NUMERICAL ASSESSMENT OF MULTIFREQUENCY MICROWAVE RADIOMETRY FOR SENSING MALIGNANT BREAST CANCER TUMORS

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1 REFERENCES 1. M. Vea-Isasa, Antenas de anuas en guía adial: Análisis, diseño y aplicaciones, doctoal dissetation, Univesidade de Vigo, Spain, M. Ando, New DBS eceive antennas, Poc Euo Micowave Conf (1994), J. Takada, M. Ando, and N. Goto, A eflection canceling slot set in a linealy polaized adial line slot antenna, IEEE Tans Antennas Popagat AP-40 (1992), M. Ando, K. Sakuai, N. Goto, K. Aimua, and Y. Ito, A adial line slot antenna fo 12 GHz satellite TV eception, IEEE Tans Antennas Popagat AP-33 (1985), A. Akiyama, T. Yamamoto, M. Ando, and E. Takeda, Conical beam adial line slot antennas fo 60 GHz band wieless LAN, IEEE AP-S 3 (1998), M. Siea-Péez, J.M. Salamanca, M. Vea-Isasa, and M. Siea-Castañe, Synthesis of ciculaly polaised multipobe feed adial line slot antenna, IEEE AP-S 2 (1998), M. Siea-Castañe, M. Siea-Péez, and M. Vea-Isasa, Design of monopulse adial line slot antennas, IEEE AP-S 4 (1999), M. Siea-Péez, M. Vea-Isasa, A.G. Pino, and M. Siea-Castañe, Analysis of slot antennas on a adial tansmission line, Int J MiMi CAE 6 (1996), M. Siea-Peez, J.M. Salamanca, M. Vea-Isasa, and M. Siea-Castañe, Synthesis of ciculaly polaized multipobe feed adial line slot aay, IEEE AP-S (1998), M. Siea-Castañe, Contibución a las Técnicas de Diseño y Análisis de Antenas de Ranuas sobe placas paalelas, Doctoal Dissetation, Univesidad Politécnica de Madid, M. Siea-Castañe, M. Vea-Isasa, M. Siea-Péez, J.A. Gacía, and J.R. Rey, Analysis and design softwae fo adial slot antennas, AN- TEM 98, 1998, pp Wiley Peiodicals, Inc. NUMERICAL ASSESSMENT OF MULTIFREQUENCY MICROWAVE RADIOMETRY FOR SENSING MALIGNANT BREAST CANCER TUMORS Magda El-Shenawee Depatment of Electical Engineeing Univesity of Akansas Fayetteville, AR Received 30 August 2002 ABSTRACT: A numeical study of micowave adiomety fo malignant beast cance tumos is pesented. The numeical esults show that the bightness tempeatue of malignant tumos exhibits a esonant behavio vesus the fequency. The bightness magnitude deceases with the tumo buial depth, howeve, the esonance fequencies depend only on the tumo s size and mateial and ae independent of the buial depth Wiley Peiodicals, Inc. Micowave Opt Technol Lett 36: , 2003; Published online in Wiley InteScience ( DOI /mop Key wods: adiomety; beast cance; computational EM; multifequency; eflectivity 1. INTRODUCTION Recently, micowave adiomety has shown potential pomise in seveal subsuface sensing applications [1 3]. Numeous wok on using multifequency micowave adiomety has been published [2, 3, 8]. In the cuent wok, emphasis will be placed on the Figue 1 Coss section of a spheical tumo buied beneath a flat aibeast inteface showing the multiple inteactions mechanism with n 2 numeical evaluation of bightness tempeatue fo malignant beast cance tumos and its behavio as a function of fequency. The basic idea of using micowave adiomety in beast cance detection involves measuing the natual electomagnetic adiation o emission fom the female beast at micowave fequencies. This electomagnetic adiation changes consideably with the pesence of malignant beast cance tumos [4 8]. In paticula, the themal activity of the female beast is a measue of the tumo gowth ate, which can povide infomation even beyond the physical paametes of the tumo such as its size, mateial, and location [6]. In [4], the authos pesented esults based on 618 nomal female patients to show the tempeatue symmety between the left and ight beasts. Theefoe, the tempeatue deviation between the left and ight beasts is often used to diagnose the beast cance in one beast [4 6]. As pesented and shown in [4 6], medical micowave adiomety has a numbe of advantages, such as ealy diagnosis of the cance even befoe the tumo mass contast is fomed, the noninvasiveness of the technique, the absolute hamlessness fo patients of all ages, and the ange (3 10 cm) of tumo buial depth. Howeve, thee ae some baies in this technique: mainly, the equied sensitivity of the eceiving antenna due to the small numbe of eceived themal signals elative to the suounding noise signals [4 6]. The objective of this wok is to computationally evaluate the bightness tempeatue as a function of the fequency, tumo size, buial depth, and location. The output of this study can be used to undestand the themal adiation phenomenon, which will aid in designing enhanced adiometes fo ealy detection of beast cance. The multiple inteaction model combined with the fast computational technique, the steepest descent fast multipole method (SDFMM), [9 10] is used hee to compute the eflectivity, and hence the bightness tempeatue, due to the pesence of a malignant tumo in the beast. The geomety of the poblem is depicted in Figue 1, whee the beast suface is assumed flat and the tumo is modeled as a sphee of adius a and buied at depth d measued fom its cente. The figue shows the position of the adiomete (applicato) in the nea zone to the beast and it shows also the multiple inteactions mechanism between the tumo and the beast suface. Fo simplicity, the thickness of beast skin laye and any inteio beast inhomogeneities ae not accounted fo in this model. Cuve-fitted data fo electical popeties of the malignant tumo and nomal beast tissues ae plotted in Figue 2 vesus the fequency ange 394 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 36, No. 5, Mach

2 the ai-flat inteface is modeled with a tuncated squae suface [9, 10] and, to eliminate the edge excitations, an incident Gaussian beam is employed. The Gaussian beam is basically is a summation of plane waves tapeed towads the suface edges [9, 10]. The size of the tuncated suface and the incident half-beam width should be much lage than the buied object. The total bightness tempeatue is efomulated to account fo the buied object as follows [2]: T B,, p, f, 2, 3, g T s 1 suf P obj /P i, (3a) Figue 2 The elative dielectic constant ( j ) vs fequency fo the nomal and malignant beast tissues obtained using equation 1 in Ref. [20] 1 10 GHz. These esults ae based on published expeimental measuement data [11]. 2. FORMULATION The bightness tempeatue T B of an isothemal medium is given by [1, 3]: T B,, p, f, 2, 3, g T s 1, (1) whee the angles and ae adiomete obsevation elevation and azimuth angles, espectively, f is the adiomete obsevation fequency, p is the polaization of the adiomete (hoizontal h o vetical v), 2 is the dielectic constant of the medium, 3 is the dielectic constant of the buied object, and g epesents the object geometical dimensions. The total eflectivity of the medium with buied object is epesented by, while the physical tempeatue of the medium and the object is expessed by T s [2]. The powe eflection coefficient o eflectivity and the tansmissivity ae defined as the nomal components of the timeaveage Poynting s vectos given by [1]: ẑ S a ẑ S ai, ẑ S at ẑ S ai, (2a) (2b) whee S a Re(E H *)/ 2 is the time-aveage Poynting vecto. The subscipts, t, and i epesent eflected, tansmitted, and incident waves, espectively, and ẑ is a unit vecto nomal to the flat inteface, as shown in Figue 1. In the case of semi-infinite medium with no buied object, eflectivity and tansmissivity can be obtained in closed foms [1]. In this case, they become functions of the eflection and tansmission coefficients upon illuminating the semi-infinite flat inteface with plane waves [1, 2]. Howeve, the cuent poblem is diffeent due to the pesence of a buied object (the tumo) in the flat medium (the beast). The idea hee is to computationally evaluate Eqs. (2a) and (2b) to obtain the eflectivity and tansmissivity, espectively, of the whole scattee (the medium with the buied object). In this case, whee the subscipts suf and obj indicate the inteface suface and the buied object, espectively. The total incident powe is given by P i, the powe eflected due to the object only is P obj, and suf is the eflectivity of the flat suface with no buied object. The multiple inteaction model pesented in [10] is used hee to compute the equivalent suface cuents on the ai-medium inteface. These cuents can be decomposed into two quantities; one is due to the extenal excitation and the second is due to the multiple inteactions with the tumo (see Fig. 1). The deviation in bightness tempeatue due to the pesence of the tumo is expessed as [2]: T B,, p, f, 2, 3, g T s P obj /P i. (3b) The suface cuents due to inteactions with the tumo ae used to compute the eflected powe P obj and hence to obtain the deviation in bightness tempeatue [12]. In pactice, this deviation epesents the diffeential in tempeatue between the left and ight beasts used to detect the cance [4 6]. 3. NUMERICAL RESULTS In example 1, the eflectivity and tansmissivity of a lossless flat medium with no buied object ae computed. The elative dielectic constant is assumed to be 2.55 and the tuncated suface is assumed to be 240 cm 240 cm. The incident and obseved waves ae assumed to be in nomal diection fo all cases in this section. The objective of this example is to validate the numeical computations of eflectivity and tansmissivity obtained using the SDFMM with those obtained using the closed foms fo semi-infinite medium excited with plane waves [1]. The atios of the time-aveage powe densities in Eqs. (2a) and (2b) ae computed using the SDFMM with esolution of 1.2 cm [9, 10, 12]. Biefly, the calculated suface cuents on the flat medium ae used to adiate electic and magnetic fields at 3 cm above and below the inteface. No dependency on this distance is obseved in the eflectivity o tansmissivity fo lossless medium. Fo lossy medium, the fields ae compensated with the attenuation facto. Howeve, smalle distances affected the accuacy of the nea-field calculations [12]. The medium eflectivity and tansmissivity ae plotted in Figue 3 vesus the x diection at y 120 cm. Excellent compaison is shown within a squae spot of 150 cm 150 cm centeed at x 120 cm, y 120 cm, which is the cente of the Gaussian beam footpint. As shown in Figue 3, the beam width is 2W 96 cm, which implies, as expected, that plane waves can be assumed within the spot aea of 2W 2W. The eflectivity and tansmissivity ae added up to unity, as shown in Figue 3. Moeove, at nomal incidence, the esults fo the vetical o hoizontal polaizations ae simila. In Figue 4, the same data of the pevious example is used and a compaison is shown fo eflectivity and tansmissivity, but in this case fo a slightly lossy medium. The elative dielectic constant hee is 3.55 j0.4 (loamy soil with 5% moistue MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 36, No. 5, Mach

3 Figue 3 Reflectivity and tansmissivity of a lossless flat medium with elative dielectic constant The solid cuves epesent the SDFMM esults fo both the vetical and hoizontal polaizations and the dotted cuves epesent the closed foms of the semiinfinite medium Figue 5 The eflectivity and tansmissivity of nomal beast tissues with elative dielectic constant of 10 j1.2 (see Fig. 2 and [20]) [1]). Because the computed time-aveage powe densities ae obtained at 3 cm below the inteface (as peviously explained), the field values in this case ae multiplied by exp(2 l ), whee is the medium attenuation constant and l 3 cm. The computed esults show excellent ageement with the closed foms in [1] and also within the same spot aea 2W 2W, simila to the pevious lossless case. In Figue 5, the eflectivity and tansmissivity of nomal beast tissues with elative dielectic constant 10 j1.2 ae computed (see Fig. 2 and [11]). Notice that the nomal beast tissues have almost the same dielectic constant in the micowave fequency ange 1 10 GHz. The esults ae plotted vesus the x diection pe wavelength and at y 4 0. The modeled suface dimensions ae , whee 0 is the fee space wavelength. Also in this example, the computed values of the tansmitted fields ae multiplied by exp(2 l ), with l 0.1 0, the nea field esolution is , and the half-beam width is W The eflectivity and tansmissivity, upon compensation with the attenuation facto, ae added up to unity as shown in Figues 4 and 5. The eflectivity in Figue 5 is lage than that in Figues 3 o 4, which is due to the lage dielectic constant of the medium, in this case 10 j1.2, as shown in Figue 2. As expected, the tansmissivity in Figue 5 is smalle than that in Figues 3 o 4, due to the lage conductivity of the medium in this case. Notice the slight oscillations in the tansmissivity and eflectivity in Figue 5, which ae due to the incease of edge eflections in this case. This could be deceased by inceasing the Gaussian beam tapeing, that is, deceasing W [9, 10]. In Figues 3 5, a validation is demonstated by computing the eflectivity and tansmissivity using the SDFMM. In Figue 6, the time-aveage eflected powe density S a due to only the malignant tumo is plotted vesus the x diection at y 4 0. The malignant tumo is modeled by a sphee of adius a 5 mm and is buied at depth of d 2 cm, measued fom its cente as depicted in Figue 1. The dielectic constant of the malignant tumo vaies with fequency as shown in Figue 2, while the dielectic constant of the nomal beast tissues is assumed constant as 10 Figue 4 The eflectivity and tansmissivity of a slightly lossy flat medium with no buied object and elative dielectic constant 3.55 j0.4 (Loamy soil with 5% moistue [1]) Figue 6 The time-aveage eflected powe density of the malignant tumo only vesus the x-diection 396 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 36, No. 5, Mach

4 as explained in Figues 3 5. As an example, the adiomete coss section was 1 cm 2.3 cm at 3.3 GHz in [4]. As expected, the total eflected powe P obj depends on the coss section aea A of the eceiving antenna (the adiomete o applicato) as shown in Figue 7(a). Fo simplicity, the adiomete coss section is assumed to be a squae with dimension anging fom to 2 0. The esults clealy show the oscillatoy behavio of tumo eflectivity vesus fequency, with peaks occuing at 3 GHz and 4.5 GHz. Also, the esults show that the smalle the obseving aea A, the lage the magnitude of the sensed tumo eflectivity. Upon multiplying the eflectivity of Figue 7(a) with the physical tempeatue T s, the deviation in bightness tempeatue due to the pesence of the tumo is shown in Figue 7(b). The physical tempeatue of beast tissues vay with a woman s age, fo example, at 50 yeas of age, the aveage tempeatue of the beast is assumed to be 33.7 C (o K), as epoted in [5]. Natually, the tumo s physical tempeatue is diffeent fom the suounding nomal beast tissues because they vay in mateial, as shown in Figue 2. Howeve, in this wok it is assumed that the physical tempeatue T s in Eqs. Figue 7 (a) The eflectivity of malignant tumo vesus fequency. The tumo adius is a 5 mm and it is buied at depth of 2 cm measued fom its cente (see Fig. 1); (b) Bightness tempeatue deviation T B due to the pesence of malignant tumo of adius a 5 mm buied in nomal beast tissues fo same data of Fig. 7a j1.2. The fequency anges fom 1 5 GHz in steps of 200 MHz, which implies that thee ae 21 cuves plotted in Figue 6. Notice that the dimension of the plane-wave squae-spot aea, as shown in Figues 3 5, anges fom 96 cm to 19.2 cm. This aea is consideed much lage than the diamete of the tumo, which is 1 cm in this case. The pupose of Figue 6 is to show that the waves eflected due to the tumo ae sensed within the spot aea of 2W 2W fo all consideed fequencies. The tumo eflected waves ae spheical waves as discussed in [2]. The emphasis of the following examples is to demonstate the behavio of themal emissivity o tumo bightness tempeatue vesus fequency. Theefoe, in Figue 7, the eflectivity due to the tumo is plotted vesus the fequency fom 1 5 GHz in steps of 200 MHz. The tumo adius and buial depth ae 5 mm and 2 cm, espectively. The tumo eflectivity is obtained by computing the tem (P obj /P i ) in Eq. (3b), which is obtained by integating the time-aveage eflected powe density S a due to the tumo and the time-aveage incident powe density S ai of the Gaussian beam ove the adiomete coss section aea A, whee A 2W 2W, Figue 8 (a) Bightness tempeatue deviation T B due to the pesence of malignant tumo in nomal beast tissues. The adiomete coss section is assumed as A ; (b) Deviation in bightness tempeatue T B due to the pesence of malignant tumo in nomal beast tissues. The adiomete coss section aea is A MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 36, No. 5, Mach

5 (3a) and (3b) is the aveage tempeatue fo the beast, which is epoted fo a vaiety of ages in [5]. In Figue 8(a) and (b), a paametic study fo the bightness tempeatue deviation T B is investigated vesus the fequency with the adiomete coss section aea A In Figue 8(a) T B is plotted fo seveal buial depths of 1 4 cm, whee the tumo adius a is assumed to be 5 mm. The esults show that the bightness tempeatue oscillates at the same fequencies egadless of the buial depth. Howeve, the bightness magnitude deceases with the buial depth incease, due to the lage attenuation in nomal beast tissues at micowave fequencies. In Figue 8(b), T B is plotted fo seveal tumo adii of 2 5 mm, buied at the same buial depth of 2 cm. The esults clealy show the bightness oscillating behavio fo all sizes, howeve, fo lage tumo adius the tempeatue peaks at lowe fequencies and vice vesa. In all examples above, the tumo was buied in the cente of the modeled beast at 4 0,4 0. In this example, the tumo is buied off cente at 3.2 0, 4.8 0, in the uppe left quadant of the beast. The tumo adius is a 5 mm and is buied at 2 cm. The deviation in bightness tempeatue T B is plotted in Figue 9 fo seveal adiomete squae coss section aeas with dimensions anging fom to 3 0. The esults show that the bightness tempeatue inceases with the incease of the coss section aea up to A and afte that it stats to decease. This obsevation contadicts the esults of Figue 7(b), whee the bightness tempeatue inceases with the decease of A. The eason of this contadiction is that in Figue 7(b) both the tumo and adiomete coss section ae located at the cente of the modeled beast. Howeve, in Figue 9, the adiomete location is kept in the beast cance, while the tumo is moved to the beast uppe left quadant at 3.2 0, This implies that fo values of A smalle than , the adiomete does not sense the tumo because it is located outside this aea. Afte expeimentation with the adiomete location, the esults show that when it is e-located and centeed exactly above the tumo, a geatly enhanced bightness tempeatue is eceived. Fo a coss-section aea equal to , the exact esults of Figue 7(b) ae obtained. This suggests that scanning the beast suface with a localized adiomete coss section is bette than obseving the bightness tempeatue fom the whole beast. 4. CONCLUSION The conducted numeical evaluation fo a beast cance tumo s bightness tempeatue shows clea oscillatoy behavio vesus the fequency. The esults show that the peaks of bightness tempeatue occu at the same fequencies egadless of the tumo s buial depth, howeve, the oscillating fequencies depend on the tumo s size and mateial. These obsevations can be used to enhance the adiomete design paametes such as the opeating fequency o multiple fequencies, the bandwidth, and the adiomete-eceiving coss-section aea. This statement is consideed a futue wok in collaboation with the NASA Langley Reseach Cente. Figue 9 Deviation in bightness tempeatue T B due to the pesence of malignant tumo in nomal beast tissues. The tumo adius is a 5mm and is located at (3.2 0, ). The adiomete coss section aea A is centeed as (4 0,4 0 ) ACKNOWLEDGMENTS This eseach was sponsoed by the NASA Langley Reseach Cente, gant no. US/NASA/NAG The autho would like to thank Ds W. Lawence, J. Johnson, M. Deshpande, and W. Munden at NASA Langley fo thei valuable discussions. This wok is suppoted in pat by NSF-ERC Notheasten Univesity, awad numbe EEC REFERENCES 1. F.T. Ulaby, R.K. Mooe, an A.K. Fung, Micowave emote sensing active and passive, volume 1: Micowave emote sensing fundamentals and adiomety, Addison-Wesley, B. Unga and J.T. Johnson, A study of micowave themal emission fom a sub-suface object, Micowave Opt Technol Lett 36 (2000), J.T. Johnson, H. Ki, D. Wiggins, and Y. 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