IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY, VOL. 3, NO. 2, MARCH 2013 207
The Helical Structure of Sweat Ducts: Their
Inﬂuence on the Electromagnetic
Reﬂection Spectrum of the Skin
Itai Hayut, Alexander Puzenko, Paul Ben Ishai, Alexander Polsman, Aharon J. Agranat, and Yuri Feldman
Abstract—The helical structure of human eccrine sweat ducts,
together with the dielectric properties of the human skin, suggested
that their electromagnetic (EM) properties would resemble those of
an array of helical antennas. In order to examine the implications
of this assumption, numerical simulations in the frequency range
of 100–450 GHz, were conducted. In addition, an initial set of mea-
surements was made, and the reﬂection spectrum measured from
the skin of human subjects was compared to the simulation results.
The simulation m odel consisted of a three layer skin model (dermis,
epidermis, and stratum corneum) with rough boundaries between
the layers and helical sweat d ucts embedded into the epidermis.
The spectral response obtained by our simulations coincides with
the analytical prediction of antenna theory and supports the hy-
pothesis that the sweat ducts can be regarded as helical antennas.
The results of the spectrum measurements from the human skin
are in good agreement with the simulation results in the vicinity of
the axial mode. The magnitude of this response depends on the con-
ductivity of sweat in these frequencies, but the analysis of the phe-
nomena and the frequencies related to the antenna-like modes are
independent of this parameter. Furthermore, circular dichroism
of the reﬂected electromagnetic ﬁeld is a characteristic property
of such helical antennas. In this work we show that: 1) circular
dichroism is indeed a characteristic of the simulation model and
2) the helical structure of the sweat ducts has the strongest ef-
fect on the reﬂected signal at frequencies above 200 GHz, where
the wavelength and the dimensions of the ducts are comparable.
In particular, the strongest spectral response (as calculated by the
simulations and measured experimentally) was noted around the
predicted frequency (380 GHz) for the axial mode of the helical
Index Terms—Electromagnetic (EM ) simulations, skin, sub-mm
wave band, sweat ducts.
ITH the advent of modern imagery of living human
skin, using methods such as optical coherence tomog-
), it was found that the human eccrine sweat duct has
awelldeﬁned helical structure , . This brought forward
the hypothesis that the sweat ducts could exhibit electromag-
(EM) behavior reminiscent of an array of helical an tenn as.
This concept was presented and expe rimentally explored in two
Manuscript received July 12, 2012; revised August 28, 2012; accepted O c-
tober 26, 2012. Date of publication December 28, 2012; date of current version
February 27, 2013. This work was supported by the Israeli Ministry of Science
under G rant 3/4602.
The authors are with the Department of Applied Physics, The Hebrew Un i-
versity of Jerusalem, 91 904, Jer usalem, Israel (e-mail: firstname.lastname@example.org uji.ac.il).
tal Object Identiﬁer 10.1109/TTHZ.2012.2227476
Fig. 1. Optical coherent tomography imaging of (a) the human skin (repro-
duced with permission from ISIS GmbH) and (b) a sketch of a helic al an-
tenna (see Balanis , reproduced with permission from John Wiley &
Sons Ltd.). The helical sweat ducts ar e embedded within th e epidermis. The
roughness between the epidermis and the dermis is of the same order of magni-
tude as the sweat ducts length.
previous works, where chang es in the electromagnetic reﬂec-
tion of the skin were observed as a result of elevated activity
of the sweat glands, in a frequen c y ra
nge of 70–110 GH z ,
. It is reasonable to assume that the morphology and electro-
magnetic properties of the skin have an impact on the reﬂected
signal in this frequency rang
e, as well as in higher frequencies
in th e sub-millimeter reg ime. To explore this assumpti on one
must consider the structure of the skin.
We consider a skin model, w
hich is composed of different
layers: 1) outermost stratum corneum (SC); 2) intermediate epi-
dermis; and 3) inner dermis. For the purposes of investigating
c response it i s necessary to take into account
the conductivity and permittivity values of each layer. This can
be achieved by evaluating the bulk and bound wa ter content in
each layer ( prev
iously detailed i n ).
One of th e p rin cipal roles o f the hum an skin is the thermoreg-
ulation of the body by sweat evaporatio n. Sweat is pro duced in
the glands, l
ocated at the bottom of the dermis layer. The ec-
crine glands are the mo st co mmon type of sweat glands, and are
distributed through m ost of our body .
vated by the nervous system the eccrine glands se-
crete the sweat liquid into the ducts—a tube-like micro organ.
The ducts deliver the sweat up to the skin surface, where it evap-
s through a pore in the SC .
The upmost section of the ducts associated with the eccrine
glands have a well-deﬁned helical structure ,  as can be
n in Fig. 1. Histological studies have sh own that about 90%
of the sweat ducts a re right-handed spirals .
In the sweat, the proton hopping can be considered as a mech-
nism for ultra-fast electrical charge mobility. Past stu dies have
2156-342X/$31.00 © 2012 IEEE
208 IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY, VOL. 3, NO. 2, MARCH 2013
Fig. 2. Three-dimensional power patterns for (a) normal node and (b) axial
(also called en d -ﬁ re) mode. Based on (see Balanis , reproduced with per-
mission from John Wiley & Sons Ltd.).
shown that the hopping timescale of protons in water is ap-
proximately 10–13 s , [ 9] , allowing the creation of an al-
ternating current in the sub-THz frequency band. In add iti on,
using macroscopic measurements of electrolyte solutions 
the conductivity of the sweat liquid, in th e sub-THz frequency
band, can be estimated to be at least 100 S/m in bulk solution.
These ﬁndings conﬁrm that the sweat ducts AC conductivity is
much higher than the conductivity of the surrounding tissue in
which the duct is embedded. Consequently, the helical struc-
ture of the sweat ducts and their electrical properties allow us to
treat the EM response of the skin organ by adopting terminology
and models taken from antenna theory . In these terms the sw eat
ducts can be regarded as an ensemble of helical antennas em -
bedded in the skin dielectric medium.
A helical antenna is a device used for radiating or receiving
EM waves, consisting of a conducting wire wound in the form o f
a helix. It was ﬁrst presented by K raus  and is broadly used
in the c om mu nication industry. This antenna can be regarded as
a hybrid between two elements: a d ipo le antenna and a loop an-
tenna. Consequently, the helical antenna has two main modes of
activation—a norm al mode and an axial (end- ﬁre) mode . In
the normal mo de the helix act s m uch like a half-wave dipole an -
tenna, effectively operating when the total length of the helix is
smaller than t he waveleng th. In this mode the helix is radiating
at an angle of 90
to the long axis of the helix [Fig. 2(a)]. How-
ever, unlike the dipole antenna the radiated ﬁeld is elliptically
polarized. In the axial mode, a resonance is created when the
helix loop circumference equals the wavelength, and the spacing
between loops is around quarter of the w avelength. The radia-
tion is emitted from the antenna in the direct ion of the lon g axis
[Fig. 2(b)]. In this mode the electromagnetic ﬁeld radiated is
circularly polarized, with the same chirality (left-hand or right
hand polarization) as the helix.
In this work the relevant mode is the axial mode, because of
the null e lect ric ﬁeld of the normal m ode in the direction of the
helix axis (perpendicular to the skin surface).
The geometrical conditions for the axial activation mode can
be summarized b y the relationships
is the helix loop circumference, is the spacing be-
tween loops and is the wavelength. In spite of the fact that
the accurate geometrical dimensions of the helix contribute to
the radiating efﬁciency, one can consider this mode valid even
in the case of deviations from the exact values due to its broad
S-matrix formalism can be used to describe a general case
where a local reference system is used to describe both incident
and scattered waves. In particular, the propagation of a plane
wave in an inhomogeneous m edia can be described in t
4 scattering matrix, by which two orthogo nal po larizations
are taken into account . In the special case of the same polar-
ization of the incidence and the scatte
red waves, the problem can
be reduced to a 2
2 scattering matrix, ,where
and f is the frequency :
Here, t he element
is the reﬂection coefﬁcient equal to
the ratio of the complex magnitu des of the reﬂected plane wave,
, to incident plane waves, :
Similarly, the electromagnetic spectra of reﬂection and ab-
sorption from the human skin in the sub-mm wavelength band
can be presented in terms of the matrix of scattering. The
term w ill describe the simulation results dealing with the reﬂec-
tion from a m ulti-layered skin model. Since the incident plane
wave impinges no rm ally on the skin, th ese results can be pre-
sented regardless of polarization.
In order to describe the frequency-dependant polarization
changes, a different approach can be used. In general, the value
of Circular Dichroism,
,isdeﬁned as the difference
between left and right circular polarizations
It can be considered as a m easure of the elliptical polariza-
tion of the reﬂected ﬁeld. Here is the left-handed
circularly polarized reﬂection coefﬁcient in a system excited by
a linearly polarized source, and
is the right-handed
circularly polarized reﬂection coefﬁcient in a system excited by
a linearly polarized source.
The initial set of simulation s ,  modeled the skin as a
3-layer planar system, where the boundaries between the layers
were well-deﬁned topologically ﬂat planes. This was acceptable
because the wavelength involved was larg er than the dimen-
sion of roughness of boundaries b etween the layers (
However, once h igher frequencies are considered the roughness
of the boundary must be incorporated into the model because
both waveleng th and roughness will be of the same order o f
The methodolo gy adopted to evaluate EM wave propagation
in t he skin, co nsisted of a p plying ﬁnite elements (in frequency
domain) or ﬁnite difference (in time domain) analysis to solve
HAYUT et al.: HELICAL STRUCTURE OF SWEAT DUCTS 209
the Maxwell equation s throughout the three layers medium, in
which the conducting helices were embedded (using CST mi-
crowave studio software).
In our previous studies the interface between the layers was
considered to be ﬂat . This led to the creation of a standing
wave between the layers, causing the absorption of the skin to
be elevated near speciﬁc frequencies. The
nitude at these frequencies was highly correlated with the ex-
pected sweat ducts activity (this elevated activity was d
physical stimulus), which was considered to be the main factor
for creating changes in the electromagnetic properties of the epi-
dermis. T his frequency-dependent reﬂection of th
Following ou r previous works , , ot
her groups have ex -
ploited a similar skin model in order to examine the EM re-
ﬂection –  and energy absorption  of the skin i n t he
sub-mm wavelength range.
Ney and Abdulhalim  suggested that spectral variations
from the skin can be explained by interference between the skin
layers, where the broad diel
ectric properties o f the layers are
changed. However, this idealized ap proach igno res the ph ysio -
logical beh avior of human skin, by proposing a dramatic change
in the dielectric perm i
ttivity of the epidermi s. Furthermo r e , a
recent study has conﬁrmed that sweat ducts do play a key role
in characterizing the spectral response of skin reﬂectivity .
The difﬁculty in
determining and separating the inﬂuence of dif-
ferent structural properties on the reﬂected signal has motivated
us to examine effects which can be created only by the unique
In this work, we shall study the behavior of EM waves
traversing through the skin. I n addition to the studied sim-
n models , , – we will focus here on the
100–450 GHz frequency band, where the wavelength is equiv -
alent to the dimensions of the helical structures. We shall
sider a sch ematic model of the skin that takes into account
the m ain details of its m orphology and the dielectric response
of its vario us layers including t he rough boundaries betw een
the skin layers, and the electrical properties of the sweat ducts.
We explored for the ﬁrsttimeauniqueasymmetrycreated
between left and r ight circular polarization of the reﬂected
signal as a result of the natural dichroism of the human sweat
ducts. We outline the frequency bands which are expected
to guide experimentalists in the study of the electromagnetic
response of the human skin. The sug gested effect of sweat
ducts on the spectrum can be used in order remotely sense
an activation of the human sweat system, and can lead to the
creation of a generic method for remote sensing of the physical
and emo tional state of human beings.
ODELS AND METHODS
A. The Model
As is clearly evident from the recent OCT images of the skin
, , the interface betw een the layers is not ﬂat. The derm al
ridges penetrate into the epidermis as papillae, which can be al-
most as large as the thickness of t he epidermis it self (Fig. 1). In
this work, the non-ﬂat boundary between the layers was taken
KIN DIELECTRIC PARAMETERS AS USED IN THE SIMULATIONS MODE L.THE
AC CONDUCTIVITY OF THE SWEAT DUCTS IS CONSIDERED TO BE MUCH
HIGHER THAN THAT OF ITS SURROUNDING EPIDERMIS
Fig. 3. Th e model side cross-section . The skin is divided into three layers:
stratum corneum (SC), epidermis and dermis. The helical sweat ducts are lo-
cated in the epidermis. Sinusoidal functions with different spatial frequencies
and amp litudes are used in o rder to mo del the non-ﬂat boundaries between the
dermis, epidermis and SC.
into accoun t, making the model more physiologically plau sible.
The boundary between the dermis and the epidermis was mod-
eled as a tw o-dim ensional sinusoidal surface (with amplitude
m). T h is was augmented by additional roughness at the
upper boundary of the e pidermis (between the epidermis an d the
SC) with am p li tude of 50
m. Adopting a non-ﬂat interface be-
tween the layers was found to be effective f or avoiding parasitic
interference effects between the layers.
The periodical shape of the layer bou ndaries, although sup-
ported by the morphology of the human skin (Fig. 1), does not
play an im po rtan t role in shaping the electromagnetic spectral
response. Th e different components of the skin were modeled
using the same dielectric properties as calculated in previous
studies . The conductivity of the sweat ducts wa s consid-
ered to be much higher than that of the skin layers, varying be-
tween zero in the absence of sweat ducts activity to 100–10 000
S/m , , , which might account for the different activa-
tion states of the sweat system in response to neurophysio log ic
stimuli. The model parameters are summarized in Table I and
B. Computation Method
The EM simulation was conducted using the CST Microwave
Studio software package, utilizing a 3-D ﬁnite-difference or ﬁ-
nite-element analysis to solve Maxwell’s equations over a mesh
210 IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY, VOL. 3, NO. 2, MARCH 2013
Fig. 4. The 3-layer skin model. The simulation is conducted over the (a) unit
cell using (b) tetrahedral mesh. Periodic boundary conditions extend the model
into the surrounding space.
of cells covering the model. A typical me th od for carrying ou t
such simulatio ns is the use of a waveguide port generating an
electromagnetic pulse which propagates in the simulated space.
The reﬂection from the simulated system is comp uted and the
spectrum is calculated using fast Fourie r tr a nsform (time-do-
In this work a different method was app lied —the model was
simulated using ﬁnite-element analysis as a frequency-selective
surface (FSS). A FSS may b e viewed as a ﬁlter of electromag-
netic waves in the frequency domain . A single mo del el-
ement is built within a unit cell. The unit cell boundary condi-
tions virtually repeat the modeled structure periodically in the
two directions along the skin surface up to in ﬁnity. An exci-
tation source of the n orm al incidence plain waves was placed
on the axis perpen dicu lar to these two directions. At this port
the differences between the outgoing and incom ing electromag-
netic radiation was measured in order to calculate the S-parame-
ters. The unit cell was deﬁned as containing one sweat duct. The
same structure was replicated in the neighboring cells through
the p eriodic boundary conditio ns (Fig. 4). Such a periodic struc-
ture allows the use of Floquet’s theorem in the computatio n
process . This results in a reduction of the s i m ulation do-
main, causing a signiﬁcant shortening of the computation time.
The concentrat ion of ducts in the skin was modiﬁ ed by changing
the size of the unit cells, effectively changing the distance be-
tween the ducts (see Section III). The FSS method allowed us to
decrease the model size calculated, an d therefo re to use a highly
accurate me sh (about 100 000 tetrahedrons in one unit cell, each
duct is built of 10 0–5 00 tetrahedrons).
The use of tetrahedral m esh was found to be computationally
efﬁcient due to the curved nature of the helical sweat ducts.
The periodic boundary conditions were found to be effective in
avoiding reﬂection s from the model edges. In addition, using
the plane wave source eliminated parasitic e ffects due to the
creation of a standing wave between the port and the model.
In order to calcula te the results for circular dichroism in the
reﬂected signal, a slightly different model was used, due to soft-
ware limitations: The model was built as a complete skin frag-
ment containing ﬁve sweat ducts (Fig. 5), and the computation
was made using a pulse excitation source (via a time-domain
calculation). The electromagnetic reﬂected ﬁeld at a larg e dis-
tance perpendicular to the skin surface (far ﬁeld) w as calcu-
lated, and the left and right circular polarized components w ere
Fig. 5. The skin model used in the c ir cu lar dichroism simulation. This simula-
tion was made using a pulse excitation source (time domain calcul ation).
Fig. 6. Schem atic rep rese ntation o f the AB-mm VNA measuring system. Ar-
rows represent the propagation of the beam from the source to the sample and
its reﬂection to the detector. A directional coupler is created by two polarizing
grids, standing at 45 deg to eac h other.
C. Experimental Setup and Method
The reﬂection coefﬁcient of the human palm was measured
using an AB-M illim etre vector network analyzer (MVNA-8 -
350, Paris, France), described in –, that can cover the
frequency range from 8 to 660 GHz. The optical path in this
setup from the source to the hand was 72 cm and the beam was
focused with elliptical m irrors ( see Fig. 6). The hand of the sub-
ject was ﬁxed at the point of focus using a special holder de-
signed to be of minimal inconvenience to the subject.
The right hand w as p laced into the holder with the bottom end
of the palm situated at the beam focus. The reﬂection coefﬁcient
of the palm was then measured as the subject w as at rest. The
measurement was made in the A SA frequency band (260–440
GHz). The measured spectrum was divided into eight separate
bands; in each one the appropriate conﬁguration of the system
was used. The recorded signal is computed in respect to a refer-
ence (a metal plate). Tw o subjects were measured, each one with
repeating 11 frequency sweeps in every frequency band. The en-
tire spectrum was then com bined from the separate bands, in a
HAYUT et al.: HELICAL STRUCTURE OF SWEAT DUCTS 211
Fig. 7. The reﬂectio n spectra of two different models of the skin (without sweat
ducts) were compared: A model with ﬂat boundaries betw een the layers (grey)
and a model including rough boundaries between the layers (black). The rough
boundaries reduce the effect of standing waves on the reﬂection spectrum above
way that the last part of the ﬁrst band was matched with the ﬁrst
part of the following band, etc. The data was then smooth ed
using a robust ﬁrst-order polynomial local regression method
(spanned locally on 5% of the data).
ESULTS AND DISCUSSION
A. Effect of the Rough Layer Bo und aries
Initially th e skin model was simulated without ducts. The in-
ﬂuence of th e periodic rough layer boundaries on the reﬂection
was investigated. The results, presented in Fig. 7,
show that at frequencies above 100 GHz the rough layer bound-
aries have reduced the interference in comparison with the ﬂat
boundaries, while the ﬁrst interferential minimum (below 100
GHz) becom es more pronounced. The simulation results ob-
tained in the low frequency range for the sm ooth boundaries
without ducts coincide with simil ar results presented in t he pre-
vious studies , , , [1 5] where ﬂat boundaries between
the layers were considered. The maximal epidermis thickness
is increased due to the introduction of rough boundaries, so tha t
the maximal thickness is 1 050
m instead of 350 mfortheﬂat
boundaries model. Th is yields a creatio n of the ﬁrst minima at
50 GHz compared to 90 GHz in the prev iou s studies.
B. Helical Sweat Ducts Response Modes
The frequency of the axial mode of the helical ducts em -
bedded in the skin model have been estimated b y means of an-
tenna theory, using
for the relative pe rmittivity of the
epidermis layer, in which the d ucts are embedded.
As the wavelength approaches the size of the circumference
of the duct, we expect the emergence of the axial-mode reso-
nance, the frequency of w hich is given by:
is the speed o f light in vacuum, and C is the duct cir-
cumference (we assume here
m). The loop spacing
based on OCT images
m slightly d eviates from
its optimal value
m but as it was mentioned above,
Fig. 8. Reﬂection spectrum from the sk in model, for different values of dis-
tances between ducts. (A) Inter-layer interferome tr y minimum is created at th e
lower frequencies band (
50 GHz). (B) The lower ﬁgure is a magniﬁcation of
the spectrum in the frequency range of 200–450 GHz. The main resonance can
be seen, corresponding to the axial mode (
380 GHz). The conductivity value
of the sweat ducts is ﬁx ed on the high-limit value of 10 000 S/m.
the axial mode activation in a helical antenna can still be con-
sidered . In order to s tudy the effect of the a xial helix mode
on the reﬂected ﬁeld, a numerical simulation of the skin mod el
with ducts was conducted (see computational method) and the
parameter was calculated. At this stage the ducts sur-
face density, which depends on the distance between th e ducts,
was the only parameter of the model that was varied. Results of
the calculati ons of thespectraofthereﬂection c oefﬁcient mod-
, for different distances between the ducts are plotted
in Fig. 8. The notable spectral variations when the distances
between ducts are changed can be ob served in the vicinity of
the estimated resonance frequency for the axial mode. Since the
values of the sweat duct length and its circumference are com-
parable, there mig ht be also an inﬂuence of the total duct length.
This can relate to a normal mode, although such effect should
be very small in the direction perpendicular to the skin surface.
Antenna theory analysis imp lies that the axial mode dominates
at a frequency of
The results also show that the distance between the ducts has
limited effect on the location (in frequency domain) of the re-
gions of spectral variations. This leads to the conclusion that the
frequency-dependent response is not related to ducts cou pling.
This is probably due to a strong attenuation of the EM ﬁeld in
the epidermis at these frequencies, which decreases the EM am-
plitude in the norm a l direction of the ducts. Besides the distance
between the ducts and the thickness o f the epidermis, the only
length sizes of the model, which correspon ds to the wavelength
range of 100–450 GH z, are related to the helical structure itself.
The fact that the reﬂectance is elevated at
240 GHz and re-
380 GHz is due to phase d ifferences in th e r e ﬂected
212 IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY, VOL. 3, NO. 2, MARCH 2013
electromagnetic ﬁeld. When charges ﬂo w between the upper
and the lower parts of the duct, a rotating current is also cre-
ated in the circumference of the duct as well. This induces an
electromagnetic wave propagating on the direction perpendic-
ular to the skin surface. The ﬁeld radiated from the ducts is com-
bined with the ﬁeld that is reﬂected from the skin surface, and
the phase between these two waves will determine whether the
reﬂection will be elevated or decreased.
C. Dependence of the Spectra l Response on the Conductivity
The sweat ducts condu ctiv ity was chosen as the parameter b y
which the sweat glands and d ucts activity is modeled. It is well
known that arousal of the human central nervous system encour-
ages the excretion of sweat from the sweat glands and trans-
porting it to the skin surface through the sweat ducts –.
This leads to al teration of the quanti ty and composition of the
sweat in th e ducts, which contribu tes to their AC con ductivity.
Hence, changes in the conductivity of the ducts can be used
as a reasonable model for investigating the effect of the sweat
system activation on the reﬂection spectrum. One must ask what
are, in this case, the limits of the AC conductiv ity? In bulk
can be estimated using the dielectric losses,
, where the DC element is assigned to
mostly proto n hopping . A s this is a diffusive motion it can
be estimated by
Ne , where N is the proton concen-
the e l ementary proton charge and is the proton
mobility (linked to the diffusion coefﬁcient,
by the Ein-
, ). At 100 GH z this es-
timation gives approximately 100 S/m at . Note, that the
similar value of conductivity was measured in th e solu tio n of
simple electrolyte KCl and NaCl at a frequency of 40 GHz, in
the concentration range of 0.01 to 1 mol/l at a room temperature
, and would be even higher a t 100 GHz. However, the dif-
fusion coefﬁcient of protons has been demonstrated to increase
once water becomes ordered. For instance the diffusion coef-
ﬁcient o f protons in ice i s 10 times higher than of protons in
bulk water at room temperature . Furthermore there is ev-
idence to suggest that in the vicinity of a lipid/water interface,
water is highly structured  an d that along such structures
ﬂuorescence spectroscopy estimated an increase in proton dif-
fusion by a factor of 10 0  in comparison to that of protons
in the bulk water. The layer of “ordered” water in the duct is
approximately a few nanometers deep , is sm all compared
to the micrometers diameter of the duct i tself. Consequently the
ratio of volu mes is of the order of 0.01. Under the assumption of
a radial homogeneity in proton density inside the sweat duct, the
contribution fro m proton hopping along the du c t s urf ace can be
estimated by a similar weighting and t h erefor e not negligible.
Using the value o f dielectric losses for water
ice (almost zero) at 300 GHz , the ratio of conductivities
between the surface layer and the b ulk i s g iven b y
which can be estimated by
Fig. 9. (top) The reﬂection spectrum from the skin model for different values
of the conductivity of the helical sweat ducts, with co nstant distance between
ducts of 700
m. The frequency regions in which helical sweat ducts affect
the spectrum does not change when the conductivity is modiﬁed. (bo ttom) For
moderate conductivity values, the effect of the sweat ducts is less pronounced,
but peak differences still co rresponds to the axial mode (
Using the values of  for the proton conductivity in bulk
water as a function of the proton concentration we h ave for a
concentration of 1 mole [H+]
quently the ratio of the respective surface and bulk c on ductivi-
. Given that bulk wate r co nductivity
is 100 S/m and that f or an electroly te solution it is even higher,
it is not un reason able to set the upper limi t of co nductivity as
10,000 S/m. Hen ce, most of the simulations were made using
the upper lim it of the theoretical conductivity values of sweat
(1000–10 000 S/m). However, the results are valid even with
lower co nductivities, as can be seen in Fig. 9 (low er) . In fact,
the main results of this paper (in terms of the spectral shape and
antenna modes) are independent of the value of the sweat con-
ductivity—as lon g as it is higher than that of the surroun ding
tissue. In short it is merely a signal-to-noise issue. Such an ap-
proach can also be used in order to predict the experimental
results of electromagnetic reﬂection from human subjects with
different levels of the thermoregulation system activity, as do ne
In this work, t he simulatio ns with different cond uctivity
levels have enabled us to identify the effect of the helical sweat
ducts in the passiv e regime, i .e., without any possible additional
modulation o f the current by another source.
When the conductivity is increased, a prominent change in the
reﬂectance spectrum was observed, especially in the vicinity o f
the axial mode resonance ( 350 –400 GHz), which was d iscussed
earlier in the paper (Fig. 9 (top)). This response region does not
shift with changes in the conductivity. This fact supports the
HAYUT et al.: HELICAL STRUCTURE OF SWEAT DUCTS 213
Fig. 10. The reﬂe c tion spectrum from the skin model, f or different values of
the diam eter of the helical sweat ducts. The ax ial mode frequency shifts as we
change the duct d iam eter, as expected
The conductivity value of the sweat
ducts is ﬁxed on the high-limit value of 10 ,000 S/m.
conclusion that this is the region of the spectral variations which
emerges from the structural properties of the helical sweat ducts.
D. Spectral Response Dependence on the Ducts Circumference
According to antenna theory, a helical antenna axial mode
center wavelength is equal to the circumference of the helix
. Therefore, changes in the circumference of the ducts in
in the absorption p eak location. As expected, the response band
originally computed at 350–400 GHz shifts to higher frequen-
cies when we decrease the diameter of the ducts and to lower
frequencies when we increase it (Fig. 10). The reﬂection peak
at 250–300 GHz also shifts when we change the diam eter of
the ducts, which is consistent with the assum pt ion that this peak
does not simply r elates to a norm a l mode resonance of the ducts.
An explanation o f this effect can be found in the fact that the
“classic” antenna theory normal mode of a helix r elat es to a lon g
and narrow helix , and this is not the case in our mo del.
As mentioned above, the fact that the circumference and the
height of the ducts are of th e same order of magnitude creates
this “impure” mode that relates to both height and diameter.
E. Experimenta l Measurem ent Results
The experimental results (See Fig. 11) give the ﬁrst indica-
tion of a measurable enhanced spectral absorption in the region
related to the axial mode (
380 GHz). Nevertheless, the ele-
vated reﬂectance region from the simu lation routine was n ot ob-
served in the frequency band (
240 GHz) correspondent to t he
normal-mode. This might be due to the fact that the measure-
ment was con ducted on ly ab ove 260 GHz, or that th e spectral
variation in this region is much weaker (than predicted in the
simulations). The exact location of the absorption local max-
imum was slightly different between the two subjects, but the
spectral shape was r obu st (in the limitations of an in vivo m ea-
surement) for each one of them separately. The shift in the re-
ﬂection minimum can be achieved in the simulation spect rum
or by changing the dielectric permittivity of the epidermis or
varying the radius of the helical duct. H ere a comparison of two
simulations was made using different values of the epidermis
dielectric permittivity (valu es of 2.6 and 2.8) and d uct co nduc-
tivity value of 1500 S/m, while all the other parameters remain
Fig. 11. The modulus of the reﬂection coefﬁcient as measured from the
skin of two subjects using the AB-m m VNA (solid lines) and as produced by
the simulation model with different values of epider mis permittivity ( d a shed
lines). In both m easurem ent sets a signiﬁcan t change in the reﬂection spectrum
was measured in the vi cinity of the frequency re gio n suggested as the axial mode
380 GHz). The spectral shape is slightly different between the two subjects,
as expected due to morphology variations between the skin of the subjects. The
simulations were made using the p arameters listed at Table I, except duct con-
ductivity (1500 S/m in both simulations) and epidermis relative permittivity (2.6
constant according to Table I. Shift in the reﬂection minimum
can also be acquired by chang ing the radius of the helical duct.
These measurements mark the starting point for future re-
search, as a larger number of subjects and measurements can
supply statistically-signiﬁcant results in order t o verify experi-
mentally the sim ulatio ns results. For such addition al measure-
ments, a time-domain system might be more appropriate, in
order to avoid the separation of the frequency range into smaller
bands as the VNA requires.
In principal , the helical structure of the sweat ducts implies
that an electromagnetic radiation reﬂected from the skin must
have speciﬁc polarization p roperties. Similar to the classical he-
lical antenna, a helical sweat duct should have a strong response
to a preferred circular polarization direction , . At the
macroscopic level, if the ducts turn direction was equally dis-
tributed to bot h di rections, the sum of the reﬂected signal was
averaged out and this property of the ducts would not b e ex-
pressed. Remarkably, studies of the morphology of the human
skin hav e clearly shown that a bou t 90% of the sweat ducts are
right-handed spirals . When exci ting the skin using linear
electromagnetic radiation (which can be expressed as superposi-
tion of tw o equal left and right circular components), this asym-
metry should be expressed in the reﬂected signal. In order to ex-
amine this phenomenon we used a similar skin model simulation
and examined the difference between the left and right circular
polarization components of the reﬂected ﬁeld. The model was
excited u sing a linearly polarized wave source, and the max-
imum amplitude of the reﬂected electric ﬁeld was examined
separately for left and right circular co mp onen ts. Plotting the
difference between these two components, one can clearly see
the circular dichroism in the same frequency bands related to
the helix modes (Fig. 12). At frequencies lower than 200 GHz,
the wavelength is larger than t he d im ensions of the ducts, and
there is no difference between the two components. At these
214 IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY, VOL. 3, NO. 2, MARCH 2013
Fig. 12. CD (circular dichroism)—The difference between the left and right
circularly polarized electromagnetic ﬁeld amplitude in the reﬂected signal, as
a percent f rom the total reﬂected electromagnetic ﬁeld amplitude. CD appears
when the w avelength approaches the structural dim ensions of the sweat duct
long wav elengths, the ﬁne helical stru cture of the ducts cannot
be expressed, and so the difference between left and right com-
ponents is zero. As the excitation wav e leng th approaches the
size of the duct (around 200 G Hz), the ratio between the left and
right components starts to change. Circular dichroism reaches a
high level aroun d 350–400 GHz, as the ducts interact with the
radiation close to their a xial mode. Such a preference for a par-
ticular polarization direction might be detected experimentally,
as sub-m m sources and detectors become more available.
In this work, the details of th e structure of the b oth the mor-
phological features and the electrical conductivity of the sweat
ducts were shown to have an important role in shaping the re-
ﬂectance spectra of the human skin in the frequency band of
100–450 GHz. Unlike other skin m odeling studies, it was shown
here that the effect of m ultilayer interference is substant ially re-
duced when the non-ﬂat boundaries between the different skin
layers are taken into account.
The performed simulations demonstrate that variations of the
spectra are observed in the vicinity of the frequencies close to
the predicted axial response m ode of th e sweat ducts (regarded
as helical antennas) at approximately 380 GHz. In addition a
lower frequency peak which appears around 240 GHz might be
a result of an impure normal mode related t o the total length o f
the helix. The results clearly show that the structure of th e sweat
ducts plays a key role in the shaping of the reﬂ ected spectra. I t
should be emphasized that the simulated passive model sweat
ducts are excited only by the incident plane wave without any
modulation of the current by addition al sources. Th e sim ula-
tion demonstrates that the frequency region of the main spectral
variations does not depen d on the conductivity value, as the in-
creasing of conductivity only am pliﬁes the effect.
In addition, due to the natural preference of the direction in
the human sweat ducts chirality, the expected circular polariza-
tion effect was supported by the simulation. This effect is pro-
nounced in the vici nit y of t he mai n spectral variations. In an ini -
tial set of measurements, the spectral variation in the vicinity of
the axial mode was observed, sup porting the hypothesis that the
helical structure of sweat ducts inﬂuences the reﬂection spec-
trum of the h uman skin at sub-mm wavelengths. It is clear that
this model have to be extended in the future for consideratio n
of strong coupling between the sweat ducts, to take into accoun t
the stochastic nature of ducts m orphology, and other parameters
of our sim pliﬁed model.
The authors thank Pro f. V. Ilyin, Prof. V. Rozenshtein,
L. Lavy, I. Segev, E. Safrai, and E. N a’am an for helpful
 A. Knuttel and M. Boehlau-Godau, “Spatially conﬁned and temporally
resolved refractive index and scattering evaluation in human skin per-
formed w ith optical coherence tomography,” J Biomed Opt., vol. 5, pp.
83–92, Jan. 2000.
 A. Knuttel, S. Bonev, and W. Knaak, “ N e w method for ev aluation
of IN VIVO scattering and refractive ind ex properties obtained with
optical coherence tomography,” J Biomed. Opt., vol. 9, pp. 265–273,
“Human sk in as arrays of helical antennas in the millimeter and sub-
millimeter wave range,” Phys. R ev. Lett. , vol. 100, p. 128102, 2008.
 Y. Feldman, A . Puzenko, P. Ben Ishai, A. Caduff, I. Davidovich, F.
Sakran, and A. J. Agranat, “The electromagnetic response of human
skin in the m illimetre and submillimetre wave range,” Phys. Med. Biol.,
vol. 54, pp. 3341–3363, Jun. 7, 2009.
 H. R. Jacubovic and A. B. Ackerman, Derma to log y,vol.1,p.66,1992.
 L.A.Goldsmith, Fitzpatrick’s Dermatology in In tern al Med icine, vol.
1, p. 155.
 S. Takagi and M. Tagawa, “Predominance of right-handed spirals in
the intraepidermial sweat ducts in man and the prim ates, ” Japan. J.
Physiol., vol. 7, p. 113, 1957.
 V. V . Krasnoholovets, P. M. Tomchuk, and S. P. Lukyanets, “Proton
transfer and coherent phenomena in molecular structures with hy-
drogen bonds,” in Advances in Chem ical Physics. Hoboken, NJ:
Wiley, 2003, pp. 351–548.
 M. A. Lill and V. Helms , “Molecular dynamics simulation of proton
transport with quantum mechanically deriv ed proton hopping r a tes
(Q-HOP MD),” J. Chem. Phys., vol. 115, pp. 7993–8005, 2001.
 R. Gulich, M. Kohler, P. Lunkenheimer, and A. Loidl, “Dielectric spe c-
troscopy on aq ueous electrolytic so lutions,” Rad. Environ. Biophys.,
vol. 48, pp. 107–114, Feb. 2009.
 J. D. Kraus, Antennas. New York: McGraw-Hill, 1950, p. 382.
 C. A. Balanis, Antenna Theory: Analysis and Design,3rd
ed. Hoboken, NJ: Wiley, 2005.
 D. M. Pozar, Microwave Engineering. Hoboken, NJ: Wiley, 1998, p.
 M. Ney and I. Abdulhalim, “Does human skin truly behave as an array
of helical antennae in the millimeter and terahertz wave ran ges?,” Opt.
Lett., vol. 35, pp. 3180–3182, 2010.
 M. Ney and I. Abdulhalim, “Modeling of reﬂectometric and ellipso-
metric spectra from the skin in the terahertz a nd submillimeter waves
region,” J Biomed. Opt., vol. 16, pp. 067006–15, 2011.
of the electromagn etic reﬂection response of human skin at W-band,”
Opt. Lett., vol. 36, pp. 4203–4205, 2011.
 G. Shaﬁrstein and E. G. Moros , “Modelling millimetre wav e propaga-
tion and absorptio n in a high resolution skin model: The effect of sw eat
glands,” Phys.Med.Biol., vol. 56, p. 1329, 2011.
 D. CST Computer Simulation Technology AG, Darmstadt , Germany,
“CST Microwave Studio suite—Ver. 2010,” [Online]. Available:
http://www.cst.com /Content/Applications/Artic le/A+Polarisation+In-
dependent+Ba n dp ass+FSS, Accessed Apr. 10, 2011
 W. Magnus and S. Winkler, “Floquet’s theorem,” in Hill’s Equa tio n.
New York: Dover, 1979, vol. 1.2, p p. 3–8.
 A. Elhawil, G . Koers, L. Zhang, J. Stiens, and R. Vounckx, “Reliable
method for material characterisa tion using quasi-optical free-space
measurement,” IET Sci., M eas., Technol., vol. 3, pp. 39–50, 2009.
 M. Mola, S. Hill, P. Goy, and M. Gross, “Instrumentation for
millimeter-wave magnetoelectrodynamic investigatio ns of low-di-
mensional conductors and superconductors,” Rev. Sci. Instrum., vol.
71, pp. 186–200, 2000.
HAYUT et al.: HELICAL STRUCTURE OF SWEAT DUCTS 215
 S. Taka hash i and S. Hill, “Rotating cavity for high-ﬁeld angle-depen-
dent microwave spectroscopy of low-dimensional conductors and mag-
nets,” Rev. Sci. Instrum., vol. 76, p. 023114-10, 2005.
 D. M. DiPasquale, M. J. Buono, and F. W. Kolkhorst, “Effect of skin
temperature on th e cholinergic sensitivity of the human eccrine sweat
gland,” J pn. J. Physiol., vol. 53, pp. 427–430, Dec. 2003.
 S. C. Landis and D. Keefe, “Evidence for neurotransmitter plasticity in
vivo: Developmental ch anges in prop e rties of cholinergic sympathetic
neurons,” Devices Biol. , vol. 98, pp. 349–372, Aug. 1983.
 A. K. M. Shamsuddin and T. Togawa, “Continuous monitoring of
sweating by electrical conductivity measurement,” Physiol. Meas.,
vol. 19, p. 375, 1998.
 D. S. Eisenberg and W . Kauzmann, The Structure and Properties of
Water. Oxford, U.K.: Clarendon, 1969.
 R. K. Pathria, Statistica l Mechanics, 1st ed. New York: P ergamon,
 S. Cuk ierman, “Proton mobilities in water and in different stereoiso -
mers of covalently linked gramicidin A channels,” Biophys. J, vol. 78,
pp. 1825–1834, Apr. 2000.
 I. Presiado, J. Lal, E. Mamontov, A. I. Kolesnikov, and D. Huppert,
“Fast proton hopping detection in ice Ih by quasi-elastic neutron scat-
tering,” J. Phys. Chem. C, vol. 115, pp. 10245–10251, May 2011, 2011.
 J. Kim, W. Lu, W. Qiu, L. Wang, M. Caffrey, and D. Zhong, “Ultrafast
hydration dynamics in the lipidic cubic pha se :? Discrete Water Struc-
tures in Nanochannels,” J. Phys. Chem. C, vol. 110, pp. 21994–22000,
Nov. 2006, 2006.
 M. Brändén, T. Sandén, P. Brzezinski, and J. Widengren, “Localized
proton microcircuits at the biological me mbrane-water interface,”
Proc. Nat. Acad. Sci., vol. 103, pp. 19766–19770, Dec. 2006, 2006.
 M. Simeonova and J. Gimsa, “The inﬂuence of the molecular structure
of lipid membranes on th e electric ﬁeld distribution and energy absorp-
tion,” Bioelectromagn., vol. 27, pp. 652–666, 2006.
 P. V. Hobbs, Ice Physics. Oxford, U.K.: Clarendon, 1974.
 W. J. Ellison, K. Lamkaouchi, and J. M. Moreau, “Water: A dielectric
reference,” J. Mol. Liq., vol. 68, pp. 171–279, 1996.
Itai Hayut received the B.Sc. and M.Sc. degrees in
physics and neuroscience from Ben-Gurion Univer-
sity of the Negev, Israel, in 2006 and 2008, res
tively, and has been working toward the Ph.D.
in Depart ment of Applied Physics at the Hebre
versity, Israel, since 2009.
His current work is focused on remote sensing
from t he human skin at sub-TH z frequencies.
Alexander Puzenko wasborninRussia,U.S.S.R.,in
1944. He received the M .Sc. degree in radio physics
and electronics and the Ph.D.degreeinradiophysics
and quantum radio physics from the K harkov State
University (USSR) in 19 66 and 19 7 9, r espectively.
From 1966 to 1983, he was with the Department
of Radio Waves Propagation and Ionosphere of the
Institute of Radio physics and Electronics Ukrainian
Academy of Sciences (Kharkov). From 1984 to 1994
he was with the Department of Space Radiophysics
of I nstitute of Radio Astronomy National Academy
of Science (Kharkov), as a senior scientist. In 1995 he immigrated to Israel, and
since 1997, he has been with The Hebrew University of Jerusalem, where he
is currently a senior scienti st at the Dielectric Spectroscopy Laboratory in the
Department of Applied Physics. H is current r esearch interests include time and
frequency domain broad band dielectric spectroscopy, theory of dielectric po-
larization, relaxation phenomena, and strange kinetics in disorder ed m ater ials,
transport properties and percolation in complex systems, dielectric properties of
biological systems and electromagnetic properties of human skin in the sub-THz
Paul Ben Ishai received the Ph.D. degree from the Hebrew University in 2009.
For the last 12 years he has been involved with the L ab oratory of Prof.
Feldman, conc entrating on dielectric research. He currently holds the position
of Director of the Hebrew University’s Center for Electromagnetic Research
and Cha racterization, situated in the Applied Physics Departm e n t . His research
topics include soft condensed matter physics, glassy dynamics, biophysics,
sub-terahertz spectroscopy and dielectric spectroscopy. In 2004, he was part of
the founding team investigating the interaction of the hu man sweat duct with
sub tera hertz electromagnetic radiation.
Alexander Polsman received the B.Sc. degree in
physics from Racah Institute of Physics, The Hebr ew
University of Jerusalem, in 2009, and is currently
of A pplied Physics, School of Computer Science and
Engineering, The Hebrew University of Jerusalem,
His researc h interests include microwave, mil-
limeter- and subm illimeter-wave technologies.
Aharon J. Agranat received the B.Sc degree
physics and mathem atics, the M.Sc. degree
plied physics, and the Ph.D. degree in phy
the Hebrew University, Israel, in 1977, 1
He is the N. Jaller Prof essor of Applied Sc
the Director of the Brojde Center for Inn
Engineering and Computer Science, a
nd the former
Chairman of Applied Physics at the H
versity of Jerusalem. From 1986 to 1
997, he was a
senior research fellow at the Cali
fornia Institute of
Technology, Pasadena. He is the au
thor of over a hundred scientiﬁc papers, and
holds over 25 patents.
Prof. Agranat is a Fellow of the Opt
ical Society of Am erica, and a recipient
of the 2001 Discover Innovation A
ward in th e area of commu nication for the
invention of Electroholograp
Yuri F e ldman was born in Ka z
an, U.S.S.R., in
1951. He received the M.S. d
egree in radio physics
ecular physics from the
Kazan State University, U
.S.S.R., in 1973 and 1981,
From 1973 to 1991, he was w
ith Laboratory of
Molecular Biophysics o
f Kazan Institute of Biology
of the Academy of Scie nc
e of the U.S.S.R. In 1991,
he immigrated to Israe
l and since 1991, he has been
with the Heb rew Univer
sity of Jerusalem, where he
is currently the Full
Professor and the Head of the Di-
py Lab oratory. He also is a Director of the Center for Elec-
ch and Characterization (CERC) and since 2002 h e is the
Secretary and Memb
er of the International Dielectric Society Board. He has
spent over 30 year
sintheﬁeld and has more than 200 scientiﬁc publications
related to dielec
tric spectr osco p y and its applications. He holds 8 p aten ts in the
areas of electro
magnetic properties of the matter. His cu rrent interests include
ctric spectroscopy in frequen cy and time domain; theory of di-
zation and relaxation; relaxation phenomena and strange kinetics
in disordered m
aterials; electromagnetic properties of bio log ical systems in vitro
and in vivo.