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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: ziskin@temple.edu 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].
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