ArticlePDF Available

Modelling millimetre wave propagation and absorption in a high resolution skin model: The effect of sweat glands

IOP Publishing
Physics in Medicine & Biology
Authors:
  • H. Lee Moffitt Cancer Center and Research Institute

Abstract and Figures

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 X™). 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.
Content may be subject to copyright.
Modelling millimetre wave propagation and absorption in a high resolution skin model: the
effect of sweat glands
This article has been downloaded from IOPscience. Please scroll down to see the full text article.
2011 Phys. Med. Biol. 56 1329
(http://iopscience.iop.org/0031-9155/56/5/007)
Download details:
IP Address: 138.26.16.5
The article was downloaded on 07/03/2011 at 05:34
Please note that terms and conditions apply.
View the table of contents for this issue, or go to the journal homepage for more
Home Search Collections Journals About Contact us My IOPscience
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 ×105m(15μm) in the Xand Ydirections and 105m(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 m1. 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 106m 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 m2was 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 m1) permittivity (kg m3)(Wm
1C1) capacity (J kg1C1)(m
b3/mt3/s)
Dermis 39 5.8 1100 0.35 3437 1.78×103
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 m1) 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 cm2under normal conditions. That is about 2.59 ×103mg cm3which
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 m3) in each voxel of the thermal simulation was created by multiplying
the SAR (W kg1) by the specific density (kg m3) 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
kT|z=0,x,y =h(T Text ). (1)
Text was set to 26 C and the convection coefficient hwas set to 15 W C1m2, assuming slow
air flow over a flat plate (Holman 1981). Blood perfusion of 1.78×103mb3mt3s1was 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 xzplane, 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 kg1(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 kg1
and 32 500 W kg1were 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 m1versus 1 S m1. Within the dermis, the SAR decays
from 32 500 W kg1to 255 W kg1(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 kg1was 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 m1at 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 kg1was calculated within the glands
versus maximum SAR of 2494 W kg1within the EPD with no SGD (figures 2and 5). In our
previous work we showed that a maximum SAR of 4500 W kg1induced 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 kg1)
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 (106mm3)
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 m2C1versus 15 W m2C1).
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 m2at 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 m2of 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.
References
Alekseev S I, Radzievsky A A, Logani M K and Ziskin M C 2008 Millimeter wave dosimetry of human skin
Bioelectromagnetics 29 65–70
Alekseev S I, Radzievsky A A, Szabo I and Ziskin M C 2005 Local heating of human skin by millimeter waves:
effect of blood flow Bioelectromagnetics 26 489–501
Alekseev S I and Ziskin M C 2003 Local heating of human skin by millimeter waves: a kinetics study
Bioelectromagnetics 24 571–81
Alekseev S I and Ziskin M C 2007 Human skin permittivity determined by millimeter wave reflection measurements
Bioelectromagnetics 28 331–9
Cukierman S 2000 Proton mobilities in water and in different stereoisomers of covalently linkedgramicidin A channels
Biophys. J. 78 1825–34
Feldman Y, Puzenko A, Ben Ishai P, Caduff A and Agranat A J 2008 Human skin as arrays of helical antennas in the
millimeter and submillimeter wave range Phys. Rev. Lett. 100 128102
Feldman Y, Puzenko A, Ben Ishai P, Caduff A, Davidovich I, Sakran F and Agranat A J 2009 The electromagnetic
response of human skin in the millimetre and submillimetre wave range Phys. Med. Biol. 54 3341–63
Gabriel C, Gabriel S and Corthout E 1996a The dielectric properties of biological tissues: I. Literature survey Phys.
Med. Biol. 41 2231–49
Gabriel S, Lau R W and Gabriel C 1996b The dielectric properties of biological tissues: II. Measurements in the
frequency range 10 Hz to 20 GHz Phys. Med. Biol. 41 2251–69
Gabriel S, Lau R W and Gabriel C 1996c The dielectric properties of biological tissues: III. Parametric models for
the dielectric spectrum of tissues Phys. Med. Biol. 41 2271–93
Holman J P 1981 Heat Transfer (New York: McGraw-Hill)
Modelling millimetre wave propagation and absorption in a high resolution skin model 1339
Johnsen G K, Haugsnes A B, Martinsen O G and Grimnes S 2010 A new approach for an estimation of the equilibrium
stratum corneum water content Skin Res. Technol. 16 142–5
Naito S, Hoshi M and Mashimo S 1997 In vivo dielectric analysis of free water content of biomaterials by time domain
reflectometry Anal. Biochem. 251 163–72
Nolano M, Simone D A, Wendelschafer-Crabb G, Johnson T, Hazen E and Kennedy W R 1999 Topical capsaicin in
humans: parallel loss of epidermal nerve fibers and pain sensation Pain 81 135–45
Peier A M et al 2002 A heat-sensitive TRP channel expressed in keratinocytes Science 296 2046–9
Pickard W F and Moros E G 2001 Energy deposition processes in biological tissue: nonthermal biohazards seem
unlikely in the ultra-high frequency range Bioelectromagnetics 22 97–105
Pickard W F, Moros E G and Shafirstein G 2010 Electromagnetic and thermal evaluation of an applicator
specialized to permit high-resolution non-perturbing optical evaluation of cells being irradiated in the W-band
Bioelectromagnetics 31 140–9
Radzievsky A A, Gordiienko O V, Alekseev S, Szabo I, Cowan A and Ziskin M C 2008 Electromagnetic
millimeter wave induced hypoalgesia: frequency dependence and involvement of endogenous opioids
Bioelectromagnetics 29 284–95
Shafirstein G, Baumler W, Lapidoth M, Ferguson S, North P E and Waner M 2004 A new mathematical approach to
the diffusion approximation theory for selective photothermolysis modeling and its implication in laser treatment
of port-wine stains Lasers Surg. Med. 34 335–47
Shibasaki M, Wilson T E and Crandall C G 2006 Neural control and mechanisms of eccrine sweating during heat
stress and exercise J. Appl. Physiol. 100 1692–701
Tillman D B, Treede R D, Meyer R A and Campbell J N 1995 Response of C fibre nociceptors in the anaesthetized
monkey to heat stimuli: estimates of receptor depth and threshold J. Physiol. 485 753–65
Walters T J, Blick D W, Johnson L R, Adair E R and Foster K R 2000 Heating and pain sensation produced in human
skin by millimeter waves: comparison to a simple thermal model Health Phys. 78 259–67
Wilke K, Martin A, Terstegen L and Biel S S 2007 A short history of sweat gland biology Int. J. Cosmet. Sci. 29 169–79
Zylka M J, Rice F L and Anderson D J 2005 Topographically distinct epidermal nociceptive circuits revealed by
axonal tracers targeted to Mrgprd Neuron 45 17–25
... A large number of dosimetry studies on human skin is available in the literature, [1], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]. A stratified model of human skin is applied in most of them [1], [3], [4], [5], [6], [8], [9], [10], [11], [12], distinguishing between different skin layers (i.e., Stratum Corneum, Epidermis, Dermis) and underlying tissues (i.e., Subcutaneous Fat, Muscle). ...
... A large number of dosimetry studies on human skin is available in the literature, [1], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]. A stratified model of human skin is applied in most of them [1], [3], [4], [5], [6], [8], [9], [10], [11], [12], distinguishing between different skin layers (i.e., Stratum Corneum, Epidermis, Dermis) and underlying tissues (i.e., Subcutaneous Fat, Muscle). Some of them also investigate the impact of skin appendages on dosimetry, like sweat glands [6], [7], [8], [12] or others [5]. ...
... A stratified model of human skin is applied in most of them [1], [3], [4], [5], [6], [8], [9], [10], [11], [12], distinguishing between different skin layers (i.e., Stratum Corneum, Epidermis, Dermis) and underlying tissues (i.e., Subcutaneous Fat, Muscle). Some of them also investigate the impact of skin appendages on dosimetry, like sweat glands [6], [7], [8], [12] or others [5]. The impact of variations of skin strata thicknesses [1], [3], [4], [9], [10], [11], or dielectric properties with age [9] in dosimetry, has also been studied. ...
Article
Full-text available
The upper part of the frequency spectrum (millimeter waves, MMW) applied by modern communications technologies (5G and beyond), makes skin the dominantly exposed tissue to electromagnetic fields. In this work, a methodology for murine skin dosimetry evaluation is presented, intended to contribute to animal studies with mice exposed to MMW radiation, in particular 27.5 GHz. A stratified skin model is proposed and the variations of the skin layers’ thicknesses during a hair cycle are measured in mice. The variations of skin layers’ dielectric properties due to age, based on the changes of total body water, are also evaluated. The impact of these variations in dosimetric metrics (i.e., mean absorbed power density, APD, and power loss) within each layer is assessed and found to be significant. Changes in the skin layers’ thicknesses throughout a hair cycle considerably affect the APD, resulting in a two-fold increase, compared to changes in the dielectric properties due to aging or due to hair presence inside the skin
... Interestingly, coiled sweat glands act as arrays of helical antennas with a resonating frequency in the THz range and influence the RF-energy absorption of millimeter and submillimetre waves into the human skin (19)(20)(21). Furthermore, a computational study suggested that the presence of sweat gland ducts resulted in an increase of SAR and temperature near to the skin epidermis during 94 GHz millimeter wave (MMW) radiation (22). The alteration in the expression of genes associated with thermal damage, oxidative stress, protein folding, inflammation and tissuematrix turnover has been reported in the skin tissues of rats collected at 6 and 24 h after 35 GHz MMW exposure at power density 75 mW/cm 2 (23). ...
... Furthermore, simulation-based computational studies have also suggested that the spatial distribution of sweat glands acts as arrays of helical antennas and may influence the penetration and absorption of incident MMW energy into the skin surface (19)(20)(21)(22). Nevertheless, due to the lower penetration depth, the deposition of 10 GHz MW energy occurs to the top layers of the skin (3). ...
Article
Full-text available
Microwave (MW) radiation poses the risk of potential hazards on human health. The present study investigated the effects of MW 10 GHz exposure for 3 h/day for 30 days at power densities of 5.23 ± 0.25 and 10.01 ± 0.15 mW/cm2 in the skin of rats. The animals exposed to 10 mW/cm2 (corresponded to twice the ICNIRP-2020 occupational reference level of MW exposure for humans) exhibited significant biophysical, biochemical, molecular and histological alterations compared to sham-irradiated animals. Infrared thermography revealed an increase in average skin surface temperature by 1.8°C and standard deviation of 0.3°C after 30 days of 10 mW/cm2 MW exposure compared to the sham-irradiated animals. MW exposure also led to oxidative stress (ROS, 4-HNE, LPO, AOPP), inflammatory responses (NFkB, iNOS/NOS2, COX-2) and metabolic alterations [hexokinase (HK), lactate dehydrogenase (LDH), citrate synthase (CS) and glucose-6-phospahte dehydrogenase (G6PD)] in 10 mW/cm2 irradiated rat skin. A significant alteration in expression of markers associated with cell survival (Akt/PKB) and HSP27/p38MAPK-related stress-response signaling cascade was observed in 10 mW/cm2 irradiated rat skin compared to sham-irradiated rat skin. However, MW-irradiated groups did not show apoptosis, evident by unchanged caspase-3 levels. Histopathological analysis revealed a mild cytoarchitectural alteration in epidermal layer and slight aggregation of leukocytes in 10 mW/cm2 irradiated rat skin. Altogether, the present findings demonstrated that 10 GHz exposure in continuous-wave mode at 10 mW/cm2 (3 h/day, 30 days) led to significant alterations in molecular markers associated with adaptive stress-response in rat skin. Furthermore, systematic scientific studies on more prevalent pulsed-mode of MW-radiation exposure for prolonged duration are warranted.
... One avenue available to investigate EM skin response is by simulation, and a number of simulation models of the skin have been proposed in order to address questions regarding energy absorption and interactions between an external impinge EM field and the human skin in this band [2][3][4][5][6][7][8][9]. However, the majority of these models ignore the detailed structure of the skin. ...
... A major subcomponent of the skin is the perspiration system, consisting of an ensemble of eccrine sweat glands distributed with varying degrees of density over the surface of the body [2]. The human skin contains 2-5 million eccrine sweat glands overall [3]. By studying dissected slices of human skin, it was revealed that the coiled sections of the sweat ducts have, with a pronounced preference (~90%), a right-handed turn [4,5]. ...
Article
The helical nature of human sweat ducts, combined with the morphological and dielectric properties of skin, suggests electromagnetic activity in the sub-THz frequency band. A detailed electromagnetic simulation model of the skin, with embedded sweat ducts, was created. The model includes realistic dielectric properties based on the measured water content of each layer of skin, derived from Raman Spectroscopy. The model was verified by comparing it to measurements of the reflection coefficient of the palms of 13 volunteers in the frequency band 350-410 GHz. They were subjected to a measurement protocol intended to induce mental stress, thereby also activating the sweat glands. The Galvanic Skin Response was concurrently measured. Using the simulation model the optimal ac-conductivity for each measurement was found. The range of variation for all subjects was found to be from 100 S/m to a maximum value of 6000 S/m with averages of 1000 S/m. These are one order of magnitude increase from the accepted values for water at these frequencies (~100 s/m at 100 GHz). Considering the known biochemical mechanism for inducing perspiration, we conclude that these ac-conductivity levels are probably valid, even though the real time measurements of sweat ac-conductivity levels inside the duct are inaccessible. This article is protected by copyright. All rights reserved.
... However, it is predicted from theoretical models that the skin's sweat gland ducts (SGD) act as helical antennas, which can potentially carry mmWaves much deeper into the body (25,26). Such deeper penetration has been confirmed, albeit at higher frequencies (94 GHz) (27). There are also predictions that transients from short pulses due to high data rates may create secondary waves called Brillouin Precursors that penetrate even deeper into the body, leading to the unwinding of large molecules, cell membrane damage and blood-brain leakage (28). ...
Article
Full-text available
The advent of fifth-generation (5G) wireless communication introduces new technology utilizing near-millimeter radiofrequency waves [i.e., with a frequency of 30–300 GHz (mmWaves)]. The long-term effects of these signals on humans and the environment are unknown. Scientific literature reviews investigating biological harm from mmWave usage have concluded . . . no in-depth conclusions can be drawn. . . and no confirmed evidence. Unfortunately, these statements of scientific uncertainty have been used by industry and government advisory bodies to reassure the public of the safety of the 5G rollout. However, the assumption that 5G technologies are safe is not an evidence-based conclusion. Why this is so cannot be easily understood from existing summaries or reviews. Therefore, this article takes one step back from reviews to the original papers, so as to provide a visible overview of the existing mmWave evidence base. It then examines how the science is being conducted and communicated, finding errors in reasoning that cloud judgements and the subsequent conclusions drawn from the existing research.
... A priori knowledge of temperature distribution within the skin appendages is essential for capturing any local or systemic thermal effects of mmWaves. The first attempt to evaluate the local temperature elevation within skin due to the presence of sweat ducts was made by Shafirstein et al. [23]. The mmWave energy was selectively absorbed by the sweat ducts due to their higher water content (≈99%), and the temperature maxima within the skin shifted from dermis to epidermis. ...
Article
Full-text available
In this study, we quantify microscale heating at the level of cutaneous nerves and capillaries due to continuous and pulsed plane-wave exposure at 60 GHz. The thermal properties of the nerves and capillaries were derived using mixture equations based on their water content. The electromagnetic problem was solved in conjunction with Pennes bioheat equation and Arrhenius equation using finite element method to evaluate the spatial and temporal evolution of temperature along with thermal damage within cutaneous nerves and capillaries. Although, the maximum power density within the nerve (41.6 kW/m3) and capillary (20 kW/m3) was 37.3% and 30.2% higher than surrounding skin for a continuous exposure at 10 W/m2, the peak temperature elevation (ΔT\Delta T) within the nerve (93.3 n°C) and capillary (90.7 n°C) occurred after 5 μ\mus and 10 μ\mus of exposure and was 19.2% and 17.7% higher than surrounding skin, respectively. The nerve and capillary attained thermal equilibrium with skin after roughly 10 ms. The maximal ΔT\Delta T within the nerve (0.5 °C) and capillary (0.25 °C) due to nano- and micro-second 60 GHz pulses with highest fluence (0.48 kJ/m2) permitted under ICNIRP guidelines was 34% and 24% higher than in the surrounding skin. Ten 3 μs 60 GHz pulses (power density = 13.4 GW/m2) separated by 10 s of cooling period were used to demonstrate the possibility of selective thermal ablation of cutaneous nerves [damage index (Ω\mathit {\Omega })=1.1)] without damaging skin (Ω\mathit {\Omega } = 0.15). The results provide valuable insights into local millimeter-wave induced heating within various skin substructures.
... 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). ...
Article
Full-text available
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.
... The electrodes are attached to the skin model, with the terminal electrode containing the target medication (Figure 1(b)). The skin model's boundary conditions as shown in Table 1, as well as the drug and electrical properties, are derived from a several literatures [7] [8]. Additionally, we established assumptions for the electrical and thermal properties of the drug, including the density, charge, and other related parameters. ...
Article
Full-text available
Transdermal Iontophoretic Drug Delivery System (TIDDS) is a non-invasive method of systemic drug delivery that involves by applying a drug formulation to the skin. The drug penetrates through the stratum corneum, epidermis and dermis layers. Once the drug reaches the dermal layer, it is available for systemic absorption via dermal microcirculation. However, clinical testing of new drug developed for the iontophoretic system is a long and complex process. Recently, most of those major pharmaceutical companies have attempted to consider computer-based bio-simulation strategies as a means of generating the data necessary to help make a better decision. In this work, we used computational modelling to investigate the TIDDS behaviour. Our interest is to study the efficacy of drug diffusion through transdermal delivery, including the thermal effect on the skin. We found that drug will be delivered more efficiently if the electrical potential and the position of electrodes are optimum. We analysed the drug diffusion time of the system using 1,3 and 5 mA DC source. In addition, we also modify the electrode distance from 10 mm to 30 mm long and analysed the effect of delivery time and d effect to the skin thermal. We conclude that, a high electrical current, as instance, a 5 mA DC, delivered the drug faster into the skin but increased the skin temperature because of skin joule heating effect. However, a 30 mm electrodes distance setting decreased the skin temperature significantly than the 10 mm distance with more than 9.7 °C under 5 mA DC and 60 minutes of operation. TIDDS enhanced drug delivery compared to oral consumption and might be suitable used for localizing treatments such as chronic disease. This work provides great potential and is useful to efficiently design of iontophoretic drug delivery system including new drugs delivery applications.
Chapter
Sweat glands (SGs) are part of the autonomic nervous system, influenced by metabolic disorders like diabetes. In this condition and during nephropathy, its morphology and sweat constituents’ changes. Monitoring these parameters could provide information on the onset of these diseases. Electrochemical and wearable techniques are available to quantify sweat elements, but there are no non-invasive technologies to assess sweat gland dimensional changes. Hence, the attempt here is to estimate morphological changes in sweat glands and correlate it to diabetes and kidney disease. Skin modeling is done and irradiated with electromagnetic radiation at 300 GHz. Three different models are constructed; one for controls, a second for diabetes, and a third for diabetic kidney disease (KD). After assigning relevant electrical and thermal properties, these models are executed by exposing them to 300 Hz electromagnetic waves. Electric field and specific absorption rate (SAR) are computed at different layers and correlated to pathological conditions. The results show that the variation in the distribution of electric field and SAR values in the SG is found to be higher as diabetes progresses. If taken ahead with practical implementation, this attempt could be helpful in preventing diabetic kidney disease.KeywordsSARSGDiabetesDKD
Article
The galvanic skin response (GSR), which is a manifestation of the activity in eccrine sweat glands, has always been an important psychological test to evaluate emotional arousal and mental stress. Although, researches have focused on the radio reflections of skin and revealed that sweat gland activity can change the reflection signal of skin, the complicated experimental settings including vector network analyzer (VNA) and even optical path design limit the further daily life application. In this paper, we demonstrate the potential of using commodity millimeter-wave (mmWave) Multiple-Input Multiple-Output (MIMO) radar for contactless GSR sensing. To simulate the reflected signals of Frequency-Modulated Continuous-Wave (FMCW) radar to the skin of different individuals, a four layered skin model focused on the sweat duct is utilized and the change of conductivity in sweat ducts is regarded as mapping of sweat gland activity. Extensive experiments are conducted, consisting of 3 different physiological status: relaxing status, mental and physical stress status. We design a beamformer to transform raw signal to space domain so that the reflection signals from the palm are separated. The principal components of processed signal are extracted to eliminate the interference caused by breathing and random noise. We evaluate the performance in terms of the correlation between the radar signal and GSR before and after stress-induced events. The experimental results preliminarily verify the feasibility of contactless GSR sensing.
Preprint
Full-text available
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.
Article
Full-text available
Three experimental techniques based on automatic swept-frequency network and impedance analysers were used to measure the dielectric properties of tissue in the frequency range 10 Hz to 20 GHz. The technique used in conjunction with the impedance analyser is described. Results are given for a number of human and animal tissues, at body temperature, across the frequency range, demonstrating that good agreement was achieved between measurements using the three pieces of equipment. Moreover, the measured values fall well within the body of corresponding literature data.
Article
Full-text available
The dielectric properties of tissues have been extracted from the literature of the past five decades and presented in a graphical format. The purpose is to assess the current state of knowledge, expose the gaps there are and provide a basis for the evaluation and analysis of corresponding data from an on-going measurement programme.
Article
The prospects of ultra high frequency (UHF, 300-3000 MHz) irradiation producing a nonthermal bioeffect are considered theoretically and found to be small. First, a general formula is derived within the framework of macroscopic electrodynamics for the specific absorption rate of microwaves in a biological tissue; this involves the complex Poynting vector, the mass density of the medium, the angular frequency of the electromagnetic field, and the three complex electromagnetic constitutive parameters of the medium. In the frequency ranges used for cellular telephony and personal communication systems, this model predicts that the chief physical loss mechanism will be ionic conduction, with increasingly important contributions from dielectric relaxation as the frequency rises. However, even in a magnetite unit cell within a magnetosome the deposition rate should not exceed 1/10 k(B)T per second. This supports previous arguments for the improbability of biological effects at UHF frequencies unless a mechanism can be found for accumulating energy over time and space and focussing it. Second, three possible nonthermal accumulation mechanisms are then considered and shown to he unlikely: (i) multiphoton absorption processes; (ii) direct electric field effects on ions; (iii) cooperative effects and/or coherent excitations. Finally, it is concluded that the rate of energy deposition from a typical field and within a typical tissue is so small as to make unlikely any significant nonthermal biological effect. Bioelectromagnetics 22:97-105, 2001. (C) 2001 Wiley-Liss, Inc.
Article
Recent studies of the minute morphology of the skin by optical coherence tomography showed that the sweat ducts in human skin are helically shaped tubes, filled with a conductive aqueous solution. A computer simulation study of these structures in millimeter and submillimeter wave bands show that the human skin functions as an array of low-Q helical antennas. Experimental evidence is presented that the spectral response in the sub-Terahertz region is governed by the level of activity of the perspiration system. It is also correlated to physiological stress as manifested by the pulse rate and the systolic blood pressure.
Article
Water content is the most vital parameter governing the overall function of the epidermal stratum corneum (SC). Thus, knowledge of the in vivo absolute water content of the SC is of great interest. We have investigated a non-invasive method for the estimation of in vivo SC water content based on transepidermal water loss measurements combined with desorption studies of SC in vitro, by means of a dynamic vapour sorption setup where relative humidity (RH) and temperature are controlled. The SC equilibrium water content of the volar forearm in our study was estimated to be 80+/-7 microg/cm2. The estimate of the water content seems to decrease slightly with increasing ambient RH. The estimated water content is a bit lower than what can be expected to be realistic. A calibration against ambient RH is most probably needed if our method is to be applied over a broad range of values of the RH in the ambient air.
Article
To permit epi-illuminated, high-resolution optical microscopy of cells in monolayer culture during unperturbed W-band (75-110 GHz) irradiation, a new class of applicator has been developed based upon WR10 rectangular waveguide components: the cells are normally plated onto the underside of a coverslip which is then placed against the under side of a waveguide flange and receives a roughly circular exposure pattern, with the +/-1 dB central spot roughly 1 mm in diameter. Constructed and tested with 94 GHz millimeter waves, water-immersion optics, and free-convection cooling, the applicator works robustly and permits SARs at the cell layer as high as 4500 W/kg before the steady-state temperature rise at the cell layer exceeds 0.5 K.
Article
Recent studies of the minute morphology of the skin by optical coherence tomography revealed that the sweat ducts in human skin are helically shaped tubes, filled with a conductive aqueous solution. This, together with the fact that the dielectric permittivity of the dermis is higher than that of the epidermis, brings forward the supposition that as electromagnetic entities, the sweat ducts could be regarded as low Q helical antennas. The implications of this statement were further investigated by electromagnetic simulation and experiment of the in vivo reflectivity of the skin of subjects under varying physiological conditions (Feldman et al 2008 Phys. Rev. Lett. 100 128102). The simulation and experimental results are in a good agreement and both demonstrate that sweat ducts in the skin could indeed behave as low Q antennas. Thus, the skin spectral response in the sub-Terahertz region is governed by the level of activity of the perspiration system and shows the minimum of reflectivity at some frequencies in the frequency band of 75-110 GHz. It is also correlated to physiological stress as manifested by the pulse rate and the systolic blood pressure. As such, it has the potential to become the underlying principle for remote sensing of the physiological parameters and the mental state of the examined subject.
Article
1. Responses to ramped or stepped temperature stimuli were obtained from fifty-three cutaneous C fibre mechano-heat nociceptors (CMHs) in the hairy skin of the pentobarbitone-morphine anaesthetized monkey. A three-layer heat transfer model was developed to describe the temperature distribution within the skin and to estimate receptor depth and heat threshold. 2. Surface heat threshold, defined as the surface temperature when the first action potential occurs, increased as: (a) the rate of temperature rise for the ramped stimuli increased from 0.095 to 5.8 degrees C s-1; (b) the duration of stepped heat stimuli decreased from 30 to 1 s; and (c) the base temperature of stepped heat stimuli decreased from 38 to 35 degrees C. These results suggest that the heat threshold for CMHs is determined by the temperature at the depth of the receptor. 3. Receptor depth estimates from responses to ramped stimuli ranged from 20 to 570 microns with a mean of 201 microns. The estimated mean receptor heat threshold was 40.4 +/- 2.2 degrees C (+/- S.D.). No correlation was observed between depth and thermal or mechanical threshold. The average receptor depth and threshold, estimated from the responses to stepped heat stimuli, were 150 microns and 40.2 degrees C, respectively. 4. We conclude that: (a) the receptor endings of CMHs occur in the epidermis and dermis; (b) temperature at the level of the receptor determines threshold; (c) temperature at the receptor ending is much lower than skin surface temperature at threshold; and (d) the tight distribution of receptor heat thresholds suggests a uniform transducer mechanism for heat in CMHs.
Article
A parametric model was developed to describe the variation of dielectric properties of tissues as a function of frequency. The experimental spectrum from 10 Hz to 100 GHz was modelled with four dispersion regions. The development of the model was based on recently acquired data, complemented by data surveyed from the literature. The purpose is to enable the prediction of dielectric data that are in line with those contained in the vast body of literature on the subject. The analysis was carried out on a Microsoft Excel spreadsheet. Parameters are given for 17 tissue types.