‘r‘lth a ‘ ‘ ‘ ‘- 1 g ’V is; ‘3; eats, t Equatic ABSTRACT AN EXPERIMENTAL AND THEORETICAL STUDY ON THE INTERACTION OF ELECTROMAGNETIC FIELDS WITH ARBITRARILY SHAPED BIOLOGICAL BODIES by Bhag Singh Guru This thesis presents an experimental verification of the numerical technique for calculating the electric field induced inside and scattered by biological systems of arbitrary shape and composition, when irradiated by an electromagnetic wave. An understanding of the induced electric field inside a biological system is very important for investigating the biological hazards of nonionizing radiations. As an introduction, the interaction of an electromagnetic field with a biological system is considered. A basic theoretical approach leading to an integral equation is introduced. Using the method of mom- ents, the integral equation is transformed into a set of simultaneous equations for numerical solution. A variety of experiments have been conducted on the regularly and irregularly shaped biological models Containing saline solutionsait var— ious frequencies of the incident electromagnetic field either at normal or end - on incidence. Effects of increasing the conductivity of a given region are considered and the induced field and absorbed power density inside adult and child's torsos are quantified. a . . u V n T. E .Ils .n.. 1 A E S . a. . A f. C S h . t. .5 .l .L f. r. a... Z .: v . Pu .u . a a a. 6L a5 The integral equation method is applied to quantify the induced electric field and absorbed power density inside cell samples and these results are verified by total absorbed power and heat dissipation tech- niques. Some chromosomal aberrations were observed experimentally in human amnion and lymphocyte cells when irradiated by microwaves with intensities lower than the safety standard. In addition, a computer program to quantify the induced electric field is described and the instructions of its use and limitations are given with a worked out ex- ample. AN EXPERIMENTAL AND THEORETICAL STUDY ON THE INTERACTION OF ELECTROMAGNETIC FIELDS WITH ARBITRARILY SHAPED BIOLOGICAL BODIES By Bhag Singh Guru A DISSERTATION submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Electrical Engineering and Systems Science 1976 To My Mother Sardarni Hazoor Kaur Guru ii n - Rive Boctc Etude flucti at M.- 4. for h Pngr ACKNOWLEDGEMENTS I offer my most grateful thanks to many persons who helped me in this project. Special thanks are extended to Dr. Kun-Mu Chen for his sincere guidance and counsel, under whose supervision this research was conducted, and to the members of my guidance committee, Dr. D. P. Nyquist, Dr. J. Asmussen, Dr. M. Siegel and Dr. P. K. Wong of mathematics depart~ ment. Thanks are extended to the Ministry of Education, Government of India, and to the Division of Engineering Research at Michigan State University for the financial assistance rendered during Master's and Doctoral programs, respectively. Thanks go to Mr. S. H. Mousavinezhad and Mr. Samual Day, graduate students in Electrical Engineering, for their technical help in con- ducting experiments whenever requested. I must sincerely thank Ms. Rebecca Scarbrough of EE/SS department at Michigan State University, who donated her typing skills so generously. Last, but not least, I am sincerely indebted to my wife, Janet, for her patience, understanding and encouragement during the graduate program. iii TV.» \I «1.. III. TABLE OF CONTENTS LIST OF TABLES . . . . . . LIST OF FIGURES . . . . . I. II. INTERACTION OF ELECTROMAGNETIC FIELD III. IV. INTRODUCTION ... . . WITH BIOLOGICAL BODY 2 1 Introduction . 2.2 2 2 Electric Field Moment Method 2.2.3 Total Electric 2.2.4 THEORETICAL AND EXPERIMENTAL RESULTS ON THE INDUCED FIELD INSIDE BIOLOGICAL BODIES THEORETICAL AND EXPERIMENTAL RESULTS ON SCATTERED 3.1 Experimental Set Up 3.2 Construction of Probe 3.3 3.4 Experimental Error . FIELD FROM BIOLOGICAL BODIES. 4.1 4.2 4 3 APPLICATIONS OF TENSOR INTEGRAL EQUATION METHOD FOR INDUCED FIELDS INSIDE HUMAN TORSO AND LOCAL HEATING . 5.1 5.2 Local Heating iv Theoretical Development . Tensor Integral Equation for the Induced Evaluation of Matrix Elements and Field Expressions for the Scattered Electric Field Induced Field Inside Human Torso . Theoretical and Experimental Results .Transformation of Integral Equation - Simplification of Tensor Integral Equation . Induced Current Inside Cylinder . Scattered fields mm 11 12 14 16 16 17 23 53 o 059 o O 59 ° '62 o o. 73 "84 . . 84 . 117 HICI IN '. VIII. SUIC- BIBI MICRowAVE EFFECTS ON HUMAN CHROMOSOMES IN TISSUE CULTURE CELLS . . . . . . . . . . . . . . . .129 Introduction . . . . . . . . . . . . . . . . . . 129 Experimental Set Up . . . . . . . . . . . . . . . 13o Preparation of Cells . . . . . . . . . . . . . . 132 Field Intensity Determination . . . . . . . . . . 133 Study Criteria . . . . . . . . .. . . . . . . . . 13g Experimental Results . . . . . .. . . . . . . . . 139 Summary . . . . . . . . . . . . . . . .. . . . . 143 O‘C‘O‘O‘O‘O‘O‘ NO‘U‘J-‘UJNH VII. A USER'S GUIDE TO COMPUTER PROGRAM FOR INDUCED ELECTRIC FIELD INSIDE AN ARBITRARILY SHAPED, FINITELY CONDUCTING BIOLOGICAL BODY . . . . . . . . . . . . . . . . . . . 147 1 Formulation of the Problem . . . . . . . . . . 147 2 Description of Computer Program . . . . . . . . 150 3 Data Structure and input variables . . . . . . 151 .4 An Example to Use the Program . . . . . . . . 157 5 Printed OUCPUt . . . o . . . . . . . . o . o 161 6 Listing of the Programs . . . . . . . . . . . 164 VIII. SUMMARY . . . . . . . . . . . . . . . . . . . . . . 189 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . 192 6.3 6.1. 7.1 .-“‘~' Ix.) Table 6.1 6.2 6.3 6.4 7.1 LIST OF TABLES Chromosomal aberrations of human amnion cells due to a microwave of 2.45 GHz with electric field intensities of 20.6 v/m for 7,12, 19 and 20 minutes respectively. Chromosomal aberrations of human amnion cells due to a microwave of 2.45 GHz with electric field inten- sities of 32 v/m for 7 min. and 41.3 v/m for 4.5 min., 8 min., and 10 min. respectively. The initial cell temperature was 22°C. Chromosomal aberrations of human lympnocyte cells due to a microwave of 2.45 GHz of various inten- sities and exposure times. Chromosomal aberrations of human lymphocyte cells due to a mocrowave of 2.45 GHz with an electric field intensity of 40.94 v/m for 3 minutes on 3 successive days. The symbolic names of input variables and corres- ponding specifications for the data files used in data structure for the program "FIELDS". vi ‘140 142 144 145 152 .... . - 3.3 3.5 3.6 3.7 3.8 3.9 LIST OF FIGURES Figure 2.1 A biological system illuminated by electromagnetic rad iat ion 0 O O O O O O O I O O O O O O O O O I O O 3.1 The schematic diagram of the experimental set up for the measurement of induced electric field inside a biological system . . . . . . . . . . . . .. 3.2 Relative electric field distribution inside an . anechoic chamber in y - and z - directions. The point (y=0, 21=0 ) is approximately 3 feet away from horn antenna as shown in fig. 3.1 . . . . . . . . . . 3.3 Insulated dipole type probes mounted with microwave detector diodes for the measurement of induced fields in vertical (b) and horizontal (b) directions . 3.4 Calibration curve for the dipole type probe loaded with a microwave detector: SWR vs. relative input power 0 O O O O O O O O O O O O I O 0 Co 0 O O O O O 0‘ 3.5 A rectangular model of 6 x 6 x 1 cm dimension containing salt solution illuminated by EM wave at end-0n inCIdence. o o o o o o o o o o o o o o o. 3.6 Theoretically induced E field in 1/2 of the rec- tangular shaped model shown in fig. 3.5. Frequency - 2.45 GHz, O=5.934 mho/m, €= 68.48780, salt con- centration = 0.5 normal. Cell size=l cm3. . . . . .. 3.7 Theoretical and experimental values of the dis- sipated power due to Ex and E2, i.e. 1/20'lExl2 and 1/20IEZI2 respectively, as a function of 2 along x-0.5 cm, x=l.5 cm and x=2.5 cm lines. . . . . . 3.8 A rectangular model of 12 x 12 x 1 cm dimensions containing 0.5 normal saline solution illuminated by an EM wave of 2.45 GHz at end-on incidence. . . . . 3.9 Theoretically induced '1? field in 1/2 of the rec- tangular model shown in fig. 3.8. Frequency 8 2.45 Gl-Iz, 0- 5.934 mho/m, €= 68.48130, Salt concentration - 0.5 normal. Cell size = 1 cm3. . . . . vii 3.11 3.12 3.13 3.16 3.17 3.18 Figure 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 Theoretical and experimental values of the dissipated power due to E and E2, i.e. kolE I2 2 x x and koIEzI , respectively, as a function of 2 along x a 0 O 5 cm. 0 O O O O O O O C O O O O O O O O O A rectangular model of 12 x 12 x 1 cm dimensions containing saline solution illuminated by EM wave at normal incidence. . . . . . . . . . . . . . . Theoretically induced x — component of E field in k of the rectangular shaped model shown in fig. 3.11. O= 5.934 mho/m, €= 68.48780, fre- quency = 2.45 GHz, salt concentration = 0.5 normal. Cell size = 1 cm3. . . . . . . . . . . . . . Theoretical and experimental values of the dis- sipated power due to Ex,%o IExlz, as a function of y along x = 0.5 cm for different frequencies conductivities and permittivities. . . . . . . . .. A rectangular model of 16 x 16 x 1 cm dimensions containing saline solution illuminated by EM wave at normal incidence. . . . . . . . . . . .. . . Theoretically induced x - component of the E field in k of the rectangular shaped model shown in fig. 3.14. Frequency = 2.45 GHz, o= 5.934 mho/m, e= 68.48760. Salt concentration 8 0.5 normal and cell Size = 1 cm 0 O C O C O O O O O O O O I O O O O O 0 Theoretical and experimental values of the dis- sipated power due to Ex,%o IEXIZ, as a function of y along x = 0.5 cm. Frequency = 2.45 GHz, o= 5.934 mho/m, e= 68.48780. Salt concentration a 0.5 normal. . . . . . . . . . . . . . . . . . . . A rectangular two layer model of 12 x 12 x 2 cm dimensions containing saline solution illuminated by EM wave at normal incidence. . . . . . . . . . . . The x - component of the theoretically induced E field in the first and second layer of biological model shown in fig. 3.17. Frequency = 2.45 GHz, 0= 5.934 mho/m, EB 68.48760, salt concentration =0.5 normal. Cell size = 1 cm . . . . . . . . . Theoretical and experimental values of the dis- ipated power due to Ex,%p'|Ex|2, as a function of y along x = 0.5 cm. Frequency = 2.45 GHz, 0= 5.934 mho/m, s3 68.48780. Salt concentration = 0.5 normal. viii 3O 32 33 34 36 37 38 40 41 42 ,é-Js 3.22 3.33 3.28 3.29 Figure 3.20 3.21 3.22 3.23 3.24 3.25 3.26 3.27 3.28 3.29 4.1 An I — shaped model containing saline solution illuminated by an EM wave at normal incidence. Theoretically induced E field in E of the I - shaped model shown in fig. 3.20. Frequency = 2.45 GHz, 0= 5.934 mho/m, €= 68.48780. Salt concentration = 0.5 normal. . . . . . . . . . Theoretical and experimental values of the dis— sipated power due to Ex, kolExlz, as a function of y along x = 0.5 cm and x = 3.5 cm. Frequency = 2.45 GHz, 0= 5.934 mho/m, €= 68.48780. Salt concentration a 0.5 normal. . . . . . . . . . . Theoretical and experimental values of the dis- sipated power due to E , 5olEyI , as a function of y along x a 0.5 cm and x = 3.5 cm. Frequency = 2.45 GHz, O= 5.934 mho/m, €= 68.48760. Salt concentration = 0.5 normal. . . . . . . . . . An I - shaped model containing saline solution illuminated by an EM wave at end-on incudence. Theoretical induced E field in 15 of the I - shaped model shown in fig. 3.24. Frequency = 2.45 GHz, G= 5.934 mho/m, €= 68.48780. Salt concen- tration = 0.5 normal. . . . . . . . . . . . . Theoretical and experimental vaiues of the dis- sipated power due to Ex, kolExl , as a function of 2 along x - 3.5 cm and x = 0.5 cm. Freq. = 2.45 GHz, 0- 5.934 mho/m, e= 68.48780. Salt concentration - 0.5 normal. . . . . . . . . . Theoretical and experimental values of the dis- sipated power due to E2, koIEzlz, as a function of 2 along x = 3.5 cm. Freq. = 2.45 GHz, 0- 5.934 mho/m, €= 68.48760. Salt concentration = 0.5 normal. . . . . . . . . . . . . . . . . . . Configuration of the probe in a finite, hetero- geneous volume conductor. . . . . . . . . . . . Equivalent circuit for probe in a finite,hetero- geneous volume conductor. . . . . . . . . . . . A finite biological cylinder of arbitrary con- ductivity and permittivity, half - length h and of square cross-section illuminated by an incident m wave 0 O O O O O O O O I C I O O O O O O O 0 ix 45 46 47 49 50 51 52 54 57 60 4.9 Figure 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 5.1 Distribution of currents (amplitude) induced in metallic cylinders by an electric field of lv/m at 9.45 GHz. Cylinder half-length: h = 0.8 cm and 1.28 cm, respectively. . . . . . . . . . Distribution of currents (magnitude) induced in metallic cylinders by an electric field of 1v/m at 9.45 GHz. Cylinder half-length: h = 1.6 cm and 2.4 cm respectively. . . . . . . . . . . . . . Maximum induced currents in different cylinders of half-lengths: h = 0.8 cm, h = 1.6 cm and h = 2.4 cm respectively as a function of cylinder conductivity . . . . . . . . . . . . . . . . . . . Total induced current along the axis of the salt water cylinder for h/Ao = 0.113, 0.227, 0.510 and 0.737. The concentration for salt solution is 1 normal at 9.45 GHz. . . . . . . . . . . . . . Total induced current along the axis of the salt water cylinder for h/Ao = 0.113, 0.227, 0.510 and 0.737, The concentration for salt solution is 5 normal at 9.45 GHz. . . . . . . . . Experimental set up for measuring the scattering from cylinders of arbitrary parameters. . . . . Comparison of theory and experiment for back- scattering from a saltwater cylinder of 1 normal at 9.45 GHz. The observation point was 15 cm from the cylinder. . . . . . . . . . . . . . . . . Comparison of theory and experiment for back- scattering from a saltwater cylinder of 5 normal concentration at 9.45 GHz. The observation point was 15 cm from the cylinder. . . . . . . . . . . . Comparison of theory and experiment for back— scattering from a brass cylinder at 9.45 GHz. The observation point was 15 cm from the cylinder. Comparison of theory and experiment for relative back-scattering from brass cylinder and a salt- water cylinder of 1 normal concentration at 9.45 GHz. The observation point was 15 cm from each cylinder. . . . . . . . . . . . . . . . . . . . . . The x - component of the induced electric field. Incident EM wave: vertical polarization, 80 MHz. 65 67 69 71 72 74 76 78 80 82 86 Figure 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.11 5.13 5.15 5.16 The y - component of the induced electric field. Incident EM wave: vertical polarization, 80 MHz. The 2 - component of the induced electric field. Incident EM wave: vertical polarization, 80 MHz. Absorbed power density. Incident EM wave: verti— cal polarization. 80 MHz. . . . . . . . . . . The x - component of the induced electric field. Incident EM wave: horizontal polarization, 80 MHz. The y - component of the induced electric field. Incident EM wave: horizontal polarization, 80 MHz. The 2 - component of the induced electric field. Incident EM wave: horizontal polarization, 80 MHz. Absorbed power density. Incident EM wave: hor- izontal polarization, 80 MHz. . . . . . . . The x - component of the induced electric field. Incident EM wave: vertical polarization, 200 MHz.. The y - component of the induced electric field. Incident EM wave: vertical polarization, 200 MHz.. The 2 - component of the induced electric field. Incident EM wave: vertical polarization, 200 MHz.. Absorbed power density. Incident EM wave: ver- tical polarization, 200 MHz. . . . . . . . . The x - component of the induced electric field. Incident EM wave: horizontal polarization, 200 MHz.. The y - component of the induced electric field. Incident EM wave: horizontal polarization, 200 MHz.. The 2 - component of the induced electric field. Incident EM wave: horizontal polarization, 200 MHz.. Absorbed power density. Incident EM wave: horizon- tal polarization, 200 MHz. . . . . . . . . . . . Relative absorption area and relative maximum in- duced field in the torso of a 1.7 m adult as func- tions of the frequency of the vertically polarized and horizontally polarized incident EM waves . . Relative absorption area and relative maximum induced field inside 1.02 m torso of a child as functions of frequency for the vertically polarized incident EM wave. . . . . . . . . . . xi Page 87 88 89 9O 92 93 96 96 97 98 99 100 101 102 104 106 A... I PKJ of. 5.30 Figgre 5.19 5.20 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.30 The x - component of the induced electric field. Incident EM wave: vertical polarization, 30 MHz. Absorbed power density. Incident EM wave vertical polarization, 30 MHz. . . . . . . . . . . . . . .. The x - component of the induced electric field in an adult torso with outstretched arms. Inci- dent EM wave: vertical polarization, 30 MHz. . . Absorbed power density in an adult human torso with outstretched arms. Incident EM wave: vertical polarization, 30 MHz. . . . . . . . . . . . . . .. The x - component of the induced electric field in an adult torso with thin neck. Incident EM wave: vertical polarization, 30 MHz. . . . . . Absorbed power density in an adult torso with thin neck. Incident EM wave: vertical polariza- tion, 30 M112. 0 o o o o o o o o o o o o o o o o 0 The x - component of the induced electric field in an adult torso with thin neck. Incident EM wave: vertical polarization, 80 MHz. . . . . . . . . . . Absorbed power density in an adult torso with thin neck. Incident EM wave: vertical polari- zation, 80 M112. 0 O O O O O O O O O O O O O O O O O A three layer biological model illuminated by vertically polarized EM wave at normal incidence. The conductivity of 11nd layer is variable. . . .. Theoretical results on the x - component of the electric field, current density and absorbed power density in k volume of IInd layer as a function of its conductivity, induced by a vertically polar— ized EM wave of 30 MHz at normal incidence. The conductivity of the surrounding layers is kept at 0.6 mho/m. . . . . . . . . . . . . . . . .. . . A three layer biological model illuminated by vertically polarized EM wave at normal incidence. The conductivity of the cells of inner columns of IInd layer is variable. . . . . . . . . . . . . Theoretical results on the x - component of the induced electric field, current density and ab— sorbed power density in k volume of IInd layer as a function of conductivity of inner cells, induced by a vertically polarized EM wave of 30 MHz at normal incidence. The conductivity of rest of the biological body is kept at 0.6 mho/m. . . . . . . . . . . . . xii Page 108 109 110 111 112 113 115 116 119 120 122 123 “Ere .. 3.31 6.2 6.3 -.“fi'b Figgre 5. 31 5.32 5.33 6.2 6.3 7.1 A two layer biological model of dimensions 6 x 8 x 2 cm containing saline solution illuminated by a vertically polarized EM wave at normal incidence. The conductivity of the shaded region may be dif- ferent than the rest of the model. . . . . . . . . . . Theoretical and experimental results on the ab- sorbed power density in region 1 as a function of the conductivity in the same region of a saltwater model, induced by a vertically polarized EM wave of 2.37 GHz at normal incidence. . . . . . . . . . . . Theoretical and experimental results on the ab- sorbed power density in region 1 as a function of the the conductivity in surrounding region 2 of a saltwater model, induced by a vertically polar- ized EM wave of 2.37 GHz at normal incidence. . . . . A schematic diagram of the experimental set up used to irradiate human amnion and lymphocyte cells to microwave radiation at 2.45 GHz. . . . . . . A typical cell sample of dimensions a=0.5cm, b=4.0 cm and c=6. 0 cm illuminated by vertically polari d EM wa e 45 GHz. 0= 1 mho/m, =8 7080 ’ if g xe ”3 “(2 cm; 0 O O O O O O O O 0 Theoretical results for the normalized x - com- ponent of the induced electric field inside % volume of cell sample as shown in fig. 6. 2. o- 1 mho/m, 88 7080, E1 = xe'32* (2/2 ) . . . . . .. A two layer biological body illuminated by EM wave at normal incidence is shown divided into 8 quadrants under symmetry conditions. Layers are shown separated for clarity purposes. . . . . . . xiii 125 126 128 131 134 136 153 During m- :he eff. cf the Bid! populated . Iaiiation . experiment the nonion them-a1 ef neathermal 51:11 the 1 ROI temple debated, u; adding to even more generates With the “Tuning that medil “3639 Eff; SIHCI an irregu; becomes a CHAPTER I INTRODUCTION During the last two decades or so there has been a growing concern on the effects of electromagnetic radiation on biological systems because of the wide spread use of high intensity electromagnetic radiation in populated areas and the much more restrictive safety standards on EM radiation exposure in U.S.S.R. The perpetual cognizance of the available experimental data on possible health hazards commend that the effects of the nonionizing EM radiation may be thermal or nonthermal in nature. The thermal effects are attributed to the increase in body temperature while nonthermal effects are ascribed by induced electromagnetic field and as such the line of demarkation from one particular response to another is not completely determined. While this controversial issue is still being debated, microwave has already found its home in medication, therefore, adding to the enormity of the already complex problem. Thus, it becomes even more important to determine the induced electromagnetic field which generates the nonthermal response and investigate the temperature at which the thermal effect appears. Since the rise in temperature in a conducting medium can be correlated to the induced electric field in that medium, therefore, a great deal of information may be obtained on these effects if the induced electric field in the medium is calculated. Since a biological body is usually a heterogeneous finite body with an irregular shape, the determination of the internal electromagnetic field becomes a difficult problem. For mathematical simplicity, the commonly and C05 thapter used models are the plane slab [1,2], the sphere [3,4,5] , the cylinder [6]and the spheroids [:7,8]. Although these simple models provide es- timates of the internal electromagnetic fields, the results have limited applicability to the biological bodies with irregular shapes and il- luminated by electromagnetic waves of microwave range. This thesis discusses a recently developed numerical technique called the tensor integral equation method which can be used to quantify the internal electric field induced by an incident electromagnetic wave inside arbitrarily shaped biological bodies. The theoretical development for calculating the fields induced inside and scattered by a finite biological body having arbitrary shape and composition when exposed to electromagnetic radiation, is given in chapter II. A concise derivationfor the internal and scattered electric fields resulting in a tensor integral equation is given. The method of moments is discussed to transform the tensor integral equation into a set of simultaneous equations for numerical solution. Chapter III is devoted to the theoretical and experimental results on the induced electric field inside biological bodies when irradiated by EM waves. In order to carry on the experiments, the experimental set up and the construction of the insulated dipole probe are outlined. Rectangular plexiglass models of various dimensions with regular and irregular shapes containing saline solutions of different concentrations are used for experiments. An excellent agreement between theory and ex- periment is obtained. An inherent experimental error assoc‘iatedwith an implantable probe immersed in finite biological body is also discussed. Chapter IV contains the theoretical and experimental results on scattered fields from finite biological bodies, when irradiated by EM ’ESCI int :t-e accurz IEHEUCS 3 scattering iihensions The a electric I are discus vertical 5 internal e 'nduced b1, and a chi] informatic Chap: 501398 in 1 M18 are aPplied U the cell 1 the exIIOSI Safety st. Chap 3‘31“ used DQIinitiO] waves. Thin biological and metallic cylinders are considered. The' tensor integral equation is simplified for thin approximations. To check the accuracy of the simplified tensor integral equation, the induced currents inside metallic cylinders are calculated and then compared with the currents induced on perfectly conducting cylinders based on Hallen's integral equation. The criterion on the assumption for a perfect con— ductor is presented. In addition, the relative amplitudes of the back— scatterings from a biological cylinder and a metallic cylinder of the same dimensions are compared. The applications of the tensor integral equation method for induced electric field and absorbed power density inside adult and child's torsos are discussed in Chapter V. Some numerical examples are given for the vertical and horizontal polarizations. It is found that the strongest internal electric field and the maximum absorbed power density are induced by vertically polarized EM waves of 80 MHz and 120 MHz for adult and a child's torsos respectively. The chapter concludes with some information on the local heating with electromagnetic waves. Chapter V1 is devoted to the effects of microwave on human chromo— somes in tissue culture cells. Human amnion cells and human lymphocyte cells are used for experiments. The tensor integral equation method is applied to quantify the induced electric fields at various locations of the cell samples. Certain chromosomal aberrations were observed, when the exposure levels were substantially lower than the permitted U.S. safety standard of 194 volts/m. Chapter VII includes a description and listing of the computer pro- gram used for the numerical evaluation of the tensor integral equation. Definitions of input variables, construction of data files and the instructions for its use are given. In addition, an illustrative example using even and odd symmetries along the z - direction for the incident electromagnetic field is worked out for better understanding. f-J I H lite DIES r: C0 be El ic tI CHAPTER II INTERACTION OF ELECTROMAGNETIC FIELD WITH BIOLOGICAL BODY 2.1 Introduction. In this chapter, the theoretical and experimental study on the interaction of electromagnetic field with biological body will be presented. The four major topics to be discussed are: a. The quantification of electromagnetic fields induced inside any arbitrarily shaped biological body, also referred to as body, the physiological system or just the system, when exposed to the electromagnetic radiation. b. The maximum and total power deposition inside the biological body under the exposure of electromagnetic radiation. c. The electromagnetic field scattered by the system and d. The electromagnetic probing of the simulated biological system during its exposure to the electromagnetic radiation. Let us first plan to concentrate on the theoretical study. Upon completion of the theoretical deveIOpment, an experimental study will be discussed to verify the accuracy of the theoretical results. 2.2 Theoretical Development. When a biological system such as human body, is illuminated by an electromagnetic wave, an electromagnetic field is induced in the inter- ior of the body and an electromagnetic wave is scattered by the body in the region exterior to the body. Since any biological body, in general, is a heterogeneous, finitely conducting with frequency dependent per- mittivity and conductivity and with an irregular shape, the distribution 5 . . >— 3. {AC '4". tons Inc-r syst Ele tiO knc r-w .A H I the ("'1 3 ,\ Em of the internal electromagnetic field inside the body and the electro- magnetic wave scattered by the body will be dependent on its physio- logical parameters, geometry, frequency and polarization of the incident electromagnetic field. The electric field induced inside the biological system is the key quantity which determines the induced current and the total power deposition inside it when exposed to electromagnetic radiations. Therefore, our theoretical approach aims to determine this induced electric field. Consider a biological system as shown in fig. 2.1, composed of heterogeneous lossy medium with an irregular shape, being illuminated by incident electric field E1. The body may further be assumed to be constructed of layers with variable permittivity and conductivity. Therefore, the parameters of the medium constituting the biological system can be expressed as: + permittivity :8 = EKw,r) -dependent on frequency and location + conductivity: 0’= oflu,r) ~dependent on frequency and location permeability: LI= 1% —permeability of free space, since the biological bodies are assumed to be essentially non-magnetic in nature. From the Maxwell's equations, both for the incident and the total electromagnetic field, a tensor integral equation is derived in sec- tion 2.2.1. This tensor integral equation provides a link between the known incident electric field Ei(;) and the unknown total induced field 5(3). As it will be clear later on in the theoretical development that the so called tensor integral equation involves the unknown total field E(;) as a part of integrand, thereby imposing difficulties in arriving at a direct solution. To circumvent the problem mentioned above, a numerical technique - Moment Method with Pulse Function Expansion of Free space ...p. E' €(1‘), O-(I'), ’10 33!. Fig. 2.1 An arbitrarily shaped biological body in free space, illuminated by an electromagnetic field. f?_ 1 . E]:- 88 vhe The kno 10c. the unknown electric field E(f) - will be employed to transform the tensor integral equation into a set of simulataneous equations. This set of simultaneous equations can then be solved for the unknown fields at different locations inside the body by known numerical techniques. An exact formulation of the tensor integral equation and its transfor— mation into a set of simultaneous equations have already been reported by Livesay and Chen [9]. Nevertheless, for the brevity of the experi— mental results, a brief outline of the theoretical development is the topic of discussion in section 2.2.1. 2.2.1. Tensor Integral Equation for the Induced Electric Field. In a source free region of free space, the electromagnetic field satisfies the following Maxwell's equations: v x E16?) = -jwuo BR?) (2.1) v x EN?) = jweo BR?) (2.2) v - E (15) = O (2.3) V +1 + _ - H (r) - 0 (2.4) where no and so are the permeability and permittivity of free space. +1 +~ +14+ The quantities E (r) and H (r) of incident field are assumed to be known every where in space and are, of course, known functions of + location r. When a biological body is illuminated by the incident electric +1+ ++ field E (r), the total electric field E(r) inside and outside the body +1" +3+ is the sum of E (r) and the scattered electric field E (r) maintained by the induced current and charge in the body. Mathematically it?) J?) + $236?) (2. 5) 9 and similarly, the total magnetic field H(;) can be expressed as 136:) e'fiiG) + ESQ) (2.6) where Hs(f) is the scattered magnetic field maintained by the induced current and charge in the biological system. Since Ei(f) is known, the problem will be solved if an expression for ES(:) is obtained. Furthermore, for the total electromagnetic field to exist at any point in space including the physiological system, it should satisfy the following Maxwell's equations: v x "E(I) = -jwuo m?) (2.7) v x E(I) = c(¥)'€(¥) + jweGfiG) (2.8) v ~[o(¥)§(¥) + jwe(?)’1§(?)] = 0 (2.9) v - fié) = 0 (2.10) From the set of equations (2.7) through (2.10), using equations (2.1) through (2.6), the following equations can easily be derived: v x E91?) -- -jwuo fisé’) (2.11) v x fish?) 406?) + 31) [E(r) - to] I EEG“) + jweo‘ESG) (2.12) Defining an equivalent volume current density 3;q(f) by Fed?) = r(?)E(?), (2.13) where T(:) = C(f) + jw[t(¥) - 80:], is the equivalent complex con- ductivity of the medium. Eqn. (2.12) can now be rewritten as vx’fiSG) = 3616?) +jOeOESG) (2.14) The equivalent current density has two components, viz. O(;)'E(;) the + ++ conduction current component while jw{€(r)-€o }E(r) is the polarization current component, and exists only inside the biological system. The terms 0f continuz and DOT Theref expres densit can Whe 10 + The equivalent volume charge density peq(r) can be expressed in terms of equivalent volume current density jeq(f) from the equationof continuity. i.e. (I) - 1-v 3 (I) (2 15) peq r — w eq r . and moreover, divergence of eqn. (2.14) gives +S+ 1 + v . E (r) = E- o (r) (2.16) Therefore, the Maxwell's equations for the scattered field can now be expressed haterms of the equivalent volume charge and volume current densities as VxEG)=—m%FG) adv v x‘fis(?> = 'Jeq(?) + jdcéts(?> (2.18) .s _1 v 'E (I) - 60pqu) (2.19) v ° fis(?) = 0 (2.20) The theoretical expression for the scattered field anywhere in space can be written as E8 j , *‘i +, 3.eg(?) (I) = P.V. j equ ) . r,r ) dV - 3jw€o (2.21) v where mi?) = ‘jw€o[+—T + WZ—{ltfl—fl'f') ko -jk ? - I' P(?;?') = e °| I 4N|I - ?'| ’ AA AA I+ = xx + yy + 22 , ko =m/“oeo and the symbol P.V. stands for the principal value of the integral obtained by excluding from the total volume V a small sphere of radius l l + <~~>—+ + ra centered at r and then taking the limit such that r; O. G(r,r') is the free space tensor Green's function. Once the expression for the scattered field is obtained, the ex- + pression for the total electric field at any point r follows from eqn. (2.5). i.e. after some rearranging .. [1 1. $7213: 1% - 2v. JT(¥')'E('§') - 66.?) av. = 13%;?) (2.22) 7' O In eqn. (2.22) Eff) is the incident electric field at any point inside the biological body and is a known quantity. E(;) is the unknown total electric field at any point inside the body. In the actual calculation, due to the complex nature of the tensor Green's function G(f,;'), it will be formidable to solve eqn. (2.22) without some simplification and approximation. The Moment Method using the pulse function expansion provides some simplification and approx- imation in solving eqn. (2.22) numerically. The details of this method are nicely reported elsewherefllfland will not be reproduced here, but in order to perserve the continuity of the topic, a simple introduction of this method along with some important results are discussed in sec- tion 2.2.2. 2.2.2 Transformation of Integral Equation - Moment Method. The integral involved in evaluating the total electric field E(f) at any point inside the volume V, eqn. (2.22), is very difficult to be performed in problems of practical interest. A simple way to obtain approximate solution is to require that eqn. (2.22) be satisfied at. certain discrete points in the region of interest. This procedure is called as point matching technique. In the Moment Method, the total volume of the biological body is partitioned into N subvolumes or cells. These subvolumes are assumed to be electrically small and in each cell .0 3. in 12 E(:) and T(f) are assumed to be constant. Therefore, the accuracy of this method depends upon the dimensions of the cell. From exper— ience, it has been found that any physical dimension of the cell should not be greater than 330’ wherexo is the free space wavelength of the incident EM field. On the other hand, due to the limited storage capacity of the modern computers, the number of small subvolumes can not be increased drastically because in each cell there exists three com— ponents (Ex’ Ey’ and E2) of the total electric field E(f). Thereby, increasing the total number of unknown quantities to 3N. These unknowns are to be determined from 3N simultaneous equations obtained by trans- forming eqn. (2.22) through the point matching techniques. These sim— ultaneous equations can be grouped into a matrix form symbolically as [Gm] I [nyl I [ze] '[Ex] [13:] [GYIJ 5 [“22] 5 [an] [ray] [2;] (2.23) ""','""'1"'" "" ”1" £6239 :[Gzy] : [Gzzt JEz]_ b[Ez 'd where matrix[G]represents a 3N x 3N matrix and[ E] and [E1] are 3N column matrices expressing total electric field and Incident electric field at the central locations of N cells. Although the elements of [G]matrix have been carefully evaluated inhILL yet expressions for their numerical evaluation are given in the next section. 2.2.3 Evaluation of Matrix Elements & Total Electric Field. In this section, the explicit expressions for the elements of each N x N submatrix [Gx x] p,q = 1,2,3 are given. The notations used in 99’ expressing these elements are = y, and x = 2. x1 = x, x 3 2 There ‘ ‘1 VI‘R‘ 13 The m,nth element of the off diagonalI'prxq] matrix is given by ..ja mn -jmu k If; ) AV e mn G o o n n 2 , x x = [(01 - 1 - 301 )6 p q 41m3 mn mn pq mn + cosOmp cosOInn (3— a2 + 3ja )] (2.24) x x mn mn P q where + + a = k R , R = Ir - r l mu 0 mn mn m n m m n xp _ xn mn x - x cost)mn = -—-——JL—- ’ C086x = R x R q mn p mn + _ m m m + _ n n n rm - (x1 .x2 , x3). r (x1. X2 . x3) AV = IdV' n Vn The n,nth diagonal element of [Gx x] matrix is given by p q nn 2jwu T(+ ) 'k G = - 6 o r11 .3 can x 2 1+ k -1 xp q pq { 3k2 ( j oan) ] o T(¥) + [DPT—L] j“’80 (2.25) .1. - 2E! 3 where an - 4" n] (After all the elements of 3N x 3N matrix are determined, the total elec- ttflc field, E(P), is determined at any point inside the body by inverting the matrix as follows: :aLCL IEIII'. is bio tri an: PI“ Io -1 — .. r- . 1 '— , T [Ex] [G ] I [ny] : ze] "E;' My]; [6...] 51,.) Etyzl 42;] Eli'2.-i [GzzJ E [Gzy' E [6221 :[E; 'J (2.26) 2.2.4 Expression for the Scattered Electric Field. The scattered electric field outside the biological body can be calculated once the induced electric field inside the body has been de- termined. The expression for the scattered electric field at any point : outside the biological body is given by Es(?) = ‘fr(?') E(I') . EI?;¥') dV' (2.27) V where E(P') is the total electric field at any point P' inside the body and is given by eqn. (2.26). Since I is an external point not located in V, G?;,?') stays finite over the range of integration. Therefore, the principal value of integration in eqn. (2.27) is not needed. Since the above equation yields the scattered field from the total body, hence it is possible to express it in terms of number of subsections of the whole biological body. Therefore, each scaler component of the scattered elec- tric field may be written as N 3 E8 G) = z >3 u? )1: (I) c (r. X n X 1’1 p n=1 q=1 q v p q ')dV' (2.28) and this integral equation can be solved by the method outlined in the previous sections. This almost concludes the discussion of the theoretical development for the induced electric field inside and scattered by the biological 15 system except some simplifications due to thin approximations. Since a theoretical development is not complete until and unless the theoretical results are compared with the existing results if their are any and checked by experiments. In the following chapters, we aim to verify the accuracy of the tensor integral equation by conducting a series? of experiments on regular, irregular and.thin simulated biological bodies. The theoretically quantified results will be compared with ex- perimental observations at various locations inside the biological body in the next chapter. .1..."ev. . .11-... 4a:.'.: and 51; BK PI ti CHAPTER III THEORETICAL AND EXPERIMENTAL RESULTS ON THE INDUCED FIELD INSIDE BIOLOGICAL BODIES. The tensor integral equation method is applied to solve the pro— blems of interaction of electromagnetic field with quite a few dif— ferent types of biological bodies in order to determine the total electric field induced inside and scattered by them. To prove the theoretical development discussed in section 2.2, of chapter 2 and to confirm the accuracy of the tensor integral equa- tion method, a series of experiments have been conducted either to measure the induced electric field inside some boxes or the electric field scattered by some cylinders. In either case, the saline solutions of varying concentrations were used to model the biological systems and were exposed to plane electromagnetic wave at different frequencies. Let us concentrate in this chapter on the set of experiments de— signed to measure the induced electric field inside the simulated models of biological systems containing saline solutions. The details of this experimental study are given in section 3.3. Sections 3.1 and 3.2 ex- plain the experimental set up and the construction of a typical probe needed to carry on the aforementioned experiments. 3.1 Experimental Set Up. The schematic diagram of the experimental set up for measuring the induced electric field in the simulated biological bodies is 16 .w. o. r. 17 shown in fig. 3.1. For simulated biological bodies, a number of ex- perimental models were constructed with plexiglass and filled with saline solutions of various concentrations. These models were placed inside the anechoic chamber and illuminated by electromagnetic wave with frequencies ranging from 1.7 - 3.0 GHz (with 1 KHz modulation). A horn antenna was used as a radiating source. The:anechoicchamber was probed in the y - and z - directions to find a region where there is no variation in SWR (SWR being inversely proportional to the electric field intensity) under free space conditions. These regions are shown in fig. 3.2 to lie eitherside by 4 cm from the center in y — direction and greater than 17 cms away from the central location along 2 — dir— ection. The central location used as reference here is approximately I3feet away from the horn antenna. The induced electric field inside the saline solution was measured by small dipole type probe loaded with microwave detector. The details for the construction of this probe are given in section 3.2. The output of the detector loaded probe was connected to SWR meter. A vertical dipole probe was used to detect the vertiCal component of the induced electric field, Ex’ and a hori- zontal probe was used to measure the horizontal components Ey and Ez. 3.2 Construction of Probe. When a biological body such as human body is exposed to electro- magnetic radiation, it is difficult to predict the electromagnetic fields induced inside the body from the electromagnetic fields outside the body because of inhomogeneous electrical properties and the irregular geometry of the body. Theoretical development on the EM fields induced inside the body is given in the previous chapter. However, it is highly desirable to devise an electromagnetic probe to directly detect these induced fields experimentally. 18 .amumhm Hmowwoaown m moans“ pHOfiw uauuooao mucousw mo uaoaousmmma Gnu you a: umm Haunoaauonxo mnu mo amuwmwv vaumaonom Una .H.m .mam <<<\< {4 VV V v opomc nouoouop :33 V commofi 309.0 ”v um Ed U eye“. .22.... 11>? I mdfidm fl ddGmud< GMOS /_' i 92.3 vv madam? we amEl'. 4111‘— uoumt ocoO vv 9330.33 ' . >>>>>>> r>> - .5 T 2 , hmuwz mam .228qu anon on”. Baum umom m 3395x393 ma 8am .oub ucfioa one .maoauuouav 1 u use 1 % ea nonemno owonooem cm powwow doausnwuuMfiv paofim owuuomao O>Humamm ~.m .wwm Eu 4 N 3 «a «a on 2 o. E a. 2 a o v a o . - 4| 11’ u - J a q u . . a . O O 0.0 9 1 0.— Eu 1.. x 9 n o v a o n - v- o- 0.. OT .06 p131; 31.113910 BAII‘BIJJ p191; 31.113313 31513219.: a ., A4) a;- u-vh. 20 The basic requirements for such a probe include (1) relatively small size, (2) sufficient sensitivity, (3) polarization independence and (4) minimum interference due to the lead lines. The first two requirements are very common in antenna theory and had been handeled very carefully for any impedence type probe. The last two require- ments are unique for this type of probe and present a great difficulty in designing the probe practically. Fig. 3.3 shows the dipole type probes mounted with detectors and lossy lead lines. The construction of each probe includes a micro— wave detector (type H.P. 5082 - 2755) with its axial wires of 5 mm length on each side forming a dipole. A pair of very thin high resistance wires (Nichrome V wire of 2 mil diameter) were glued on to the long but thin stick of plexiglass and were wound and soldered on the axial wires of the microwave detector at one end and connected to the output wires (shielded gramophone wires) at the other end. The high resistance lead wires were needed to minimize the interference of the lead wires with the incident electromagnetic wave. Since the probe and part of the lead wires were to be immersed in the finitely conducting saline solution for measurement of the induced electric field, therefore, it was necessary to insulate the probe and the lead wires. A commercially available Klyron transparent spray was used to provide the needed in- sulation. After the construction of the probe, it was necessary to precal- ibrate it as the microwave diode detector may not be a square law de- tector needed for the optimum operation of the SWR meter. Such a cal- ibration curve is shown in fig. 3.4. A vertical dipole probe and a horizontal dipole probe, as shown in fig. 3.3 were constructed and 21 'H “'6 mm 7r 74 output leads A? ‘—plexiglass stick 1 p—hlgh reststance —'F w1res 80.6cm 3mm H——25Acm :3: FE microwave detector (b) Fig. 3.3 Dipole type probes mounted with microwave detectors for the measurements of induced fields in the vertical (a) and horizontal (b) directions. 22 .uosoe apnea o>wumaou .m> mzm "nouuwump m>msou0Ha m spas vopmoa onoua mazu mHoaHp Gnu uom w>u=u coaumunaamo <.m .wwm Came; 1‘ poison “5&5. o>fim~ou a. h. o. n. v. n. N. —. o n - u N - - - . ms pexnseam 23 then calibrated for the measurements of the vertical and horizontal components of the induced electric field. 3.3 Theoretical and Experimental Results. The experimental results on the induced electromagnetic fields inside some simulated biological models are compared with the theoretical values of the induced fields obtained from the tensor integral equation method. This comparison is shown in figs. 3.5 to 3.27 and is the topic of discussion of this section. In fig. 3.5 a rectangular plexiglass box with dimensions of 6 x 6 x 1 cm, containing 0.5 normal saline solution is illuminated by a microwave of 2.45 GHz with a vertically polarized field and at end-on incidence. The total volume is divided into 36 subvolumes and each cell is 1 x l x 1 cm in dimensions. Fig. 3.6 indicates the theoretical values for the x - and z - components of the total induced field at the centers of the cells. The y - component is neglected as it is very small compared to the other two components. In the calculations, conductivity is assumed to be 5.934 mho/m and permittivity is assumed to be 68.48780. These values of the conductivity and permittivity correspond to a 0.5 normal solution at 2.45 GHz [11]. Due to the synnnetry along x - axis, only upper portion of the model is shown in fig. 3.6. The upper part of fig. 3.7 shows the comparison of the theoretical and experimental results for the dissipated power due to Ex’ k0] Ex I2, as a function of 2 along x = 0.5 cm, x = 1.5 cm, and x = 2.5 cm lines. The lower part of fig. 3.7 shows the theoretical and experimental values of the dissipated power due to Ez, % OIEZI2 , as a function of 2 along x = 0.5, 1.5, and 2.5 cm, lines. It is observed that the patterns of the dissipated power are quite complicated functions of location and these patterns PI Fig. 3.5 A rectangular model of 6 x 6 x 1 cm containing salt solution 24 )( Mr... I o 2"" ' I \\ ’ ' l I I ’I’. L’ ' \ I: I \ ,’ I ‘1 I ) I I V/ K / /u&————————- 6 crn / .4 illuminated by an EM wave at end-on incidence. 25 . 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E x : 015 cm 0 e: 68.48760 g1 3 _____ .3---” ...... Z - 6 ‘ -10,- \ O I 6 ‘f'EJZ- - . I’m .\.\ -‘- ____ _" I" 'ZO_ .\. ’.—_,_._,." \.\.-.’.’.,’ l 1 4 £ 1 1 1 J l I -3 -Z -l 0 l 2 3 ZZ---—§- ( crn ) (dB) ,/."“""-‘.~.\ ~10. -l4 1. mg -181- -ZZ_. Fig. 3.7 Theoretical and experimental values of the dissipated power due to E and E2, i.e. %OIEXI2 and EUIE I2 respectively, as a function of 2 along x = 0.5 cm, x = 1.5 cm, x = 2.5 cm lines. 27 show no similarity from one another, but the agreement between the theory and experiment is excellent. However, it is noted in fig. 3.7 that the experimental results on %O|EZI2 are not available near the edge of the box because it was not possible to measure Ez at these locations with a horizontal probe of finite dimensions. Fig. 3.8 shows a rectangular plexiglass biological model in the shape of a rectangular box of 12 x 12 x 1 cm, containing 0.5 normal saline solution and is illuminated by a microwave of 2.45 GHz with a vertically polarized field and at end - on incidence. In this example, the total volume of the biological model is divided into 144 subvolumes, i.e. 4 times the number of subvolumes considered in the previous example. The idea of carrying on this experiment was to determine if there are any significant changes among the induced field variations, when similar looking biological bodies of same thickness, one having twice the size of the other in other two planes, but with the same bio— logical parameters, are exposed to electromagnetic radiations of the same frequency. Fig. 3.9 shows the theoretical values of the induced fields for the x - and z - components at the central location of each cell. The y - component of the induced field is neglected because it is very small as compared to the other two components. Again, owing to the symmetry of the biological model, as shown in fig. 3.8, along x - axis, there- fore, the theoretical values of the induced fields (magnitudes and phase angles) only for the upper part of the biological model are shown. In the theoretical calculations of the induced fields, conductivity and permittivity of the saline solution are assumed to be 5.934 mho/m and 68.4878o respectively. 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NE. . . . x 30 X A (dB) .- freq = 2.45 GHz El ' ’1 cm 01- 6": 5.934 mho/m T : i c: 8.487‘ _.- : , . 6 ° H1. g-’f__°_é_€:n__._.z m: -10 _ ' l -20 - <7 2 zlExl ‘ -30 .. - l :4 1 :2 L 10 l i I h l z,__———a>- (crn) (dB) . -20 .. b C _30 _ x = 0.5 crn 2 —.— Theory EFZI ’ Exp. . -40 l 1 n 1 n l 1 1 n n I -6 -4 -Z 0 Z 4 z,__—_———-» ( C01) Fig. 3.10 Theoretical and experimental values of the dissipated power due to E and E , i.e. EUIE I2 and kOIE I2 respectively, as x x z a function of 2 along x = 0.5 cm. 31 correspond to 0.5 normal salt concentration at 2.45 CHz. The upper part of fig. 3.10 shows the comparison of the theoretical and experimen- tal results for the dissipated power due to Ex’ % OIEXIZ, as a function of z along x = 0.5 cm line. The lower part of fig. 3.10 depicts the com- parison of the theoretical and experimental results for the dissipated power due to E2, %GIEz|2, as a function of 2 along x = 0.5 cm line. It is again observed that the patterns of the dissipated power are quite complex functions of location and moreover, the field induced at one location in a body of small dimensions may be quite different than the field induced in a similar body at the same location but of higher dimensions. This can be visualized by comparing the results shown in fig. 3.7 and fig. 3.10. You will recall that fig. 3.7 shows the theoretical and experimental results for the dissipated power for 6 x 6 x 1 cm bio? logical body. From the comparison, it is obvious that for the x = 0.5 cm line and for lzl_<_3 cm, the patterns for the dissipated power are in no way similar to each other, which does indicate that the induced fields are strong functions of the size of the biological body. More about this will be said when we examine the results for certain irregular shaped biological bodies. After carrying on series of experiments for the end - on incident electromagnetic wave, our next task was to observe the changes in the induced electric field when the biological model was exposed to electro- magnetic wave at normal incidence. To be consistant, we irradiated similar models having the same 0.5 normal concentration at 2.45 GHz. Fig. 3.11 shows a rectangular biological model of 12 x 12 x 1,cm at 2.45 GHz (i.e. U = 5.934 mho/m and€= 68.48780). Again, the total body 32 o \ ////// 1\\\\\\ flu" fit——12 cm ‘2; '6‘ Fig. 3.11 A rectangular model of 12 x 12 x 1 cm dimensions containing saline solution illuminated by EM wave at normal incidence. 33 X' 4 Ex(v/m) I I I T I I I I I I . I I ' ' ' ' i , .0389 ; .0304 i .0259 : .0322 : .0329 I .0345 I---_-L____J _____ ' L i I I ' I'"‘ -1 -..---. ----- I I I l I - I . ' I i .0501 I .0387 : .0388 I .0482 . .0384 ; .0545 I I l . i. ...... ..l. ...... I--__...__'. ...... .l ..... .I ...... I ' I I I ' ' I : I I I .0526 : .0462 : .0472 - .0585 1 .0292 : .0853 I I I I I I ..... 1 ...... .--—---: ...... . ..... .. ...... I I I I i : I i ' .0561 : .0555 : .0506 : .0614 I .0171 I .1235 I L ...... L----_% ...... I ...... 4-----1 ...... I I I ' I I ' ' ' ' I I ' I i .0667 : .0626 , .0513 I .0601 I .0183 } .1604 I I I I I I. ..... _.._..... ---__|..__.._I---.._- _____ 7 t , I T " 7F I I I ' | I I .0754 I .0653 ; .0516 I .0589 I .0257 I .1851 1cn1 I -6}.-___J_-_-_I _____ 1___-_1 _____ . _____ LY F-rlcrn-u— Fig. 3.12 Theoretically induced x - component of i field in k of the rec- tangular shaped model shown in fig. 3.11. O= 5.934U7m, €= 68.48780, frequency =32.45 GHz, salt concentration = 0.5 normal. Cell size = 1 cm . 34 freq = 2.032 GHz X 0’: 8.422 mho/m=(l N) l l e: 62.24 c T I 0 I E = 015 cm L._..” 1:22 0.5 crn ‘8 ‘pY ~* lcrnf (dB) —.-—Theory *i J- 5 Exp. T I<——12 cm —H -15 . 2 p 2? ZIExI .25 1 1 1 l 1 1 1 l I l -6 -4 -2 O 2 Y ——> (cm) (dB) 0 O freq = 2.032 GHz -10" G: 6.0 mho/m =(0.8 N) C: 65.3 £0 - Z 4 .4 2 Y —-D-- I cm I (dB_)1 - Q freq = 2.45 GHz 0 a": 5.934 mho/m = (0.5 N) _ 5: 68.487 ‘0 -20 ' 2 - ‘EIExl 1 L 1 j 1 1 1 1 1 1 1 '30-6 -4 -2 0 2 4 6 Y————.» (cm) Fig. 3.13 Theoretical and experimental values of the dissipated power due to Ex’ 3 0 IE I2, as a function of y along x = 0.5 cm, for dif- ferent frequencies, conductivities and permittivities. 35 is divided into 144 cells with a cell size of 1 x 1 x 1 cm. The theore- tical values for the x - component of the total induced field at the central location of the cells are indicated in fig. 3.12. In this case, y - and z - components of the induced field were fairly small as compared to the x - component and therefore, are not shown. Due to the symmetry of the biological body in the XY plane, only the induced fields at different locations of the body in one quadrant are shown in fig. 3.12. The bottom curve of fig. 3.13 shows the experimental and theoretical values for the dissipated power due to Ex’ %OIEXI2, as a function of y along x = 0.5 cm line. The field variations in x - dir- ection are, of course, different compared to end - on incidence for the same model as shown in fig. 3.10. We considered, the same biological model to be exposed to a microwave at 2.032 GHz having 0.8 and 1.0 normal saline solutions. The top and the middle curves of fig. 3.13 indicate the theoretical and experimental values of the dissipated power due to Ex’ kOlExl 2, as a function of y along x = 0.5 cm line for 1.0 normal and 0.8 normal salt solutions. For each case, in fig 3.13, the particular values of the conductivity , permittivity and the fre— quency, of the incident; field are indicated. The distribution of the dissipated power is shown to change quite significantly even though the frequency, conductivity and the permittivity are changed only slightly. In all the three cases the agreement between the theory and experiment is excellent except at the very edge of the model. This discrepancy will be considered in section 3.4. A large rectangular model is shown in fig. 3.14, being exposed to a microwave of 2.45 GHz at normal incidence. This biological model has the dimensions of 16 x 16 x 1 cm and is further subdivided into // f/////// /// //////// 16 cn1 //////// ///// /7//// f/////// /\\\\\\\\ L/) Fig. 3.14 A rectangular model of 16 x 16 x 1 cm dimensions con- taining saline solution illuminated by EM wave at normal incidence. 37 (Vlm) E? T -._._L,.Y .1711 lcnn 7. . 2. w a. n .U . nu " 7. n .8 . .3 _ 4. . 2. 7. . 7. . nu . o, . m .8 _ 7. 2. . I. . n. . 7. 4. _ 0 _ .I. _ .I. _ .1 . .I. . .I. . .l. C o _ o . o _ o a o u o - o - — 1 ...... ‘-|"|"I'-'-'-*ll'-'*"-'-'-""'r'----.-l'l' . . . _ .4 Z . 1 . 7 7 . 6 . OI . 8 . .I. .8 .I . 7. . .3 . 7. . 4. . n. . nu _ .3 . 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O C .3 . n. 7. . 0, . ,o . 4. . lo . n. _ 7. . 4. . .3 . .3 . 2. . .1 . 7. . .3 2. _ 4. . .3 _ .3 . .3 . a. . .3 . a. . 0 _ 0 . 0 . O . 0 . 0 . 0 . 0 _ o . o . o “I o u o n o . o . o 1 _ 5 - 0 . 4 c 2 . 2 o n n 6 — 6 — 8 — 1 c 8 a Z n 0 o 4 5 7 8 . 6 . 5 . 5 . ID _ 7 . n. . .U . .U . nu . n. . n. . .U . nu o _ o n o _ o . o . o . o . o — Frequency = 2.45 ...). Salt concentration = 0.5 normal Fig. 3.15 Theoretically induced x - component of the E field in k of the 68.48780. 3 1 cm . GHz,0= 5.934 21/111, 8-.- rectangular shaped model shown in fig. 3.14. and cell size = 38 .Hmauoc m.o u coaumuucmoaoo uamm .om mwm.wo nwx.a>3.¢mm.m no .Nmu mq.~ n zoamsvoum .ao m.o u x wQOHm % mo coauod=m 8 mm .m_ m_ow . m ou one .8303 vmummwmmfiv m:u mo mmSHw> Hmuawawummxw wan Hmowumuomnp o“.m .wwm AEUV I .x. .w o v N D NI .1 .Y wI omI _ . q q q . . q . u _ . q . . ...... o T Tull Eu ... III. .. .mxm Eu A! m .3093. IOI . Amp. N ‘Jr .IIIIIIIIa IIIIIII 1 Eu m.o n x Eu mud .... x H——w39I——-—I 39 256 subvolumes and each subvolume has a size of 1 x 1 x 1 cm. Due to the symmetry in the XY plane, only % of the total biological model is consideredfor the theoretical calculations. The x - component of the induced field in this biological body having 0.5 normal salt concentration with<3= 5.934 mho/m andEZ= 68.487E%)at 2.45 GHz, is shown in fig. 3.15. In fig. 3.16, the distribution of the dissipated power due to Ex’ aolExlz, in this particular model is shown. Again, in this case an excellent agreement between theory and experiment is obtained except at the edge of the model. After obtaining excellent results for the thinner biological models, it was decided to consider a thicker model with dimensions of 12 x 12 x 2 cm as shown in fig. 3.17. The purpose of this study is to see how the induced electric field decays as the incident wave penetrates the biological body and to observe the accompanied change in the field dis- tribution pattern. The total volume of the biological model, with each cell of 1 x 1 x 1 cm, is divided into 288 cells. Therefore, the model can be classified as having two layers in the z - direction with each layer of one centimeter thickness. The x - component of the induced electric field in the first and second layers are shown in fig. 3.18. The conductivity and relative permittivity, corresponding to 0.5 normal saline solution at 2.45 GHz, are assumed to be 5.934 mho/m and 68.487 respectively. Again due to the symmetry in the XY plane, only one quadrant of the total volume for each layer is shown. Fig. 3.19 shows the theoretical and experimental results for the dissipated power due to Ex’ 5013x125 as a function of y along x = 0.5 cm line passing through the centers of the first and second layers. The dissipated power in the first layer is several decibels higher than that in the second layer 4O first layer secondlayer s . s s x s l‘ I \\ \\ \ S \ \ ":'-"k"\""‘ s z I ILIIPII ..I I s \ \l s 4 \ V Fig. 3.17 A rectangular two layer model of 12 x 12 x 2 cm dimensions con- taining saline solution illuminated by EM wave at normal incidence. 41 .mao H u oNHm HHwo .Hmauoc m.o u coaumuucmoaou uamm .omqu.wc um .E\b.qmm.m nb .Nmo mq.~n mucmsvoum .n..m .mHm aH asosm Hovoa HmonOHOHn mo swam. ucoowm can umufim wnu cH UHQH: +umoswaH maamoHuouoonu wnu we uaoaomaou I x 658 w.. m .mfim ”.52... ozoowd _ mm»... ..mm... _I .1.|EIuI.I.1.I- III III -I 1.11 11 InhomHIIIIIII-IIIIIIIIII ... .1 I... ..m. .I .. ._ .14. .. .u .. ...... . E... 8.: .88. _ $8 88. _ S8; 38. 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X” 42 (dB) 1'» O 1 X" stIHMIIaycr A first layer kt . [ 2cm I ‘ .1 1F 1 I : 4 1 x = 0.6 cmn X2. 015 cm (8 {...---.ALY FIrst Layer .1 —.—Theory .Exp. V Second.Laycr —.—Theory - "" - EXP. Fig. 3.19 Theoretical and experimental values of the dissipated power due to E , kOIE I2 as a function of y along x = 0.5 cm. Frequenc? = 2.45 GHz, 0= 5.934‘U1m, €= 68.48760. Salt concentration = 0.5 normal. 43 as expected. An interesting observation, however, is that the distrib- ution pattern of the dissipated power differ significantly in these two layers. An excellent agreement between the theory and the experiment is also observed in this case. After examining the induced fields inside the regular shaped rectangular bodies to a great extent, the case of irregular bodies is considered next. An I - shaped model with dimensions as shown in fig. 3.20 was constructed with plexiglass material and was illuminated by a 2.45 GHz microwave at normal incidence. The model was filled with 0.5 normal saline solution for carrying out the experiment. Fig. 3.21 indicates the theoretical values of the induced electric field at the central locations of the cells. The cell size was 1 x 1 x 1 cm and the total model was divided into 192 cells, but due to the symmetry only k of the total volume is shown. The amplitude and phase angles of the x - and y - components of the total induced electric field grace the figure whereas the z - component, being very small, is neglected. Fig. 3.22 shows the comparison of the theoretical and the experimental results for the dissipated power due to Ex’ EOIEXIZ, as a function of y along x = 0.5 cm and x = 3.5 cm lines. Patterns of the dissipated power are quite complicated functions of the location but the agreement between the theory and the experiment is excellent. Fig. 3.23 shows the theoretical and experimental results for the dissipated power due to Ey,%0IEyI2, as a function of y along x = 0.5 cm and x = 3.5 cm lines. In the next example, we exposed the same I - shaped biological model filled with 0.5 normal saline solution to a microwave at 2.45 GHz at end - on incidence. The geometry of the problem is as shown in fig. 3.24. In fig. 3.25 because of symmetry, the amplitude and the 44 \ s " "§" .. “x . \\ 192‘ Fig. 3.20 An I - shaped model containing saline solution illuminated by an EM wave at normal incidence. 4S J _ O _ O 04.— 07 O8 0 o 01 8 — o— o o 71.m ,0 2871 018 170 4.H“ 211 A35 8 . 6 .12 03 .43 4 . .2. 3.1 .8 4. _n.. .0 .Q,. R. .R. 1.. v. o. 0. ... o. ."o. o. .0 ... -.0.--.0....m--.0w.. ..mh-.m:.-mm 07 2. . . . 7 8 E. 13.5..(1.1 01 no ,0 .U 0, .n. ,0 ...0 .b . c 0. 0. u... o. no. 0. no. ... .IT1 r|"--"-'-""' """-' """ ' C _ . n. . 01“ QT. . o n. ’ 020.031.“. ..7muo.08",m.,..m . . 8 Q/ 8 4. 7.3 7. . o 77. 74. _ ...... u .7... 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Theoretically induced 8 field in k of the I - shaped model shown in fig. 3.20. €= 68.48780. Frequency = 2.45 GHz, 0= 5.934‘U/m, Salt concentration = 0.5 normal. 3.21 Fig. 46 IX x: 0.5 cm [—— f —.—’I‘hcory 41ch x — 3.5 cm (dB) * i O .. E 4cm 10 1 k-—-IZcrn -'* .4 40* ' H 0 2 ET . z‘E.| -20" J_ 1 1 1 1 1 4 L I -6 .4 -Z O 4 6 'Y -—————a-» ( crn ) (dB) 0“ x = 3.5 crn —.—Theory Exp. -10. 2 %Fx‘ _. o o -20[ v 1 1 . l L 1 1 1 l l . a . Fig. 3.22 Theoretical and experimental values of the dissipated power due to E , 80|E I2, as a function of y along x = 0.5 cm and x = 3.5 gm. Frgquency = 2.45 GHz. 0= 5.934 vim, €= 68.48780. Salt concentration = 0.5 normal. 47 )r ‘1ka 4C") X: 3-4 r‘nL x: 0.5 C111 1 * x=0.5 cm -—O-—Thcory 4cn1 L-'-’ Y Exp. X 4cm 1C EfilL l-r-12crn--Dfi (dB) 1? 4H)’ - M ~30'- . .' . . E? 2 2| yl _40 l 1 l 1 l l l l l -6 -4 -2 o 2 4 6 'Y-——--—-"' (crn) (dB) x = 3.5 cm -10" -..—Theory _ Exp. 0 O - 0 2H)” . . Z O O 9333'] ' 1 1 1 1 J_.__L__._l 1 1 l 1 -30 _4 -Z 0 2 4 6 Y ____.. (cm) Fig. 3.23 Theoretical and experimental values of the dissipated power due to E , l§CIIE I2, as a function of y along x = 0.5 and x = 3.5 cm. Frequency = 2.4; GHz, 0= 5.934 U/m, €= 68.48760. Salt concentra- tion = 0.5 normal. 48 phase angle for the x - and z - components of the total induced elec— tric field for the upper part of the model are shown. In this case, the y - component of the induced electric field was comparatively smaller than the other two components. In fig. 3.26 the comparison of the theoretical and experimental results for the dissipated power due to Ex’ kOlExlz, as a function of 2 along x = 3.5 cm and x = 0.5 cm lines is shown. It is observed that the patterns of the dissipated power as functions of location are entirely different from the case of normal incidence. Nevertheless, an excellent agreement between the theory and experiment does exist. (It is noted that in the end - on incidence case, the z — axis correspond to the y — axis of the normal incidence case.). Fig. 3.27 shows, once again, the close relationship between the theoretical and the experimental values of the dissipated power due to E2, kOIEzIZ, as a function of 2 along x = 3.5 cm and x = 0.5 cm lines. As evidenced by the above mentioned examples, the tensor integral equation method has been completely confirmed by the experiments as far as the field induced in any arbitrarily shaped biological body exposed to electromagnetic wave are concerned with the minor exception at the very edge of the biological body. The discrepancy between the theory and the experiment at the edge of the biological body is essentially due to the inherent error in the probe measurement. This is the point of discussion in the next section before we proceed further to check the accuracy of the tensor integral equation method for the scattered field. 49 \‘\\\\9. x v) 2. X) \\\\\ "1L Fig. 3.24 An I- shaped model containing saline solution illuminated by an EM wave at end-on incidence. SO .Hmauoa n ooHumuucoocoo unm .owmw0.wo um .a\osa 0m0.m n0 .umo m0. Nu zocoavoum .m .me :H 030:0 H0005 coamnm 1 H 050 m0 0 :H 0H0Hmm +000000H HmoHuouomzh mN. m me N ‘|lll Ilul'lulnfilcllllflll. Inllll.|ll|.||o IIIIQJlllloll1|luo|I1 1* N 0N 0.03H00 .3H0 . 00 .H3H0.0H H.03H0_00 03 30.0..0 0 02.0.0 .0N-H.0 0 - 00Mm00. ”WWW-.0 0000030.H00._ ”00%: 0mm... .0NNmm00.03H3Hm000 0N.m.N.HH..0 ...0H - . - _ ...-.- 0 ----0300......m ...-0.2-. ..0. 000.0,. - ..-H. 0.0.30.0 03 .33H-NH0H .0NH..N _ 0N .00HH.03 .NH0 .H00.3 . 0.0.0 .N0-0._00 .30H0.0.00 .0NH- .0 000m... 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N330.- -. --0N30 -.--N.330- .. 0.3030 .- - N330. ..--0NHH..-.--NNOH..-.--N3N-H-. - ---030.-. 30H.00..0N .030..0H ..030 .03 .NN0 .0 H.000 ..0N .33: 00 .30. 00 .NNH0...00 0N.0 0.00 0H0-0.. 0 .330. 0N 3.0. 02: 0: 33H. 33H. . H._N300 03N0. 0.N000_ 30:. 0.3:. 3020 . 0.0NN0. HH00 0N .N0.0..00 .0030 0 .33 .00 030.. 00 .0N. .0 0.-3H0_ 0N-33N0 .30. 03 .33H0..0 0 .N0H0_0N ..300 .00 .030 0N .0N0. ..-0HN0-r-03HH...1330003E-.033N0Nm0.N330- ---0H00---0N.NHH-.-0H3HJ--03NH.-..--0NNH- 0N .0HH0....0H 0:003 .220 ..H .00NH0.3 3.N3H0..0H .32.... 0.0 .000 .0HHH0.0H H.-3N 0 00 .00. .0H .03-00533 002.. 303? 33NH. 3000. .0 30. 3.3.... 33.. 0H.3N00 00.00NH 03:. _ 330.. N330. H000.03N0H00.300H0_:0.HNH.0m03.0HH0% 0.H700.1.03H0..0.00H.0_0N.0N-0. 0.3030. 00.30 .E0: 0003. R00. H.NNo: . oomowow. RS. Eco-.0 HNmo.. HHmo. 0.omNH RS. X‘J 51 )( 0 _ E: 4 c x : §.5 crn * I ' +4 4 CH1 x - 423?} Z PI -10.. C 0' ill? I x = 3.5 crn —.—Theory 1- EXP. . -30 1 l 1 1 1 1 1 1 1 1 1 -6 -4 -Z 0 2 4 6 Z. -—-———-- ( can) ((113) o I O -10 020 - x = 0.5 crn fIEXIZ ... — Theory .40 " Exp. - O .50 1 1 1 1 1 1 1 1 -6 -4 02 0 2 4 6 Z.-—-—--i>- ( crn ) Fig. 3.26 Theoretical and experimental values of the dissipated power due to E , kolE I2 as a function of 2 along x = 3.5 cm and x = 0.5 Em. Fr’e‘q. 2.45 GHz, o= 5.934 U/m, €= 68.487€o. Salt concentration 0.5 normal. ad E: I 4 cnn + x=0.5cm 4 cn1 Z x = 3.5 cnn * (dB) —O—The0ry 4 cm lcm """""- EXP. ! -lO _ H——12 car—H z _ ' %|Ez| . -20 " . -30 1 l l l . l 1 j -6 -2 O 6 ‘Z ——————i- (crn ) = 0.5 crn (dB) _._Theory Exp. a20" -30 r- . 2 $sz 1 I 1 n 40-6 .2 0 Z ———.- ( cm ) 52 Fig. 3.27 Theoretical and experimental values of the dissipated power due to E , kOIE I2 as a function of 2 along x x = 0.5 Em. Frczaq. = 2.45 GHz, o= 5.934 v/m, e= 68.48780. Salt concentration = 0.5 normal. 3.5 cm and 53 3.4 Experimental Error. When a probe is immersed in a finite biological body to measure the induced electric field, the output of the probe becomes location - dependent especially at the edge of the biological body. To show the existance of this factual phenomenon, let us consider the finite geo- metry as shown in fig. 3.28. A finite biological body occupies a region V of space and is characterized by the electrical parameter €<¥), 0(f), and U0. It is illuminated by an incident wave with an electric field E1. A thin wire probe, immersed in V, lies along the contourf} location along "S" probe is designated by the variable with origion s=0 at the probe ter- minals. suis a unit tangent vector to at any point. I0 and V0 are the current and voltage at the probe terminals, to which a load impedence ZL is connected. The incidence electric field Ei(:5 excites an induced elec- tric field ER?) in the body V, and this electric field subsequently ex— cites a current distribution I(s) = ID f(s) in the probe wire where f(s) is a current distribution function with f(0) = 1. The induced probe current [(3) maintains a secondary field Ep in the body. Thus the total electric field inside V in the presence of the probe is E's) = E(r’) + EPG) (3.1) +'+ +- + The function of the probe is to measure E(r) and not E'(r). Indeed this is the case, as can be seen from the following development. The boundary condition on the tangential electric field at the probe surface requires that §.E(§) = 0, except at the slice gap terminals: §.E'(’§) =v 5(3) =IOZ 6(3) (3.2) 54 .uouosvaoo wasao> msomcomoumumn .ouwcfim M GA «noun mnu mo cowumnawwmcoo w~.m .wwm A H u a: 82? c “Conan—o moo—ohm pounce. o 3: H u 3 H 0: .Eb .Ew > macho o .H um >+ IIIIHIWIHI II oogop on in: ‘III Ilium”- ”dugousmmgc ommfio> Gm owflfio> 355cm“ n ANoH u 0> o acouuso Atmofivddcdhuou u H I ..H monocomes. 0mg .. N em 55 where V = I Z , as shown in fig. 3.28. o o L Integrating eqn. (3.2) we have I f(s) a. E'(s) ds = I 2 (f(0) = 1) (3.3) f o L with eqn. (3.1),eqn. (3.3) becomes f f(s) s. E(s) ds + ff(s) s. E (3) ds = I Z (3.4) f { p o L Since the first integral of eqn. (3.4) represents the total driving force for the probe current, we can define an equivalent probe deriving voltage as Veq = {f(s) §. E(s) ds (3.5) It is noted that E(S) is the internal electric field at the probe loc- ation, in the absence of the probe, and is the key quantity to be meas- ured. The second integral of eqn. (3.4) is the integration of Ep(s), which is porportional to lo. We can therefore, define an internal impedance for the probe as .._L. "" zin — — Io {f(s) s. E£§s) ds (3.6) This zin is the input impedence of the probe when it is used as a radia- ting antenna imbedded in a finite biological body. With eqns. (3.5) and (3.6) substituted in eqn. (3.4), we get or 56 I = Ve + Zin ZL (3.7) Eqn. (3.7) leads to an equivalent circuit for the probe, as shown in fig. 3.29. This circuit differs from the conventional equivalent circuit for a receiving antenna in that Z is a strong function of heterogeneity in of the medium because f(s) is a function of electrical parameters at the location of the probe. The probe response is equal to the terminal voltage and can be ex- pressed as + V Z Vo(r) = I Z = 89 L 7111??“ 2L ZL f + = f(s) §. E(s) ds Zin(;)+ZL ’ = $56?) . {f(s) §ds _ ZL + zin(r)+zL for a small probe (3.8) Eqn. (3.8) clearly indicates that the probe response is proportional to the internal electric field, E(f), at the probe location in the absence of the probe. However, it also shows the proportionality constant be- tween Vo(;) and ii?) to be a strong function of probe location for the following reasons. Firstly, Zin(;§ as defined in eqn. (3.6) is a func- tion of location because E%(s) produced by the probe current is dependent on the relative position of the probe in the body and the body geometry, and secondly, the distribution function for the probe current, f(s) is dependent on the electrical parameters (8 (r),0 (r)) at the location of the probe. It is noted that in a homogeneous medium such as in our 57 Zin(r) V6438"? Fig. 3.29 Equivalent circuit for probe in a finite, heterogeneous volume conductor. 58 experimental models,8 and 0 remain constant so thatf(s) will remain constant. However, Zin(?) is still a strong function of the location in a homo- geneous finite body. A simple experiment can indicate that Zin(;) changes most rapidly near the edge of the body. Thus, the proportionality constant between Vo(;) and E(;) may undergo a rapid change near the edge of the biological body leading to an inherent experimental error at this location. Therefore, a location dependent probe calibration factor is needed before an imp- lantable probe can be used to accurately measure the internal field in— duced inside a finite biological body. CHAPTER IV THEORETICAL AND EXPERIMENTAL RESULTS ON SCATTERED FIELD FROM BIOLOGICAL BODIES. In this chapter, the tensor integral equation method is applied to determine the scattered field from finite biological cylinders with arbitrary conductivity and permittivity and metallic cylinders, illumin- ated by a plane electromagnetic wave. The nature of electromagnetic scattering from a biological cylinder is studied in comparison with that from a metallic cylinder. The theoretical results obtained from the tensor integral equation method for the induced currents in the metallic cylinder are compared with the results obtained by King[12]for the cur— rents induced on perfectly conducting cylinders based on Hallen's inte- gral equation. 4.1 Simplification of Tensor Integral Equation. The geometry of our problem is a rectangular cylinder with length 2h and square cross - section with one side of 2a, having conductivity o(;), permittivity C(f), and permeability no. This cylinder is il- luminated by a plane wave with its electric field E1 parallel to the axis of the cylinder as shown in fig. 4.1. Under this illumination, 3 total electric field and therefore, current are induced inside the cylinder. The total induced electric field is given by eqn. (2.22). The resultant current in the cylinder determines the field scattered by the cylinder and a general expression for the scattered electric field is given in eqn. (2.28). Equations (2.22) and (2.28) can further be simplified if the thin cylinder 59 60 -fi-:& I? w.‘ 61?) Y “a"; €(r) '/ Pk) .1 b--1Y ~42. V Fig. 4.1 A finite biological cylinder of arbitrary conductivity and per- mittivity, half-length h and of square cross-section illuminated by an incident EM wave. 3?? I'E ta SU 9‘] “he 61 approximations are made. The case of thin cylinders having arbitrary conductivity and permittivity is considered next. If the thickness 2 a of the cylinder is much smaller than the free space wavelength A0, it is therefore, reasonable to assume that only the x - component of the induced electric field is significant in- side the cylinder of length 2 h. In other words, it is assumed that By = E2 = 0, where Ey and E2 are the y - and z - components of the total induced electric field. With this assumption, eqn. (2.22) can be reduced to a scaler integral equation as given below. TS;2 + _ + ++ V: i —> [l.+- ijeo ] Ex(r) PV li(r) Efo) Gxx(gr)dv Ex(r) (4.1) where Gxx(r,;') is a component of tensor Green's function+5(f,;'). If the cylinder is partitioned into N subvolumes, each with volume Avm along the x - axis, eqn. (4.1) can be reduced to a set of N simul- taneous equations by matching the field at the center point of each subvolume as detailed in the previous chapters. These N simultaneous equations can be written in matrix form as 11 12 1N1 , . 1 , 21 22 2N i Gxx Gxx ... Gxx Ex(x2) Ex(x2) (4.2) o $- - ' N1 N2 ‘NN ' 1 ' chx Gxx ' ° ' Gxxd Ifixo‘N) LEx (KN). where xm denotes the center point of the mth volume. 62 The diagonal elements of the [Gxlematrix are expressed as . ‘ 'dx ) mm _ Zqu T(x ) _. . _ _ __ m Gxx — - o m [exP( Jkoam)(l+Jkoam) lJ [1+ 3:———-s] (4.3) 2 Jweo 3k 0 I 3AV -- here a = m 3 w In Mr (4.4) The off diagonal elements of the [Gxx] matrix are given by Gmn = -ijoko eXp(-j¢mn) (1+ a xx 2w «3 j mn) where «mn = ko lxm - xn I (4'6) Ex(xm) is the x - component of the induced electric field at the center of the mth subvolume and E:(xm) is the x - component of the incident electric field at the same point. Since the incident electric field E: is a known quantity, therefore, Ex at any point along the cylinder can be determined from eqn. (4.2) by any standard technique. 4.2 Induced Current Inside Cylinders. The general expression for the equivalent free space current density (')1 1 b eq r s g ven y Lvlr Ld (MG) «(3%) - [on + w (e6?) '60)] M) (4.7) where if?) is the total induced electric field inside the biological body at location E: In the case of thin cylinders the only component of total induced electric field it?) is Ex(x). Therefore, the total equivalent induced current density inside the cylinder is Ix(x) = A [0(x) + jw(8(x) ’80)] Ex(x) (4.8) where A is the cross - sectional area of the cylinder. Ix(x) is the current which produces the scattered field outside the cylinder. 63 Ix(x) consists of a conduction current, AOEx, and a polarization cur- rent Au£:-gb) Ex' In a metallic cylinder, the conduction current pre- dominates while polarization current is a dominating factor in a low- loss dielectric cylinder. For a biologicalcylinder the ratio of the conduction current to the polarization current is dependent upon the biological material and the frequency of the incident wave. In this chapter, theoretical results on the induced currents in biological and metallic cylinders are presented. To check the accuracy of the tensor integral equation method for the thin cylinders, the results are compared with King's results which are obtained from the Hallen's integral equation. King's result on the total current in a perfectly conducting, circular cylinder of radius a and half length h induced by incident electric field 31, is given as 1 3” E Ix(x) = 36%6——- [:WdD(cosBox - cos 80h) -deuI(cos%Box - coskBoh)] (4.9) Q = wdD[wduR COS Boh - wu(h)] + j wD(h)wduI (4.10) h ‘i‘dD= (1 - cosliBoh)“l 5 (cos 15 Box' - cos 3580b) [K(0,x') - K(h,x')]dx' -h (4.11) wduI = (l - coslsBohf-l J:(cosBox' - cosBoh)[KI(0,x') - KI(h,x')]dx' (4.12) wduR = (l - cosBoh)-1 J¢l(cosBox' - cosBoh)[RR(O,x') - KR(h,x'i]dx' 'h ‘ (4.13) Wu(h) = 1:1(cosBox' - COSBoh) K(h,x')dx' (4.14) WD(h) = J¢1(coskBox' - cos%80h)K(h,x')dx' (4.15) -h ‘ K(x,x') =—%-e—jBoR with R =IJéx - x')2 + a2 (4.16) 64 : l KR(x,x ) R cosBoR (4.17) 1 - R sinBoR (4.18) KI(x,x') In fig. (4.2),the distributions of total current induced by a unit incident electric field in metallic cylinders of square cross-section are calculated based on the tensor integral equation (T.I.E.) method. These results are then compared with that in perfectly conducting cir- cular cylinders of corresponding dimensions based on eqn. (4.9). The two metallic cylinders considered for the calculations based on T.I.E. have the dimensions of 2 a = 1.6 mm, h = 0.8 cm and h = 1.28 cm. Relative dielectric constant is assumed to be unity whereas the conductivity o= 1.57 x 107 mho/m. The incident electric field is polarized along the x — axis of the cylinder and has the intensity of 1 v/m at 9.45 GHz. The numerical results on the total induced current are indicated by the solid circles. To apply King's result, i.e. eqn. (4.9), in calculating the induced current, the two metallic cylinders are slightly modified. The cylinders are now assumed to have circular cross - sections with a diameter of 2a = 1.6 mm and of the same lengths. The conductivity of the cylinders is assumed to be infinity. The intensity, polarization and the frequency of the incident wave are assumed to be same as in the previous case. The results for the total induced currents in these two cylinders are shown by solid lines in fig. 4.2. In general a good agreement is obtained between the results based on tensor integral equation method and King's formula. The main disagreement however, between these two methods is the currents at the ends of the cylinder. Because of finite cross - sectional area of the cylinder, the tensor integral equation method yields a finite current at the cylinder ends while King's formula always gives zero current at the ends of the cylinder. 65 h = 0.8 cm (.ZSZXJ UlA) 2a 20.16 cm 140%- f = 9.45 GHZ O = 1.57 x IOU/m e _ r’ 1.0 O 10(* 0 2'5 0) h [-4 8 ... 6° ' -o—T.I.E. ' S .9 K. 1ng . 20‘ l I l 0 .2 .4 .6 .8 (cm) location along the cylinder (AA) -.— ToIoEo ~ King h = 1.28 cm .403 80 _ ( x0) 3 ‘ o g 0 :3 40- . o '53 +0.» 0 0 1 1 1 1 l 1. 0 .2 .4 .6 .8 1.0 1.2 location along the cylinder (cm) Fig. 4.2 Distribution of currents (amplitude) induced in metallic cylinders by an electric field of l v/m at 9.45 GHz. Cylinder half-length: h: 0.8 cm and 1.28 cm, respectively, 66 Fig. 4.3 shows two more results being compared for the longer metal— lic cylinders with h = 1.6 cm and 2.4 cm respectively. At the frequency of the indicent wave of 9.45 GHz, these half lengths of the two cylinders correspond to 0.504 40 and 0'756Ao respectively, whereko is the free space wave length. Other dimensions of the cylinders are the same as in the previous example and so is true for the incident field. As shown in fig. 4.3, a good agreement between these two sets of results is again obtained. This agreement tends to confirm the accuracy of the present tensor integral equation method as applied to thin cylinders. In fact, this agreement was not expected in the outset, because in the employment of tensor integral equation method, the induced current was implicitely assumed to be distributed uniformly over the cross - section of the cylinder. This assumption is a poor approximation of the actual situation where the induced current should concentrate on the surface of the cylinder at the frequency of 9.45 GHz for the metallic cylinders. This surprisingly good agreement, even under a very poor approximation would enhance our confidence in the accuracy of the tensor integral equation method when it is employed to calculate the induced current in cylinders of finite conductivities where the assumption of a uniform current distribution over the cross - section of the cylinder is, of course, justified. While calculating numerically the total induced current on the square metallic cylinders using tensor integral equation method, very high but finite conductivity was used for the calculations, while the King's result is based on perfectly conducting cylinder with infinite conductivity. Common question which would be asked in this regard is - - How good is this approximation of considering a material with very 67 .>Hm>wuomommu Bo c.~ was So c.~ n a "Suwamalmamn umvcaaxo .nmu m¢.m um a\> H mo waowm ofiuuomao am an wumvcfiaho ofiHHmuma ca voosvaw onouacmmav muamuuao mo cowusoauumwn m.q .wfim AEUV Al anaemic ofi mdofim coflmuofi o¢.~ 3d No; mo.“ *4... cm; or. N». aw. em. 00 I . m... . . . . .4 D mddvfil O O . ow m OMOHOH|.I . A J o o o .. m C O o . cm a 202.; animus . O O - 2a A 50 V ‘1 noccmlo 05 macaw dofldoou o. a v4 NJ 0. H m. c. v. N. so _ a a q - u a . l o w manna rem; mag C no ‘- .m.H.Hl.ol A038; .5 a; "a . AS: 68 high but finite conductivity as having infinite conductivity? Generally, in the study of interaction of an electromagnetic field with metallic body, it is a part of common practice to assume the metallic body to be perfectly conducting. Since the conductivity is a variable parameter used in the tensor integral equation method, therefore, we are in a position to help re— solve this controversy. The question is, how high should the conductivity of the body be before the body can be assumed to be a perfect conductor? To answer this question, the maximum amplitudes of the total induced currents in three square cylinders with dimensions of 2a = 1.6 mm and h = 0.8 cm, 1.6 cm and 2.4 cm have been calculated as functions of cy- linder conductivity as shown in fig. 4.4. It is seen that total induced current in the cylinder increases roughly linearly as the conductivity of the cylinder increases from a small value up to 103 mho/m. However, when the conductivity of the cylinder reaches beyond 103 mho/m the total induced current in the cylinder stays almost constant, independent of the increase in conductivity. This implies that when the cylinder con- ductivity is higher than 103 mho/m, the induced electric field inside the cylinder decreases linearly as the conductivity is increased. One more important information which can be obtained from this result is that when a conducting body has the conductivity of 103 mho/m or higher, it can be approximated as a perfectly conducting body since the total induced current in such a conducting body is the same as that in a perfectly conducting body of the same dimensions. Before we pass on to the scattered field observations, it is quite important here to determine the distribution of the induced currents inside low conducting cylinders. Fig. 4.5 shows the distribution of the 69 (pA) h=0.8 cm (.25210) 100 ’ ' h=2.4 cm (.7563?) 80 P ‘ h= 1.6 cm (.504AO) 60 r b )( 40 ~ E1 f% IImaxl - *i 1 H 2 h ""."Z 20 ‘ freq = 9.45 GHz HV cross-section: 0.16 cm sq. -H No.16 cm 0 l l l l 1 10 102 103 104 105 106 107 conduc tivity —y.. (mho/ m ) Fig. 4.4 Maximum induced currents in different cylinders of half-lengths: h = 0.8 cm, h = 1.6 cm, and h = 2.4 cm respectively as a function of cylinder conductivity. 70 total induced currents in four saltwater cylinders. The dimensions, i.e. thickness and normalized lengths are as given in the figure. The salt concentration of these cylinders is 1 normal and the corresponding values of the relative permittivity and conductivity at 9.45 GHz are 50.0 and 20.37 mho/m respectively. The incident electric field at 9.45 GHz has the intensity of l v/m and is in the direction parallel to the axis of the cylinder. The selections of the dimensions of the cylinder and the frequency of the incident electric field were dictated by the experimental models and set - up. The distribution of the induced cur- rent is roughly cosinusoidal for the shorter cylinders and more compli- cated shifted cosinusoidal for the longer cylinders. It is noted that since the cylinders have a finite cross - sectionalqarea, the induced current in the cylinders do not go to zero at the ends. This point is different from those results obtained from Hallen's integral equation where the currents at the end are forced to vanish. Fig. 4.6 depicts the distribution of the total induced currents in the same four salt cylinders as in the above example, but with higher salt concentration of 5 normal. The increase in salt concentration causes significant changes in permittivity and conductivity. The relative permittivity and conductivity in this case at 9.45 GHz are 23 and 31.67 mho/m respectively. These changes in the permittivity and conductivity lead to some changes in the amplitude and the distribution of the total induced currents in the cylinders. These changes are particularly significant in longer cylinders. It is mentioned in passing that the tensor integral equation method can also be used to calculate the induced current in an inhomogeneous cylinder. (11A) 20 III 0 0 (11A) 60‘ 40 III 20 h (AA). III h = .113 x0 .227 )0 wA) . 20 III 71 Salt Concentration =1N 6,: 50 r 0': 20. 37 mho/m 2a 21.6mm i Ezlv/m freq = 9.45 GHz h .737 )b Fig. 4.5 Total induced current along the axis of the salt water cylinder for h/A = 0.113, 0.227, 0.510 and 0.737. The concentration of salt golution is 1 normal at 9.45 GHz. 72 Salt concentration 2 5 N h = .113)» WA) 0 er 2 50 20b III 0': 31.67 mho/m 0. 2a = 1.6 nun) O .2 X/XO El: 1 v/m freq 2 9.45 GHZ (11A) 60" h: .227 7.0 40- III 20- 0o I .3 x/AO .510).O 11:.73'1).o Fig. 4.6 Total induced current along the axis of the salt water cylinder for h/A = 0.113, 0.227, 0.510 and 0.737. The concentration of salt solgtion is 5 normal at 9.45 GHz. 73 4.3 Scattered Fields. After the total induced current in the cylinder is determined, this current is used to calculate the field scattered by the cylinder in space. Experiments have been conducted to measure the scattered field from var- ious saltwater and matallic cylinders. These experimental results are then compared with the numerical results obtained by solving the tensor integral equation for the scattered field. Theoretically, the scattered field at any point :0 outside the bio— logical body is given by eqn. (2.27) in general and by eqn. (2.28) in different components form. Again, applying the thin cylinder approximations as mentioned earlier, only the x - component of the induced current is significant. Under these assumptions, the scattered field ES(;;) can be simplified to +3 + -*' + +' + +' ' E (r0) = {f(r ) Ex(r ) Gxx (ro,r ) dv or +3 + n +1 I E (to) = nil-r (in) ExG'n)I (zxx o,r ) dv (4.19) v Eqn. (4.19) being a special case of eqn. (2.28), therefore, this equation can be solved numerically by the same techniques applicable for eqn. (2.28). Experiments have been conducted to measure the scattered field from finite cylinders of various saline solutions of different concentrations and metallic cylinders. Fig. 4.7 shows the schematic diagram of the experimental set up. The experiment was conducted at 9.45 GHz with l KHz modulation. The signal from a Klystron source was fed into the first terminal of a four terminal magic tee after passing through an isolator and an attenuator. The second terminal of the magic tee was connected to a horn antenna 74 .mumuoamumm zumuufinpm mo mnmvcfiamo Eoum wcfiumuumum mnu wcHHSmmmE How an own Hauamafluoaxm n.q .me poem." ocoO cohmtfim Louflofl poemscmwfim COMuNCwEhQu LQCSu E - 2 “L \)o \ I I Au..— AI... ‘ A mo”. 2me nouoouofl .2 was» dado”. dd Geo: n638d£0 303033 >} 75 through a tuner. The third terminal of the magic tee was connected to a termination via a tuner. The fourth terminal of the magic tee was con- nected to a detector and tflunito a SWR meter. If the system is well tuned, a half of the signal is radiated into the anechoic chamber through the horn antenna and the other half of the signal ends up in the termination. In the absence of the scattering cylinder, no radiation signal is reflect- ed back into the horn antenna and the system can be tuned in such a way that nearly zero signal is channeled into the fourth terminal of the magic tee and thus, no reading or only a noise level is recorded by the SWR meter. When the cylinder is introduced, the scattered field from the cylinder enters into the horn antenna and this scattered field can go through the fourth terminal of the magic tee and be detected by the SWR meter. Relative magnitudes of the scattered fields from cylinders of different dimensions can be directly measured by the readings of the SWR meter. For the absolute magnitude of the scattered field from a cylinder, the scattered field can be compared with that of a reference cylinder such as metallic cylinder. In our experiment, the spacing between the cylinder and the horn antenna was kept to be 15 centimeters. Fig. 4.8 shows the theoretical and experimental results on the backscattered field from a saltwater cylinder of 1 normal concentration at 9.45 GHz. The experimental model of the cylinder has a circular cross - section with a diameter of 1.8 mm and variable length from 2 cm to 7 cm. The electrical properties of the cylinder at 9.45 GHz for 1 normal concentration are, e= 50.6:0 and cr= 20.37 mho/m. The observation point of the backscattered field is 15 cm from the cylinder, because the spacing between the cylinder and the horn antenna was kept at 15 cm during the experiment. For the theoretical model, a square cylinder with 76 mnu 80pm Eu mH me uaaoa :owum>pmmno one .Nmu mc.m um aofiumuunwoaoo Hmauoa H nHHho umumsuHmm m aoum wawumuumomuxomn How uamaHumaxm paw muomnu mo comfiumaaou m.q .mHm oa\:~ m.N o.~ m.H o.H m. o q . q q 1 u q q q T OH _2M_ Ho. H _mm_ ”mucoumumn mm o . 1 NH .Ygflfimm "a w. LN 2m .mxm I . HuH X. . s 3 502? lol . m. L m u. HmW 1 oHnm 88 on ”MN 1 83:8 hm.om ub wH ..H 1 7: cm .1 w are 34. u we: . EB 77 a thickness of 1.8 mm and of corresponding lengths were adopted. The backscattered field is plotted as a function of cylinder length in decibels. The zero decibel reference for [Eslis chosen to be 0.01 {Ei|. Theoretical results are shown by solid circles joined by a solid line. and the experimental results are given by solid triangles. In this fig- ure a good agreement between theory and experiment is observed. The important finding of these results are: 1. The scattered field increases nearly monotonically for low loss cylinders as the cylinder length is increased. 2. No distinctive resonance peak at resonance lengths (2h = (n+1)§_) are observed. 2 From these results it appears that no strong longitudinal electro— magnetic resonance can be excited in a low loss slender biological body. Althoughtu)distinctive resonance is observed in the scattered field, yet the computation of the total absorbed power in the cylinder does show that there exists a weak maxima at resonance length. More will be said in this regard when we will try to find out the induced fields and total power induced inside human models as functions of frequency and polari- zation of the incident electromagnetic wave. In fig. 4.9, the theoretical and experimental results on the back- scattered field from a salt-water cylinder with 5 normal salt concentration at 9.45 GHz are shown. The increase in the salt concentration causes changes in the electric properties of the cylinder. The relative permit- tivity and conductivity in this case are 23 and 31.67 mho/m respectively. Except for these changes, all other parameters of the cylinder are the same as in the previous example. Similar results are obtained in this case also. A good agreement between the theory and experiment is obtained, 78 .nwccHHmo one aoum so mH mmB uaHoa coaum>uomno may .Nmu m¢.m um GOHumuuamoaoo Hmauoa m mo umeeHHzo HoumauHmm m Bonn wawuouumomaxomn pow uaoafiuoaxm can mucosa mo comwummaoo m.q .me oi: N . . . .H m. o mHN‘ d OHN . mfid q o: 1 q . OH rm: Ho. n WM_ "ouconowmu Me 0 l . .NH Ifi.I&Lg1TI MN 1 q E m. a N _ HmH s .1. . .3 EXHI m r M 43023.1? 1 m H4. Am in: such w.H u MN 1 .wH E\0HHE hoém Mb u use 3.0 n 3: 1 EB 79 thereby dictating that backscattered field does increase monotonically with the increase in length of the cylinder and no distinctive resonances are obtained. After conducting the experiments with low loss cylinders yielding the monotonic increase in the scattered field with increasing length and the missing of the resonance peaks at the resonance lengths, it becomes necessary to conduct few more experiments to measure the backscattered field from high loss cylinders. The purposes of these experiments are - (l) to check the accuracy of the tensor integral equation method from the viewpoint of scattered field, (2) to see the existance of maxima at resonance length for the metallic cylinders and (3) to provide a com- parison with the backscattering from the biological cylinders. A re— sult for such an experiment is shown in fig. 4.10. In this case the brass cylinders with various lengths of 1.6 mm diameter were used. The electrical parameters for these cylinders are as given in the figure. The backscattered field was measured at a distance of 15 cm from the cylinder. The theoretical results are plotted in a solid line with circles and experimental results are in triangles. The agreement between the theory and the experiment is quite remarkable in view of the fact that the theoretical results are based on rather poor approximation of uniform distribuxion of the induced current as stated earlier. In this figure we do observe the well known phenomenon that a metallic cylinder exhibits strong resonances at the resonant lengths of the cylinder. This phenomenon was found missing in the saltwater cylinders. So far the results, as shown in figs. 4.8 through 4.10, depict the relative amplitude of the backscattered field as a functioncfifcylinder length either for the saltwater or for the metallic cylinder. Therefore, 80 .hmeeHHmo may aouw so mH was ucHoo aowumtomno 09H. .55 mq.o um umwGHHau manna m aoum wefiuouumomcxomn pom unmafipooxo use muoonu mo cowHumaaoo oH.¢ .mHm 0.2: N m.N o.N m.H o.H m6 - o 1 H a . J‘ 1 a q d 4 H 4 .mme ldl 1 ‘ ‘ 43023. ll. . ..NH j‘lmN +-—;:=,—a-1 IE neosxoeg a r . 1 . .3 u. m _HM_ Ho 1 mm_ .oodououou mp c aw H6: d 55 o.H "mm 0 Nb 1m.— 4 < 835: 50H x mm H o u . 4 w l 4 are $4. ... v9: 33 _L 81 it becomes desireable to provide some information on the absolute mag- nitude of the backscattered field from a biological cylinder. For this reason the backscattering from a saltwater cylinder and brass cylinder of the same length (with slightly different diameters) were measured under the same experimental conditions and the results were then com— pared. These results are shown in fig. 4.11. The solid circles and the solid line indicate the experimental and theoretical results for the 1.8 mm diameter saltwater cylinder with 1 normal concentration. On the other hand, the solid squares and the dotted line show the experimental and theoretical results for the brass cylinder of 1.6 mm diameter. A good agreement between the theory and experiment is obtained in either case. The most interesting observation from the fig. 4.11 however, is that a metallic cylinder may scatter more field than a biological cylind- er at the resonance lengths, but at off resonance lengths a biological cylinder may scatter more field than a metallic cylinder. This phen- omenon is not obvious from the physical intuition. As evidenced by the results discussed in this and the previous chapters, the tensor integral equation method has been confirmed com- pletely by experiments with a minor exception at the very edge of the biological body for the induced field. The discrepancy between theory and experiment at the edge of the biological body was essentially due to an inherent error associated with the probe measurements as discussed in section 3.4 of chapter 3. Therefore, we are now in a position to justify the results obtained numerically from the tensor integral equa- tion method for those complicated geometries for which experimental data can not be easily obtained. One of these experimentally unavailable configurations is the human body. Therefore, in the next chapter, the 82 .uvaHHmo some aoum Eu mH mm3 ucHOQ cowum>ummno any .Nmu mq.m um aOHumuucmuooo Hmsuo: H mo umvcHHmo umumzuHMm m use pochHku mmmun m Scum wcwumuumom Hump m>Humeu you unmaHumoxm can huomnu mo aomHummaou HH.q .th 0A E N mom CON mod OOH moo o T A q A q q 1 _ H OH I. . L _ M_Ho. 1_ NH .ooconouou mo 0 I . 1 . 1111!: . .m‘. m4: Iv .Iln' I s LNH / H I H I / .H 1 m. a / H x. [I s 4 I! .mm , WsH 1¢H m 5N T I m. H1. 1 J. 88 o; umm m g .3931; mmdun .udoEHuonHXMIII o S 1 H nooaHHtHo manna ..HuooHHHu .111 SE w.H H mm noanH>o JwH oGHHMm Z H .ucoEHuoenmlOl GoflsHOm oGHHmm 2 H ..Huooah. . £5 34. new: 53 83 tensor integral equation method is applied-—(1) to quantify the induced electric field and absorbed power density inside an adult torso, and (2) the localized heating capabilities of electromagnetic wave. CHAPTER V APPLICATIONS OF TENSOR INTEGRAL EQUATION METHOD FOR INDUCED FIELDS INSIDE HUMAN TORSO AND LOCAL HEATING The salient features of chapter 3 and chapter 4 were to develop some confidence in the tensor integral equation method as discussed in chapter 2. Although the biological models considered for theoretical and exper- imental verifications were not as complex as many biological bodies be, yet the results of the preceding chapters have manifested the validity of the tensor integral equation method. This cogent evidence perpetuates an assurance in the certainty of the results for the electromagnetic fields induced inside and scattered by very complex shaped biological systems. Although the list of applications of the tensor integral equation method can be of infinite extent, yet this chapter, by and large, deals with the induced fields inside human torso and localized heating of a tissue in a biological system. 5.1 Induced Fields Inside Human Torso. After the accuracy of the tensor integral equation method is con- firmed, this method was applied to quantify the induced electric field and absorbed power density inside an adult torso with a height of 1.7 meter and of different shapes. Incident electromagnetic fields of var- ious frequencies ranging from 10 - 500 MHz have been considered. Ex- tensive results have been summarized in a reportllB] . For brevity, only few examples are given in this section. 84 induc along elect inci ins 85 Fig. 5.1 shows the x - component of the internal electric field induced inside a human torso of height 1.7 m with 70 cm arms resting along the body, by an electromagnetic wave at 80 MHz with an incident electric field of 1 v/m polarized in the x - direction and at normal incidence. The corresponding values of conductivity and permittivity are given in the figure. These values are obtained from the tables in [14] for high water contents. The strongest electric field induced inside the torso is about 0.426 times the incident electric field and is located at the hatched area as shown in fig. 5.1. In the numerical cal- culations, the two layered torso is divided into 124 subvolumes with each subvolume being 10'X10'x10 cm in dimensions and the field intensity was calculated at the centers of the cells. Due to the symmetry, only one half of the torso is shown. Even by using the symmetry conditions, the size of the matrix was so big that with the existing techniques it was difficult to handle it at one time. To overcome this limitation, even and odd symmetry along the z - axis was employed. That is the incident wave was decomposed into its real and imaginary parts and the program was modified to run using the real and imaginary parts as the incident fields intensities. Each time the results were stored on the magnetic disk and later on these results were combined in such a way so as to yield the induced fields in the first and second layer respectively. The accuracy and the validity of using the even and odd symmetry was checked by test samples with easy to handle matrix size. This technique was used for the frequencies above 50 MHz, whereas for the frequencies lower than or equal to 50 MHz, the incident electromagnetic field was assumed to be 1 v/m everywhere in space and only kth of the human body was considered due to the symmetry in the z - direction. This assumption 86 freq = 30 MHz 559,4," 6 O”: 0.84 '07!" 30:3,1‘ I I € =- 80.0 €0 P.4 7 I 1’, I '1 4811.15 1: 42.1 E'= I V/m I1”""I":':--:TI/ . I Izoztzz.zi9o.51,1 -_—:.----I--—_I 0 : IO cm L242 335-25121 1" - l 1 b -;g cm 1267;254:5132 [,1 c = cm I—---.—-- ,---1 I d =I70 cm L275 {32.01121 / I---"-'1-'-" dL‘E‘i’EI'4'mPE: "3 lzso V. 48.0 I? -—-- o | Ito-H) 237 L--H’I I I I221 xi I.-- Ex(mvlm) 12.9%.,» '178 A 1121 / *1 y In". H i:69.8:8.87 lst Layer Fig. 5.1 The x - component of the induced electric field. 307 x I183 ,1 , I - r"'1 T [250 118. 1:28. 8 I""I""'"" 1326'34. 661. 5 L- --r_-_1r___. I382'143. 1 '82 .8, W “““ * 26/37.3I81.5 It“ 4.--..4—H... I zz.z§56.8 . 1---...” "" L388 /’ 30.6 I366 f/ 'r... — .1 '339 1 --1' r--‘ |269 .‘ p--— 226 / '175 / I97.4§11. 2nd Layer EM wave: vertical polarization, 80 MHz. Incident 87 ' I15 1 o ‘ ' o ,’ freq = 80 MHz :tffx b r----' . 00.2 1 6.: 0.84 U/m I-8-.-5-4-I(’I ‘ I-----‘I/ I I 6' =80.0 60 19.77, L, 110.1 , - I"' : I" : : ' '33-4:70-4 45-5 34.41728' 8.6 ,1 E = I V/m I‘""T""I"'""/ I ___1____:':1-__.w , 1 £24.; 3:48 .4I3o. 3 ,1 L25’5I50'5332'3/I ...... 1'____.V . _—-r———r--— I o ,0 cm I15.8131.5_JI20.6,1 !17.1§33.4:21.7 (,1 = '----:--- .---1' I----.----1---- 1 c b =30 cm 1'6 85:12-629-24 ,1 {7.93:13. £18.46 ,1 C :70 cm r-“r-"+""1' r---:'---. n" d -170 cm p.9z:11.5:..71',1 [5.11L10.o_§4.so',1 - ..--I L’""'"""' I-_--1 ....... d. I17. 6:3703: 18. 5 ’13 I1501'3408§1905-fl/i . 1 r" [—1 '6072 ’A .89 / \( l5.65 I, 7.85 —.—.——17 “a O r--.” L.98 ll l6047 /’ ......” [.--—V I Ii’:°.°./ 6:1/ I I 1: . Eff-7311” y (mv/ m) 7:63", '7.70 ,4 I8.78 ,‘ ,x I""' I' E1 I8.44 x 19.75 z r»- .1-- 110.2 [12.1 *i Y I’""""f"'_'| 1"" I iison I50.8 I35.o:57.4 W lst Layer 2nd Layer Fig. 5.2 The y - component of induced electric field. Incidence EM wave: vertical polarization, 80 MHz. 88 I .7. freq = 80 MHz L233." 6 I 0": 0.84 '07!" “117:1," & I 6 =80.0 60 116.4, I. . r‘" 1' , . , 5‘: 1 vlm p.518. .88110. .3/ I4.6'L14.65£4.27/1 -..-T ------ -- I----1-“~ I8.55I5.46I6.44 {3.776.318.3115 1 a - IO cm I‘D-133374 69 A I3.11E1.27' 1 .69/ 1. '36 rm?" 1-"1 c C ‘70 :3: I§°63:'970-§§°86(" 12.381138 12°44 .4 = ---1--- ---- r----:----,---' I d =I70 cm E.O3I1.77I1.45/ I1.57LZ.61i4.0o/J 1 "-1 ""1”" 1"“: "-1—-" d {136314. 88:1.86 ,‘3 £1.33 4.92:5.05 ,1 "I" """ "" """"" l 1 . 7 '5049J}/ 4034/ \( '1027 [I 11.5 ___ I‘d-90 5"" '7029 1‘ !2.94 ,’ IL--.” r,___r l 19:52.." 423/ I11.6 . E (mv/m) r_-_”/ 2 '13.7 ,4 ,x I'"" F 115.8 ,1 z I"’" 117.4 .. y 1---. H 1:19.2§14.o lst Layer Fig. 5.3 The 2 - component of the induced electric field. Incidence EM wave: vertical polarization, 80 MHz. 89 T" '1 ‘ freq : 80 MHZ [133/ b }2_°.6.-r’ l i 1 6’: 0.84 U/m ffg/ ‘ £7.51, I 0 € :1 80.0 6'0 14,9 , 24,1 x .1 I . r'" 1 ." 1 1 5': 1 Wm 19.70:2.21: 1. .66/ !26.7|2.38i1.35 ,1 F"‘"I"'1"‘ "' “'"""““'“ {17.451 2.013. 84 ,1 '4.9:l.58EZ.0%/‘ ______ _:__-_V | .. _..r_.__'..__ 1 l 2408:0702. 6.36 4 ! ' | ’1 o = 10 cm L--.:_--_§-__.x .f’lziilii'é-Pi, C l b =30 cm 150.1:.349:7.37 ,4 :72 81.899:3.4 / c :70 cm r---:----:-—--'/////1-4/—--{---- d =17O cm 31.797116. .191; 6. A(”23533012. 182/1 I ---' ---! ------ d 2265:. 677:3. 40 1A3 !71 0 0725:1152 1” l r' 1 ! Fl 1 l26.3 ,1 1( [63.4 ,/ .475 V ____, lea->90 l "4 I23.7 ,1 56. 4 ,4 | '1---- |ZO.6’/ 'fs. .4 /’ ...2 3 --- !17.1/ P (mw’m ’ 39.7 x [...--47 r———d/ '13-4 1 I30 5 A x l'"" "" 19.71 ,1 21 4 ,1 ? z r——— ’ --.-.1' '6031 ’1‘ '1300 «D, y l‘“‘+—" 1"“. H 1:2.58E1.20 !4-53:1148 lst Layer 2nd Layer Fig. 5.4 Absorbed power density. Incident EM wave: vertical polari- zation, 80 MHz. freq: 80 6': 0.84U/m E =' 30 60 fizz] v/m Cl : 1C) b :30 c :70 cm d .1170 cm "’ Z " 13” iii ‘X Fig. 5.5 The x - component of induced electric field. 1 . 9O f—‘Tm {11.41'J !17. 7 ‘ b 1.---.11’ & l2.2. , 1' f'": f I 122. 0'14. 4:16. 8 .......... U d {15.6 15, 57: 33-3. / .1721, 28.5/ had) I17.7 ,‘ 1.. '17.3 ,‘ IST IAYFR 123. 25 10.5 '1810' l """"" :-'—" 1,. ......... .1! E12. 3:12.810: I '16. 4'8. 85112. 7 .v ' J E43 15.971243”, O‘K-Q-Dl Ex (mv /m) I I I E_11._3.1 ! 70 g /A 1—--——1 !Z I ‘1’ r"“. 1 I I .2 2119 _4_:_1_8..2. :160719067:16o I__,,-:__--L..-- ‘15. 3'7. 30 26 4 l- —————— J—g-4 I | I 18-. .36 3 '34 L9. : '7 117.5 ,’ 8.9 !4.90§2.4 2ND IAYVR Horizontal polarization, 80 MHz. Incident EM wave : 91 152 1—1’ ;‘ freq = so MHz 1.7.1.1114 b 17,-.125/ 1 . 6‘: 0. 84 U/m [1:25 1 15.31%, . I 6 '1 8° 60 5.281 ,1’ I110 L—T"7 . r..-- ' I r‘——1 T. 1 . 1 E = I W I21 27:? _4 3913/ 1329:3358? 1‘ I I 1 I39. 9.36. 0126.1 ,1 147. 0140. 7:28. / . “-f'rniu-1' 1" “1'""1'"" ’ a 3 10 cm !52.4: 45. 3.3013/ I531149 z :32 0’,’ b :30 cm I ' 4 -70 Cm P2:§"§91é§- L3_z:§/’ d 1:170 cm 159.0319 9132 0,1 --------- r I dI54. 7147. 8314,13 L——--1F -———4' 1 1 I 1 1.91.2.721' 11 0 /O ‘( 1 Isa->1)0 .6.451 [——fl 1.7-9.131" —>12Z ‘ k Ei '8.2§1/ 0.811.1/ Y 1 1 ,~ FLJKL/4 12 (nnv/rn) QLQ8_1I +1 1 1 V 1 1 H FZJLB—JVI E52541, 1 ; I .X }.8.:_—.L’_—1 tic-8.4 1:37.83293 {36.81300 lsr [AYFR 2N1) [AYP‘R Fig. 5.6 The y — component of induced electric field. Incident EM wave: Horizontal polarization, 80 MHz. 1req: 811 0:0.11 5:] 0:10 5:30 1170 c1117 / \"“ freq: 80 MHz 1 = 0.8-1 U/m E: = 80 6: O Ei: I v/m CI : IC) Cf" t) :J3C’ CT" :70 cm d =17O cm d 1 92 -..-...u—n—n—y .82313.06:6.91 ...... _-_..'---q -_ —.—-- .7643.15 W. 00 I L99: 5 '14)} ’ l ,1 244.1 6.55 " had) dléér’ l1.74 ,1 L--4' 189/ r..- J ISFLAYFR Fig. 5.7 The 2 - component of induced electric field. y lI----| H 152425971 lst Layer H-O-DI --J--_-P-__ I I I 7.57I9.72:11.7’ F"‘F—”r"" I I m513.5:3.4351.77 VI.— I 510. 5'22. 5523. 5, | 2nd Layer Fig. 5.11 The 2 - component of the induced electric field. EM wave: vertical polarization, 200 MHz. 98 ' 52 86 2.0 A . I; freq : 200 MHZ 5..-.8./ 5.----. l . b 55 93 1 a“: 1.28 ulm 56_._1_35, 5 ;_.'.-../ 5 =' 56.5 60 510.7 , 57.34 , «5— , 5"" 5 5"": T 5'- 1 v/m 511 .452.95: 1. 50 ,4 55.8956675131/ - [.---5--- 5..--..1' --- {.-.--5-..-- :6 38 10 .755. 60 ,4 52.3352.8456.78 ,4 ...... .5---4 4V ...— _-r__._t__.__../ | ' 5 o = 50 cm 55:5?fii1653};/5 55113533955313" _ 5 I 1 C b ";g cm '1’73510'8g6i/r" :5 .'47 1 .60514. 8 / c - cm ----- r---5---: ---. d =770 cm 53 7956 .045141 ,1 55.6451 .24.11 .4 ,2 ..--5L. ....... I —————————— 4' d53.5.5.635097 27,53 52.111350525/ ...--51 ..... r 5......_1 ---—5! i | i 1 I2.50 .4 1.46/0»! 5.268 / .695 .——.——1' .—-——-17 k-a-H) I3021 ,‘ I0729 I] ---57 ___.f 5 F 6.42 '1‘ 2.32 // 511.6 7 P"“‘”’“‘ 5 4.73 ,1 r__-J’ b..../ '15.8 4 56.45 4 x 1---- 1 Ei 515.6 ,4 6.06 ,4 z 1—- 5 y 2006 ”5 I3084 -> "'“.‘—"5 1"" H 553665.629 51-48538 lst Layer 2nd Layer Fig. 5.12 Absorbed power density. Incident EM wave: vertical polari— zation, 200 MHz. freq : O": 200 MHZ 1.28U/m 6 = 56.5 €o E3: 1 Wm OzIO 13:30 cm cm :70 Cm d :I7O cm 99 ~—--'-—-O. -513 #137 .‘ L----’—+r I 3 b L7.--9x 3 I 593/ {I 1’": 389932139855,“ I--__.'f-__-|---_3v I i ' p§.z:é-_431§-.9./1 I : . I30. 23 14. 1'30. 9 / 1362.4. 7.53 L..___£_—J agar 34-1/0: had) ,41.8/ 1”"‘1 1.39.13" l 38—2203/ ' A P11" Ex (mV/m) i.].'...O—4V/ I I |_1_o_9_3, ISFIAYFR J; ;W I. -—.1-— I ‘0‘ H45 90‘ Tu I f M \ :‘—'-rm I I. I. 78.l_j_5. I I I -... 3 7O :10. 5, 28.5.0188125. 3 -—_:——— '|.'———‘ -.- co...— Fig. 5.13 The x - component of induced electric field. wave: horizontal polarization, 200 MHz. 2N1) l /\ v I" R Incident EM 100 3.7 3.7: ' 1 | ,1 freq 1'. 200 MHZ 3.4.9.2133 b 3.4.211 . . I 1 0‘: 1. 28 U/m LZ_&..-/ 3 3115M I I .. , I , € - 56.5 Q !9 8 I ll .19....7 / . :1 “. I F : : E': I W 3151319512294," 3"” 5-4-7- 9:21 3.," I 3 . 3 E !80. 1161. 9'32. 'Or" |_1_3§_:_86_. _533_5_. .5,” "--.—--1-'— ' l ' I 3 I ' l A . I ’4 . ' I (t!) 2 IO cm !Z§ZLI_7§L%3§§L€3 35.23.623.53:§3 35-12! C 30 cm .| I I A I ' ' l‘ C , 70 cm 79-1.;.79.§:_4._:zx {9.3.281 8345 51/ I I I I I d ‘770 cm %o4i_4.7_§:§§-_1/ 3.141-308 9:45.51." I ' 3 d ////2 3 , ! : ' 2 154/122 ' 2.3.! 3 12,113 54.3.. I u. 11 -- i 3 1 I3}:6 v '4 9 ‘ V \( 3.2} -8-4!’/ V had) | 1 46 4 ,2: '4_ _05/ i r 4 I 1.5.3:..4. r, 3.5.9.9.. ’ —> A k Z?’ 's_0__2./ 359.9./ I I ,1 Y 33.22%“! EY (mv/m) 331-2, [.7 319.2 ,1 ' '8.84 x .x I'"-". 1373.4: 75.1 L—uu—I‘I—I-i IST [AYFR 2N1) I A\' Hz Fig. 5.14 The y~- component of induced electric field. Incident EM wave: horizontal polarization, 200 MHz. freq : 200 MHz O':1.28 ulm 6 =' 56.560 Ej::I KING 0 :10 on b :30 cm (I :17!) crn d =I70 cm Fig. 5.15 The 2 - component of induced electric field. d 1 I . 101 4.. §9.lé-.9 321...} I' . 'I ‘ —...-- ...—.3 -+ I I I 1 ' 3 31.36114611613 ' I 33.72;_1§._1_;15.5 , l I l‘-CHH 3_ . 34.09/35! I lea-H) L.? !_3_:§- I A .5.:95/ 376,313,” Ez (mv/m) '8.86/ r---I 311.0; 33. ISFIAYFR U0 T 00 ND Kb 19.--?“ wave: horizontal polarization, 200 MHz. 2N1) I A Y 1‘12 Incident EM 102 I331 freq = 200 MHZ 32314.5/ b 0": 1.28 U/m L433." 3 ""I I e =‘ 56.5% !6.06/ ‘7 ' rr F i VK/észnfizJ 7.31'1.7431.24 ’ E = 1 VI," f9d%rl--—-I-"‘VI ”.1”, . I I 36.7232.65!1.17 / 3.3 5.99:L_g,l’ I""."°"I"" I " F I . . l l A o = I0 cm 3339332233393, 3411.63/ C .. I ' b '30 cm I4.39:4.4421.72 .4 .131. 94 3/ c :70 cm I»-..T--_3_--.r .3.... I ' I .. 4..46'2.211 721 X 70 .2 01 , d -170 cm //‘""I““' .- -__'___, d I? 12:10. “3343/3 6-44133331/‘3 . i FLLZE 3433.13" 820 o\’ I/ 3 Ito-~12-o 2.50 1‘ I“"‘ I 2041 ’ L——4I 15.72 / 1"“ 3 $0.0 A P’(nnN/n1) ---.I’ '1;._1_3,II '7. 76 / l~---. 3 3 136.013435 33.3 36.21 IS'I‘ [AYFR 2ND lAYl-‘R Fig. 5.16 Absorbed power density. Incident EM wave: horizontal polar— ization, 200 MHz. 103 location of the strongest induced field varies with the frequency and polarization of the incident electromagnetic wave. Fig. 5.17 shows the total absorbed power in terms of the relative absorption area, Ar’ and the maximum induced electric field relative to the incident electric field,IE&ax/[EH, as functions of frequency for both vertical and horizontal polarization. The relative absorp- tion area is defined as (total power absorbed / incident power density) / total surface area, since the heat dissipation capability of human torso is essentially determined by the total surface area of the torso. It is noted that the subscript V stands for the vert- ical polarization and H for the horizontal polarization in fig. 5.11 From these results it is evident that a weak resonance occurs at around 80 MHz for a vertical polarization and this implies that the strongest field is induced in a human torso when the torso height is about 0.453 A0 where A0 is the free space wavelength of the incident elec- tromagnetic wave. For the horizontal polarization, the induced elec— tric field and the absorbed power tend to increase monotonically with the frequency first and than rather stay constant for frequencies higher than 170 MHz, it is true that for frequencies lower than 100 MHz, the induced field for the vertical polarization case is much stronger than that for the horizontal polarization. However, for the higher frequencies,a horizontally polarized electromagnetic wave can induce a stronger field than a vertically polarized electromag— netic wave does inside a typical human torso as indicated in fig. 5.17. The effect of the size of the biological body is also an impor- tant factor in determining the total induced electric field inside it«at a given frequency. A torso with the same number of cells as in £963 2M «c0305 venwufloa Efimucouwuos wad woumuflom 3303p?“ 05 mo >ocoswonm 05 mo msomuocsm mm :35 ct. .H .m «0 canon. 05 cm 303 pounce—#558338 obflmflou van «on.» Gown—mucus: ”532.6% 3 .m .wwh ANEEV 02w? £3305 mo >ocosvouh 2:” Sn . _ . . OI ’ I I ~ .‘ 2:: My. .. . e x . ...../ .. s .\ _ a as. ...v. r x - .....4/ .6 u t d ...:...........a.. z 0’ ~.\ . __3 / / fix .2- z 2. . ... d, b ...... / l.\ e ’ d \ Q Ir o'o'o'o' 1%” \. x x 2 Ii iiii-Iiiiii...i..lu . .Q - e.— In” mod "among [Jam P311051! um“ I“! OSIIJIS ‘umn 105 the afore—mentioned human torso but with the reduced cell size of 6 x 6 x 6 cm was considered to demonstrate the biological body influence on the induced electric fields. This typical torso would correspond to an ideal- ized torso of a child with a height of 1.02 meters. The head in this case is 12 cubic cm and the arm length is 42 cm. In this case the inci- dent electromagnetic wave of various frequencies ranging from 10 - 300 MHz is considered. Fig. 5.18 shows the total absorbed power in terms of the relative absorption area and the maximum induced electric field relative to the incident electric field as function of frequency for the vertical polar- ization. The relative absorption area and the relative maximum induced electric field have been defined earlier. From this figure it is obvious that a weak resonance occurs at around 120 MHz and this implies that the strongest field is induced in a child's torso when the torso height is about 0.408 A0 at 120 MHz. These results indicate that the frequency at which the strongest field can be induced in a biological body is in- versely proportional to the size of the body for the vertical polarization. It is noted that the idealized homogeneous models used for human and child torsos do not account for the skin, fat and bone layers at their particular locations, but the generalized parameters used correspond to muscle, skin and tissues with high water contents as summarized by Johnson et. a1.[14]. Furthermore, the models do not deal with heat diffusion prOper- ties of the torso such as conduction, respiration and blood circulation. The contribution of the results presented here lie in the fact that they distinctively show the areas of possible maximum power deposition inside the human torso and the effect of size forthe induction of the strongest .m>m3 2m ucoowoaw vmuwumaoa Adamofiuuo> osu pow hoamsvouw on» mo mcofiuoasw mm vaflso m wo ompou z No.H mufimafi vamfim vooowsa aaaflxma o>wumamu mam mono aowumuomnm m>fiumamm wH.m .me 106 A 3.22 V vim? “G039: no raucozwouh V. 0.0 0mm 4 T a q Gin-vN . 4 « AVA—V.H CWOH J m B 1? .. S a. T a“ O .... m a. CI 1 I: ...... m. ~.o,. 1., _nm_ ..moH mam Ill .. e a I x“ lama“. X \ EH. m P . II 9 1.. E 01/ u w. MoO.- [.1 INOIH e w... w d o . r m w o .¢pa J w T u m. . M .2 - a 107 field in a torso. Although these results grossly give an insight into what can happen when a human body is exposed to a given electromagnetic radiation and thus provide very crucial information to learn more about the biological hazards of microwave, yet due to the complexity of human body, these results may not necessarily pertain to man. So far we have considered the human torso having all the cells con- stituting it of the same dimensions and similar shapes. Let us now con- sider the effect of different shapes and different cell sizes of the human torso on the induced electric field and the total power absorbed when the torso is exposed to vertically polarized electric field of inten- sity 1 v/m at 30 MHz. These results are, of course, discussed in detail in the report [liL but just to show the effect of these changes in the shape of human torso, only x - component of the induced electric field and total power absorbed are added here. Figs. 5.19 and 5.20 show the x - component of the induced electric field and power density induced in each cell of the human torso when the arms are resting against the body. In this case all the cells have the same dimensions. The max- imum intensity of the x - component and the maximum power density are shown by hatched lines in all the cases. Figs. 5.21 and 5.22 show the x - component of the induced field and the total induced power density in each cell of the same size torso with the arms in the extended position. A considerable change in the field induced in the arms region is evident. In figs 5.23 and 5.24 the x - component of the induced electric field and total power density induced in each cell are shown. It is noted here that the configuration is similar to as shown in figs. 5.19 and 5.20 except that the dimensions of the cells constituting the neck region of the human torso have been changed to 5 x 5 x S cm. Although maximum freq: 3o Mhz 6: 100 Eo <3'=:0.6 'ijnn Cflfl Cflfl CH” CH” IFI v/ m 108 J7 Ex ( mv/anb :14.5 :17.3 n 'L——J -—-‘ !75. I I '86.5'7.84:13.4 ,f I L---«'----»--- I I I I l98.5:12.8;16.2 4 L---,-__r,__ | l ‘ : I’ .108 34.7.17. ,. I.--.I_-.._:..-.. I I V I I !123 :12.z;16.1 ---1__4__mv: I I I129 '7.66:13.9 ,1 W -- E132 ,f 10.4 H I) I I130 --d '126 pf I '/ E118 {mi LEO-81’? !94.6 y? L‘ Fig. 5.19 The x - component of induced electric field. wave: vertical polarization, 30 MHz. Incident EM 109 X ,x I If If_—-| f _ .516 I. b req- 3° Mhz “-4 Ix‘ 1.13 7‘ 6: 100 60 . _____ , I, /, h.69 I““J’_" 6— 0.6 wm I— . 1L/ :l) 2 .25' .058I. 099/! . """""" I, E'= I v/m '33119‘2‘3 99.3.4” I LI P ( mw/mfirh _5_2_:_07_7_1§_,0"93 r/I I C I £1.07I I.071_'I ._09_3 /' I ___.- —/ I/ I4 .'56 .049I. _079 /" d -___4- /l‘ / 4.98'.021I-058 ,‘ 0= 10 cm __., : b l; I:flé/z: V i 035/ == 3() CHW EMLMéIq - = 70 cm d=l70 cm *i E , k fii JL Fig. 5.20 Absorbed power density. Incident EM wave: vertical polarization, 30 MHz. 110 *x I I \ Tf‘“. b I, I I37 I freq: 30 Mhz I":""-" 6-100 :57.9,: H— C ’1 — 60 I ..... I 21’ 7 .1” .2.” I” II, elf I 72.1 ,--—.——, --, "7 -~--7 ",4— - I- I I, 4’ / I, I, ‘l I "°°""”" “L: I i ': ‘: II ' L94.7:18.1I3.86i3.23:3.53:3.68;3.83;3.8215.11 i V E=I V/m I118j3Z.O/:’ I"”:""' I/ l128 I31.2 .’- ""'I"“' I; I136'275 ," E (mv/m) I_____ '__._..I’: X I '3 u“ d I143 l21.6 ,1 ...J..__!. l I ' 148.131 0= IO cm I J/ I? I" .. 30 cm I“, ':’. = 70 cm 147 ,4" -___ r I d=I70 cm I I," ”39.x“. I.130 I L-"III I Z I J/ "F I 5' 1131/: -> I L" k 103 _ ' I T ->i ‘1 H :1 r --’Y Fig. 5.21 The x - component of induced electric field in an adult torso with outstretched arms. Incident EM wave: vertical polariza- tion, 30 MHz. 111 T f—‘I/I I I " .45 . freq: 3o Mhz IMPI b 6:10060 : ----- x. fi, r , , , 'I I I l I I I I I157 ""‘7"—-f--7‘-'7‘--7---7‘--,4- . = 0.6 -..- I x 1’ ./ ’ ’ +I " I Wm I . g I g I I . ,r . |2.77I.737 ;1.06 I.997:.816I.610IL.402§.224 1.088 5 If"? IA E: I V/m I4.18I.326 ’4’ [.--—4-----I 0‘ I :/ l4.95:.297 ,1 {MIN ,5.58:.230 ,1. P ( mw/m3 ) F'" """ ”I” d l6.lZ'.l41 1 J l f" In” 6.54 .053 0= IO cm I I V/ ,4" I = 30 cm ’ZZ’B ,7?" = 70 cm l6.47I ___- II d: I70 cm I I/ '5087 ’4' A 01 0 ha 0 \ ---¥ \ N \ \ TI Fig. 5. 22 Absorbed power density in an adult human torso with outstretched arms. Incident EM wave: vertical polarization, 30 MHz. 112 X I T T ', b 25.1 It freq: 30 Mhz I-" : I ,35.9 6:100 60 ' .3:” I x I .7 '- -—/4--- 0’: 0.6I17m Ih J f I,‘ '51.7:11. 1'17. 8 ,I . L---—:—---:—---J " E': 1 v/m I66.7:16. 2520 .6 ,I’ i——--;t----E----4V I, .80 .5.17. 221 .0 II' C r,I :,a E 1 x (mvlm) 93.—49.6: .2.2 (LIA |/ I103 '13. 2; '.17 8 X cI I---—1-—-:—--MI4 . 4’ a: 10 cm 112 8.16:14.¢1 1 b= 30 cm = 70 cm d=170 cm E' k +i H Fig. 5.23 The x - component of induced electric field in an adult torso with thin neck. Incident EM wave: vertical polarization, 30 Ma. 113 X ,4" I T _1’ I I i0198 ’? b freq: 30 Mhz .--- : L404 6:100 60 ' 2:93., I ,' I 2.05'- ——/4--- O’: 0.6 Wm IL .4 fit I 7 1.803;.092'.151 ,1' l- ' ' i , ---§---—:----1r I]. E: 1 v/m I1 .35I.109: 148 VI I195..113I145I,I C I”"I""“" "" I ’ P (mw/m3) 'LZ. .57:.097I .126 II/ .....r--—:L—-—d’ I ’4 I3.1BI .065; .098 ,I’ d 1..._I.__I..../I4 .3.77I.030;. 06 ’7’ i 0= 10 cm ; b= 30 cm . D C= 70 cm d=l70 cm *5 E .. It +i H Fig. 5.24 Absorbed power density in an adult torso with the thin neck. Incident EM wave: vertical polarization, 30 MHz. 114 induced x - component of the total electric field and power density are shown to lie elsewhere (in the hatched region) yet comparatively a local maximum does exist in the neck region as compared to the re— sults in the previous cases. Furthermore, a small change in the dimensions of any cell does effect the total electric field and power density induced in the neighboring region. This further strengthen the belief that the geometry of the biological body plays a major role in determining the total induced field and so on. To end the discussion on human torsos, one more result on the induce field and power density at 80 MHz with the different dimensions of the cells constituting the neck region is considered. In this case, each cell in the neck region is 5 x 5 x 5 cm whereas the rest of the cells in the torso have the dimensions of 10 x 10 x 10 cm. Only the x - component of the total induced electric field and the total in- duced power density are shown in figs. 5.25 and 5.26. When these re- sults are compared with the results obtained at 80 MHz for the case when all the cells constituting the torso have the same dimensions as shown in figs 5.1 and 5.4., the existance of the local maximum in the squeezed neck region is evident. Moreover, the change either in the induced field or the total power density in the neighbouring region of the neck is clearly visible. Therefore, from these aforementioned results, it can be concluded that the results obtained pertaining to one particular configuration of human body may not be generalized. Above all, as the human body is not that simple physically as discussed in all the illustrations, therefore, a small change in the cell size here and there may greatly effect the patterns of the fields induced. Nevertheless, it may be a :10 cm b=30 cm C :70 cm d =I7O cm E’ z 17’ Fig. 5.25 The x - component of induced electric field in an adult torso with thin neck. Incident EM wave: vertical polariz— I137. 115 L..-- I60. I55 --. r182 “17112.9 I r---I---«-—-+ I I179 I20 .5I75. 1 r---.---+---‘ I231 I23. 81107 -4 I I.---I—— I 1 "- 1267 L24.2I121 ...-L ..... ---J L287 120.9I114 ...... +---‘ d, ation, 80 MHz. dI287I13.I.5852 3 I——-- «m1 ----‘I I I. l7.79 47.2 0.; I“ Ito-H) 1.2.6.94" I254 ,1 I234 ,1 E (mv/m) ran—-47 X i309 ,/ |180 ,1 H46 1---. 1:84.8I11.9 lST LAYER I l167J26.6I24.3' .0.-- '-I----:--- . I L261 I45 .7I48.0 . - "F”‘T""" I338 353 .4I68.z, r ''''' 1”“ 1 I393 I53 .0 '77.6 I I423 l44.24I72.9 W “““““ I :4279 6.3 I52.8 F” 7 I418 29.2 P——‘ I402 ,1 {.---I 378 ,1 I----1' 347 ,I r-" I308 ,1 ‘ I115 514.9 2ND LAYER (4:7 116 '644 I I- ,I ..928 ,1 freq = 30 MHz l,__,, I) I'm" I . I2.40 0‘: 0.84 07m J66 I I- H§£g 'Q3‘ 6 :80.0 60 [fl 1 :25 1 f - 1 1 1. F‘ : .1 E'- 1 v/m 5.17:2 5,5 '1 ,5: / 112.213.00:1.55 I13.8I 1 .52I2 .96 ,1 i_29.1I2.47I1.64 *— ------ -.:———-4 .4' i - —-—:——-——:————-1V 4 I o .-.- IO cm Elf; 9.6.2.? 11.1. ,’ :9 LEIE '_°_8_:E :33. I b 30 cm I'30 1: 472I6 ‘ I64 8I1 49:2 66 c=70 cm -:-}.--A : Igéfll r.-:-iy.:.-_Il..:--.r d -170 cm L34.sI. 235:5 4.8 ,1 I75. 0| .8634I2. 25 - ————————— 4V ——————— . : . WWI. {313:6I. 447I3. 13,“; I26. .563. .547I1. .26 1 ' 1 'I ,32.8 ,1 .955/ ~( I73.3 / .433 ___—4' “0&0 i——-—d' [30,4 ,4 .67.8 KI I I” " 27.1 ,1 60.0 I L--.4' ..--.1, l 3 ' .23.0 [A P (mw/m ) 50.5 v" I311. .X | El l28.6 ,1 z "-1’ I1706 II :71 7 I . .6.27:2.04 l 1 151‘ LAYER 2ND LAYER Fig. 5.26 Absorbed power density in an adult torso with thin neck. Incident EM wave: vertical polarization, 80 MHz. 117 worthwhile to mention here that the present computer program can handle the case of human torso being divided intolfl) cells and each cell having different conductivity, permittivity or the physical dimensions than all other cells. 5.2 Local Heating In the recent years microwave has crept into the arena of medicine and its applications in that area are twofold - heating of the tissue and diagnostic. The electromagnetic heating includes rewarming of the refrigerated blood, thawing of frozen human organs and the production of differential hyperthermia etc. The diagnostic applications include the noninvasive diagnostic of lung diseases such as pulmonary edema and emphysema using microwave radiation. Here in this study we are mainly concerned with the former application, i.e. the selective heating of a local tissue in a biological body by electromagnetic radiation of high frequency, generally in the range of 3 - 30 MHz. Recently, a new technique involving high frequency radiation with high loss materials such as stain? less steel balls has been reported[15] to concentrate the heat in a selective region more efficiently and effective while the temperature of the rest of the body is lowered by 250 c. Lowering the temperature of the body, of course, results in reducing the metabolic rate which effects directly on the diffusion of the injected high loss material. According to the report, the high loss material is injected into the region needed to be heated by electromagnetic radiation. In other words, by making a region more lossy than the rest of the body, the concentration of heat in that doped region can be obtained. To an electrical engineer, the situation seems to be bit incompatible, because by increasing the conductivity of a certain region, one suspects to obtain decreasing electric field intensity in that region which in 118 turn may result in reduced power in that region. These simple conclusions may be drawn from the concept of continuity of the induced current in the high loss region and the surrounding area. To check the validity of these conclusions, let us pose a question - Is it true that with an increase in conductivity of a certain region of a biological body, the induced electric field intensity and the total power absorbed in that re- gion decrease? Let us try to answer this question theoretically, using tensor inte- gral equation method. Consider a biological body of dimensions 24 x 24 x 18 cm as shown in fig. 5.27. The body is subdivided into 48 cells with each cell being 6 cubic cm. The whole body is illuminated by a vertically polarized plane wave with electric field intensity of 1 v/m at 30 MHz. Owing to the symmetry in the x - y plane, only % volume of the biological body is shown divided into cells. The layers in z - direction are labelled as, I, II and III layer. For the high water contents of human body, the conductivity and permittivity at 30 MHz are 0.6 mho/m and 100 so respectiv- ely. Our objective is to observe the changes in the induced electric field intensity, volume current density and power density of II layer as a fun- ction of its conductivity. The theoretical results are shown in fig. 5.28. The conductivity of other two layers is kept at 0.6 mho/m. Only the x - component of the total induced electric field and volume current density are shown while other components, being relatively small, are neglected. It is clear from fig. 5.28 that when the conductivity of the II layer increases, the current density in that region increases for a while but then stays al- most constant and on the other hand the induced electric field and the 119 / I - I I i '0'. E". -'::3‘ ' ". ":_:-;' : | " c...:.l::.& I I: '-‘::-.: “4 1 wsufin E I ' l- U I \ s ' II' .4"ch ‘ 4’. a l?’ ':‘ Q : |\\ 1’ D‘s-115353... ,” N K I ‘ \‘ v’ I C: .5:-.5:; ’ +1 I '. 0 ...-v E / J ’2 Fig. 5.27 A three layer biological model illuminated by ver- tically polarized EM wave at normal incidence. The conductivity of IInd layer is variable. 120 P -40 -50 -—60 -7o 0_ ______________ 3 _-80 0‘ “‘~-~------ 3..-80 1 10 100 1 1° 10° 0' 0 Ex_ 8: 4. 0- 1 10 100 1 1° 100 U U IInd layer Fig. 5.28 Theoretical results on the x — component of the electric field, current density and absorbed power density in k volume of IInd layer as a function of its conductivity, induced by a vert- ically polarized EM wave of 30 MHz at normal incidence. The conductivity of surrounding layers is kept at 0.6 mho/m. 121 total power density show decrease. This decrease in electric field in- tensity and the total power density is in accordance with intutive results explained earlier. The above development outlines, to what happens to the induced fields within a layer when the conductivity of the whole layer is changed. Let us now see, to what happens when the conductivity of part of the layer undergoes a change. Again, consider the same biological body being ex- posed to the same electromagnetic field at the same frequency. In this case, our aim is to observe the changes in the induced electric field intensity, volume current density and power density absorbed by the IInd layer when the conductivity only of the shaded region as shown in fig. 5.29, changes. This shaded region of the IInd layer runs all the way in x - direction and has a symmetry in the y direction (Iyl§_6 cm). The theoretical results are shown in fig. 5.30. Again, the x - component of E field and volume current density are shown, and due to the symmetry only k volume of IInd layer is shown, and the cells are numbered as 5,6,7, and 8. The conductivity of cells 5 and 7 undergoes the change whereas the conductivity of cells 6 and 8 stays at 0.6 mho/m. From fig. 5.30, it is clear that with the increase in conductivity, Ex and P go down in cells 5 and 7 and show little increase in cells 6 and 8, whereas Jx stays almost constant in all the cells. From the above results, it is obvious that by increasing the con- ductivity of a selected region in a biological body, it may IKfiibe POSSible to increase power absorption in that region when exposed to electromag~ netic radiation at 30 MHz with the size of the body comparatively very small to the wavelength. To verify the theoretical observation, exper- iments were conducted on some models of saline solutions exposed to 122 24cm \-—— Fig. 5.29 A three layer biological model illuminated by vert- ically polarized EM wave at normal incidence. The conductivity of the cells of inner columns of IInd layer is variable. 123 Ex -Z—- Jx P Ex -§—- Jx P 7 .I -30 74+ -30 ~ 6 .. -40 8 ------------------ 6 . -40 I I I: '''''''''''''''' 5 1- -50 4b 4 I- 40 -60 OI 3“ -70 l 10 100 l 10 100 O O _5__ _§__ Ex ..... Ex (mvl m) Jx P Ex_ -.-----..---------..--- Jx P _ -""" Jx (ma lmz) 7" -3C " 7‘? -30 - ._ . ...) 11 ------------------ 8 P 61b -40 I 4 54.. '30 4.. -60 3dr -70 I 1 1 l 10 100 I II Layer Fig. 5.30 Theoretical results on the x - component of the electric field, current density and absorbed power density in k volume of IInd layer as a function of conductivity of inner cells, induced by vertically polarized EM wave of 30 MHz at normal incidence. The conductivity of rest of the biological body is kept at 0.6 mho/m. ‘ 124 microwave radiation. Due to experimental limitations and non-availability of reliable equipment at lower frequencies, these experiments were carried out at 2.37 GHz and the experimental set up, as shown in fig. 3.1, was used. Fig 5.31 shows a rectangular box of dimensions 6 cm x 8 cm x 2 cm, divided into 48 cells and forming two layers in z - direction with a cell dimension of 1 cm x 1 cm x 1 cm. The shown box has a partition in the middle, shown dotted, to form a column of dimensions 6 cm x 2 cm x 2 cm and is separated on either side by the plexiglass material. When this rectangular box is used to simulate a biological body, then the column can be filled with a different conductivity solution than the rest of the model. This rectangular model was illuminated by plane electromagnetic wave (with l KHz modulation) polarized in x - direction at 2.37 GHz and propagating in z - direction. The saline solution used as reference had 0.08 normal concentration with O= 2.2 mho/m and Er = 76.72 at 2.37 GHz. Fig. 5.32 shows the theoretical and experimental results on the absorbed power density in region 1 (i.e. column) at the location of x = 0.5 cm, y = 0.5 cm and z = 0.5 cm; due to Ex’ gl-IEXIZ, as a function of conductivity of region 2 of a saltwater model, induced by a vertically polarized EM wave of 2.37 GHz at normal incidence. The concentration of region 1 was kept at the reference level, while the concentration of region 2 is varied from 0.08 normal to 3.0 normal. It is noted that ex- perimental measurement point lies in region 1 and the first layer. The experimental results as shown by solid circles are in good agreement with the theoretical curve. From this figure it is clear that with the increase in conductivity of the surrounding region 2, the absorbed power 125 cm . . 09 S .0 fl ""° :°-:"-.‘-3°-°.'.'.: \ \’ 9° Fig. 5.31 A two layer rectangular biological model of dimensions 6 x 8 x 2 cm containing saline solution illuminated by a vertically polarized EM wave at normal incidence. The conductivity of the shaded region may be different than the rest of the model 126 62532: Hon—no: um 35 nm.~ m0 963 mu consumaoa Samoan—pot, m .3 coupon.“ .Hmvoa “unusuamm m mo N aowwmm wawvasouuam a“ muu>auo=vcoo man mo cowuoasm a mm H dogwom a.“ huamcmv uoaoa vonuomnm on» so muaomou Housmaauonxo woo Hmofiumuoofi. mm.m .me AS305»: A «3 N cofiwom no 33:03:50 3 2 E 2 2 m o v N _ u u q q u q q a a q q — u - u 0N! N cowwom .— dodmmm C 1_de IN N cgwmm 03.2.3», INb Naommom 03.3.19, u w H 2.. 83:8 ~.N u b .1 O H Acgwom NFAX. n w 53 NED hm.~ n uudoswouu 3 o; anp Ansuap Jamod paqaosqe X I 113-Z) {“01393 U! (X 21:11 127 density in region 1 increases. Therefore, it may be concluded from this experiment that in order to increase the power absorption in a given region, the conductivity of the surrounding region should be increased. The next experiment demonstrates to what happens when the afore- mentioned model is exposed to the same electric field but the salt con- centration of region 1 is changed from 0.08 normal to 3.0 normal, whereas thesaLt concentration of region 2 is kept to be at the reference level. Fig. 5.33 shows the experimental and theoretical results on the absorbed power density due to Ex’ % UIIEXIZ, in region 1 as a function of its conductivity at the location of x = 0.5 cm, y = 0.5 cm, and z = 1.5 cm. Although this experiment was a bit difficult to be performed without disturbing probe's position, yet the experimental results are in good agreement with the theory. From fig. 5.33 it is obvious that power ab- sorbed does show some increase in the beginning, but later on it droops down. This implies that there exists an optimum conductivity at which the local electromagnetic heating will be most effective. 128 623325 Hon—nos um 35 nmd mo 963 mm omuwuoaom hHHooauuoer o .3 mounts.“ .Hovoa umuosuamm a mo :3on made .23 ca huu>auo=vaoo 23 mo cones—am o on H seamen ea minnow meson wonuomao on”. do 3.250..— Houaoafiuoaxo use Hoowuouoofi. mad .wam Anions: A “3 u commom «0 33:03:80 2 2 3 3 3 m o v N . . _ d _ . q . . T 1 . . 4 :1 80 m .~ u N 80 m.o n g» macho no nodudqu omunm IICII Lmul .CoonH. \VJ .2- x Nmo FMoN nu >Ud05v0n—H 1 Md! . I w 1 E: 2.4:. u H d daemom Bagufir u w N daemom ( IIEIIIDE) 11101893 u} x3 03 anp Ansuap Jamod paqaosq'e Z I CHAPTER VI MICROWAVE EFFECTS ON HUMAN CHROMOSOMES IN TISSUE CULTURED CELLS 6.1 Introduction. Although a great deal of experiments have been done and the results have been reported on the electromagnetic effects on various tissues of the body, yet only few studies have been performed on the effects of elec- tromagnetic radiation on the living cells. Many existing papers have been cited by Michaelson [16] and Johnson and Guyha] . A more relevant study on microwave - induced chromosomal effects in Chinese hamster cells has been conducted by Janes, et. al.[17]. moreover, the studies by Stodolnik - BaranskaIlB], Chen, Samuel and Hoopingarilgland Guru, Chen and Hoopingarned: 20]have demonstrated an effect of microwave radiation on human lymphocytes and chromosomal aberrations of Chinese hamster and human cells respectively. In almost all these studies, the radiation ex- posures were expressed in terms of power intensity of the incident elec- tromagnetic wave. This specification is ambiguous for the following reasons: The non-thermal, cytological damage to chromosomes is probably dependent directly upon the intensity of the electric field inside the cells. Furthermore, the actual induced electric field at the location of the cells which are usually immersed in a liquid medium and confined in plastic tissue culture flask is a strong function of the geometry and electric properties of the cell sample (cells and liquid medium in the flask) and the frequency and polarization of the incident electromagnetic wave. It is true that the same microwave can induce completely different 129 130 electric fields inside a cell sample if only the geometry or the orien- tation of the cell sample with respect to the incident electric field is slightly changed. Therefore, in this chapter, the actual induced elec- tric field at the location of the cells was carefully quantified and chromosomal aberrations were then analyzed in terms of this electric field. For the experiment human amnion and lymphocyte cells were used. Cells were exposed to a microwave of 2.45 682 at various intensities over various periods of time inside of a closed and matched waveguide system. Observed chromosomal aberrations were carefully analyzed. In section 6.2, a brief discussion of the experimental setup used to expose the living cells to microwave is given. Section 6.3 explains the treatment given to the cells before and after their exposure to microwave radiation. The quantification of the induced electric field inside the cells with a check on total absorbed power is the topic of discussion in section 6.4. Section 6.6 yields the imformation needed on the chromosomal aberrations induced by electromagnetic radiation when studied under certain probability criteria as explained in section 6.5. Finally, section 6.7 sums up some of the important results obtained in this study. 6.2 Experimental Set Up The experimental set up used for this study on the effects of elec- tromagnetic radiations on human amnion and lymphocyte cells is schematically shown in fig. 6.1. The cells, which were grown in liquid medium and confined in plastic tissue culture flasks, were placed inside of a closed and matched waveguide system. The output from a microwave generator at 2.45 GHz was amplified by a travelling wave tube amplifier before it was fed to the waveguide. Two directional couplers were employed to monitor 131 .35 n<.~ um oofiuofivou 2630..."an ou mHHoo 3.39.3.5: was defines amass museums: ou mom: asuom Housoaauomxo man no Enema: cause—anon < H.0 .wfim ZOHH§>om8 incic tion matc syst be I den was int 083 gr SE t1 132 incident, reflected and dissipated powers. To ensure the minimum reflec- tion from the wave guide system an impedence tuning stub is used to match the input impedence of the wave-’guide system and the total system was precalibrated for the overall power losses. The TEIO mode was excited in the waveguide. The cell sample could be placed either perpendicular or‘parallel to1the direction of the inci- dent Frfield inside the waveguide. In this study the former configuration was used and this fact was taken into account for determining the actual intensity of the induced electric field at the different locations of the cell sample. 6.3 Preparation of Cells Human amnion cells commonly known as AV3 tissue culture cells were grown in eagle's minimum essential medium supplemented with 132 calf serum. These cells were exposed to microwave of various intensities over various periods of time. After the exposure the cells were allowed to grow for 24 hours and their growth was stopped at the metaphase stage with colcemide. The cells were then removed from the container with trypsin and collected in a test tube by centrifuging. These cells were then swelled by adding 12 solium citrate at room temperature for three minutes. Cold carnoy fixative ( 1 part glacial acetic acid to 3 parts reagent grade methanol) was used to fix the cells. The fixative was replaced 5 times at intervals of 3,5,8, and 10 minutes. The cells were then collected by centrifugation and resuspended in 8 m1. fixative and placed on slides dipped in cold methanol. The slides were then flamed and cells stained for chromosomal analysis. Human lymphocyte cells were obtained from the fresh blood. The blood was allowed to settle and the serum plus leucocytes pipetted into chrc {UN men of aft GE? 81 we 133 chromosome medium 1A (Grand Island Biological Company). Replicate cul- tures were established at the same time and cultures selected for treat- ment were irradiated within two hours of culture establishment in most of the cases. The cultures were harvested for lymphocytes at 68 hours after initiation. Two hours prior to harvest 10 mg/ml colcemide (CIBA- GEIGY) was added to the cultures to arrest mitosis in metaphase. This allowed for a greater number of cells suitable for analysis. The cells were fixed to microscope slides, stained with Giemsa stain and examined microscopically for chromosomal aberrations. The aberrations were class- ified under a 16 point system and the results compared between the treat- ments. 6.4 Field Intensity Eetermination The actual field intensities at the locations of cells were quan- tified by the following three steps: (1) The cells were immersed in a liquid medium and confined in a tissue culture flask. The flask was then placed inside the closed and matched waveguide system in such a way that incident electric field was perpen- dicular to the surface of the liquid medium. To determine the actual induced electric field at the location of the cells, the tensor integral equation.method was used. The details of this method are given in chapter 2.Based on this tensor integral equation method, the distribution of the total induced field in a typical cell, as shown in fig. 6.2, is calculated. the that cells are actually immersed in the liquid medium. The total cell sample volume including the liquid medium has the dimensions of 0.5 x 4.0 x 6.0 cm. For the calculation of the induced electric field,the total volume is is divided into 96 subvolumes with a subvolume size of 0.5 x 0.5 x 0.5 cm. 134 AMNFV b.6410 m n Hm .ow. oh aw .a\oaa H n b .85 mqé m0 963 SM nonrandom 53.3325 .3 mousse—SH: so 061.0 0 was so oé n a .60 m.o n o maowmsoafiv mo madame Soc .3393 ¢ «.0 .wam to $311 wit cei 135 The incident field is polarized in the x - direction and corresponds to the electric field in a wave guide for T1310 mode. Since the cell sample is placed symmetrically in the wave-guide with its center aligned with the center of wave-guide in y - direction and the dimensions of cell sample in that direction are small compared with the dimensions of wave-guide, therefore, the magnitude of the incident field is assumed to be constant over the entire body. Due to the symmetry only one half of the volume is shown. Fig 6.3 shown the normalized x — component of the induced field inside the biological body, having conductivity 0- 1 mho/m and permittivity 6= 70 so at 2.45 GHz. It is seen in fig. 6.3 that the distribution of the electric field is rather uniform in the central part of the cell sample with a slight increase around the edge of the sample. The value of the fi field at the central part of the cell sample is close to the value of E:o IE1(;) U |6+36 This agrees with the value deduced from the boundary condition on a thin layer of liquid medium as our cell sample. If the cell sample is placed in the waveguide in such a way that the incident electric field is parallel to the surface of the liquid medium, the induced electric field at the location of the cells will be increased by one order of magnitude from the case shown in figs. 6.2 and 6.3. (2) The incident, reflected and dissipated powers of the waveguide system were carefully monitored. The system was then precalibrated for power losses. With these actual measured powers, the actual power absorbed LE 1 ma. m... 2 mgfls 4 mo m o 2 so . c mm Y o _a. a. Exi a xv o as. n m u . ... ....“ o 4 . .l. . . w u 5 1.1m 2 . l . .l. . 5 . .4. . — N A u m M1 . 2 . Z . l . 1 . 2 1 . a - i 0 . 0 . 2 . . .I. . . .I. . 0 _— vuI . .. .. . O . 0 _ 2 . 2 M . l . O . 6 nm 3 . . .----T---.----. . . . n . _o .o .2 h... 2 5 . 5 . 3 . Z . . . .iu'lJlllL . 0 . l . l . 5 _ 5 . l . 0 . . Ill! r c . . 0 . .I. . 5 0 - 9 . . 0.1 8 .. . 0 l . 5 . 5 . l . . fri . . _ o u 0 n O . m _ l . .l. . M... . 5 . “.4 . 6 tf . .I. . . 6 . 5 . 8 . 7 . . . . III; I e . 0 0 . l . l . .:4 a. 6.. 6 . 7 ..1 . co) . n . n 0 n 0 . m. . m. _ l n ...w . 5 . 5 u 5 . ......” 1“ uflu '--'1"-- O O . O . o l l l d / .I. . 6 n l . 8 . IJIIIIAIIII‘ . ”I u .h. . u . . 0 t1 8“ u 5 p 7 --- "' ' O . 2 . l . m . 5 u 5 . 6 . 5 n . . JIIILIII. mm 92 0 . O . . l 1 . 5 5 4 . 4 . . . ... otlJ . . . . 0 . 0 u 0 l _ l n 5 . 5 . 5 ..9 ..1 e E c u o . o u o n 0 O _ m u 1 . w . 4 u l “f e Ilurullrl ._ . . . . . . . 0 . 0 . l . Z O Bax 'LI'IL . O . O 3 I'lrll'L' -' O I IIL 6 am .1. F iun at eq1 Pa 137 by the cell sample was determined using the relation P = P - P - Pc1188 — abs inc ref loss Power absorbed Total Power Power ' Power by the cell sample - power reflected dissipated loss 1 incident in matched the load system (6.1) (3) The actual absorbed power by the cells (cells and the liquid med- ium) was checked by using the equation of conservation of energy. For a biological system under the exposure of electromagnetic radiation, the equation balancing the power in the system is given as 1211st = 55 6 o(¥')| EEG?) [2 dV' . aug- + hcAc(T-To) + hrAr('l‘-Tw) (6.2) Power absorbed by Time rate of eat transfer Heat transfe the biological syste volume heat y convection by radiation increase where T is the temperature of the cell sample, T0 is the initial cell sample temperature and TV is the temperature of the surrounding walls. hc and hr are heat transfer coefficients for convective and radiative transfers; Ab and Ar are effective areas of convection and radiation respectively. Mlis the mass of the biological system and C is the average system heat capacity. If the time rate of temperature increase at T-To is carefully measured, the right hand side of eqn.(5,2) can be approximated by the first term CM.(dT/dt) , and thus P can be calculated. In our ex— abs periment, the dimensions of cell samples are standardized so that only 138 a few test samples are needed for conducting this experimental verifi- cation. It is important to note that in all other cell samples under exposure, the measurement of the temperature increase rate should be avoided because the thermocouple may induce a strong local electric field in the cell sample and it may, in turn, cause some serious arti- facts. The temperature of the cells may be monitored intially and after the exposure. The value of Pabs thus calculated was comparable with that obtained from eqn. (6.1) which in turn was comparable with power absorbed obtained by using numerically calculated Epfield from step (1). In our study, the results obtained from these three steps agreed closely, therefore, implying the validity of fiffield at the 10- ' cation of the cell obtained by solving the tensor integral equation. 6.5 Study Criteria After exposing a number of samples to the microwave, the next task was to study the results by using certain probability criteria. Since the number of samples exposed to electromagnetic radiations was less than 30 for the majority of the cases, the use of student t-test was preferred. Our objective was to make inferences concerning the difference between the two population means obtained from the data for the controlled and the exposed cell samples. The comparison was done at 95% confidence interval or 52 probability level. The small sample statistical test for the difference between the two means is as follows: §1'§2 Test statistic: t --——————-] s[l+.l; (6.3) n1 n2 139 (n -1) s2 + (n -1) s2 2 1 1 2 2 where S = (n1 + n2 - 2) (6.4) n - 2 d 82 a 21 (Y1 ' ’1) a“ 1 1:1 n1 -1 (6.5) n - 2 $2 - 2:2 (y1 - yz) 2 i=1 n -1 (6.6) 2 n1 and n2 are the numbers of observations, §1 and §2 are the means and 1 and 82 are the standard deviations for the samples 1 and 2 respect- ively. S is the pooled estimate variance and the denominator in the S formula for 82, (n1 + n2 -2), is called the number of degrees of freedom assiciated with $2. The critical value of t was obtained from the tables[21]corresponding to (nl + n - 2) degrees of freedom at 2 952 confindence interval or 52 probability level. The experimentally obtained values of t by using eqn. (6.3) were then compared with the critical values of t obtained from tables for drawing some inferences. For the experimentally obtained values of t, their corresponding probability values were also mentioned because that information is frequently quoted in the literature for reference purposes. 6.6 Experimental Results Experimental results are summarized in tables 6.1 to 6.4. Table 6.1 shows the results of chromosomal analysis of the control and ir- radiated human amnion cells. The cells were exposed to a microwave with an intensity of 20.6 volts/ m at 2.45 GHz for times varying from 140 Table 6.1 Chromosomal aberrations of human amnion cells due to a microwave of 2.45 GHz with the electric field inten- sity of 20.6 v/mfor 7,12,19 and 60 tginutes respectivly. The initial cell temperature was 22 C. TYPE figfiROL 7 12 19 60 OF M131. M131. M131. MINd iS.D. 30 C 33 C 31 C 30.5 C CHROMOSOMAL ABERRATIONS CHROMOSOME BREAKS 0. 01:0. 0 0. 0 0. 0 0. 0 0. 0 CHROMOSOME * GAPS 0.0:0.0 0.0 0.0 0.0 1.5:0. 7 CHROMATID 3. +3. 0 4. 0 3. 35 2. 0 2. +0. 7 BREAKS 5’ 5 5" CHROMATID 2Q * GAPS 0. 2510. 35 1.0 1.4 0.0 3. 5:2. 1 SATELLITE Assoc. 70 75.18. 2 6o 0 8. 5 lo. 0 0. 01:0. 0 ACENTRIC 4. 5:3.1 4. 0 l. 4 0. 0 0. 010. 0 FRAGMENTSl zoo CELLS PER TREATMENT/TEST * PR OBABILIT Y LEVEL. SIGNIFICANT LY HIGHER THAN THE CONTROL AT THE 5% hm... , 5t: mim inc sli cer the CE [10 St ir 141 5 to 120 minutes. Results for four different times (7,12, 19 and 60 minutes) are tabulated. The control samples were kept at 37°C in the incubator. Chromosomes of the control cells were analyzed on two slides each containing 200 cells and chromosomal aberrations in per— centile were: Expressed in terms of means and standard deviations of the means. The irradiated cells were analyzed on one slide having 200 cells. The coromosomal aberrations of the irradiated cells which were noticeably higher than the control at 52 probability level are marked as stars(*). It is obvious that those cells exposed to the electric field intensity of 20.6 volts/m over a period of 60 minutes or longer seemed to suffer considerably higher chromosomal aberrations. Noticeable aberrations include chromosome gaps, chromatid breaks and chromatid gaps. It is worthwhile to note here that the temperature of the irradiated cells was kept lower than 37°C during the exposure period so that the chro- mosomal aberrations induced by the electromagnetic radiations were non- thermal in nature. Table 6.2 depicts the results of possible chromosomal aberrations induced in AV tissue culture cells by a 2.45 GHz microwaves of relat- 3 ively higher intensities than those of table 6.1. The intensities were 32 volts/m for 7 minutes and 41.3 volts/m for 4.5,8 and 10 minutes. Again the temperatures during the experiments were either 37°C or lower. The chromosomal aberrations of the irradiated cells were compared with the chromosomal aberrations of the controlled cells at 95% confidence interval. The results indicated that at 32 volts/m for 7 minutes and at 41.3 volts/m for 8 minutes or longer, the irradiated cells suffered significantly higher chromosomal aberrations. 142 Table 6.2 Chromosomal aberrations of human amnion cells due to a microwave of 2.45 61-12 with electric field intensities of 32 v/m for 7 min. and 41.3 v/m for 4.5 min., 8 min., and loomin. respectively. The initial cell temperature was 22 C. TYPE CONTROL 3; WM 1. 3V7M41.3v/M 41.3V/M OF MEAN 7 MIN. ASMIN. 8 MIN. 10 MIN. 0 o o o CHROMOSOMAL i S. D. 33 C 33 C 36 C 37 C ABERRATIONS CHROMOSOME BREAKS 0.010. 0 0. 0 0.0 0. 7* 0.5* CHROMOSOME GAPS 0. 0:0. 0 0. 0 0. 0 0. 7* 0. 0 CHROMATID BREAKS 0. 010. 0 4. 0* 2. O 2. 05 l. 5 CHROMATID GAPS 0.5.10. 7 4.0* 0.0 2.. 75* 1.5* SATELLITE ASSOC . 3. 012. 8 18. 0* l4. 0* 6. Z 6. 0 ,ACENTRIC FRAGMENTS l.5;_+_0.7 4.0 0.0 1.4 1.0 200 CELLS PER TREATMENT/TEST WERE ANALYZED. *SIGNIFICANT LY HIGHER THAN THE CONTROL AT 5% PROBABILITY LEVEL. exper: micro‘ to 42 the c stand ing v chrom somal gaps, humar for ‘ if tt cult‘ 25 h( hour, did I was I The I for 1 Culat thoS the 6.7 radj 143 Table 6.3 shows the average result of sixteen different sets of experiments for human lymphocyte cells. These cells were exposed to microwaves with intensities ranging from 20.6 volts/m for 40 minutes to 42.84 volts/m for 5 minutes at 2.45 GHz. Chromosomal aberrations in the control and irradiated cell samples were expressed in means and standard deviations. The value of t using eqn.(6,5) and the correspond- ing value of the probability level P were also tabulated for each chromosomal aberration. It was found that the most significantchromoh somal aberrations observed at 52 probability level included chromosome gaps, chromatid breaks and settalite associations. Table 6.4 exhibits the results for the successive exposure of human lymphocyte cells to a microwave with an intensity of 40.94 volts/m for 3 minutes on three successive days. This study was aimed to determine if there was any remarkable difference in terms of damage at different culture stages of the cells. The cells were exposed after 1 hour, 25 hours, and 49 hours of their initiations and then harvested after 68 hours of their initiations. The study seemed to indicate that there did not exist any stage during the culture stage of the cells which was more susceptible to the microwave radiations than the other stages. The numbers tabulated in the table give the percentage of damage seen for the different types of chromosomal aberrations along with the cal- culated values of t and the corresponding probability levels P. Again, those aberrations marked as star (*) show significant differences from the control at 52 probability level. 6.7 Summary It appears that human amnion cells when exposed to an electromagnetic radiation of 2.45 082 at the level of 20.6 volts/m for 60 minutes or 41.3 Ia 144 Table 6.3 Chromosomal aberrations of human lymphocyte cells due to a microwave of 2.45 032 of various intensities and exposure times. TYPE OF ‘CONTROL EXPOSED T P CHR OMOSOMAL MEAN_+_ MEANi ABERRATIONS s. D. s. D. CHROMOSOME ‘ BREAK 0. 6i1-1 1. 3_+_1. 3 1. 08 0.30 CHROMOSOME GAP 1. 8:1. 3 3. 712. 1 2. 33 0. 04* CHROMATID 2. 4+2. 5 6. 8+3. 2 3. 25 0. 005* BREAK " " CHROMATID 15. 4+5. 5 22. 3+8. 3 2. 03 0. 0 GAP - - 6 SATELLITE + + ... ASSOC. 5.5__2.2 9.3_4. 3 2. 33 0.04 ACENTRIC FRAGMEN'ISI 1. 2+1. 9 0. 9:0. 9 0. 368 0. 63 CELLS EXAMINED AT FIRST IN VITRO CELL DIVISION MICROWAVE EXPOSURE RANOED FROM 20. 6v/M FOR 40 MIN. TO 42. 84 v/M FOR 5 MINUTES. AVERAGE RESULTS FOR 16 DIFFERENT SETS OF EXPERIMENTS. *SIGNIFIES THE VALUES NOTICEABLY DIFFERENT FROM THE CONTROL AT 5% PROBABILITY LEVEL. 145 Table 6.4 Chromosomal aberrations of human lymphocyte cells due to a microwave of 2.45 GHz with an electric field intensity of 40.94 v/m for 3 minutes on 3 successive days. TYPE OF TREATMENT AT HOURS AFTER CULTURE CHROMOSOMAL INITIATION ABERRATION CON- 1 HR. 25 HR. 49 HR.TROL T P CHROMOSOME BREAK 0 1 o 0 0.55 0.6 CHROMOSOME 2 3 GAP 4 1 1 1.1 0. CHROMATID BREAK 9 11 9 3 2.97 0.024: CHROMATID CAP 23 24 18 22 -.8 .9 SATELLITE ASSOC. 19 18 16 6 3.4 0.01* ACENTRIC FRACMENTS ° ° 1 0 0. 5 0. 6 ALL TREATMENTS WERE HARVESTED AT 68 HRS. AFTER INIT IATION. lOOCELLS/TREATMENT TEST WERE ANALYZED. a SICNIFIES THE VALUES NOTICEABLY DIFFERENT FROM THE CONTROL AT 5% PROBABILITY LEVEL. 146 volts/m for 8 minutes or longer may suffer some chromosomal aberrations. Same kind of phenomenon was observed in human lymphocyte cells where intensities of 20.6 volts/m for 40 minutes or 42.84 volts/m for 5 minutes were sufficient to show some significant chromosomal aberrations. It is ffirther stressed that these chromosomal aberrations were non- thermal in nature as the temperatures of all the cell samples were kept either at 37°C or below during the exposure durations. The most sig- nificant point is that these exposure levels were substantially lower than the permitted U.S. safety standard of 194 volts/m. duc has the tie to bo th CHAPTER VII A USER'S GUIDE TO COMPUTER PROGRAM FOR INDUCED ELECTRIC FIELD INSIDE AN ARBITRARILY SHAPED, FINETELY CONDUCTING BIOLOGICAL BODY. This chapter explains the computer program used to quantify the in- duced electric field at various locations of the biological system, based on tensor integral equation method. In addition to the listing of the program, an example has been worked out to help understand the sequen- tial.order of control data files and a sample print out. 7.1 Formulation of the problem. The very first step in the numerical formulation of the problem is to visualize the shape, dimensions and the orientation of the biological body with respect to the incident electromagnetic wave. In this program, the incident electromagnetic wave is assumed to be a simple plane wave polarized in the x - direction with the electric field intensity of l v/m. Mathematically, the incident electric field may be expressed as .E1(;) - Q ejkoz - ‘Q (cos koz - jsin koz) (7.1) where k0 is the free space wave number and the wave is propagating in + z - direction. The incident electric field may illuminate the body either at normal incidence or at end - on incidence. The arbitrarily shaped biological body is divided into N small sub- volumes with each subvolume cubic in size for the optimum results. Further- more, the side of cubic subvolume should not be greater than kAo where A0 is the free space wave length of the incident electromagnetic field. 147 148 The maximum Size of the matrix the program can handle is 120 x 120. Since there are, in general, three components of the induced electric field in each small subvolume, therefore, the maximum number of subvolumes, without any simplifications, can not be greater than 40. This imposes a restraint on the physical size Of the biological body. Hence to be within the limits of the above mentioned program, as the frequency of the incident field increases the physical dimensions of the biological system should decrease. Since most of the biological bodies possesshuge volumes comr parable to many wavelengths of the incident wave at high frequencies, the program finds the least versatility unless some simplications are imr bedded into it. Some of the simplifications are already provided by nature in the form of symmetry, i.e. right half being the mirror image of left half in most living biological bodies such as, rat, cat and human beings etc. If these symmetrical properties are exploited to full extent, the 8—fold increase in the size of the biological body can be obtained. In other words, under these symmetric conditions the total volume of the biological system may be divided into 8 similar looking segments and here after called quadrants, then the induced electric field is calculated in one of these quadrants and the results are transformed very carefully into the rest of the quadrants of the body. More about these quadrants will be be said in the next section. Another way of increasing the actual number of subvolumes and still be within the aforementioned limits is to put a restraint on the induced electric field components. In general, for any form of the incident electric field, there exists three components of the induced electric field inside a biological system. However if the system is thin in any 149 direction, the induced component of the electric field in that direction may be comparatively smaller than the other conponents and therefore, may be neglected. An example for this type of thin approximation is the case Of thin cylinder . The thin cylinder may be considered having small subvolumes stacked one upon another. Hence, it has many cells in one direction whereas, only one cell in other directions. If the incident electric field is polarized in the direction of many cells, then intuitively we expect only that component of the induced electric field which is parallel to the incident electric field stronger than the other components. Therefore, if we neglect other components just in the outset, we can in- crease the number of subvolumes by a factor of three. It is, however, pointed out here that a sample run be executed to verify the applicability of thin approximation. Finally it can be concluded that with the symmetric conditions and thin approximation, the size of the actual biological system may be 24 times the size otherwise handled by the present computer program. After visualizing the symmetry conditions and deciding the number of components of the induced electric field, the next step in the numerical formulation of the problem is the specification of the location of each subvolume, its physical dimensions and the electrical parameters. All the physical and electrical parameters for a cell may be different than the rest of the cells. The central location of each cell is thén internally computed and the incident electric field intensity is automatically spec- ified. As stated earlier, the program is written for plane wave with in— cident electric field polarized in x - direction. However, other types of incident electric fields may be used with few changes in the main pro- gram. 00 vi ti OI 150 7.2. Description of computer program. The computer program is coded in FORTRAN-IV and can be compiled on any FTN. compiler. The main program is symbolically named as "FIELDS" with input and output formats on any undefined logic units in conjunc- tion with "TAPEl" and"TAPE2". "TAPEl" and "TAPEZ" are two logic units onto which some of the results are buffered out depending upon certain commands to be discussed later. Program "FIELDS" uses the following complex function and subroutines for the numerical evaluation of induced fields inside a biological system: "GMAT" - - is a complex function which calculates the elements of G matrix based on eqns. (2.24) and (2.25) as discussed in chapter 2. "RFN" - - is a subprogram which calculates the distance between one cell and another everytime the complex function "GMAT" is called by the main program "FIELDS". "CMATPAC" is a subprogram which calculates the induced electric field in each subvolume by solving N x N matrix. It is actually a Gauss-Seidel method for solving a system of N equations in N unknowns. "ANGLES" This subprogram, as the name suggests, determines the phase angles between real and imaginary parts of the induced electric field in each subvolume. A listing for the main program "FIELDS", the complex function "GMAT" and subprograms "RFN", "CMATPAC" and "ANGLES" is given at the end of the chapter. The listing for the subroutines appear in the order they are called by the main program. It is noted that "$" sign is used to separate one fortran statement from another on one card. data sect: and pro: 7.3 and 111 to 01 151 Before, we jump to use the main program, the structure of the input data files and their relative input variables are explained in the next section, because the understanding of the sequential order of the data files and the format specifications is a must in order to utilize the computer program effectively and efficiently. 7.3 Data structure and input variables. The sequential structure of the data files, the format specifications and the symbolic names of the variables appearing on each file are out- lined in table 7.1. Fig. 7.1 shows a sample biological body we will refer to from time to time. The biological body is divided into 8 quadrants and the center of the body is assumed to be the reference point. The body has two layers in z - direction and these layers are shown separated just for the clarity purposes. In actual calculations of the induced electric field we will assume that the first and second layer touch each other. It is highly important to identify the order of quadrants and their numbering system. For this program, the quadrants are numbered in the clockwise order beg- inning with the second layer as shown in fig. 7.1. The location of each subvolume is read with respect to the reference point. Note that the symmetry conditions exist in this case if the electrical properties and physical dimensions of each cell in first quadrant are.same as their counterparts in other quadrants. In this example, it is assumed that all the cells have same physical dimensions and electrical parameters. Under the symmetrical conditions, it is always intended to solve for the induced fields in first quadrant and then interpret the results in other quad- rants. Before we go any further in determining the induced fields, let us first understand the sequence of the data files. 152 Table 7.1 The symbolic names of input variables and corres- ponding specifications for the data files used in data structure for the program "FIELDS". File NO. Card No.(sfiSymbolic name Columns Format 1 l NDIV 1 11 2 1 COMP 1-6 A6 Q(J) ,J-1,8 11-18 8A1 FMEG 21-31 F10.0 SCAT 41-45 A5 3 l NX 1-2 12 NY 6-7 IZ NZ 11-12 I2 4 1 N 1-3 I3 5 l-N AMX 1-10 F10.3 AMY 11-20 F10.3 AMZ 21-30 F10.3 RLEPI 31-40 F10.3 SIGI 41-50 F10.3 DXCM 51-60 F10.3 DYCM 61-70 F10.3 DZCM 71-80 F10.3 153 .momonuso huwumao mom oumumaom CBOnm mum muomma .mCOfiuHoaoo huuoaahm noon: muamuomsv w Ousa wooa>fio cacao mu menopause Hmauoc um o>m3 2m ho voumawaoaaa soon Hmowwoaowo ushma Oau 4. H.N .me / 2---- W \ \ .’m /' \O --L-- x HOhOH umuww ushoa waooom 154 There are in all five data files. Each file consists of at least one data card. The maximum number of data cards in any file is equal to the number of cells the biological system is divided into. Under this division the first four files have one data card each whereas file numr her five has N data cards, N being the number of subvolumes of the bio- logical system in first quadrant. The information on each data file should be as explained below. First Data File: - This data file has only one data card which defines a symbolic name "NDIV" under I - format. NDIV - determines the further subdivisions of each side of a subvolume for more accurate results. Any number from 1 to 9 in the first column of the data card may be used. Dividing each side into "NDIV" subdivisions results into (NDIV)3 sub- small volumes, for the integration purposes, of each cell. It has been seen from experience that number 2 gives fairly good results as compared to even higher numbers and still keeps the computer computations down. It is noted that number 2 will subdivide a small cell into 8 sub-small cells for integration in numerical evaluation of elememts of [G] matrix. Second Data File: - consists of only one data card and it defines the number of components of the induced electric field, the number of quadrants used, frequency of the incident wave and the type of the inci- dent field. 4 "COMP" being the code name for the components of the induced elec- tric field may have any one of the following forms: "X-ONLY" for x - component of the induced electric field. The other components are assumed to be negligible. This code may be used for the case of thin cylinder considered in chapter 4. H1 "XANDY." flx’Y’Z. H 155 for x - and y - components of induced electric field. Under this assumption, the z - component is assumed to be fairly small. For instance, the thin biological bodies considered in chapter 3. in general, for all the components of the induced electric field. This is the code most oftenly used, unless it is made certain that thin approximations hold. It is stressed here, that any other information supplied to the code "COMP" will abort the program. (XJ),J=1,8 is the symbolic name for the quadrants. The maximum number of "FMEG" quadrants one can use under symmetric conditions is 8 where- as the minimum number of quadrants to be:specified is 1. When specifying only quadrant 1, note that we are not making use of any symmetry at all. Therefore, quadrant l is always specified. If we are using quadrants 1,4,5, and 8 under the symmetric conditions, then the numbers 1,4,5 and 8 are punched in columns 11, 14, 15 and 18 of the data card and filled with blanks in the remaining columns. reads frequency of the incident electromagnetic wave in MHz under F - format. Therefore, 2450.0 punched in the respec- tive columns will state that the frequency of the incident wave is 2.45 GHz. The last information on this data card is the specification of the type of incident electromagnetic wave. The symbolic name "SCAT" is reserved for this information under A - format. The followings are the permissible codes for the type of incident field. 156 "EXPKZ" for the exponential variation Of the incident electric field as given in equation (7.1) "COSKZ" for the real part of the exponential form of the incident electric field. "SINKZ" for the imaginary part Of the exponential form of the incident electric field. "EINCX" for the uniform incident electric field over the entire space. Any other code will abort the program. "SINKZ" and "COSKZ" type of incident field variations are needed when the biological body is div- ided into 8 quadrants. The induced fields for these two incident fields are combined in such a way so as to yield the exact induced fields in first and second layemh It is noted, however, that the induced fields in first and second layensmay be computed directly by using "EXPKZ" type of variation for the incident field with only 4 quadrants, only if the size of resultant matrix is within the handling capacity of the present program. Third Data File: - consists of one data card which defines the maximum number of cells in x -, y -and z - directions under I - format. This information is an integral part of the symbolic names "NX","NY" and "NZ" respectively. Although this imformation is not needed for actual cal- culations by the program yet, it helps to imagine the shape, size of the biOlogical system at a later date. Fourth Data File: - contains only one data card with very important imformation on it. It tells the computer about the total number of cells being considered. The code name for this information is "N" and read under I - format in the first three columns of the data card. 157 Fifth Data File: - this is the only data file involving more than one data card. In this case there are as many as "N" data cards. This set of data cards helps simulate the biological system and is the backbone of the numerical formulation of the problem. Each card contains the follovdng information: "AMX","AMY AND"AMZ" These codes correspond to the maximum boundaries of a cell in the x -, y - and z - directions in centimeters with reference to origion. This information is supplied by the programmer under F - format. "RLEPI" and "SIGI" are the codes for relative dielectric constant and conductivity (mho/m) of the cell. "DXCM","DYCM" and "DZCM" are the symbolic names for the dimensions of the cell in x 4, y - and z - directions in centimeters. Since each cell is a cube, the columns for "DXCM", "DYCM" and "DZCM" will contain the same information. This completes the detailed structure for the data files needed to specify all the necessary information for the quantification of induced electric field inside any arbitrarily shaped biological body. An exam- ple is worked out in the next section for the induced fields inside a biological body as shown in fig. 7.1. 7.4 An example to use the program. Let us now try to determine the electric field induced inside a bio- logical system, as shown in fig. 7.1, by an incident electric field as given by eqn. (7.1). Although this problem can be solved by considering only 4 quadrants since the number of cells in the first quadrant cons- tituting both the layers is comparatively small yet, we will use all the 8 quadrants in order to understand the logic of decomposing the plane prc thI me VC 158 propagating wave into two standing waves. Let us further assume that the frequency of the incident wave is 2.45 GHz and the electrical para- meters of the biological body are €=5050 and 0=5.94 th/m with a cell volume of l x l x 1 cm. There are in all 32 cells but only 4 cells con- stitute the first quadrant. As stated earlier, the program will be run in two parts and each time the results for the induced electric field will be stored on magnetic storage discs, hereafter referred to as "TAPEl" and "TAPEZ" due to the corresponding "COSKZ" and "SINKZ" variations in the incident electric field. These results are then combined in such a way so as to yield the theore- tical values of the induced fields in two layers. With the aids of section 7.3 and table 7.1, the sequential order of the data files due to "COSKZ" type variation of the incident electric field is as follows: File No. Information on the file. 1 2 2 x,y,z. 12345678 2450.0 COSKZ 3 02 02 01 4 004 5.1 1.0 1.0 1.0 50.0 5.94 1.0 1.0 1.0. 5.2 1.0 2.0 1.0 50.0 5.94 1.0 1.0 1.0 5.3 2.0 1.0 1.0 50.0 5.94 1.0 1.0 1.0 5.4 2.0 2.0 1.0 50.0 5.94 1.0 1.0 1.0 Note that'File No3'column is just for reference and furthermore, File No. 5 contains 4 data cards since the number of cells in quadrant l are 4. Before the program is actually executed we must add an extra control card in order to catalog "TAPEI" due to "COSKZ" type of variation in 159 the incident electric field. Let us assume that the main program is already on the magnetic disc under the permanent file name (PFN) "FIELDS INSIDE BODIES". In this case, the list Of the control cards needed for the execution of the program is as under: Card No. Its purpose Information on the card 1. authorization to use the computer PNC. 2. job card B,CM170000,T450,RG1,JC2500. 3. pass word PW-BHARAT 4. identification name HAL,BANNER,GURU 5. calling the PFN ATTACH,LGO,FIELDSINSIDEBODIES. 6. execute the program L00. 7: create the disk CATALOG,TAPEI,FIELDSDUETOCOSKZ. 8. end of control cards 7/8/9 *This control card is needed only when using "COSKZ" or "SINKZ" type of variation in the incident electric field. The main program uses "BUFFER OUT" statement for creating the mag- netic storage disc, "TAPE1"in the "COSKZ" case. To recall this disc a similar statement known as "BUFFER IN" will be used. A unit check at the end of either statement identifies end of the file. More information about these unformatted ways of writing and reading a sequantial data with efficiency may be obtained from any computer handbook. but this know- ledge is not necessary for using the program. The first disc for the induced electric field due to "COSKZ" type of variation in the incident electric field has been cataloged under a permanent file name "FIELDS DUE TO COSKZ". In order to create a second disc due to "SINKZ" type of variation in the incident electric field we have 'to rerun the above program.with the only change in the second file for th CI 160 the type of incident field in the data structure and card no. 7 for creating a new disc, "TAPEZ".These cards should look like- File No. Information on the file. 2 x,y,z. 12345678 2450.0 SINKZ Control card - 7* CATALOG,TAPE2,FIELDS DUE TO SINKZ. The second disc "TAPEZ" has now been created under a symbolic name "FIELDS DUE TO SINKZ". After creating both the tapes, we are now in a position to combine these results, on the induced fields due to "COSKZ" and "SINKZ" variations in the incident electric field, in such a way so as to yield the theore- tical values of induced electric field in the first and second layer. Another program called "COSINKZ" is written to interface the two tapes. The output of this program is the induced electric field with magnitude and phase information in quardrants 1 and 5. It may be borne in mind that the magnitude of the induced field in quadrants 2,3 and 4 is the same as in quadrant 1 and the magnitude of the induced field in quad- rants 6,7 and 8 is the same as in quadrant 5. The phase information in other quadrants may be obtained by intuition. The data file structure for the program "COSINKZ" is as follows: First Data File: consists of only one data card with the information on total number of cells "N", the number of components of the induced elec- tric field "COMP" and the frequency of the incident wave "FMEG" in MHz. This information is given in l-3,5-1o and 11-20 columns of the data card under I, A and F -formats for "N", "COMP" and "FMEG" respectively. 161 Second Data File: is actually a set of as many data cards as there are number of cells in consideration of the biological system. Each card in this set contains the information for the relative dielectric constant "RLEPI", conductivity (mho/m) "SIGI" and the physical dimensions "DXCM", "DYCM", and "DZCM" of the cell in centimeters. The format for this in- formation is arranged in such a way so that the Fifth Data File of the main program may be used as it is. This helps avoid the duplication of the same information. Summing all that up, the sequential order of data file structure for the above example to log in "TAPEl" and "TAPEZ" using "COSINRZ" will be: File No. Information on the file. 1 004 x,y,z. 2450.0 2.1 1.0 1.0 1.0 50.0 5.94 1.0 1.0 1.0 2.2 1.0 2.0 1.0 50.0 5.94 1.0 1.0 1.0 2.3 2.0 1.0 1.0 50.0 5.94 1.0 1.0 1.0 2.4 2.0 2.0 1.0 50.0 5.94 1.0 1.0 1.0 It may be noted that the first three columns of information in Second Data File are of no importance for the execution of the program "COSINKZ? In order to run the program*with the above data structure, the con- trol cards should incorporate the following commands to attach "TAPEl" and "13512132" before the "LCD" command card. ATTACH, TAPEl, FIELDS DUE TO COSKZ. ATTACH, TAPEZ, FIELDS DUE TO SINKZ. 7.5 Printed output. The most important data on the output file is the echo of the data from the input files in addition to the required output. The purpose of doing so is mainly two-fold, firstly, it provides an immediate check 162 on the data used for the input variables and secondly for further future references. Blending these requirements into our numerical formulation for the induced fields inside an arbitrarily shaped biological system, the following data needs to be reproduced on to the output files every- time the program "FIELDS" is logged in. Firstly, the maximum boundary limits of each cell as read in through the symbolic code names "AMX? "AMY", and "AMZ" and the dimensions of each cell "DXCM", "DYCM" and "DZCM" in centimeters in the x —, y - and z - directions respectively. Secondly, the internally calculated coordinates in the x -, y - and z - directions for the central location of each cell, its volume and its permittivity and conductivity. Thirdly, the components of incident electric field in each cell and the type of its variation . Fourthly, the most needed result for the induced electric field and power density in each cell in addition to the frequency of incident field and total power absorbed by the biological system. Finally, the real and imaginary parts of each component of the in- duced electric field in each cell along with its absolute magnitude and phase angle. Since the program.”FIELDS" is run twice for "COSKZ" and "SINKZ" type of variations in the incident field in order to catalog "'JAPE 1" and "TAPE 2", therefore, each time a output file is generated in accordance with the above-mentioned subdivision of the output format. The printed output due to "COSKZ" type of variation in the incident electric field is shown on pages 166 and 167 . Most of the input variables are echoed on page 166, whereas the absolute values of the components of 163 induced electric field, power density in each cell and total absorbed power are shown on page167. The real and imaginary parts of each com- ponent of the induced electric field is the data buffered out onto 'VIAPEI". This information along with magnitude and phase angle for each component of the induced field is the last part of the output file and is suppressed here, it will be reporduced from "TAPEI" by using the program "COSINKZ?. The printed output due to "SINKZ" type of variation in the incident electric field is shown on pagesl68 and 169. Most of the input variables are echoed on page l68,whereas the absolute values of induced electric field components, power density and total power absorbed are shown on page 169. In this case, the real and imaginary parts of each component of the induced electric field are buffered out on ”TAPEZ". Once again, this information in addition to magnitude and phase angle for each come ponent is the end part of the output file and is not shown here, since it may be produced from "TAPEZ" by using the program "COSINKZ'.’ Once the files "'TAPEI" and "TAPE2" are created, it 18 now possible to combine these files in a systematic way to obtain induced fields in each layer due to exponential variation of the incident electric field. The program "COSINKZ" does this job for us. The data file structure for this program has already been explained. Therefore, by attaching the files "TAPEI" and"TAPfl", the output file generated by "COSINKZ" is explained below with numbers 1,2 etc. corresponding to new page of the output file. 1. The input data variables are again reproduced for verification as shown on page 170. This information is self explainatory. 2. The buffered in values for the real and imaginary parts of the induced 3. 164 electric field components due to "COSKZ" type of variation in the incident electric field from "TApgln with the magnitudes and phase angles are shown on the same page. The buffered in values for the real and imaginary parts for the in- ° duced field components due to "SINKZ" variation from "TAPEZ" with magnitudes and phase angles are shown on page 171. 4-5.The absolute values for the induced electric field components, power density and total absorbed power due to exponential variation of the incident electric field are shown on pages 172 . for the first layer and second layers respectively. 6-7.The real and imaginary parts for the induced electric field compon- ents with the magnitude and phase angle in the first and second layers due to exponential variation in the incident electric field are shown on pages 173 and 174 respectively. For a quick check on the bufferedin values of the induced electric fields from "TAPEI" and "TAPEZ", a comparison among the origional values from the output files due to "COSKZ" and "SINKZ" be made. In the end, it is left to the user to verify these results on the induced electric fields inside first and second layers by considering only four quadrants and exponential nature of the incident electric field. This will help develop the confidence in using "FIELDS". 7.6 Listipg of the programs. A FORTRAN listing of the programs "FIELDS" and "COSINKZ" for come pilation on CDC-6500 begins on page 175. The listing for the program "FIELDS" and its subroutines precedes that for "COSINKZ" and its sub— routines. The subprogram are listed in order of their first appearance . in the main programs. "$"signs have been used most often to separate two 165 FORTRAN statements from one another on a computer card. "*"signs have been imbedded into the program for additional comments and for separation of input and output formats etc. If compiled, the program "FIELDS" re- quires 1265008 storage units of core memory whereas "COSINKZ" uses 34660 8 approximately. oflIU Z— I: .-H: THE PARAMETERS OF EACH CELL AS READ IN ARE GIVEN BELOW IN CNS. 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The understanding of the induced electric field at various locations inside the system is very important for investigating the biological hazards of nonionizing radiation. As an introduction, the interaction of an electromagnetic field with a biological system was considered. A basic theoretical approach leading to a tensor integral equation was introduced. The method of moments was used to transfer the tensor integral equation into a set of simultaneous equations for the electric field induced inside and scattered by the biological system. This set of simultaneous equations was solved by a well known standard technique. Experimentswere conducted to verify the theoretical results on the induced electric field in regularly and irregularly shaped biological bodies. Saline solutions of different concentrations were used to model the biological body. A very good agreement between theory and experiment was reported when the saline solution models were exposed to vertically polarized plane wave of various frequencies at normal and end - on in— cidence respectively. The results for the scattered field from a cylinder were compared theoretically with King's formula and also verified experimentally for 189 190 different concentrations of saline solutions modelling the biological cylinders. In each case a good agreement between theory and experiment was reported. The integral equation method was further employed to quantify the induced electric field intensity and absorbed power density inside modelled adult and child's torsos for vertically and horizontally polar- ized plane waves. The effects of torso geometry on the induced fields were also considered. Then the tensor integral equation method was used to obtain information on electromagnetic wave local heating. The theoretically obtained results were experimentally confirmed at microwave range to obtain very good agreement between theory and experiment. Lastly, the tensor integral equation method was used to quantify the induced electric field at various locations of the cell samples. These results were experimentally verified by the total power absorbed and heat dissipation techniques. Experimental results on chromosomal aberrations of human amnion cells and lymphocyte cells were reported, when these cell samples were irradiated by microwaves with intensities lower than the safety standard. Under the student t - test probability crieteria certain chromosomal aberrations were observed at some low intensity levels of the microwave. In addition, a computer program to quantify the induced electric field was described with an example and instructions for its use. The limitations of the numerical technique were discussed and some ap— roximations to overcome these limitations were pointed out. Since the numerical formulation of most of the practical problems end up in inverting an enormously large matrix, the wayouts to extend the applicability of numerical solution are searched. A new computer 191 program which can handle twice the size of present matrix has been written based on partitioning scheme. The listing of this very expensive wayout may be obtained from the author. Although lot of different experiments have been reported usingan incident plane electromagnetic wave, yet there exists a great demand to carry on the theoretical and experimental research for the quantifi- cation and measurement of internal electric field in finite arbitrarily shaped biological bodies having arbitrary composition, when the body is irradiated by non-uniform electromagnetic fields. Furthermore, the human torsosdiscussed were grossly simplified with all the cells having similar electrical and physical composition in almost all the cases. Since human body is very complex and there is a noticeable lack of experimen- tal data on the induced fields inside human body, consequently, a useful topic for further research would be that of conducting experiments on human models, having inhomogeneous composition and with cells of various dimensions. BIBLIOGRAPHY 8. 10. ll. BIBLIOGRAPHY Schwan, H.P., Radiation biology, medical applications, and Radiation hazards, in Microwave Power Engineering, Edited by E.C. Okress, Vol. 2, pp. 215 - 232, Academic Press, New York, 1968. Lehmann, J.F., A. Guy, V.C. Johnston, G.D. Brunner, and J.W. Bell, "Comparison of relative heating patterns produced in tissues by exposure to'microwave energy at frequencies of 2450 and 900 megacycles.‘ Arch. Phys. Med. Rehabil., Vol. 43, pp. 69 - 76, 1962. Shapiro, A.R., Lutomirski and H.T. Yura, "Induced fields and heating within a cranial structure irradiated by an electromagnetic plane wave? IEEE Trans. Micr. Th. Tech. MTT - 19, pp. 187 - 196, 1971. 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