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Reflection and Penetration Depth of Millimeter
S.I. Alekseev, O.V. Gordiienko, and M.C. Ziskin*
Center for Biomedical Physics,Temple University Medical School,
Millimeter (mm) wave reflectivity was used to determine murine skin permittivity. Reflection wasmeasured in anesthetized Swiss Webster and SKH1-hairless mice in the 37–74 GHz frequency range.
Two skin models were tested. Model 1 was a single homogeneous skin layer. Model 2 included fourskin layers: (1) the stratum corneum, (2) the viable epidermis plus dermis, (3) fat layer, and (4) musclewhich had infinite thickness. We accepted that the permittivity of skin in the mm wave frequency rangeresults from the permittivity of cutaneous free water which is described by the Debye equation. UsingFresnel equations for reflection we determined the skin parameters best fitting to the reflection data andderived the permittivity of skin layers. The permittivity data were further used to calculate the powerdensity and specific absorption rate profiles, and the penetration depth of mm waves in the skin. In bothmurine models, mm waves penetrate deep enough into tissue to reach muscle. In human skin, mmwaves are mostly absorbed within the skin. Therefore, when extrapolating the effects of mm wavesfound in animals to humans, it is important to take into account the possible involvement of muscle inanimal effects. Bioelectromagnetics 29:340–344, 2008.
Key words: murine skin permittivity; millimeter wave dosimetry; skin modeling
the mm wave interaction with murine skin. Therefore,the aims of the present study were to determine the
Therapeutic application of millimeter (mm)
permittivity of murine skin using mm wave reflectom-
waves in medicine [Rojavin and Ziskin, 1998] has
etry and to calculate the power density (PD) and specific
stimulated great interest in understanding the mecha-
absorption rate (SAR) profiles as well as penetration
nisms of biological action of mm waves. Recently, mm
depth of mm waves in murine skin based on homoge-
wave effects on the immune system, tumor metastasis
neous and multilayer skin models. To evaluate the
and mm wave induced hypoalgesia have been exten-
influence of hair on murine skin permittivity, we used
sively studied in mice [Radzievsky et al., 2000, 2001,
2004; Makar et al., 2003, 2005; Lushnikov et al., 2004;Logani et al., 2006]. The reported actions arise frominduced systematic effects that result from the shallow
penetration of mm waves into the skin. To determine theprimary targets for mm wave action, it is first necessary
to determine what biological structures are within
Millimeter wave reflection was studied in
the penetration depth of mm waves. Furthermore, to
two strains of mice: male Swiss Webster mice, body
extrapolate the biologic effects found in mice to
weight approximately 20–25 g (obtained from Taconic,
humans, it is necessary to know the mm wave intensitydistribution in both murine and human skin. Both of
these tasks require accurate dosimetry. Dosimetry
Grant sponsor: NIH NCCAM; Grant number: P01-AT002025.
calculations are based primarily on the geometry and
*Correspondence to: M.C. Ziskin, Center for Biomedical Physics,
Temple University Medical School, 3400 North Broad Street,
Recently we have reported the results of a study of
Philadelphia, PA 19140. E-mail: firstname.lastname@example.org
human skin permittivity using mm wave reflectometry[Alekseev and Ziskin, 2007] and human skin dosimetry
Received for review 9 August 2007; Final revision received
[Alekseev et al., 2008]. Permittivity was determined for
both homogeneous and multilayer skin models.
We did not find in the literature any permittivity
Published online 25 January 2008 in Wiley InterScience
data specific for murine skin nor any detailed analysis of
Germantown, NY) and female SKH1-hairless mice,
frequency range results mostly from the polarization
body weight approximately 22–25 g (obtained from
of free water molecules [Grant, 1982; Foster and
the Charles River Laboratories, Wilmington, MA). The
Schwan, 1986; Gabriel et al., 1996a].
animals were housed in plastic cages in the Central
The permittivity of each skin layer (i) was
Animal Facility at Temple University. The Institutional
described by the Debye equation with a single
Animal Care and Use Committee of Temple University
relaxation time t equal to that of pure water at skin
approved the experimental protocols. All experiments
were conducted under anesthesia with a mixture of
ketamine (95 mg/kg), xylazine (10 mg/kg), and
acepromazine (0.7 mg/kg). Reflection measurements
were made on the caudal dorsum and flank areas of
where o ¼ 2pf, f is the frequency, j ¼ (À1)1/2, De
both strains of mice. On the Swiss Webster mice, these
regions were shaved on the day preceding the measure-
1i the magnitude of the dispersion of the free water
ments. We used 10 animals of both strains in each
1i the optical permittivity, eo ¼ 8.85 Â 10À12 F/m, si
the skin ionic conductivity. The permittivities of the fatand muscle layers were selected in accordance with
The methods and techniques used for mm wave
reflection measurements were the same as described inour recent publication [Alekseev and Ziskin, 2007].
To fit the theoretical equations for calculating the
Reflection was measured at the open-ended waveguide
power reflection coefficient R in different models to the
applied to the caudal dorsum or flank area of murine
reflection experimental data, we used the least-squares
skin in the 37–74 GHz frequency range. Reflection
technique. The standard deviation of the differences be-
measurements were performed at ambient room temp-
tween the calculated values and the measured values in
erature of 22–24 8C and relative humidity of 15–30%.
the final fit was used as a measure of goodness of fit.
The optical permittivity and ionic conductivity,
and the thickness of the SC played an insignificant
role in the fitting procedure. Taking into account that the
optical permittivity of the solid fraction of skin and pure
The skin temperature was measured using a
water were equal to 2.5 and 5.2, respectively, the optical
thermocouple of the IT-23 type (Physitemp, Inc.,
permittivity for each skin layer was approximated as
Clifton, NJ) immediately before and after each
reflection measurement. Average temperature of these
two values was used for the permittivity calculation.
The skinfold thickness was measured using a Starrett
where wti is the weight fraction of the total water content
micrometer (L.S.Starrett Co., Athol, MA). To deter-
of skin layer i. The weight fraction of total water was set
mine the thickness of skin, the skinfold thickness was
equal to 0.33 for the SC [Imokawa et al., 1991] and 0.6
divided by two. The skin thickness was also measured
for the viable epidermis and dermis layer [Duck, 1990].
with the micrometer directly in euthanized mice. Both
The ionic conductivities of the SC and the viable
epidermis and dermis were set equal to 0 and 1.4 S/m,respectively [Alekseev and Ziskin, 2007].
In determining skin permittivity we varied two
parameters, the permittivity increment Dei, and the
In modeling mm wave interaction with skin, we
thickness di. The thickness of the SC was fixed equal to
applied a homogeneous unilayer and a four layer skin
its typical literature value of 0.015 mm [Warner et al.,
model. The four layer model contained (1) the stratum
1988]. The thickness of the fat layer was determined as
corneum (SC), (2) the viable epidermis plus dermis, (3)
the difference between the total skin thickness meas-
fat layer, and (4) muscle which had infinite thickness.
ured experimentally and the thickness of the epidermis
We made several assumptions. First, the skin layers
used in both models were considered to have distinct
A sensitivity analysis showed that a 10% variation
plane boundaries. Second, the skin layers contained
in reflection measurements resulted in a variation of Dei
different amounts of free water. Third, permittivity of
within10% and di within15%. The least-squares fit was
biological tissue, including skin, in the gigahertz
considered to be acceptable if the SD was no more than
Æ15%. The results of reflection measurements are
TABLE 1. Parameters of Murine Skin Models Giving the Best
presented as mean Æ SD (n ¼ number of independent
Millimeter waves were considered to be at normal
incidence to the skin surface. To calculate the power
reflection coefficient (R) and power density profile
PD(z) as a function of skin depth we applied the Fresnel
equations [Born and Wolf, 1975; Alekseev and Ziskin,
2000, 2007]. The penetration depth d was calculated as
d ¼ c/o Á n00 where c is the velocity of light.
The mean thickness of skin including the thick-
ness of the fat layer in the caudal dorsum and flank
areas was 0.37 Æ 0.03 mm in the Swiss Webster mice
and 0.38 Æ 0.06 mm in the SKH1-hairless mice. The
mean skin surface temperature at the same sites was
The stratum corneum and the rest of epidermis plus dermis are
32.8 Æ 0.4 8C in the Swiss Webster mice and
denoted as SC and EÀ þ D, respectively; d is the thickness and s is
30.3 Æ 0.5 8C in the SKH1-hairless mice.
the ionic conductivity of the skin layer. In homogeneous skin (model 1),
The dependence of the power reflection coeffi-
EÀ þ D stands for the whole skin. Other symbols used in the tableare given in the ‘‘Methods Section’’.
cient measured in the hairy murine skin on frequency
is shown in Figure 1. The difference between thereflection data obtained from the caudal dorsum or flankareas was statistically insignificant. Reflection from
Table 1 used with the Debye Equation (1) determine
hairless mice was slightly greater than from hairy mice
permittivity of the homogeneous skin or permittivity of
( 7.4%). The data obtained from both strains of mice
skin layers in the multilayer skin model. They were
were well fitted to the homogeneous or multilayer skin
further used to calculate the reflection, PD, and SAR
models. The parameters of the homogeneous and
profiles, and the penetration depth of mm waves in
multilayer skin models giving the best fit to the data
are presented in Table 1. The electrical parameters of
The power reflection coefficient and penetration
depth calculated for the plane mm waves at thetherapeutic frequencies are given in Table 2. At eachof three frequencies tested, the penetration depth of thehairy skin was 9.0–9.7% less than that of the hairlessskin. Since the penetration depth is inversely propor-tional to attenuation, this result implies that hairlessskin is approximately 9.5% more attenuating of mmwaves than is hairy skin. The R and d values can be usedto evaluate SAR in homogeneous skin. Once the
Depth of Plane Millimeter Wave Electromagnetic Field inMurine Skin at Therapeutic Frequencies
Fig. 1. Power reflection coefficient versus frequency for hairy mur-
ine skin. Symbols are experimental data.The error bars represent
SD at n ¼10. Solid lines are fits to the four layer skin model. Reflec-
tion curves for hairless murine skin were similar to those of hairy
murine skin but the values of the power reflection coefficients were6.3 ^ 7.4% higher.
Calculations were made using the homogeneous skin model.
Fig. 3. Frequency dependence of the PD and SAR at a depth of d1(the front surface oftheviable epidermis), d2 (therear surface ofthe
Fig. 2. Power density (PD) profiles within hairy murine skin
dermis), and d3 (the front surface ofthe muscle) ofthe hairy murine
calculated for 42.25 and 61.22 GHz using the one (dashed line)
skin.Calculations were made for a plane wave at the incident PD of
and four (solid line) layer skin models. In the four layer model,
1 denotes the SC, 2 is the viable epidermis plus dermis, 3 is the fatlayer, and 4 is the muscle. Calculations were made for the planewave at the incident PD of 10 mW/cm2. The PD profiles within thehairless murine skin were close to those shown on the graph.
the deeper muscle layer and at the rear surface of thedermis, the SAR values were close to each other. Atboth regions the changes of SAR with frequency were
incident PD, I, is defined the SAR at a depth of z can be
not as pronounced as on the epidermal layer.
calculated as follows [Gandhi and Riazi, 1986]:
In modeling the mm wave interaction with murine
The results of calculation of the PD profiles for the
skin we used plane wave exposure and simplified skin
two therapeutic frequencies 42.25 and 61.22 GHz in
models. The heterogeneity within each skin layer and
hairy murine skin are shown in Figure 2. The PD
non-parallel internal boundaries would affect the
profiles obtained for the hairless murine skin showed
calculated results. However, we do not expect a signi-
little difference. Millimeter waves penetrated deep
ficant influence of these factors on the PD deposition in
enough to reach the muscle, that is, 42.5% and 32%
the skin and underlying tissue as the heterogeneous and
of mm wave energy entering the skin at 42.25 and
multilayer models resulted in similar results. This can
61.22 GHz, respectively, was absorbed within the
be explained by the small difference in water content of
muscle. In the skin layers with lower water content, that
different tissue layers except for the SC and fat layers.
is, with the higher wave impedances, the SC and fat, the
The thin SC and fat layers produced a small effect on the
PD was lower than in the viable epidermis and muscle,
PD deposition [Alekseev et al., 2008].
Reflection from both hairy and hairless murine
The changes of the PD with frequency in the
skin was lower than from human skin [Alekseev and
different layers of skin were small (Fig. 3). The SAR
Ziskin, 2007]. This result can be explained by the lower
values increased notably with the frequency at the
free water content of murine skin in comparison with
surface of the viable epidermis. At the surface of
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