IEEE TRANSACTIONS ON ANTENNAS AND...

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 62, NO. 3, MARCH 2014 1293

Sensing Depth of Microwave Radiation for InternalBody Temperature Measurement

Robert Scheeler, Student Member, IEEE, Edward F. Kuester, Fellow, IEEE, and Zoya Popović, Fellow, IEEE

Abstract—This paper investigates modeling of the interaction ofhuman tissues with a probe antenna situated on the surface of theskin. The goal is to differentiate temperature changes at differentdepths under the skin for passive radiometric measurements of in-ternal body temperature. An improved metric is defined in orderto differentiate thermal power radiated from a specific part of thetissue relative to the total thermal power received by the probe an-tenna. The frequency range between 0.5 and 3 GHz is investigateddue to the sensing depth that can be achieved for a given receiversensitivity. The general approach is to validate full-wave finite ele-ment method (FEM) EM simulations with a spectral-domain anal-ysis for layered lossy dielectrics with a dipole at the interface be-tween two of the layers. This was successfully done for a dipole on awater half-space and a stack of three tissues (skin, fat, andmuscle).A new type of multifrequency probe was designed for 1.4, 2.7, and4.9 GHz operation, and the predicted impedance validated exper-imentally. To the authors’ knowledge, this is the first time that thenear-field received power of a dipole probe placed in contact withlossy layered media is examined as a function of frequency. This isshown to be significantly different than the plane wave case, andis necessary knowledge for the design of a portable radiometer formicrowave internal body thermometry.

Index Terms—Biological tissues, dipole antennas, electromag-netic propagation in absorbing media, microwave radiometry,multilayered media, spectral domain analysis.

I. INTRODUCTION

M ICROWAVE radiometry for noninvasive temperaturemeasurements is based on near-field power recep-

tion, and holds promise to achieve the spatial resolution andsensing depth necessary for a variety of medical applications,including cancer detection [1]. Monitoring drug deliveryfor cancer treatment [2], hyperthermia temperature control[3], and hypothermic neural rescue of infants suffering fromhypoxia-ischemia [4] also utilize noninvasive near-field radio-metric measurements. Additionally, near-field applicators areused in microwave hyperthermia treatment [5] and nonmedicalapplications such as food processing [6].

Manuscript received March 19, 2013; revised October 21, 2013; acceptedNovember 29, 2013. Date of publication December 20, 2013; date of currentversion February 27, 2014. This work was supported in part by an NIST andUniversity of Colorado Graduate Fellowship in Measurement Science and En-gineering and in part by National Science Foundation Grant ECCS 1202193.The authors are with the Department of Electrical, Computer, and Energy

Engineering, University of Colorado, Boulder, CO 80309-0425 USA (e-mail:[email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TAP.2013.2295595

Fig. 1. Dipole probe placed on the skin connected to a microwave radiometerto measure subsurface tissue temperature. The tissues are represented by layersof complex permittivity dielectrics .

Of critical importance for both receiving and transmittingapplications is accurate knowledge of the power within a fewwavelengths of the antenna as seen in Fig. 1. The dipole antennareceives thermal power radiated by the tissue layers situated inthe near field and, therefore, it is more appropriate to think ofthe dipole as a transducer. The received power is filtered bythe dipole impedance with a predetection bandwidth , andin this paper we are considering a narrowband response. Thedipole feed is connected to a total power radiometer as shownin Fig. 1. The signal is received using a square-law detector andan integrator with an integration time . To measure the tem-perature of, e.g., a portion of the muscle in Fig. 1, it is neces-sary to find the portion of the power received by the antennadue to the specific heated muscle, relative to the total receivedthermal power. This in turn will depend on the imaginary partof the permittivity of the tissues, as well as on the thicknessesand real part of the permittivity. To this end, we define an im-proved sensing depthmetric, and show its dependence on tissueparameters. Typical values for the dielectric properties are givenin Table I. In the literature, simplified propagation models areused that assume a plane wave with an exponentially decayingfield [5], [7], or are determined by a 3-D electromagnetic sim-ulation software. We applied a spectral domain analysis to thisproblem of a dipole for passive near-field radiometry, and wedemonstrate that simple propagation models cannot be used toaccurately predict the physical temperature through inversion ofthe radiometric measurements.A common antenna for near-field microwave thermometry is

a waveguide aperture and has widely been investigated for ra-

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1294 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 62, NO. 3, MARCH 2014

TABLE IDIELECTRIC PROPERTIES OF HUMAN TISSUES AT

MICROWAVE FREQUENCIES [12]–[14]

diating into stratified biological tissues [8]–[10]. In near-fieldmicrowave radiometry for temperature measurements, multiplefrequencies are used to achieve spatial resolution. The sensingdepth is dictated by the frequency that achieves the deepestsensing, which is often assumed to be the lowest frequency. Thisassumption is accurate for plane waves propagating in a lossymedium; however, this is not always the case for near-field an-tennas as demonstrated by Cheever et al. [11] for small wave-guide apertures. A printed dipole probe is more useful than awaveguide when size, flexibility, and cost are requirements asfor a portable microwave thermometer. Here we demonstratethe design of a new type of multifrequency dipole probe for 1.4,2.7, and 4.9 GHz operation, accompanied by experimental val-idation of the predicted impedance.Previously developed spectral domain analysis methods are

adapted to the case of a receiving dipole in the presence of astratified tissue medium. Assuming the dipole is matched toa radiometer with a finite sensitivity, sensing limitations aredetermined as a function of frequency, tissue properties, andthickness. Human tissues are often approximated by multilayerplanar dielectrics [8]–[10], [15]. Low-loss stratified media havebeen investigated in the context of multisubstrate microstripantennas and transmission lines [16], [17]. Spectral domainmethods to determine the fields as a superposition of TE andTM fields have been used to investigate dipoles in stratifiedmedia [16]–[18] and dipoles on a lossy half-space [19]. Galejs[18], [20] and Dvorak et al. [21] utilized Hertz vector potentialsto determine the fields, and are used in this paper since they areappropriate for inhomogeneous lossy dielectrics.The paper is organized as follows. In Section II the problem

of a dipole in a stratifiedmedium is defined, and the fields are de-termined by a spectral domain analysis. The input impedance ofa dipole is determined by a variational method using an approx-imate current density. Next, in Section III, the Poynting vectoris used to define a sensing depth for the purpose of a medicalmicrowave radiometer. Section IV validates the equations de-termined in Section II and III by investigating a dipole on a dis-sipative half-space, and the results are compared to commercialsoftware (Ansys HFSS). Section V investigates the frequencydependence of a dipole on a three layer medium of skin, fat,and muscle. The single dipole is extended to a triple probe ona skin, fat, and muscle three layer medium in Section VI, andmeasured results are given. Finally, conclusions are drawn inSection VII for applying these results to a near-field medicalmicrowave radiometer.

Fig. 2. Stratified media consisting of layers of complex permittivity materialswith current source at . The source is embedded atthe interface between layers and . It is assumed that layers and

extend to and respectively.

II. SPECTRAL DOMAIN ANALYSIS

In this section the fields in a stratified lossy medium are for-mulated for a dipole represented by in Fig. 2. For known elec-tromagnetic properties of the materials and layer thicknesses,the amplitude and reflection coefficients can be calculated. Theinduced EMF method is then applied to find the driving pointimpedance of the dipole.

A. Fields in a Stratified Medium

The spectral domain approach used in [18], [21] is appliedto the stratified medium in Fig. 2 that is infinite in and andbounded in . It is convenient to express the fields as a super-position of TE and TM (to ) modes. For this reason Whittakerpotentials (Hertz vectors with only -components) will be usedto express the fields in the th layer. The Whittaker potentialsare defined as

(1)

where and are scalar potentials in the th layer. For a gen-eral medium with both electric and magnetic current sources,the total field is a superposition of the partial fields [20], [21]related to the potentials by

(2)

(3)

where . The dielectric is assumed to be complexcharacterized by the complex permittivity

. The subscripts and denote the electric andmagnetic Hertz potentials respectively. and are solutionsto the homogeneous Helmholtz equation

(4)

SCHEELER et al.: SENSING DEPTH OF MICROWAVE RADIATION FOR INTERNAL BODY TEMPERATURE MEASUREMENT 1295

Taking the Fourier transform defined in (46) of Appendix A(transform fields are denoted by a tilde) of the wave equationsin (4) yields the transform of the Helmholtz equation

(5)

where

(6)

and and are the and spatial transform variables respec-tively. The terms containing the transformed potential rep-resent TE fields and those containing represent TM fields.The solution to the differential equation (5) can be expressed asa superposition of plane waves propagating in the positive andnegative directions. Therefore, the spectral domain Whittakerpotentials expressed in terms of the forward and reflected wavesare

(7)

(8)

where . The source free boundary conditions dic-tate the continuity of the tangential electric and magnetic fieldswhich will be utilized to determine the unknown amplitude co-efficients and reflection coefficients . In thespectral domain the boundary conditions are

(9)

where . In the source free region the boundary condi-tions at for TE and TM fields are decoupled and the unknownscan be determined by substitution of (7) and (8) into (9), yieldingexpressions for the TE and TM amplitude coefficients

(10)

(11)

and reflection coefficients

(12)

(13)

Next, the boundary conditions at will be solved todetermine the unknown amplitude coefficients ,and . First, it is assumed that there is no magnetic current

and the surface current is from a thin sheet so currentonly flows in the and directions. The boundary conditionsare

(14)

Substituting (7) and (8) into (14) and solving for and

(15)

(16)

where and are related to (15) and (16) by

(17)

(18)

Thus, the fields can be solved if the current distribution isknown. Also, it is assumed that the stratified medium has afinite number of layers in the positive direction andin the negative direction such that and

. To solve for the fields, the followingprocedure is used• Assume a current distribution along the dipole, and de-termine its spatial Fourier transform .

• Calculate the reflection coefficients and from (12)and (13) starting with the outermost layers (and ) and recursively calculate untilthe reflection coefficients at layers and aredetermined.

• Calculate the amplitude coefficients in layers andfrom (15) to (18) using the calculated reflection

coefficients.• Finally, calculate the amplitude coefficients in each layerfrom (10) and (11).

B. Input Impedance of a Dipole

Having determined the fields of a current element in the pres-ence of a stratified medium, the driving point impedance of thedipole can be determined by use of the induced EMF method[22]. A thin linear dipole of length and width will be con-sidered. If the dipole is narrow such that , it is assumedthat current only flows in the direction such thatand . Then the input impedance can be writtenin Fourier integral representation as

(19)

where is the Fourier transform of the current density,and

(20)


A variational solution for the impedance is given in Appendix Bthat follows the method presented by Galejs [18], [20]. The so-lution uses a two term trial function that consists of a sine andshifted cosine with unknown amplitudes. The amplitudes aredetermined by imposing the stationary character of the inputimpedance such that a small change in the current about its cor-rect value gives a zero first order change in the impedance.

III. POWER FLOW AND SENSING DEPTH

The aim of this analysis is to determine the power densityprofile for a transmitting dipole into a lossy stratified medium,which results in a metric for the sensing depth of the same dipolein receive mode. First, the time-average power flow through aplane of infinite extent in the and directions is determinedfrom Poynting’s theorem as

(21)

Utilizing Parseval’s formula for the Fourier transform, the timeaverage power flow can be written in terms of the transformedfields as

(22)

where the transformed fields are given in (47) of Appendix A.The goal of this analysis to determine the sensing limit for adipole when utilized as an antenna for a near-field medical mi-crowave radiometer. The principle of operation for a microwaveradiometer is to measure blackbody radiated power emitted byall matter based on its temperature. This radiation is defined byPlanck’s blackbody radiation law for spectral brightness ,given by the Rayleigh-Jeans approximation [23] for the mi-crowave region

(23)

where

Boltzmann’s constant joule/ K)

Absolute temperature (K)

Wavelength (m).

The emitted power over a bandwidth is given by .Thus, by measuring the power radiated in a bandwidth , thetemperature of a body can be measured. A near-field probe orantenna placed in contact with a lossy medium (human tissues)couples the blackbody radiation into the receiver. The antennameasures a weighted volume average brightness temperaturewithin the sensing volume . The spatial temperature distribu-tion is defined as at point , and the antenna brightnesstemperature is given by

(24)

where and are the lower and upper half-space efficien-cies defined below. The weighting function defines thecontribution from point at a temperature to the overallantenna brightness temperature. The weighting function is ob-tained from the antenna reciprocity theorem as the power ab-sorption rate

(25)

for a transmitting antenna, where is the power dissipationat point . Additionally, the efficiencies are defined from (22) as

(26)

Thus, it can be seen that the term is the contribution fromthe upper half-space of a constant temperature . Given thegeometry assumed in Fig. 2 which assumes a stratified mediumthat is infinite in extent in the and directions and assumingthe tissues under test will be characterized by a constant tem-perature in the and directions [24], (24) can be reduced to a1-D expression

(27)

where

(28)

For a nonideal antenna with radiation efficiency the antennanoise temperature at the terminals of the antenna is given interms of the physical antenna temperature as

(29)

Using the definition of the antenna temperature, a metric for thesensing depth of the receiver will be defined in a similar manneras that presented by Bocquet et al. [10].Consider an antenna placed at the interface between free-

space and the human body. The human body is approximatedby a stratified medium characterized by a temperature distribu-tion as shown in Fig. 3. The antenna temperature is givenby (27) and (29) as

(30)

Next, suppose that at a depth the tissues below this depth aresubjected to a uniform increase in temperature as shown inFig. 3, then the antenna temperature is given by

(31)


Fig. 3. Definition of sensing depth for a dipole on a lossy stratified half-space. Temperature changes with depth in the tissue layers while it is constantin the upper half-space.

or the change in antenna temperature contributed by the layersdeeper than due to a uniform increase in temperature from

to is

(32)

The signal sensitivity to the change in the layers situatedbelow is

(33)

Each individual measurement has uncertainty associated withit. This uncertainty is given for a total power radiometer as [23]

(34)

where is the receiver noise temperature, is the prede-tection bandwidth, and is the integration time. Thus, the un-certainties in the first and second measurements are

(35)

Assuming that each measurement is statistically independent,the uncertainty in is

(36)

If is very small, then resulting in the totaluncertainty

(37)

Therefore, to resolve a temperature change at a depth thetemperature contribution must be greater than . The max-imum sensing depth is then defined by

(38)

Fig. 4. Flat dipole of length and width on a dissipative half-space.

The left hand side of (38) represents the power absorbed by thematerial below normalized to the total power absorbed for

. This quantity is also equal to the real power flowingthrough a plane located at . Therefore, (38) is simplifiedby using the definition for the real power passing through aplane given by (22), resulting in the following sensing depthexpression

(39)

(40)

To summarize, detecting a temperature change depends uponthe probe and the receiver. Therefore, it is essential to considerthe power flow from the probe , the nonideal receiversensitivity , and the desired incremental temperature resolu-tion . It may also be noted that the probe is assumed tobe matched to the receiver. If this is not the case, mismatchedcomponents may be accounted for in a standard way such as pp.404–412 of [23] or [25]. In the following sections the sensingdepth is determined assuming the probe is perfectly matched tothe receiver.

IV. ALGORITHM VERIFICATION

To illustrate the properties of a dipole in the presence of alossy stratified medium, the spectral domain technique will firstbe applied to a dipole of length and width at the interfacebetween free space and a lossy medium as shown in Fig. 4. Inresearch for medical applications a water bath is often used todemonstrate temperature detection because the dielectric prop-erties of water are similar to those of human tissues. Water isa medium that is easily controlled in a laboratory environment,and is a standard phantom material [7], [11], [26]. The disper-sive electrical properties of water can be represented by a Debyemodel [27]–[29] and Fig. 5 shows the real part of the relativedielectric constant and the conductivity over the frequencyrange of 250 MHz to 5 GHz. The values were calculated usingthe single Debye model in [28] for 25 C and 37 C, which is thenormal body temperature. In the remaining numerical results,the 25 C values are used.For the two layer problem, the function (20) appearing in (53)

simplifies to

(41)


Fig. 5. Real part of the relative dielectric constant and the conductivityof water over the frequency range of 250 MHz to 5 GHz calculated using thesingle Debye model in [28] for 25 C (blue) and 37 C (red), which is normalbody temperature.

Using (56) the input impedance of a dipole on a half-space canbe found. The propagation constant along a dipole situatedat the interface between two media used in the expression forthe current will be given by an effective complex propagationconstant [30], [31]

(42)

Therefore, will be used to determine theelectrical length of the dipole.

A. Theoretical Results

First, the spectral domain technique is applied to a dipole ona lossy half-space and the results are compared to Finite El-ement Method simulations using Ansys’ commercially avail-able HFSS software. The lower half-space medium is charac-terized by the dielectric properties shown in Fig. 5. To achievean input match dB the length of the dipole waschosen to be . Additionally, to maintain the assumptionof current being uniformly distributed in , the width of thedipole was chosen to be . To numerically eval-uate the integrals in (53) a Gauss-Legendre quadrature integra-tion routine available in the mpmath [32] Python library wasused. The integration was carried out along the real axis as thecomplex poles are removed from the real axis, and the upperbound on the infinite integration was truncated at . Theantenna driving point impedance was determined using the in-duced EMF method from 250 MHz to 3 GHz and using HFSS.The results are shown in Fig. 6. Results from HFSS are within4.7 for the resistance and within 1.1 for the reactance ascompared to theory.Next, the sensing depth for a dipole on a lossy disper-

sive half-space is determined by first finding the power flowingin the lower half-space. The power flow is a function of the cur-rent density in (48) for which only the ratio is known from(55). Normalizing the current density to the current at the inputyields an expression in terms of the ratio . A -dependent

Fig. 6. Impedance versus frequency for a dipole at the interfaceof a lossy half-space characterized by a relative dielectric constant and conduc-tivity from Fig. 5.

effective transfer resistance (similar to that defined by Galejs[33] and Sec. 12.3 of [20]) may be defined as

(43)

The real power passing through a plane in the lower half-spaceis normalized to the total power radiated by the antenna whichmay be written in terms of the ratio of the distance dependenteffective transfer resistance to the input resistance as

(44)

where is the input resistance. It may also be noted that adipole placed in contact with a high dielectric constant half-space is very directive towards the dielectric such that the ratioof power radiated into the lower and upper half-spaces varies ap-proximately as [34]. As a result, or in other words

. The integrals in (43) are calculated using thesame method described for the input impedance. Fig. 7 demon-strates very good agreement (within 3%) between numericalsimulation and theory.To determine the limitations for this particular example, the

sensing depth is calculated from (40) and shown versus fre-quency as a function of the ratio of the receiver sensitivityto the incremental increase in temperature . Fig. 8 showsthe sensing depth for the dipole on a dispersive lossyhalf-space compared to the case of an incident plane wave on the


Fig. 7. Theoretical results compared to simulated results for the normalizedpower level versus of a dipole above a lossy dispersive half-spaceat 500 MHz 1.5 GHz, and 3 GHz. Theory and simulation are within 3% of eachother for each of the frequencies.

Fig. 8. Sensing depth as defined by (40) versus the ratio of the receiversensitivity to the incremental increase in temperature for a dipoleon a lossy half-space. The three frequencies (1 GHz, 1.5 GHz, and 3GHz) shownare compared to a plane wave assumption that the power decays as .

same half-space. The plane wave assumption is that the powerdecays as , and all the power accepted into the an-tenna is radiated into the lower half-space. From Fig. 8 it can beseen that for larger sensitivity ratios the sensing depth is muchsmaller for the near-field case as compared to a plane wave.The frequency dependence of the sensing depth is different forthe two cases, but increases with decreasing frequency. Thenear-field behavior differs greatly from the plane wave case forlarge sensitivity ratios. The results have important implicationsin the design of microwave radiometer for near-field tempera-ture measurements that utilize a dipole in contact with a lossymedium.

V. DIPOLE ON SKIN, FAT, AND MUSCLE

After validation with numerical simulation for a simplephantom, the sensing depth of a dipole above a three layermedium consisting of skin, fat, and muscle is quantified. As inthe previous section, the dipole is assumed to be in contact withthe skin layer. The thickness of the skin is assumed to be 2 mm,fat 10 mm, and the muscle is assumed to be infinite in extent asseen in Fig. 9. In this section the electromagnetic properties ofthe tissues are given in [12], [13], and the dielectric propertiesat a few frequencies are shown in Table I. To compare dipoleson the surface of a lossy dielectric, the electric length of thedipoles are chosen to be , as this length is matchedwell to a 50 generator. The input impedance is found using

Fig. 9. Three layer tissue model consisting of skin, fat, and muscle.

Fig. 10. Comparison of theory to simulated results for the impedance of adipole above a three layer medium comprised of 2 mm of skin, 10 mm

of fat, and muscle.

the variational solution method from Section II-B. The inputimpedance is shown in Fig. 10. The simulated results fromHFSS are within 6 of the theoretical values for both theresistance and reactance from 500 MHz to 3 GHz.Next, the sensing depth is determined. The general equa-

tion for the power flowing in a stratified medium is given inAppendix C, and was used to determine the power flowingthrough a transverse plane at some depth in the layered medium.The sensing depth is shown in Fig. 11, demonstrating a de-crease in sensing depth for an increase in frequency over asensitivity ratio from 0.15 to 0.35. However, betweenthe sensitivity ratio 0.1 to 0.15 the sensing depth is greater at1 GHz than 500 MHz. This demonstrates the inaccuracy in as-suming a plane wave propagation. Additionally, it is importantto know the sensitivity ratio when choosing frequencies thatwill achieve a desired sensing depth.The three layer medium was repeated for 1 mm of skin and

2 mm of fat for a dipole. The results shown in Fig. 12demonstrate similar sensing depth behavior if the sensitivityratio is close to 0.1. However, there is a greater sensingdepth if the sensitivity ratio is greater than 0.2. It is also ob-served that the sensing depth is greater as frequency increaseswhen compared to the 2 mm of skin and 10 mm of fat medium.These two cases were examined to give an example of how thesensing depth may change due to tissue variability between sub-jects. Intersubject variability can be estimated using a virtualpopulation such as that provided by the IT’IS Foundation [35].To illustrate the dependence of sensing depth on the sensi-

tivity ratio , an example will be given for the two tissue


Fig. 11. Sensing depth as defined by (40) versus frequency and the ratio ofthe receiver sensitivity to the incremental increase in temperature for a

dipole above a three layer medium comprised of 2 mm of skin, 10 mmof fat, and muscle.

Fig. 12. Sensing depth as defined by (40) versus frequency and the ratio ofthe receiver sensitivity to the incremental increase in temperature for a

dipole above a three layer medium comprised of 1 mm of skin, 2 mmof fat, and muscle.

TABLE IISENSING DEPTH (MM) AT VARIOUS FREQUENCIES FOR SENSITIVITY RATIOSOF 0.2 AND 0.1. TWO DIFFERENT THREE LAYER MEDIA ARE CONSIDERED:(A) 2 MM SKIN/10 MM FAT/MUSCLE, AND (B) 1 MM SKIN/2 MM FAT/MUSCLE

stacks previously considered: (a) 2 mm skin/10 mm fat/muscle;and (b) 1 mm skin/2 mm fat/muscle. Consider a receiver sensi-tivity K. If the desired detectable temperature change

K, then the sensitivity ratio seen in the right hand sideof (40) will be 0.2. The problem may be analyzed in the recip-rocal case where the antenna is transmitting. Thus, the goal isto find where the signal radiated by the antenna has decayed by80% assuming . The sensing depth for a few frequen-cies from 500 MHz to 2.5 GHz are listed in Table II showing adecreasing sensing depth as frequency increases for tissue stack(a). For tissue stack (b) the sensing depth increase slightly from500 MHz to 1 GHz then decreases.

Fig. 13. Three frequency probe with balun feed network. The overall dimen-sions of the probe are 30 mm 30 mm neglecting the balun.

Next, consider the receiver sensitivity improving toK, resulting in a sensitivity ratio of 0.1. Note

that the same sensing depth could be achieved for Kand K yielding a sensitivity ratio of 0.1. This canbe seen in (40) as the sensing depth is a function of the ratioof receiver sensitivity to change in temperature. In the caseof a sensitivity ratio of 0.1 Table II demonstrates an increasein the sensing depth from 500 MHz to 1 GHz for tissue stack(a). However, for tissue stack (b) the sensing depth decreasesacross the whole frequency range. Table II demonstrates howsensing depth is a function of receiver sensitivity, change intemperature, and near-field weighting functions.

VI. THREE-FREQUENCY PROBE DESIGN

In order to experimentally validate the simulations, a three-frequency probe is designed as shown in Fig. 13, assuming a1-mm thick skin layer, 2-mm thick fat layer, and infinitely thickmuscle layer. The frequencies are chosen to be in the 1.4, 2.7,and 4.9 GHz quiet bands allocated to radio-astronomy [23] inorder to avoid RF interference in future radiometry measure-ments. The probes are designed to be as collocated as possibleso that their power dissipation patterns coincide spatially in thetissue stack. For this reason the two lower frequency probes arebent as shown in Fig. 13. The probes are made on a RogersRO-4350B 0.762-mm thick substrate with , and eachdipole is fed with a microstrip tapered balun. The dipoles aremeasured in vivo on the abdomen with the first author servingas a volunteer. The probe was placed in direct contact with theskin of the abdomen. It was held against the skin by hand, andmild pressure was applied to ensure contact. The reflection coef-ficient of each probe was measured separately using an AgilentTechnologies E8364C network analyzer with the other probeports terminated in matched 50 loads.The measured results for the three probes are shown in

Fig. 14(a) demonstrating a match better than dB for eachprobe at the respective design frequencies. The measuredresults are compared to HFSS simulations in Fig. 14(b), wherethe electromagnetic properties of the tissues used in the simu-lation are given in [12] and [13], and the dielectric propertiesat a few frequencies are shown in Table I. Although agreementis shown only around the design frequency for each probe forclarity, the measured and simulated results agree well over theentire frequency range from 1 to 6 GHz. It should be notedthat the pressure of the probe on the tissues affects the input


Fig. 14. Measured (a) input match for the triple probe. The match is betterthan dB for each probe at their respective design frequencies. The mea-surements are compared to HFSS simulations in (b).

match as the probe must make uniform contact. Also, the probeperformance will vary if placed on a subject where the layersmodeled do not reflect the physical dimensions of the subject’stissues.Finally, the simulated power dissipation is shown in Table III.

The values are normalized to 1 W power accepted at each of thedipole ports, where the accepted power is given by the differ-ence between the incident and reflected powers. In each case,over 50% of the power accepted into the probe is dissipated inthe 1-mm thick skin layer. The lowest frequency probe dissi-pates the most power in the muscle. Less than 10% of the poweris dissipated in the fat layer, and this percentage decreases withincreasing frequency in this particular case.

VII. CONCLUSION

The results from this paper are important for designing adipole probe to achieve a desired sensing depth for near-fieldmicrowave thermometry. An improved sensing depth metric isdefined to determine the sensitivity limitations for thermal ra-diation measurement of deep seated tissues in the body and inthe near-field of the dipole. The sensing depth is not only a func-tion of the near-field power dissipation, but is also dependent onthe receiver sensitivity and the desired temperature resolution

.To analyze the frequency dependent behavior of a dipole

used for near-field microwave radiometry, a simplified modelof a dipole in a lossy stratified medium is used. The mediumis assumed to be uniform and infinite in extent in the andtransverse planes while discontinuous in . A finite number

of layers are assumed where the outermost layers extend to

TABLE IIIPOWER DISSIPATION INTO A THREE LAYER MEDIUM OF SKIN (1 MM),FAT (2 MM), AND MUSCLE. NORMALIZED TO 1 W AT THE ANTENNA PORT

infinity. A spectral-domain technique is applied to determinethe input impedance and sensing depth, defined in terms ofthe dipole near-field weighting functions, the total powerradiometer sensitivity, and the desired temperature resolution.The technique is verified for the general case of a dipole on

a water half-space by comparing impedance and normalizedpower dissipation to commercial FEM software, Ansys HFSS,with good agreement. The results enable design of other typesof probes for a desired sensing depth by extending the theory toa three layer human tissue model of skin, fat, and muscle. Theinput impedance is validated with Ansys HFSS.From the presented model, an optimal frequency can be de-

termined for a desired sensing depth and tissue stack. However,a number of practical constraints will also affect the frequencychoice. For example, overall size and location of probe dic-tated by the application will impose constraints on the choiceof frequency. Additionally, bodies vary from patient to patientchanging the performance of the probe. For this reason, twoexamples were given of different skin and fat thicknesses. In-tersubject variability can be estimated using a virtual popula-tion such as that provided by the IT’IS Foundation [35]. Fi-nally, the ambient radio frequency spectrum is congested, de-grading the achievable signal to noise ratio (SNR) at many fre-quencies that might otherwise be optimal for passive sensing.The multiband probe presented in the paper takes into accountsome of these constraints. The three chosen frequencies (1.4,2.7, and 4.9 GHz) are allocated quiet bands for earth sensingand radio astronomy and will minimally degrade the SNR. The4.9 GHz frequency is intended for surface skin measurements,as the sensing depth is small.

APPENDIX A

Substitution of the Whittaker potentials (1) into the time-har-monic vector wave equations (2) and (3) yields expressions forthe fields in the th layer

(45)


To solve the fields, a spatial Fourier transform technique is ap-plied using the Fourier transform pair given by

(46)

where the tilde represents the transformed fields. Applying theFourier transform yields expressions for the spectral domainfields:

(47)

APPENDIX B

A variational solution to the input impedance can be foundusing the induced EMF method. This is the same as presentedby Galejs [18] and Sec. 9.1 of [20] and is summarized here forclarity. To determine the input impedance the antenna currentdensity is represented by the trial function

(48)where

The Fourier transform of (48) is given by

(49)

where

(50)

(51)

Substituting (49) into (19) yields

(52)

where

(53)

and and/or . Dividing the numerator and denom-inator of (52) by yields an expression in terms of the ratio

(54)

The impedance is stationary such that a small change in the cur-rent about its correct value will cause a zero first order changein the impedance. The stationary nature of the impedance is uti-lized to find the ratio by requiring .Performing the differentiation and solving gives

(55)

(56)

where

(57)

APPENDIX C

The expression for the power flow, or real power passingthrough a plane in the -th layer of a stratified medium is givenfrom (22) using the transformed fields in (47) as

(58)

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Robert Scheeler (S’12) received the B.S. degree inelectrical engineering from the North Dakota StateUniversity, Fargo, ND, USA, in 2008, and the M.S.and Ph.D. degrees in electrical engineering from theUniversity of Colorado, Boulder, CO, USA, in 2011and 2013.His research interests include low-noise receivers,

on-chip noise calibration standards, monolithicmicrowave integrated circuit design, wireless energyharvesting, and noninvasive core body temperaturemeasurement using microwave radiometers.

Edward F. Kuester (S’73–M’76–SM’95–F’98) re-ceived the B.S. degree from Michigan State Univer-sity, East Lansing, MI, USA, in 1971, and the M.S.and Ph.D. degrees from the University of Colorado,Boulder, CO, USA, in 1974 and 1976, respectively,all in electrical engineering.Since 1976, he has been with the Department of

Electrical, Computer and Energy Engineering, Uni-versity of Colorado, where he is currently a Professor.In 1979, he was a Summer Faculty Fellow at the JetPropulsion Laboratory, Pasadena, CA, USA. From

1981 to 1982, he was a Visiting Professor at the Technische Hogeschool, Delft,The Netherlands. In 1992 and 1993, he was an Invited Professor at the ÉcolePolytechnique Fédérale de Lausanne, Switzerland. He held the position of Vis-iting Scientist at the National Institute of Standards and Technology (NIST),Boulder, CO in 2002, 2004, and 2006. His research interests include the mod-eling of electromagnetic phenomena of guiding and radiating structures, appliedmathematics, and applied physics. He is the coauthor of one book, author ofchapters in two others, and has translated two books from Russian. He is a co-holder of two U.S. patents and author or coauthor of more than 90 papers inrefereed technical journals.Dr. Kuester is a member of the Society for Industrial and Applied Mathe-

matics (SIAM) and Commissions B and D of the International Union of RadioScience (URSI).

Zoya Popović (S’86–M’90–SM’99–F’02) receivedthe Dipl. Ing. degree from the University of Bel-grade, Serbia, Yugoslavia, in 1985, and the Ph.D.degree from the California Institute of Technology,Pasadena, CA, USA, in 1990.Since 1990, she has been with the University of

Colorado, Boulder, CO, USA, where she is currentlya Distinguished Professor and holds the HudsonMoore Jr. Chair in the department of Electrical,Computer, and Energy Engineering. In 2001, shewas a Visiting Professor with the Technical Univer-

sity of Munich, Munich, Germany. Since 1991, she has graduated 50 Ph.D.students. Her research interests include high-efficiency, low-noise, and broad-band microwave and millimeter-wave circuits, quasi-optical millimeter-wavetechniques for imaging, smart and multibeam antenna arrays, intelligent RFfront ends, and wireless powering for batteryless sensors.Prof. Popovic was the recipient of the 1993 and 2006 Microwave Prizes pre-

sented by the IEEE Microwave Theory and Techniques Society (IEEE MTT-S)for the best journal papers. She received the 1996 URSI Issac Koga Gold Medaland was named an NSF White House Presidential Faculty Fellow in 1993. Shewas the recipient of a 2000 Humboldt Research Award for Senior U.S. Scientistsfrom the German Alexander von Humboldt Stiftung. She was elected a ForeignMember of the Serbian Academy of Sciences and Arts in 2006. She was also therecipient of the 2001 Hewlett-Packard (HP)/American Society for EngineeringEducation (ASEE) Terman Medal for combined teaching and research excel-lence. She also received the IEEE-MTT Distinguished Educator award in 2013.

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