work offers a new direction in the
understanding of the absorption of mm-waves in the human skin. However, in their studies,
the effect of the SGD on the specific absorption rate (SAR) and resulting temperature increase
was not investigated. The objective of this work was to model the effect of SGD on SAR and
temperature increase due to exposure of skin with SGD to mm-wave radiation.
2. Methods
2.1. Electromagnetic modelling
The SEMCAD X (Schmid & Partner Engineering AG, Zurich, Switzerland) finite differences
time domain (FDTD) software was used to simulate the propagation and interactions of 94 GHz
Modelling millimetre wave propagation and absorption in a high resolution skin model 1331
Figure 1. Cross section of the waveguide (blue) and the skin geometry (green and brown) showing
the SGD (yellow) embedded in the EPD and dermis. A conformal elongated grid was used to mesh
the SGD. The green grid in the background is the mesh in the EPD region.
electromagnetic (EM) radiation in a three-dimensional numerical model of the skin containing
a few SGD. A cylinder of 8 mm in diameter and 1.38 mm high was used to simulate the skin
anatomy. The cylinder consisted of a 0.03 mm upper layer representing the SC, a 0.35 mm
intermediate layer representing EPD, anda1mmthickdermisatthebase. FiveSGDofhelical
shape were embedded linearly, with 370 μm separations, within the EPD and extended into
the dermis (figure 1).
Each helix (SGD) was 0.3 mm high and 0.12 mm in diameter. The sweat ducts themselves
were 0.04 mm in diameter coiled into four equally spaced turns. The rectangular waveguide
(WR-10) was modelled to deliver 94 GHz EM radiation, 3.21 mm wavelength in air, to the
skin model. The waveguide, 14 mm long with 2.45 mm ×1.27 mm dimensions, was located
at the centre of the skin disc. An EM source was placed 13.6 mm away from the mouth of
the waveguide to generate EM waves propagating in a TE10 mode towards the waveguide’s
mouth, which was positioned 0.02 mm from the surface of the SC. The entire model was
encompassed within a geometrical box (bounding box) with padding of 0.25 of the maximum
wavelength on all side. The bonding box bounds the volume in which the EM radiation
was allowed to propagate. The properties of the space between the faces of the box and
the skin and waveguide geometries, were those of air. Uniaxial perfectly matched layers
boundary conditions were applied to the bounding box faces. Medium boundary strength
(>95% absorption) was specified on all the sidewalls of the bounding box and high absorption
(>99% absorption) was set for the top and bottom faces of the box, above the waveguide and
below the skin model. A progressive grid with 2.645×106voxels was used to mesh the entire
geometry (skin and waveguide). The overall grid size was determined by refining it to the
point where any further refinements resulted in changes of no more than 5% in the results.
Thus, the accuracy of the simulation is ±5%. Within the geometrical model the minimum
steps of the grid were 1.5 ×10−5m(15μm) in the Xand Ydirections and 10−5m(10μm)
in the Zdirection. Using analytic modelling presented elsewhere (Pickard and Moros 2001)it
can be shown that for a forward travelling 94 GHz plane wave, the wavelength is 1.15 mm in a
biological tissue with relative permittivity of 5.8 and conductivity of 39 S m−1. Therefore, the
maximum grid size was 0.1 mm which is less than 1/10 of the wavelength. The glands were
meshed with a conformal triangular grid with 10−6m resolution (1 μm) as shown in figure 1.
There were 436 voxels in each SGD and 221 in each of the SGD extensions.
A forward power of 30 mW that translates to 9.3 kW m−2was delivered from the
waveguide towards the skin. The EM properties for each skin constituent at 94 GHz that were
used are listed in table 1. These properties were calculated using Gabriel and Gabriel empirical
equation and data (Gabriel et al 1996a,1996b,1996c), which are included in the SEMCAD
software. The EM properties of the content inside the sweat glands were assumed to be those
of saline (at 94 GHz) and were taken from Pickard et al (2010). Note, that the ac conductivity
1332 G Shafirstein and E G Moros
Tab l e 1 . Electromagnetic and thermal properties of the various skin structures used in the model.a
Thermal Specific Blood
Conductivity Relative Density conductivity heat perfusion
Region (S m−1) permittivity (kg m−3)(Wm
−1C−1) capacity (J kg−1C−1)(m
b3/mt3/s)
Dermis 39 5.8 1100 0.35 3437 1.78×10−3
EPD 1 3.2 1200 0.21 3600 none
Stratum
corneum 0.0001 2.4 1000 0.21 3600 none
Gland 83 3.9 1000 0.53 4190 none
aThe relative permeability was 1 for all regions.
oftheSGD(83Sm
−1) is close to the maximum value (100 S m−1) measured in water for
proton hopping (Cukierman 2000). The SAR distribution was calculated for two cases: (1)
equating the SGD properties to the EPD and dermis (i.e. effectively having no glands) and (2)
setting the glands properties equal to saline’s properties. The exact same geometry and grid
were used in both cases. The transient EM simulation was conducted until it reached steady
state.
Noteworthy, Johnsen et al (2010) found that the water content in the SC is 0.076–
0.0863 mg cm−2under normal conditions. That is about 2.59 ×10−3mg cm−3which
represents an extremely low volume fraction. Thus, from a practical point of view the SC can
be considered as nonconductive layer, as assumed by Feldman et al (2009) and Alekseev et al
(2008) in this study.
2.2. Thermal modelling
The temperature increase due to the EM radiation was computed by importing the calculated
three-dimensional SAR field into the bio-thermal solver module of SEMCAD. The same skin
geometry and grid that were used for the EM simulations were used in the thermal simulations.
The heat source (W m−3) in each voxel of the thermal simulation was created by multiplying
the SAR (W kg−1) by the specific density (kg m−3) of the respective tissue in each voxel. The
thermal property values were assumed to be independent of the EM field and were taken from
Shafirstein et al (2004). The initial condition for the temperature (T) was 32 ◦C following
Alekseev and Ziskin (2003). Dirichlet boundary conditions (T=32 ◦C) were applied to the
bottom of the skin cylinder and the circumferential cylinder wall. The boundary condition on
the top surface of the cylinder, the surface of the SC facing the waveguide, was
−k∇T|z=0,x,y =h(T −Text ). (1)
Text was set to 26 ◦C and the convection coefficient hwas set to 15 W C−1m−2, assuming slow
air flow over a flat plate (Holman 1981). Blood perfusion of 1.78×10−3mb3mt−3s−1was set
in the dermis with arterial blood temperature of 36 ◦C. The transient thermal simulations were
run until steady state was reached, usually about 20 s.
3. Results
The EM simulation reached a steady state in 20 cycles. The SAR distribution for no SGD
(case 1) is shown in figure 2, which plots the x–zplane, through the middle of the skin model
(no SDG).
Modelling millimetre wave propagation and absorption in a high resolution skin model 1333
Figure 2. Cross section of the 94 GHz irradiation induced SAR distribution. The A–B line is the
depth at which the SAR distribution was plotted along the distance from the centre in figure 5.
Figure 3. Cross section of the 94 GHz irradiation induced SAR distribution with SGD. The A–B
line is the depth at which the SAR distribution was plotted along the distance from the centre in
figure 5.
Figure 3shows the calculated SAR distribution through the middle of the skin model,
bisecting the SGD. Maximum SAR of 288 000 W kg−1(see figure 5) was calculated at the
upper coil of SGD embedded in the EPD.
In figure 4we present the SAR profile as a function of distance from the surface, for
the case of no SGD. The SAR is minimal at the SC layer, due to the very low conductivity
of this skin constituent (it was assumed to be dry). Maximum SAR values of 2494 W kg−1
and 32 500 W kg−1were calculated in the EPD and dermis, respectively. Within the EPD,
with no SGD, the SAR decreases as a function of depth due to the attenuation of the electric
field (E-field). However, a rapid increase in the SAR is seen at the epidermal/dermal junction
(figure 4). This increase is due to the relatively high electrical conductivity of the dermis in
1334 G Shafirstein and E G Moros
Figure 4. The SAR distribution as a function of distance from the surface of the skin with no SGD.
Figure 5. The SAR distribution along the line A–B as shown in figures 2and 4for the geometry
with no SGD and with SGD.
comparison to the EPD, i.e. 39 S m−1versus 1 S m−1. Within the dermis, the SAR decays
from 32 500 W kg−1to 255 W kg−1(figure 4) due to the E-field attenuation in the dermis.
The effect of the SGD on the SAR is clearly seen in figure 5where the SAR linear
distribution bisecting the SGD is plotted at depth of 100 μm from the top surface (along line
A–B in figures 2and 3). A maximum SAR of 288 000 W kg−1was calculated within the
central SGD. The SAR in the adjacent SGD was slightly lower, due to the E-field distribution
in reference to the centre of the waveguide and geometry. The SAR inside the SGD with
saline was about one order of magnitude higher than the SAR at the same location but with
properties of the embedding tissue.
The resulting temperature distributions, for the SAR shown in figures 2and 3, are shown
in figure 6.
It can be clearly seen that the presence of the SGD resulted in an increase of temperature
within the EPD towards the SC (figures 6(A) versus (B)). At the EPD/SC junction the
temperature increase was 5.9 ◦C and 6.9 ◦C for cases 1 and 2, respectively (figure 7(A)). Near
Modelling millimetre wave propagation and absorption in a high resolution skin model 1335
(A)
(B)
Figure 6. The temperature distribution within a cross section of the skin geometry with no SGD
(A) and with SGD (B). The lines A–B and C–D indicate the depths of which the temperature
distributions were plotted against the distance from the centre in figure 7.
the epidermal/dermal junction the maximum temperature increase was 6.8 ◦C and 7.3 ◦Cfor
cases 1 and 2, respectively (figure 7(B)). A steady state temperature increase was achieved in
20 s in both cases (figure 8).
The maximum temperature difference between the two cases was less than 0.5 ◦Cat,
steady state, t>20 s (figure 8).
4. Discussion
In this work, we investigated the effect of helical SGD on SAR and temperature distribution
during 94 GHz irradiation of skin. The simulations employed a geometry of the skin and SDG
that is similar to the one presented by Feldman et al (2009). Unlike Feldman et al, however,
we assumed that the conductivity of the content of the SGD (i.e. sweat) was similar to saline,
83 S m−1at 94 GHz, according to our previous work (Pickard et al 2010). Our results are in
general agreement with the theoretical analysis and clinical measurements of Feldman et al
(2009). The simulations clearly show that SGD act as high absorption sites for mm-wave
1336 G Shafirstein and E G Moros
(A) (B)
Figure 7. (A) The steady state temperature distribution along line A–B at the EPD/SC junction
(see figure 6) and (B) along line C–D, in figure 6,attheEPD
/dermis junction.
Figure 8. The maximum temperature increase as a function of time at the EPD/dermis junction
for the geometries with and without SGD.
radiation (figure 3). A maximum SAR of 288 000 W kg−1was calculated within the glands
versus maximum SAR of 2494 W kg−1within the EPD with no SGD (figures 2and 5). In our
previous work we showed that a maximum SAR of 4500 W kg−1induced a temperature increase
of 0.5 ◦C inside a small chamber containing cells (Pickard et al 2010). Assuming a linear
relationship between SAR and steady state temperature increase, a maximum temperature
increase of about 32 ◦C within the centre SGD would be expected. However, the calculated
maximum temperature increase was only 7 ◦C (figure 8). This discrepancy can be explained
by careful examination of the model. In the EM simulation the high SAR (288 000 W kg−1)
was extremely local (<0.013mm3) at the tip of the gland which included only a few voxels.
In the thermal simulation these few voxels represented a very small heat source (∼10−6mm3)
with extremely high surface area to volume ratio that induced rapid heat dissipation, thereby
resulting in a lower temperature increase when compared to the results of Pickard et al (2010).
Modelling millimetre wave propagation and absorption in a high resolution skin model 1337
A steady state temperature was reached after about 20 s of continuous exposure to the
94 GHz irradiation (figure 8). This is a longer time in comparison to the results presented
in Pickard et al (2010) where thermal equilibrium was obtained after 10 s. However, in that
work the overall radiated volume was smaller and the heating was more uniform (without the
SAR spikes due to SGD) than the present one. In addition, the rate of heat dissipation to the
ambient air by convection was much higher (h=750 W m−2C−1versus 15 W m−2C−1).
These two effects explain the shorter time required to reach thermal equilibration in Pickard
et al (2010).
The calculated maximum temperature, in this work, is in agreement with temperature
increase measured in skin of healthy volunteers exposed to 94 GHz radiation (Walters et al
2000). In that human study, a skin temperature rise of roughly 10 ◦C was measured after a
3 s exposure to 18 kW m−2at 94 GHz radiation. In our simulation, a temperature increase of
about 4.5 ◦C (figure 8) was calculated for a 3 s exposure at 9.3 kW m−2of 94 GHz radiation.
Assuming a linear relationship between the temperature increase and the forward power, it can
be concluded that our predicted temperature increase is in agreement with the measurements
reported in Walters et al (2000).
Our results also suggest that the majority of the mm-wave radiation is absorbed in the
EPD and upper dermis while the SC does not contribute to the temperature increase. This
result is not in full agreement with the analysis of Alekseev et al (2008), who calculated the
SARs in response to mm-wave radiation (at 42 and 61 GHz) in the skin of the forearm and
palm of hands. They assumed that the amount of free water in the SC is the key parameter
that affects the reflection of the EM waves from the palm and forearm. They postulated that
the differences in SAR between the forearm and the palm was due to the difference in the
thickness of the SC, 0.015 versus 0.42 mm for forearm and palm, respectively (Alekseev et al
2008). Thus, thicker SC translates to higher water content and higher absorption in the palm
in comparison to the forearm. We posit that the differences in the SARs between the palm
and the forearm are due to the differences in the density of SGD in these regions (Wilke et al
2007). Sweat gland density in the palm is about five times the density in the forearm (644
versus 134 SGD per cm2) (Wilke et al 2007). Our results suggest that an increase in number
of SGD would result in higher average SAR. Sweat is about 99% water and 1% salt and amino
acids; hence, it is plausible that the increase of sweat gland density in the palm will result in
a more hydrated SC that will affect the reflection of the EM waves, as observed by Alekseev
et al (2008). In this sense, our results are in agreement with their observations.
In the context of nociception research our finding is important because it shows that
temperature increases due to mm-wave irradiation are more superficial than those based on
models of multiple homogeneous layers without SGD. The temperature maxima were moved
towards the EPD which is known to be populated by pain nerve fibres and heat-sensitive
keratinocytes (Tillman et al 1995, Zylka et al 2005, Nolano et al 1999, Peier et al 2002). This
situation is closer to a more common situation in life, that is direct contact with a hot surface,
indicating that exposure to high power mm-wave irradiation should result in instantaneous
acute pain responses similar to those resulting from direct contact with a hot object but without
direct heating of the SC.
Only five SGD were embedded in our model due to computational requirements. It is
surprising that only five glands, linearly distributed, would have a clear steady state effect on
the resulting temperature distribution. It can be speculated that the effect of a two-dimensional
array (e.g. 25 glands in a 5 ×5 array) would have an even more pronounced effect, thus moving
the temperature maxima even more superficially than shown in this paper. This effect of the
SGD, demonstrated here for the first time, may be involved in the hypoalgesia effect recently
1338 G Shafirstein and E G Moros
reported in the literature (Radzievsky et al 2008). We are now actively seeking to extend our
computational capabilities to improve our models and continue our studies.
5. Conclusions
In this modelling study, we present the effect of SGD on the SAR and temperature increase
during skin exposure to mm-wave radiation. Our results agreed with previously published
data (Feldman et al 2008,2009, Walters et al 2000, Alekseev et al 2008) and suggest that
SGD may act as absorption sites of mm-waves. The inclusion of SGD in the EPD resulted in
a large increase in the local SAR, a moderate increase of the absolute bulk temperature and a
shift of the temperature maxima towards the EPD.
Future studies will quantify the effect of a larger array and varying density of SGD on
the absorption of mm-waves in the skin and the effect of thermal regulation via nearby blood
vessels and skin wetness due to profuse sweating.
Acknowledgments
This work was supported by a research contract with the Office of Naval Research (N00014-
09-1-0028).
We thank Schmid & Partner Engineering AG, Zurich, Switzerland for providing the
SEMCAD X software for this study. We extend special gratitude to Peter Futter, Dr Esra
Neufeld, Dr Pedro Crespo Valero and Maria del Mar Mi˜
nana at the SEMCAD support group
for their helpful discussions and support. We thank Dr Ben Ishai for the fruitful discussions.
We also extend gratitude to our collaborators, Dr William Pickard from WUSTL, Dr Michael
R Cho from UIC and Dr Hemant S Thatte from HU.
This study was also supported in part by the NSF and Arkansas Science and Technology
Authority grant number G1–35321–01.
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