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Ricard, Thomas A.
Active and passive microwave radiometry for transcutaneous measurements of temperature and oxygen saturation
h [electronic resource] /
by Thomas A. Ricard.
[Tampa, Fla] :
b University of South Florida,
Title from PDF of title page.
Document formatted into pages; contains 123 pages.
Dissertation (Ph.D.)--University of South Florida, 2008.
Includes bibliographical references.
Text (Electronic dissertation) in PDF format.
ABSTRACT: In this work we explore two novel uses of microwave technology in biomedical applications. Introductory material on the electrical properties of biological tissues is presented to form the groundwork for the basic theory behind both techniques. First, we develop a technique that uses 60 GHz signals to detect changes in blood oxidation levels. Several atmospheric propagation models are adapted to predict oxygen resonance spectra near this frequency. We are able to predict and observe the changes in these levels as the blood ages up to 48 hours. Identical testing procedures performed using arterial blood gas (ABG) calibration samples with controlled oxygen levels show similar results to those obtained as bovine blood ages. We then discuss a potential application of this technique to the detection and diagnosis of skin cancer. The second application involves non-invasive measurement of internal body temperatures.Conventional methods of body temperature measurement provide a numerical value for a specific location on the body. This value is then applied to the remaining body systems as a whole. For example, a measurement of 37¨ C obtained orally can possibly lead to the erroneous conclusion that temperature is normal throughout the body. Temperature measurements made on specific internal organs can yield more information about the condition of the body, and can be invaluable as a tool for performing remote diagnostic evaluations. We explore the use of microwave radiometry in the low GHz spectrum to show that temperature information can be obtained directly and non-invasively for internal organs. We use the principles of black-body radiation theory combined with the reflection and transmission characteristics of biological tissues to predict the temperature delta that would be externally measured, given specific changes in the internal temperature.Data taken using a microwave radiometer and planar structures made with biological phantoms are compared to analytical results, showing that detection of internal temperature changes of can be performed externally in this manner.
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Co-advisor: Thomas Weller, Ph.D.
Co-advisor: Jeffrey J. Harrow, M.D.
x Electrical Engineering
t USF Electronic Theses and Dissertations.
Active and Passive Microwave Radiometry for Transcu taneous Measurements of Temperature and Oxygen Saturation by Thomas A. Ricard A dissertation in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Electrical Engineering College of Engineering University of South Florida Co-Major Professor: Thomas Weller, Ph.D. Co-Major Professor: Jeffrey J. Harrow, M.D. Shekhar Bhansali, Ph.D. Lawrence Dunleavy, Ph.D. Nagarajan Ranganathan, Ph.D. John Whitaker, Ph.D. Date of Approval: July 18, 2008 Keywords: bioengineering, bioelectromagnetics, oxy gen resonance, skin cancer, radiometric thermometry Copyright 2008, Thomas A. Ricard
Dedication When I left my industry position in Connecticut and relocated to Florida in order to resume my formal education, I was far from the o nly person who was affected by that decision. I would like to dedicate this work to th ose persons closest to me who rearranged their lives so that I could be where I a m today: my parents, Jean and Armand Ricard, my wife, Gina Harris Ricard and my daughter s, Bernadette Allison and Amanda Valentine Ricard.
Acknowledgments If it takes a village to raise a child, it certainl y takes a small community to produce a dissertation. I am grateful to the follo wing persons whose assistance and advice proved invaluable during my research and the preparation of this work: My dissertation committee, especially Drs. Thomas W eller and Jeffrey Harrow. Ms. Gina Ricard B.S. RRT NPS, Hillsborough Commun ity College, Tampa Mr. Bernard Batson, IGERT and Bridge to Doctorate P rograms, USF Mr. Robert Roeder, Raytheon CompanyDr. Sanjukta Bhanja, Department of Electrical Engin eering, USF Dr. Joel Strom, Professor of Internal Medicine, USFDr. Neil Fenske, Department of Dermatology, USFMs. Karin Banach, Department of Dermatology, USFFunding for my studies and research were provided i n part by the NSF IGERT grant number DGE-0221681, by a grant from the Skin Cancer Foundation and by the Raytheon Company.
i Table of Contents List of Tables iii List of Figures iv Abstract vii Chapter 1 Introduction 1 1.1Organization and Contributions 4 Chapter 2 Electrical and RF Properties of Biologi cal Materials 6 2.1Properties Database 6 2.2Complex Permittivity 7 2.3Conductivity 13 2.4Attenuation 15 2.5Intrinsic Impedance 17 2.6Conclusion 19 Chapter 3 Microwave Sensing of Blood Oxygenation 20 3.1Oxygen Resonances 203.2Resonance Modeling Techniques 223.2.1Reduced Line Base Model 223.2.2Theory of Overlapping Lines 283.2.3Modeling Evaluation 323.3Blood Oxygen Characteristics 333.4Approximation Results 36 3.5Blood Resonance Measurements 373.6 Blood Permittivity Measurements 51 3.7 Software Simulation Results 54 3.8Skin Attenuation 57 3.9Application to Skin Cancer Detection 583.9.1Motivation 59 3.9.2Dimensional Requirements 603.9.3Background/Literature Review 613.9.4Impedance Spectroscopy 613.9.5Visible Light Spectroscopy 623.10Future Work 63 3.11Conclusion 63
ii Chapter 4 Radiometric Sensing of Internal Organ Temperature 65 4.1History and Background 66 4.2Radiometry Review 67 4.3Propagation Model 71 4.4Biological Model 73 4.5Results of Analysis 77 4.6Verification 78 4.7Measurement Sensitivity 88 4.8Limitations of Present Study 914.9Future Work 92 4.10Conclusion 93 Chapter 5 Summary and Conclusion 94 5.1 Summary 94 5.2 Conclusion 95 List of References 96 Appendices 101 Appendix AElectrical Properties of Various Biologic al Materials 102 Appendix BMATLAB Code for Oxygen Resonance by Reduc ed Line Base Method 106 Appendix CMATLAB Code for Oxygen Resonance by Theor y of Overlapping Lines 109 Appendix DBovine Blood Permittivity Data 111Appendix EAgilent 37397 Vector Network Analyzer Spe cifications 121 Appendix FMathCAD Code for Planar Biological Struct ure 122 About the Author End Page
iii List of Tables Table 2-1Four Term Cole-Cole Parameters for Select Biological Materials 11 Table 3-1Quantum Parameters Affecting Oxygen Resona nces 21 Table 3-2Liebe Parameters for Oxygen Resonance Line s 27 Table 3-3Rozenkrantz Parameters for Oxygen Resonanc e Lines 31 Table 3-4BTPS Conditions for Arterial Blood 36 Table 3-5Complete Rapid QC Solution Level Descriptions 47 Table 4-1Propagation Constants for Skin and Fat at 1.4 GHz 76 Table 4-2Permittivity Comparison for Biological Mat erial Phantoms at 1.4 GHz 79
iv List of Figures Figure 2-1Complex Permittivity of Select Biological Materials 12 Figure 2-2Conductivity of Select Biological Materia ls 14 Figure 2-3Attenuation of Select Biological Material s 16 Figure 2-4Intrinsic Impedance of Select Biological Materials 18 Figure 3-1Sea Level Atmospheric Oxygen Modeling Eva luation 32 Figure 3-2Oxygen Partial Pressures from Air to Tiss ues 35 Figure 3-3Comparison of Oxygen Attenuation (Absorpt ion) Results Under Arterial Blood Conditions 37 Figure 3-4Oxygen Resonance Sample Test Setup 38 Figure 3-5Bovine Blood Resonances from 50 65 GHz (Sample Age 90 Minutes) 39 Figure 3-6Distilled Water and Ethanol Resonances fr om 50 65 GHz 40 Figure 3-7Bovine Blood Resonances from 50 65 GHz 41 Figure 3-8Blood Response Changes with Age (Integrat ion Analysis) 42 Figure 3-9Blood Response Changes with Age (Moving A verage Analysis) 43 Figure 3-10Bovine Blood Resonances with O2 Attenuation Superimposed 43 Figure 3-11Bovine Blood Resonances with O2 Attenuation Superimposed (60 61.5 GHz) 44 Figure 3-12Non-Oxygenated Material Responses with O2 Attenuation Superimposed 46
v Figure 3-13Complete Calibration Sample Responses wi th O2 Attenuation Superimposed 48 Figure 3-14Antenna Shorting Plate/Test Fixture 49 Figure 3-15Blood Oxygen Calibration Sample Data Usi ng Test Fixture 50 Figure 3-16Non-Oxygenated Materials Data Using Test Fixture 50 Figure 3-17Permittivity Test Probe in Sample 53 Figure 3-18Blood Loss Tangent 54 Figure 3-19Test Simulation in HFSS 55 Figure 3-20HFSS Simulation of Bovine Blood Response 56 Figure 3-21Resonance Comparison: Blood Simulation, Measurement and Calibrator Data 57 Figure 3-22Predicted Signal Attenuation in Skin as a Function of Frequency 58 Figure 4-1Blackbody Spectral Brightness as a Functi on of Frequency and Temperature 68 Figure 4-2Plancks Law and Rayleigh-Jeans Approxima tion at T = 310 K 69 Figure 4-3Emitted Power vs. Temperature Over a 300 MHz Bandwidth 71 Figure 4-4Simplified Biological Model 74Figure 4-5Two-Layer Biological Structure 7 5 Figure 4-6Emitted vs. Internal Temperatures for a B iological Structure 78 Figure 4-7Total Power Radiometer Block Diagram 80 Figure 4-8Total Power Radiometer Antenna 8 1 Figure 4-9TPR Antenna Frequency Response 8 1 Figure 4-10TPR Test Bed Schematic 84 Figure 4-11Input TTL Switch Configuration 85
vi Figure 4-12Radiometric Temperature of a Biological Phantom Construct 88 Figure 4-13Effect of Skin Permittivity Variations o n Emitted Temperature 90 Figure 4-14Effect of Fat Thickness Variations on Em itted Temperature 91 Figure A-1Complex Permittivity of Various Biologica l Materials 103 Figure A-2Conductivity and Loss Tangent of Various Biological Materials 104 Figure A-3Attenuation and Phase Characteristics of Various Biological Materials 105
vii Active and Passive Microwave Radiometry for Transcu taneous Measurements of Temperature and Oxygen Saturation Thomas A. Ricard ABSTRACT In this work we explore two novel uses of microwave technology in biomedical applications. Introductory material on the electri cal properties of biological tissues is presented to form the groundwork for the basic theo ry behind both techniques. First, we develop a technique that uses 60 GHz sign als to detect changes in blood oxidation levels. Several atmospheric propagation models are adapted to predict oxygen resonance spectra near this frequency. We are able to predict and observe the changes in these levels as the blood ages up to 48 hours. Ide ntical testing procedures performed using arterial blood gas (ABG) calibration samples with c ontrolled oxygen levels show similar results to those obtained as bovine blood ages. We then discuss a potential application of this technique to the detection and diagnosis of sk in cancer. The second application involves non-invasive measur ement of internal body temperatures. Conventional methods of body tempera ture measurement provide a numerical value for a specific location on the body This value is then applied to the
viii remaining body systems as a whole. For example, a measurement of 37 C obtained orally can possibly lead to the erroneous conclusion that temperature is normal throughout the body. Temperature measurements made on specific in ternal organs can yield more information about the condition of the body, and ca n be invaluable as a tool for performing remote diagnostic evaluations. We explore the use of microwave radiometry in the low GHz spectrum to show that temperature information c an be obtained directly and noninvasively for internal organs. We use the princip les of black-body radiation theory combined with the reflection and transmission chara cteristics of biological tissues to predict the temperature delta that would be externa lly measured, given specific changes in the internal temperature. Data taken using a micro wave radiometer and planar structures made with biological phantoms are compared to analy tical results, showing that detection of internal temperature changes of can be performed externally in this manner.
1 Chapter 1 Introduction The form and function of the human body have been s tudied for millennia, using a variety of methods and technologies as they were adapted and became available. Some of these methods have included visual, chemical, me chanical and, more recently, radiological and computational techniques. The fie ld of microwave engineering, having been refined in the mid-to-late 20th century, remains a relatively undeveloped tool for the study of the bodys surface and internal characteri stics. In this work, we present the analysis and results of several potential implement ations of the use of microwave signals to sense changes and abnormalities in and under the skin. The techniques we will explore are microwave spectr oscopy and microwave radiometry. The study of spectroscopy in this work is directed toward the detection of oxygen resonance lines by examining the signal refl ection characteristics of oxygenated blood at frequencies around 60 GHz. While the stud y of oxygen resonances has a long and rich history in relation to communications and radar engineering , we are unaware of any previous effort to apply this phenom enon to the study of blood. Similarly, work has been performed only recently in characterizing the resonant frequencies of blood near 60 GHz .
2 Signal reflection generally occurs at points of cha nge in the impedance presented to the signal during propagation. Typically, these changes are due to material properties in the propagation path or to changes in the struct ure in which propagation is taking place. In the biomedical field, changes in structu re cannot always be accurately characterized; consequently, we will focus on the p roperties of the materials through which the signal is propagating. Signal reflection is quantified by the unitless ref lection coefficient G which is defined in terms of the material intrinsic impedanc e h by  0 0h h h h+ = G, (1-1) where h0 indicates the intrinsic impedance of the original material through which the wave is propagating and h is the impedance of a different material on the ot her side of a boundary. Since the complex value of the intrinsic impedance h is dependent on the complex material permittivity e we devote a large portion of Chapter 2 to the sub ject of permittivity and its uses in material characterizat ions and analysis. Assuming that h (and h0) are constant with frequency (which is a reasonabl e assumption for small bandwidths), we would expect G to likewise remain constant with frequency. However, the reflection coefficient dec reases considerably at resonant
3 frequencies, not directly due to changes in materia l impedances, but to quantum energy changes at the molecular level , . Chapter 3 is devoted to the study of this resonance phenomenon in oxygenated blood. We show that changes in signal reflection c haracteristics are related to those documented in atmospheric propagation studies, and can be detected for small volumes of material. The primary motivation for this area of research is the early detection of skin cancer. While conventional techniques such as exci sion and biopsy are quite effective in determining the presence of malignant activity, thi s approach is not without its drawbacks. For example, excision is invasive by na ture, and as such can be a source of intimidation to some patients. Time is also a fact or, since the excised material must be examined in vitro often at a different location from the patient, t o obtain a diagnosis. Cost can be a major problem for those patients with out health insurance coverage. The technology developed in this work may provide a mea ns to non-invasively produce immediate results at little or no cost to the patie nt. Chapter 4 deals with microwave radiometry, which is based on the principle of blackbody radiation: the phenomenon of all objects with a non-zero absolute temperature to emit RF energy. Emission of this energy occurs at very low signal levels over an extremely wide frequency range, with the peak ampli tude and frequency of blackbody emission dependent on the absolute temperature of t he object , .
4 In Chapter 4 we investigate the implementation of r adiometry to the measurement of internal body temperatures; specifically, the te mperatures of vital organs and tissues of astronauts during extended missions in space. In o rder to analyze a multi-layered structure to determine the characteristics of an in ternal layer, we must take into account such factors as material propagation and impedance and multiple boundary reflection coefficients. Transmission and reflection phase ch aracteristics must also be considered if an accurate coherent model is to be achieved. We show the results of a first approximation analys is and compare those to data collected using a simple 1.4 GHz radiometer. The t est structure consists of planar layers of biological phantoms that have similar electrical properties to those of muscle, fat and skin tissues.1.1Organization and Contributions We begin in Chapter 2 by introducing key concepts t hat describe interaction between microwaves and materials, and characteristi c values for common tissues. Chapter 3 is devoted to the detection of tissue oxy genation by the means of sensing oxygen resonances in the microwave frequenc y range. In this chapter we present the results of several resonance approximation tech niques and show measurements confirming the validity of the basic theory. In pr esenting this information, we demonstrate the basic technique of a real-time, non invasive method for determining
5 tissue oxygenation. The primary motivation for thi s study is the detection of malignant activity on and just below the skin, but other appl ications, such as the studies of psoriasis and burn and wound healing are discussed. Chapter 4 presents an application of microwave radi ometry. The technique is applied to the detection and quantification of inte rnal organ temperature changes. After a brief review of radiometric theory and principles, we show the results of analyses of simple planar structures and the correlation of the se results with the measurements made using a microwave frequency radiometer. This study was initiated as part of a space suit design for astronauts on extended journeys, and as such has great potential toward the advancement of space exploration and future human c olonization of other planets. This technique also has potential applications in the fi elds of surgery, critical health monitoring, and fire detection. It is our hope that this material may provide some new directions for the use of microwave techniques in biological and medical appl ications, and may ultimately serve toward a betterment of the human condition.
6 Chapter 2 Electrical and RF Properties of Biological Material s In this chapter we will review some of the basic me chanisms of the interactions between radio frequency (RF) and microwave energy a nd biological tissues and materials. Those interactions with which we will b e concerned include the effect of skin and subcutaneous materials on the propagation chara cteristics of microwave signals. In order to ensure a thorough presentation of the prop erties that affect signal propagation within the body, we must begin with a review of com plex permittivity and show how other properties, such as conductivity, attenuation and impedance can be derived from this quantity. Information that is specific to a p articular technique is presented in later chapters, that is, spectrographic and radiometric m aterial will be relegated to Chapters 3 and 4, respectively.2.1 Properties DatabaseMuch of the numerical information presented in this work is derived from the data and formulas contained in Compilation of the Dielec tric Properties of Body Tissues at RF and Microwave Frequencies, compiled by Gabriel and Gabriel for Kings College in London . One intent of this report was to de rive models for the frequency
7 dependence of the dielectric properties of the tiss ues investigated . The report presents the parameters for and uses a four-term Cole-Cole m odel  to account for the dispersion levels found in wide-band frequency stud ies of biological material behavior. Forty-four types of material are characterized in t his report, including body fluids, tissues and organs. Computation of the material characteristics can be accomplished by any number of means. However, a ready-made implementation of the Gabriel model is available: the Tissue Dielectric Properties Calculator spreadshe et by Anderson and Rowley for Telstra Research Laboratories . This spreadshe et provides rapid evaluation of the Gabriel model over the frequency range of 10 Hz to 100 GHz, and was used to obtain the data for many of the tissue characteristics plots i n this work. Plots corresponding to representative biological materials are included as part of the development in this chapter; more are contained in Appendix A.2.2 Complex PermittivityAny discussion of the interaction of RF and microwa ve fields with biological materials and tissues must take into account the co nstitutive parameters of these materials. As discussed in , these parameters include electric permittivity in Farads per meter (F/m), magnetic permeability in Henries per meter (H/m), and conductivity in Siemens per meter (S/m).
8 Permittivity and permeability are represented as co mplex quantities as follows:e = j, (2-1) andm = m¢ jm, (2-2) respectively. Since the human body is considered to be nonmagneti c and transparent to magnetic fields , the behavior of magnetic fiel ds and their effect on biological materials and processes need not be considered here Consequently, we can assume a scalar value of 1 for the relative permeability of any materials under discussion, and use the free-space permeability (0) value of 4 x 10-7 H/m wherever permeability forms part of a relationship. The permittivity value e is a product of the complex relative permittivity er and the permittivity of free space (e0 8.8542 x 10-12 F/m). Thus,e = e0er (2-3) or, in complex notation,e¢ je = e0(er¢ jer) (2-4)
9 The relationship between the real and imaginary com ponents of the complex permittivity is often referred to as the loss tangent and is exp ressed as tan q = er / er¢ (2-5) In materials in which er is a function of frequency, the value of this func tion reaches a local maximum at a frequency f correspond ing to a relaxation time t where the relationship between frequency and time is defined by t (seconds) = 1/ ( 2pf ) (Hertz) (2-6) It has been shown  that er¢ is a function of frequency if er is non-zero at any point in the frequency domain. If er reaches a single maximum value as a function of fr equency, then the real and imaginary components of the compl ex permittivity can be approximated by a first order Debye equation, expressed as ¢+ + =r r re t w e e e2 2 0 r1 (2-7) and ( ) 2 2 0 r1 t w wt e e e+ = ¢¢ r r (2-8)
10 respectively, wherew = 2 p f is the radian frequency,er0 is the relative permittivity at zero frequency, an d reis the relative permittivity at infinite frequency (also called the optical dielectric constant) . Since biological tissues and materials have constit utive parameters that exhibit generally non-linear behavior as a function of freq uency, more relaxation times (and consequently, higher-order equations) are needed in order to model the frequency dependence of permittivity with reasonable accuracy The analyses contained in this work are based on a fourth order Cole-Cole expressi on for permittivity, which is () 0 ) 1( 4 1 0/ 1we s wt e e w eaj jmm m m+ + D + == (2-9) whereDem is the value of the frequency-dependent change in permittivity,tm is the corresponding relaxation time,am is a fitting parameter, ands represents ionic conductivity .
11 The values of each of the parameters in equation (2 -9) are shown in Table 2-1 for various biological materials. Table 2-1 Four Term Cole-Cole Parameters for Select Biologica l Materials (Adapted from )Tissue e De1 t1 a1 De2 t2 a2 Blood4.00040.008.8420.100 50 3.1830.100Dry Skin4.00032.007.2340.0001100 32.4810.200Fat (Infiltrated)2.500 9.007.9580.200 35 15 .9150.100 Heart4.00050.007.9580.1001200 159.1550.050Muscle4.00050.007.2340.1007000 353.6780.100Tissue s De3 t3 a3 De4 t4 a4 Blood0.2501.00E5 159.155 0.200 1.00E7 1.592 0.000 Dry Skin0.0000.00E0 159.155 0.200 0.00E7 15.9 150.200 Fat (Infiltrated)0.0353.30E4 159.155 0.050 1.00E 7 15.9150.010 Heart0.0504.50E5 72.343 0.220 2.50E7 4.547 0.000 Muscle0.2001.20E6 318.310 0.100 2.50E7 2.27 40.000 NOTES:The units of t1, t2, t3 and t4 are picoseconds (pS), nanoseconds (nS), microsecon ds ( m S) and milliseconds (mS), respectively.Infiltrated fat refers to fatty tissue that contain s tissues of a different type (blood vessels, dermis, muscle, etc.), and as such represents a mor e physiologically realistic model than does pure (uninfiltrated) fat.
12 Figure 2-1 illustrates the frequency dependency of the permittivity of the materials whose parameters are given in Table 2-1 a nd approximated using equation 2-9. Figure 2-1 Complex Permittivity of Select Biological Materials Blood1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 234567891011 Log Frequency (10x = Hz)Relative Permittivity Real Imaginary Dry Skin1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 234567891011 Log Frequency (10x = Hz)Relative Permittivity Real Imaginary Fat (Infiltrated)1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 234567891011 Log Frequency (10x = Hz)Relative Permittivity Real Imaginary Heart1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 234567891011 Log Frequency (10x = Hz)Relative Permittivity Real Imaginary Muscle1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 234567891011 Log Frequency (10x = Hz)Relative Permittivity Real Imaginary
13 Once the complex permittivity for a material has be en established (by experimentation, numerical methods, literature sear ch or other means), determination of the remaining parameters needed to characterize and predict propagation behavior through the material can be achieved through fairly simple calculation. 2.3 ConductivityAs shown in , the complex relative permittivity er is directly dependent on the material conductivity s that is 0we s e= r (2-10) where f p w 2 = is the radian frequency (radians per second). Con ductivity is easily determined from equation 2-10 using =re we s0, (2-11) where conductivity s is in units of S/m. The conductivities of select biological materials, determined using equations 2-9 and 2-11 and the dat a from Table 2-1, are shown in Figure 2-2.
14 Figure 2-2 Conductivity of Select Biological Materials Fat (Infiltrated)0.01 0.1 1 10 100 234567891011 Log Frequency (10x = Hz)Conductivity (S/m) Muscle0.1 1 10 100 234567891011 Log Frequency (10x = Hz)Conductivity (S/m) Blood0.1 1 10 100 234567891011 Log Frequency (10x = Hz)Conductivity (S/m) Dry Skin0.0001 0.001 0.01 0.1 1 10 100 234567891011 Log Frequency (10x = Hz)Conductivity (S/m) Heart0.01 0.1 1 10 100 234567891011 Log Frequency (10x = Hz)Conductivity (S/m)
15 2.4 AttenuationThe attenuation constant a (not to be confused with the fitting parameter a in equation 2-9) is most often calculated from theory in units of nepers per meter (n/m), where one neper is approximately equal to 8.686 dec ibels (dB). For the purposes of this work, where we will be dealing with tissue and orga n layers more conveniently measured in millimeters (mm), we will use the conversionadB/mm 0.008686 an/m. (2-12) Attenuation as a function of frequency is determine d using  )1 ) / ( 1 ( 22 /¢ + ¢ =r r r r m nce e e m w a, (2-13) or, recalling that biological materials are conside red to be non-magnetic (and substituting equation 2-5), )1 tan 1 ( 22 /+ ¢ =q e w ar m nc, (2-14)
16 where c is the speed of light (approximately 2.997925 x 108 meters per second). Note that when tan q is zero (implying a scalar permittivity by equatio n 2-5), equation 2-14 reduces to zero. Figure 2-3 shows the bulk attenuation of some biolo gical materials in dB/mm, as a function of frequency. Figure 2-3 Attenuation of Select Biological Materials Dry Skin Attenuation1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 234567891011Log Frequency (10x = Hz)Attenuation (dB per mm) Heart Attenuation1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02 234567891011 Log Frequency (10x = Hz)Attenuation (dB/mm) Infiltrated Fat Attenuation1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 234567891011 Log Frequency (10x = Hz)Attenuation (dB/mm) Muscle Attenuation1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 234567891011 Log Frequency (10x = Hz)Attenuation (dB/mm) Blood Attenuation1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 234567891011 Log Frequency (10x = Hz)Attenuation (dB/mm)
17 2.5 Intrinsic ImpedanceThe last material property of general interest that we will investigate is that of intrinsic impedance (h). This is understood to be a different quantity t han characteristic impedance ( Z ), since the intrinsic property deals only with the parameters of the material in question and does not necessarily take into acco unt the effects of geometry or boundary conditions. The intrinsic impedance of free space is found by t aking the square root of the ratio of free-space permeability and permittivity; numerically it is given byh0 376.73 ohms. (2-15) For non-magnetic materials with scalar permittivity the intrinsic impedance is the freespace impedance divided by the square root of the r elative permittivity of the material: r oe h h=. (2-16) To account for the effect of complex permittivity a s found in biological materials, we use 
18 n r ¢ =q e m htan 1 1 j (2-17) The magnitude of the intrinsic impedance of select biological materials is shown in Figure 2-4. Figure 2-4 Intrinsic Impedance of Select Biological Materials Infiltrated Fat1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 234567891011 Log Frequency (10x = Hz)Intrinsic Impedance (Ohms) Dry Skin1.E+00 1.E+01 1.E+02 1.E+03 234567891011 Log Frequency (10x = Hz)Intrinsic Impedance (Ohms) Heart1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 234567891011 Log Frequency (10x = Hz)Intrinsic Impedance (Ohms) Muscle1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 234567891011 Log Frequency (10x = Hz) Intrinsic Impedance (Ohms) Blood1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 234567891011 Log Frequency (10x = Hz)Intrinsic Impedance (Ohms)
19 2.6 ConclusionWith the development of the properties of conductiv ity, attenuation and impedance (upon measurement or approximation of the complex permittivity), we are now ready to show the application of these properti es to studies of specific cutaneous and subcutaneous phenomena, particularly oxygenation an d the measurement of internal body temperatures.
20 Chapter 3 Microwave Sensing of Blood Oxygenation The effect of oxygen spectral absorption on radio s ignal transmission in the atmosphere is a well-documented phenomenon  [3 ]. A series of closely-spaced and often overlapping spectral lines around 60 GHz, ref erred to as the 60 GHz oxygen complex, has been accurately modeled for the predic tion of atmospheric attenuation of RF signals. We will examine several approximation methods in this chapter, and evaluate their applicability to model the signal re flection characteristics of oxygenated blood. After a comparison of the modeling results with experimental test data, we will discuss the potential application of this technique to the detection and diagnosis of skin cancer. We begin with a brief introduction to the molecular resonance mechanism from a quantum mechanical point of view, before moving on to resonance modeling, its application to physiological conditions and potenti al applications of resonance detection. 3.1 Oxygen ResonancesResonances are induced by electromagnetic fields, a s the energy contained in the field is used to produce transitions in quantum ene rgy states. Oxygen exists in a natural state in molecular form, with two oxygen atoms comb ining to create an O2 molecule. This molecule is paramagnetic, with a permanent mag netic moment. Diatomic molecular
21 spectral absorption is determined by the energy lev els dictated by quantum numbers, as shown in Table 3-1, which was created using informa tion from . Table 3-1 Quantum Parameters Affecting Oxygen Resonances Quantum NumberDescriptionBehavior in O2 Molecule LElectronic Axial NumberEqual to zero KOrbital Momentum NumberOnly odd values allowed, must remain constant duringtransition for microwaveabsorption SMolecular Spin Transition Number 1 JTotal Angular Momentum (K+S)J = K-1, K, K+1 All allowable orbital numbers (K = 1, 3, 5 ) and s pin transitions (S = -1 0, 0 1) result in absorption lines near 60 GHz, with the ex ception of the transition (K = 1, J = 0 1), which corresponds to approximately 118 GHz 
22 3.2 Resonance Modeling TechniquesThe exact characteristics of oxygen resonance are i nfluenced by such parameters as temperature, pressure and water vapor content [1 ]. These factors very greatly between atmospheric and meteorological measurements and tho se conditions found in human physiology. These differences in measurement condi tions lead to significant discrepancies between atmospheric oxygen absorption lines and blood oxygen resonances. Two methods of O2 resonance approximation are examined: the reduced line base model of Liebe  and Rosenkrantz theory of over lapping lines . Each of the methods uses a set of major O2 spectral line frequencies, with line width, streng th and interaction determined by such parameters as oxygen partial pressure (pO2), water vapor partial pressure (pH2O) and temperature. 3.2.1Reduced Line Base Model Liebes method is a practical means of approximatin g oxygen absorption at frequencies below 350 GHz, and is based on evaluati on of the imaginary part N( f ) of the complex refractivity. The absorption coefficient a is determined from this quantity usinga = (2w/ c )(10log e ) N( f ) (dB per mm) (3-1)
23 wherec 2.997925 x 108 is the free-space speed of light, e 2.7182818 is the natural logarithm base, f is the frequency is GHz, and N( f ) is the imaginary portion of the complex refractiv ity. The quantity N( f ) is approximated as ) ( ) ( ) ( ) ( f N f N f F S f Nw d i i i¢¢ + ¢¢ + ¢¢ (3-2) wherei is an index counter of the spectral line used in t he calculation, Si is the strength of the i th line, Fi( f ) is the shape factor of the i th line as a function of frequency, and Nd( f ) and Nw( f ) are the dry and wet continuum spectra, respective ly. The line strength Si is calculated using) 1( 3 12t a i iie pt a S-= (3-3)
24 wherea1 i is the line width coefficient for the i th line as given in Table 3-2, p is the atmospheric pressure in millibars (mbar), t is the temperature coefficient given by 300/Temp ( Kelvin), and a2 i for the i th line is given in Table 3-2, and the line shape factor Fi( f ) is given by n r D + + + D + D + D =2 2 2 2) ( ) ( ) ( ) ( ) ( ) ( ) ( f f f f f s f f f f f f s f f f f Fi i i i i i (3-4) wherefi is the frequency of the i th line as given in Table 3-2,Df is the width of the line, and s is a line interference correction factor. The term line width as used above refers to the s pectral width (in Hertz) of a specific resonance line. The width is affected by a variety of factors, including excitation quantum level uncertainty, atmospheric pressure bro adening, Doppler broadening and Zeeman broadening (due to the earths magnetic fiel d) . In equation 3-4, the line width factor Df is found using
25) 1.1 (8.0 3et pt a fi+ = D (3-5) wherea3i is the width coefficient of the i th line from Table 3-2, and e is the water vapor partial pressure in millibars, and s is found usingia ipt a s54= (3-6) where coefficients a4i and a5i are given in Table 3-2. The dry air continuum function Nd(f) is given by + + + = ¢¢-5.1 5.1 5 11 2 2 5 2) 10 2.1 1( 10 4.1 ) 60/ ( 1 ) / ( 1 10 14.6 ) ( pt f f d f d fpt f Nd (3-7) where d is a line width parameter determined by8.0 4) 1.1 ( 10 6.5 t e p d + =. (3-8)
26 Finally, the wet air continuum function Nw(f) is given by5.1 2 1.1 10 3 2.6 810 3.2 ) 3. 30 ( 10 8.1 ) ( f t pe fet et p f Nw - + + = ¢¢ (3-9) Values for the coefficients specified in equations 3-3 through 3-6 are given in Table 3-2. An implementation of the Reduced Line Base Method, written in MATLAB, is shown in Appendix B.
27 Table 3-2 Liebe Parameters for Oxygen Resonance Lines (Adapted from ) i fia1ia2ia3ia4ia5i 151.50346.087.748.905.601.8 252.0214 14.146.849.205.501.8 352.5424 31.026.009.405.701.8 453.0669 188.8.131.525.301.9 553.5957 124.704.48 10.005.4 01.8 654.1300 228.003.81 10.204.8 02.0 754.6712 391.803.19 10.504.8 01.9 855.2214 631.602.62 10.794.1 72.1 955.7838 953.502.12 11.103.7 52.1 1056.2648 548.900.01 16.467.74 0.9 1156.3634 1344.001.66 11.442.972 .3 1256.9682 1763.001.26 11.812.122 .5 1357.6125 2141.000.91 12.210.943 .7 1458.3269 2386.000.62 12.66 -0.55 -3.1 1558.4466 1457.000.08 14.495.970 .8 1659.1642 2404.000.39 13.19 -2.440.1 1759.5910 2112.000.21 13.603.440 .5 1860.3061 2124.000.21 13.82 -4.130.7 1960.4348 2461.000.39 12.971.32 -1.0 2061.1506 2504.000.62 12.48 -0.365.8 2161.8002 2298.000.91 12.07 -1.592.9 2262.4112 1933.001.26 11.71 -2.662.3 2362.4863 1517.000.08 14.68 -4.770.9 2462.9980 1503.001.66 11.39 -3.342.2 2563.5685 1087.002.11 11.08 -4.172.0 2664.1278 733.502.62 10.78 -4.482.0 2764.6789 463.503.19 10.50 -5.101.8 2865.2241 274.803.81 10.20 -5.101.9 2965.7648 153.004.48 10.00 -5.701.8 3066.3021 80.095.229.70 -5.5 01.8 3166.8368 39.466.009.40 -5.9 01.7 3267.3696 18.326.849.20 -5.6 01.8 3367.90098.017.748.90 -5.801.734 118.7503 945.000.00 15.92 -0.13 -0.8 NOTES:All a1 coefficients are to be multiplied by 10-7. All a3 and a4 coefficients are to be multiplied by 10-4.
28 3.2.2 Theory of Overlapping LinesRozenkrantzs formulation is an attempt to reduce t he complexity of the resonance calculations by simplifying the spectral line width pressure relationship as expressed in other approximation methods. Using th is method, the absorption functionkO2(f) (which is analogous to the attenuation coefficient a in section 3.2.1) is found using F T P f fO¢ =-300 1013 10 61.1 ) (2 82k (dB per mm) (3-10) wheref is the frequency in GHz, P is the pressure in millibars, and T is the absolute temperature in Kelvin. The function F¢ accounts for line strength and spectrum shape. A s ummation is used over odd values of the quantum number N (only the first 39 terms are considered significant), and F¢ is determined by [ ]= + ++ + + F + + = ¢39 ... 5,3,1 2 2) ( ) ( ) ( ) (N N N N N N b bf g f g f g f g f Fg g (3-11)
29 where gN (f) is given by N N N N N N Nf f Y f f P d f g2 2 2) ( ) ( ) ( ) (g g+ + = (3-12) and FN is n r + + = F-T N N N TN300 )1 ( 10 89.6 exp )1 2( 300 10 6.43 3 (3-13) The quantities gb and gN in equations 3-11 and 3-12 are nonresonant and res onant line width parameters, respectively, and are expressed a s 89.0300 1013 49.0 =T Pbg (3-14) and 85.0300 1013 18.1 =T PNg. (3-15) In equation 3-12, the quantities dN+ and dNare the amplitudes of the fN+ and fNlines, respectively, and are given by
30 5.0)1 2 )(1 ( )3 2( n r + + + =+N N N N dN (3-16) and 5.0)1 2( )1 2 )(1 ( n r + + =-N N N N dN. (3-17) Values for the resonant frequencies fN+ and fNand interference parameters YN+ and YN-are given in Table 3-3. An implementation of the O verlapping Line Method, written in MATLAB, is shown in Appendix C.
31 Table 3-3 Rozenkrantz Parameters for Oxygen Resonance Lines (Adapted from ) Frequencies (GHz)Interference (mbar-1) N fN+ fNYN+ YN156.2648 118.7503 4.51-0.214 358.446662.4863 4.94-3.78 559.591060.3061 3.52-3.92 760.434859.1642 1.86-2.68 961.150658.3239 0.33-1.131161.800257.6125-1.03 0.3441362.411256.9682-2.23 1.651562.998056.3634-3.32 2.841763.568555.7838-4.32 3.911964.127855.2214-5.26 4.932164.678954.6711-6.13 5.842365.224154.1300-6.99 6.762565.764753.5957-7.74 7.552766.302053.0668-8.61 8.472966.836752.5422-9.11 9.013167.369452.0212-10.3 10.33367.900751.5030-9.87 9.863568.430850.9873-13.2 13.33768.960150.4736-7.07 7.013969.488749.9618-25.8 26.4 NOTE:All YN+ and YNcoefficients are to be multiplied by 10-4.
32 3.2.3 Modeling EvaluationIn order to verify the proper implementation of equ ations (3-1) and (3-10), we used the source code shown in appendices B and C, r espectively, to evaluate a welldocumented atmospheric condition: that of 60 GHz at tenuation at sea level and ambient temperature, using conditions of Standard Temperatu re and Pressure (STP) . The results for each approximation method are shown in Figure 3-1. The frequency, magnitude and shape of the atmospheric oxygen atten uation curve are in excellent agreement between methods, and with those data prev iously published  . Figure 3-1 Sea Level Atmospheric Oxygen Modeling Evaluation 0 2 4 6 8 10 12 14 16 50515253545556575859606162636465 Frequency (GHz)Attenuation (dB/Km) Liebe Rosenkrantz
33 3.3Blood Oxygen Characteristics In section 3.2 we presented two means of oxygen res onance approximation using methods of atmospheric attenuation modeling, and ve rified each of those methods by comparing their results with those already publishe d for sea level atmospheric attenuation. Before we can apply these equations t o estimate the effect of resonances due to tissue oxygenation, we must first investigate th e quantitative differences between atmospheric conditions and those that exist within the human physiology. Only then may we be able to apply the proper parameters that will yield a usable model of the responses expected from human tissue. In order to adequately describe the oxygenation of blood and quantify the differences between blood and atmospheric oxygenati on, however, we must first present some basic material on the relevant aspects of the physiology of the respiratory system. These aspects include changes in oxygen and water v apor content during inspiration (breathing in), conditions within the lung, and the blood-gas barrier within the alveoli and terminal capillaries. Within a mixture of gasses, such as the atmosphere we breathe, there exists a set of partial pressures: each corresponding to one of the gasses in the mixture. Daltons Law states that the partial pressure of a specific gas within a mixture is the same as if that gas alone occupied the total volume, in the absence of the other gasses. Stated another way, we can consider the partial pressure of a sing le gas in a mixture to be the
34 contribution the pressure of that gas makes to the total pressure of the mixture. For example, the pressure of the earths atmosphere at sea level is approximately 760 millimeters of mercury (760 mmHg). Oxygen comprise s about 21% of the atmosphere by volume, so the partial pressure of oxygen (pO2) at sea level is the product of concentration and total pressure, or about 0.21*760 160 mmHg . Upon inspiration, atmospheric air is warmed and moi stened until the water vapor partial pressure (pH2O) is 47 mmHg . The increase in water vapor co ntent reduces the dry gas pressure from 760 to 713 mmHg. This in turn reduces the pO2 from 160 mmHg to 0.21*713 150 mmHg. Once the inspired air has reached the a lveoli for transfer to the blood, the pO2 has fallen to approximately 100 mmHg . This i s due to the continual transfer of oxygen from the inspired air to the non-oxygenated blood. (The term non-oxygenated is used here in a relative se nse, because venous blood typically has a pO2 of about 40 mmHg; lower than that of arterial bloo d but non-zero, nonetheless). Blood is very efficiently re-oxygenated as it passe s through the alveolar capillaries, so that the pO2 of arterial blood is also 100 mmHg . Figure 3 -2 shows a schematic representation of oxygen partial pressure as it pro gresses from the atmosphere, passes through the lungs and blood, and ultimately reaches body tissues .
35 Figure 3-2 Oxygen Partial Pressures from Air to Tissues (Used with Permission) By convention, blood gasses are measured at any tem perature and pressure, then converted to the values they would have at body tem perature (37 C) and pressure (sea level minus water vapor pressure), known as Body Te mperature Pressure Saturated (BTPS). This condition includes the parameters and values shown in Table 3-4 .
36 Table 3-4 BTPS Conditions for Arterial Blood Temperature37C pO2100 mmHg* pH2O47 mmHg *Standard sea level atmosphere assumed. 3.4Approximation Results The data and equation sets for the Liebe and Rozenk rantz approximation methods were evaluated over the frequency range of 50 to 65 GHz, and the results are shown in Figure 3-3. Partial pressure data as given in Tabl e 3-4 for arterial blood were used. A comparison of Figure 3-1 for sea level atmospheric oxygen and Figure 3-3 for arterial blood oxygen shows an attenuation of the resonance peaks under blood conditions and the emergence of separate resonance lines due to lo wer blood pO2 . The results for the expected oxygen resonances in arterial blood de monstrate excellent agreement between the approximations, with major spectral res ponses between 58.3 and 62.4 GHz and a peak at approximately 60.4 GHz.
37 Figure 3-3 Comparison of Oxygen Attenuation (Absorption) Resul ts Under Arterial Blood Conditions 3.5Blood Resonance Measurements We obtained samples of fresh bovine blood from a lo cal slaughterhouse for testing. The sample was prepared using a standard sodium heparin preservative  and kept refrigerated when not under test. Data were c ollected using an Anritsu 37397C Vector Network Analyzer (VNA) calibrated for a sign al reflection measurement (S11) using a short-open-load (SOL) method with the VNA t est port 1 serving as the reference plane. A 60 GHz 1 square aperture horn antenna and waveguide-coaxial adapter performed the signal input and output functions. T he sample was placed into a small ziplock poly bag, which was positioned on a steel shor ting plate. The antenna aperture was then placed directly on the poly bag, as shown in F igure 3-4. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 505152535455565758596061626364 Frequency (GHz)Alpha (dB per km) Liebe Rozenkrantz58.3 GHz 60.4 GHz 62.4 GHz
38 Figure 3-4 Oxygen Resonance Sample Test Setup Blood exhibits a number of resonances in the range of 50 65 GHz, as shown in the return loss data plot of Figure 3-5. Major res onance lines occur at approximately 51, 54, 55, 58 and 65 GHz. Although the causes of thes e lines are not yet known, it is suspected that the spectra of non-oxygen blood comp onents are contributing factors. For example, Rogacheva et al. have speculated that the 55 and 65 GHz resonances are due to the hydrogen-bond networks of subsurface water in p roteins . Horn Antenna Blood Sample Reflective Plate
39 Figure 3-5 Bovine Blood Resonances from 50 65 GHz (Sample A ge 90 Minutes) (Error Bars Indicate Sample Variability, N = 6) We are able to offer supporting evidence to the arg ument that some of the response peaks observed in this frequency range are due to the presence of water. Figure 3-6 shows a plot similar to that shown in Figure 35, except that the bovine blood sample has been replaced in turn with distilled water and ethanol. A comparison of these two plots reveals that distilled water also displays re sponse peaks at approximately 51, 54 and 55 GHz, while the ethanol trace is relatively flat at these frequencies. Subsequent data, which appear later in this section, suggest that th e frequencies of the peaks may be dependent on the test setup structure, particularly the thickness of the blood sample. 0 5 10 15 20 25 30 35 40 505152535455565758596061626364 Frequency (GHz)Return Loss (dB)
40 Figure 3-6 Distilled Water and Ethanol Resonances from 50 65 GHz With the exception of the frequency region near 60 GHz, the blood resonance characteristics are largely unchanged as testing is repeated after 24 and 48 hours, as shown in Figure 3-7. A slight upward frequency shi ft in the 24 and 48 hour data is compensated in Figure 3-7 by shifting the curves do wnward approximately 112 MHz and 262 MHz, respectively. Although a cursory examinat ion in the area near 60 GHz might suggest a change in response with time, we performe d an integration of the differences over time in 1 GHz increments to ensure there was a delta. This integration was performed using the algorithm =GN i iN1, (3-18) 0 5 10 15 20 25 30 35 40 45 505152535455565758596061626364 Frequency (GHz)Return Loss (dB) Distilled Water Ethanol
41 where N is the number of datapoints taken per GHz of frequ ency sweep. Since data were collected in intervals of 0.0375 GHz, N is approximately equal to 27. Comparisons were made between the reflection magnitude data from fre sh blood to that at 24 hours age (Figure 3-8a) and to that at 48 hours age (Figure 3 -8b). In both cases, the response difference reached a maximum value around 60 to 62 GHz, giving objective evidence of maximal change in that range of frequencies. Figure 3-7 Bovine Blood Resonances from 50 65 GHz 0 5 10 15 20 25 30 35 40 45 505152535455565758596061626364 Frequency (GHz)Return Loss (dB) 90 minutes old 24 hours old 48 hours old
42 a.) b.) Figure 3-8 Blood Response Changes with Age (Integration Analys is) (a = Fresh to 24 hours, b = Fresh to 48 hours) A moving average analysis of the data also shows a maximum change in response over time. The analysis was performed over 50 data points using each set of differences in the magnitude gamma data, as used for Figure 3-8 The results of this analysis are shown in Figure 3-9a (for the first 24 hours after extraction) and Figure 3-9b (for the first 48 hours after extraction). As with the integratio n analysis, the results of the moving average analysis show that the maximum change in re flected magnitude over time occurs in the frequency range of 60 to 62 GHz. 0.00 0.02 0.04 0.06 0.08 0.10 505152535455565758596061626364 Frequency (GHz)|Delta Gamma| 0.00 0.02 0.04 0.06 0.08 0.10 505152535455565758596061626364 Frequency (GHz)|Delta Gamma|
43 0 5 10 15 20 25 30 35 40 505152535455565758596061626364 Frequency (GHz)Return Loss (dB)0 1 2 3 4 5 6 7 8Alpha (dB per mm x 1E6) Bovine Blood Liebe Approx.a.) b.) Figure 3-9 Blood Response Changes with Age (Moving Average Ana lysis) (a = Fresh to 24 hours, b = Fresh to 48 hours) When we superimpose the Liebe approximation on the resonance data, as in Figure 3-10, the contribution of O2 resonance to the blood response becomes evident. Figure 3-10 Bovine Blood Resonances with O2 Attenuation Superimposed (Measured Data Quantized in Scale on Left, Oxygen A ttenuation on Right) 0.00 0.02 0.04 0.06 0.08 0.10 505152535455565758596061626364Frequency (GHz)|Delta Gamma| 0.00 0.02 0.04 0.06 0.08 0.10 505152535455565758596061626364Frequency (GHz)|Delta Gamma|
44 0 5 10 15 20 25 30 60.060.561.061.5 Frequency (GHz)Return Loss (dB)-0.5 0.5 1.5 2.5 3.5 4.5 5.5 Theoretical Alpha (dB/KM) 90 minutes 24 hours 48 hours Liebe O2 Approx. Sample Age:It is apparent by examination of Figure 3-10 that t he resonances at 51, 54, 55 and 64.5 GHz are not caused by the presence of oxygen in the blood. In Figure 3-11, the frequency range of 60 61.5 GHz is examined more closely. The presence of a different system of units between the left and right y-axes in Figures 3-10 through 3-11 and Figure 3-13 is not in tended to imply a numerical equivalency between the two quantities. They are pl aced in juxtaposition simply to demonstrate that the return loss and attenuation pe aks in blood occur at substantially the same frequencies. Figure 3-11 Bovine Blood Resonances with O2 Attenuation Superimposed (60 61.5 GHz) (Measured Data Quantized in Scale on Left, Oxygen A ttenuation on Right) The theoretical resonance curve and the curve at 90 minutes sample age show good agreement in terms of relative peak amplitudes width and spacing. The frequency
45 difference of about 300 MHz between the approximati on and data at 90 minutes is attributed to the shift in measurement reference pl anes that was incurred with the addition of the waveguide-coaxial adapter and horn antenna. As expected due to the effect of aging, degradation of the oxygen content is evident after 24 hours. This effect is predicted by the metabolic rate of drawn blood at 4C. Since the pO2 of in vitro blood decreases by 0.01% volume every 10 minutes , th e oxygen partial pressure is reduced by approximately 1.5 volumes percent over a twentyfour hour period. Correspondence between the oxygen response and resonance approxima tion curves is almost non-existent at 48 hours sample age. We performed several series of tests in order to ve rify that the results suggested by the preliminary data are due to oxygen resonance and variability rather than a secondary effect. In one set of tests, we subjecte d samples of materials lacking the oxygen molecule to the identical test procedure and conditions under which we measured the blood samples. These materials included:Distilled water (H2O) Isopropyl alcohol (CH3CHOHCH3) Ethanol (C2H6O) The test results for these materials are shown in F igure 3-12. The results demonstrate the differences between the expected O2 resonances and the spectral response of each of th e
46 non-oxygenated materials, in that the double peak r esponse of the oxygen approximation is missing from each of the materials under test. Figure 3-12 Non-Oxygenated Material Responses with O2 Attenuation Superimposed We also subjected samples of Complete Rapid QC arterial blood gas calibration solution  to the identical test procedure and c onditions under which we measured the bovine blood samples. Complete is a tri-level buff ered bicarbonate solution with specific values of pO2 for each level, as specified in the manufacturers data sheets and summarized in Table 3-5. 0 5 10 15 20 25 30 35 40 45 60.060.561.061.5 Frequency (GHz)Return Loss (dB) Distilled Water Ethanol Isopropyl Alcohol
47 Table 3-5 Complete Rapid QC Solution Level Descriptions Complete LevelpO2 (mm Hg)Blood Condition Similarity 1 139 145Atmospheric pO2 (Hyperoxygenated) 2 91 102Arterial pO2 (Normal O2) 3 22 25Depleted pO2 (Hypooxygenated) The test results for these materials are shown in F igure 3-13. The figures show a similar pattern between the Complete data and the bovine bl ood data shown in Figures 3-7 and 311, in that the two resonance peaks between 60 and 61.5 GHz decrease in amplitude with decreasing levels of oxygen. This supports our con tention that oxygen is the cause of the shifting peaks in the bovine blood data in Figure 3 -7.
48 Figure 3-13 Complete Calibration Sample Responses with O2 Attenuation Superimposed (Measured Data Quantized in Scale on Left, Oxygen A ttenuation on Right) A question was raised during the course of the rese arch as to the effect of the surrounding atmosphere on the validity of the measu rements. Observing Figure 3-4 carefully, we note that the antenna aperture does n ot come into direct contact with the metal shorting plate. Consequently, the test struc ture as implemented does not represent a shielded enclosure, and atmospheric effects may b e introduced to the data by means of the antenna sidelobes. To preclude this possibilit y, we designed a shielded fixture similar to an offset short, which would minimize antenna si delobe leakage by placing the antenna aperture completely and directly in contact with th e shorting plate. An aperture-sized recess is located concentrically with the aperture shelf, which allows several milliliters of 0 5 10 15 20 25 30 35 40 60.060.561.061.5 Frequency (GHz)Return Loss (dB)0 1 2 3 4 5 6 7 8Alpha (dB per mm x 1E6) Hyperoxygenated Normal (Arterial) Hypooxygenated Liebe
49 test liquid to the subjected to 60 GHz irradiation. The fixture and its implementation are shown in Figure 3-14. a.)Fixture as designedb.) Fixture with liquid c.)Fixture with antenna Figure 3-14 Antenna Shorting Plate/Test Fixture Data obtained when using this fixture are shown in Figure 3-15, for Complete Level 1 and Level 2 solutions (hyperand normal oxygen lev els, respectively). The test was also repeated for non-oxygenated materials as in Figure 3-12; these results are shown in
50 Figure 3-16. The presence of the characteristic double peak, with decreasing magnitude corresponding to decreasing oxygen level, is evidence of the validity of the prior test data (Figures 3-5 to 3-7). a.)50 65 GHzb.)60 62 GHz Figure 3-15 Blood Oxygen Calibration Sample Data Using Test Fix ture a.)50 65 GHzb.)60 62 GHz Figure 3-16 Non-Oxygenated Materials Data Using Test Fixture 0 2 4 6 8 10 12 14 505152535455565758596061626364 Frequency (GHz) Return Loss (dB) Hyperoxygenated Normal O2 0 1 2 3 4 5 6 7 8 9 10 60.060.561.061.562.0 Frequency (GHz)Return Loss (dB) Hyperoxygenated Normal O2 0 2 4 6 8 10 12 14 16 18 60.060.561.061.562.0 Frequency (GHz)Return Loss (dB) De-Ionized Water Methanol 0 2 4 6 8 10 12 14 16 18 505152535455565758596061626364 Frequency (GHz)Return Loss (dB) De-Ionized Water Methanol
51 Figure 3-15 offers further evidence of a shift in p eak frequency due to thickness of the test material. In Figure 3-13, where the da ta were collected using the plate setup of Figure 3-4, the calibrator solution with normal oxy genation levels displayed response peaks at frequencies of 60.6 and 61.4 GHz. Figure 3-15b shows the result of the same solution tested in the fixture shown in Figure 3-14 Under this condition, the frequency of the upper peak has shifted to 61.9 GHz. The mos t significant difference between these two conditions is the thickness of the calibrator s ample under test. When tested with the shorting plate as a backing, the sample thickness w as approximately 2.5 mm. The test chamber in the fixture has a depth of 4.5 mm. Sinc e the difference in sample thicknesses corresponds to approximately 0.4 wavelengths in fre e space (and an even greater percentage of wavelength in the sample material), t his magnitude of change in the signal path length could certainly contribute to such a sh ift in response frequencies. 3.6Blood Permittivity Measurements The successful measurements that had been conducted to this point involved the construct of a relatively thin planar layer of bloo d backed by some form of metallic short circuit. This configuration was chosen for several reasons: to accommodate the horn antenna aperture of approximately one square inch w hile simulating as closely as possible the small amount of blood expect in vivo and to provide a highly reflective background against which any resonances would be readily obser ved. However, we could not discount the possibility that this construct may in troduce its own set of resonances due to
52 the physical dimensions of the fixturing in combina tion with the propagation characteristics of the material under test. In order to verify that the resonances we observed were due to the properties of blood oxygenation and not the test methods, we meas ured the permittivity of bovine blood in bulk, 24 hours after extraction, using ope n-ended coaxial probes. No reflective ground plane was used, and the thickness of the blo od layer was not constrained as it was during resonance testing. For this series of tests we used the slim form probe option of the Agilent 85070 Dielectric Measurement System as controlled by the Agilent E8361C vector network analyzer. The probe consisted of a 6-inch length of RG405 semirigid coaxial cable, with one end terminated with a 1.85m m coaxial connector and simple flush cut which served as the calibration reference plane on the opposite end. The calibration procedure was provided by the Dielectric Measuremen t software, and consisted of a reflection (S11) calibration using short (copper strip), open (air ) and load (deionized water) as impedance references. The permittivity t est probe implementation is shown in Figure 3-17.
53 Figure 3-17 Permittivity Test Probe in Sample The blood permittivity test results are shown graph ically in Figure 3-18. The curve shows a plot of the blood loss tangent as a f unction of frequency, as defined by equation 2.5, with the Gabriel database approximati on ,  shown as a dashed line. This ratio maintains a relatively constant value of approximately 1.2 to 1.4 with frequency, with the exception of two prominent nonlinearities, centered at approximately 61.2 and 61.8 GHz. These non-linearities are not p redicted by the results of the fourthorder Cole-Cole expression (eq. 2-9). Again, it wo uld appear that the primary resonant frequencies have changed from earlier results; howe ver, as previously mentioned, the thickness of the test sample was not constrained in the test setup of Figure 3-17, while it had been during testing per Figures 3-4 and 3-14.
54 Figure 3-18 Blood Loss Tangent (Blood Age 24 Hours) 3.7Software Simulation Results Finally, we simulated the reflection response of a planar blood layer using Agilent High Frequency Structure Simulator (HFSS) software, version 11. Blood was simulated using the permittivity data from Figure 3-18 in tab ular form (as shown in Appendix D) as data file inputs. Due to the frequency-dependent n ature of the electrical characteristics of blood, a discrete sweep was used, requiring a compl ete electromagnetic solution to be computed at each test frequency. Figure 3-19 show s the simulation setup; the antenna dimensions were based on physical measurements of t he antenna shown in Figure 3-4. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 505152535455565758596061626364 Frequency (GHz) Loss Tangent (e"/e') Loss Tangent (Meas.) Loss Tangent (Calc.)
55 The bottom of the test sample, which is not visible in the figure, is modeled as a perfectly reflecting plane. This simulation was based on the test setup of Figure 3-4. Figure 3-19 Test Simulation in HFSS The results of the simulation are shown in Figures 3-20 and 3-21. Figure 3-20 shows the simulated blood response from 50 to 65 GH z. Since the blood sample used to take the permittivity data in Figure 3-18 was 24 ho urs old, a comparison was made with the measured blood data taken 24 hours after extrac tion. The figure shows good correspondence between the two curves.
56 Figure 3-20 HFSS Simulation of Bovine Blood Response The major peaks in the simulated and measured respo nses in Figure 3-20 coincide quite well, both in terms of amplitude and frequenc y. The minor peaks are less pronounced in the simulation than in the measured d ata. This could be due to the finite nature of the permittivity data that defined the bl ood material (401 points from 50 to 65 GHz), to the fact that the simulation frequency set did not coincide with that of the permittivity data (due to computational restraints) or to a combination of the two factors. In Figure 3-21, the HFSS simulation is plotted with the bovine blood and Complete calibrator data corresponding to normal ar terial blood oxygenation. The close 0 5 10 15 20 25 30 35 40 45 50515253545556575859606162636465 Frequency (GHz)Return Loss (dB)HFSS Simulation Bovine Blood (Measured) O2 Resonances
57 correspondence between the three curves in this fig ure justifies our conclusion that blood oxygenation may be directly detected by means of th e 60 GHz oxygen resonance complex. Figure 3-21 Resonance Comparison: Blood Simulation, Measurement and Calibrator Data 3.8Skin Attenuation None of the preceding analyses or results are of be nefit to an in vivo test situation if the attenuation inherent in the skin precludes d etection of the data. In order to ensure that this is not the case, we revisit equation 1-14 and use the data in Table 1-1. In Figure 3-22, the expected attenuation of skin at 60 GHz is shown to be about 18 dB per mm. In section 3.9 we will show that useful in vivo data can be obtained at millimeter penetration depths. Allowing for the fact that we are using re flection measurements, this means that 0 5 10 15 20 25 30 35 406 0. 0 6 0. 2 6 0. 4 6 0. 6 6 0.8 6 1.0 61.2 6 1 .4 6 1. 6 6 1. 8 6 2. 0Frequency (GHz)Return Loss (dB) HFSS Simulation Blood Sample (Meas.) Normal O2 Calibrator
58 the 60 GHz signal travels through approximately 2 m m of skin, giving an expected attenuation of 36 dB. This value is within the dyn amic range of commercially available test equipment, as shown in Appendix E . Figure 3-22 Predicted Signal Attenuation in Skin as a Function of Frequency 3.9Application to Skin Cancer Detection The ability to detect blood oxygen could be of adva ntage in the detection of skin cancer. Angiogenic activity in the vicinity of tum ors is well documented , . Angiogenesis refers to the ability of living tissue to initiate the construction of new blood vessels to provide oxygen and nutrients for growth. Research has shown that angiogenesis is required for cancerous tumors to gr ow and metastasize. One potential use of blood oxygen detection in this application is to employ elevated oxyhemoglobin levels 0 5 10 15 20 25 510152025303540455055606570 Frequency (GHz)Attenuation (dB/mm)
59 as a marker for increased blood flow, thereby detec ting possible angiogenic activity near a suspected tumor. Our intent is to increase the i ncidence of early screening and detection, by developing a technology that will ind icate malignant areas painlessly, noninvasively and in real time, thereby reducing finan cial and anxiety-based impediments to cancer screening.3.9.1Motivation The presence of skin cancer is a common yet deadly phenomenon, especially in a climate such as that found in Florida, where the co mbination of intense sunlight and yearround outdoor activities greatly increases the chan ces of overexposure to ultraviolet rays. The following facts are provided by the Skin Cancer Foundation : More than 1.3 million skin cancers are diagnosed ye arly in the United States. One in 5 Americans and one in 3 Caucasians will dev elop skin cancer in the course of a lifetime.Survival rate for those with early detection is abo ut 99%. The survival rate falls to between 15 and 65% with later detection depending o n how far the disease has spread. In the past 20 years there has been more than a 100 % increase in the cases of pediatric melanoma.After thyroid cancer, melanoma is the most commonly diagnosed cancer in women 2029.
60 3.9.2Dimensional Requirements The goal of this effort is to detect lesions before they have metastasized. According to the Tumor, Node, Metastasis (TNM) syst em of classification , melanoma rarely metastasizes when its thickness is less than 1 mm. This corresponds to tumor classification levels T1a and T1b, which repr esent the newest, or least developed tumors. In practical terms, this sets an upper lim it of 1 mm for the depth penetration requirement of this technology. This is on the ord er of typical epidermal thickness in areas where skin cancer commonly develops: 0.5 mm o ver most of the body  to 0.05 mm on the eyelids and postauricular areas . The spatial resolution necessary for this technolog y to be effective is determined by the criteria set forth in the Asymmetry, Border, Color, Diameter and Evolution (ABCDE) guidelines of self-examination . These guidelines state that any skin growth greater than 6 mm in diameter could be abnor mal. Consequently, this requires the spatial resolution of this technology to be capable of detecting abnormalities no larger than 6 mm in diameter. The technology described in this chapter is capable of meeting both these dimensional requirements. As shown in the previous section, the attenuation of skin in the 60 GHz oxygen complex is about 18 dB per mm. G iven an early-stage tumor depth of 1 mm, this will result in a reflected signal att enuation of about 36 dB, which does not
61 preclude detection using existing equipment. Secon dly, the free-space wavelength of a 60 GHz signal is approximately 5 mm, which is less than the size of the tumors being detected. Further, this wavelength will decrease i n body tissues due to a non-unity value of relative permittivity, increasing the signal res olution capability further into the useful region below 6 mm.3.9.3Background/Literature Review Previous techniques for non-invasive skin examinati on include low-frequency impedance measurements and visual light spectroscop y. 3.9.4Impedance Spectroscopy Beetner et al. looked at detecting basal cell carcinoma using imp edance spectroscopy. They successfully classified skin sa mples as being normal, benign lesions or malignant basal cell carcinoma by focusing on sk in lesions ranging from 2 to 15 mm diameter . The study showed that, while impeda nce differences were found between malignant lesions, benign lesions and normal skin, the differences were not sufficiently conclusive to establish clear identification of the lesion based solely on impedance measurements. This was attributed to the relativel y small size of the lesions compared with that of the contact probe.
62 In a similar study that compared basal cell carcino ma to benign pigmented cellular nevi, berg et al. also concluded that statistical differences exist between the impedance of common skin lesions and that of normal skin, although further development is needed for the technique to be usefu l as a diagnosis tool . 3.9.5Visible Light Spectroscopy Other research efforts have used lightwave technolo gy to determine the malignancy of skin lesions. Mehrbeolu et al. used light at wavelengths of 500 to 800 nm to differentiate benign skin lesions from those exhibiting malignancy . However, due to the limited depth of penetration inherent in using frequencies of this wavelength, this technique is limited to those tumors which lie directly on the visible surface of the skin. Cui et al. proposed the use of wavelengths longer than those of visible light, in order to increase the penetration depth of the sign al. This proposal is reasonable, considering the reflection and transmission charact eristics of viable skin. As wavelength increases (implying decreasing frequency), the refl ection coefficients decrease. This decrease results in greater effective depths of pen etration for longer wavelength (lowerfrequency) signals, while maintaining attenuation a t workable levels . Cuis proposal led to this area of research, using microwave signals, which until now has been relatively unexplored. We have shown that microwave signals provide the spatial resolution needed to detect Level T1 tumors while maintaining signal attenuation
63 sufficiently low as to obtain data at skin depths a ssociated with cutaneous and subcutaneous malignancies.3.10Future Work We would like to repeat the resonance measurements already performed using an antenna with a smaller aperture than that being use d. The present antenna has an aperture size of approximately 645 mm2 (one square inch); this is satisfactory for the bu lk measurements being made to date, but larger than ma ny Level T1 tumors and can lead to in vivo test results that are ambiguous or false. The use of a smaller radiating and receiving aperture will allow us to verify the spat ial resolution of the 60 GHz signal, and will confirm the utility of this technique for iden tifying malignancies that are the size of skin cancers. With the success of a small aperture antenna this research should, with appropriate regulatory approval, progress to animal studies (for example, characterization of papilloma virus in laboratory mice).3.11Conclusion We have demonstrated a method for the measurement o f oxygen in blood by detecting changes in the 60 GHz resonance spectra. This may be useful in performing non-invasive measurement of tissue oxygenation or h emoglobin concentration in the vicinity of tumors. This technique can be employed for evaluation of a variety of other
64 skin conditions in which oxygenation levels play a part, including but not limited to the study of burn and wound healing, contact-induced pr essure points and the detection and treatment of psoriasis .
65 Chapter 4 Radiometric Sensing of Internal Organ Temperature Microwave radiometry is based on the principle of b lackbody radiation: the phenomenon of all objects whose absolute temperatur e exceeds zero to emit electromagnetic energy. Emission occurs over an ext remely wide frequency range, encompassing wavelengths in the radio, infrared, op tical, ultraviolet and x-ray spectra. The detection and quantification of this radiated e nergy in the microwave frequency range, and its subsequent conversion to temperature is referred to as microwave radiometry. Receiving these emissions in the RF/mi crowave spectrum involves working with signals possessing extremely low power levels and time-varying characteristics similar to those of noise. In fact, we will show t hat the RF power emitted by an object at a non-zero absolute temperature is identical to the thermal noise power of a resistor : P = kTB (4-1) whereP is the thermal noise power in watts, k 1.381 x 10-23 joule/K is Boltzmanns constant, T is the temperature in Kelvin, and B is the frequency bandwidth in Hertz.
66 Signal emission as a function of temperature has im plications for non-contact temperature measurement. The primary motivation in this work is that of internal organ temperature measurement during extended missions in space. 4.1History and Background The study of radiometry began with Plancks theory of blackbody radiation, first introduced in the late 19th and early 20th centuries. Non-biological applications of microwave radiometry included radioastronomy and re mote sensing. Suggestion of the use of microwave radiometry to the fields of biolog y and medicine first appeared in the 1970s. In 1974, Bigu del Blanco et al proposed using radiometry to detect changes of state in living systems . Carr also reports th at radiometry was used in breast cancer research in the 1970s. Early theoretical work in tissue radiothermometric measurement was performed in the 1980s by Plancot, et al (1984), Miyakowa, et al (1981), and Bardati, et al. (1983) . It was reported in 1989 that radiome try in biological applications was being studied with limited but pro mising results . Research in the field moved quickly in the 1990s w ith the development of lownoise transistors capable of operating to 10 GHz. This eliminated the costly and complex need for low-temperature noise sources, which used liquid nitrogen or liquid helium for cooling . By 1995, it was reported that microw ave radiometry was being used to
67 perform rheumatological activities in joints, breas t cancer detection and abdominal temperature pattern measurements .4.2Radiometry Review The ideal signal source for the study of radiometry is the physically unrealizable concept of a blackbody. A radiator of this type is one that is perfectly opaque (no transmission) and absorbs all incident radiation (n o reflection), at all frequencies. Since a blackbody is a perfect absorber, it must also be a perfect radiator at all frequencies, in order to maintain a constant temperature. Plancks radiation law describes the spectral brigh tness of a blackbody in terms of frequency and temperature : n r = 1 1 22 3 kT hfe c hf B, (4-2) whereB is the spectral brightness in Watts/m2/steradian (sr)/Hz, h 6.626 x 10-34 joules is Plancks constant, f is the frequency in Hertz, and c 2.997925 x 108 m/s is the free-space velocity of light.
68 Figure 4-1 shows a parametric plot of equation 4-2 for frequencies in the low GHz range. The curves in the plot represent absolute t emperatures relatively near the normal physiological temperature of the human body (98.6 F, or 310.15 K) and show variations in blackbody brightness with temperature and freque ncy. Figure 4-1 Blackbody Spectral Brightness as a Function of Freq uency and Temperature Several approximation methods exist in order to sim plify the computation of equation 4-2. One method that is particularly usef ul for the microwave frequency range is the Rayleigh-Jeans approximation, expressed as [ 50] 22 l kT B = (4-3) 0 2 4 6 8 10 12 12345678910 Frequency (GHz)Brightness (W/m^2/Hz/sr) x 1E18 T = 290 K T = 320 K
69 where l = c/f is the freespace wavelength of the blackbody emiss ion. Figure 4-2 shows a comparison of Plancks Law and Rayleigh-Jeans appro ximation results, showing excellent correspondence in the low GHz frequency r ange. Figure 4-2 Plancks Law and Rayleigh-Jeans Approximation at T = 310 K The mathematical simplicity of the Rayleigh-Jeans a pproximation of Plancks Law allows for the derivation of a convenient expre ssion for the power radiated by a blackbody emission. Given that the detection bandw idth D f is sufficiently narrow to allow the assumption of a constant brightness value with frequency, we can express the received power as  p rA f kT P W D =2 l (4-4) 0 1 2 3 4 5 6 7 8 9 10 12345678910 Frequency (GHz)Brightness (W/m^2/Hz/sr) x 1E18 Planck's Law Rayleigh-Jeans Approximation
70 whereP is the received power in watts, Ar is the antenna area, and Wp is the antenna solid pattern angle. Since the antenna solid pattern is the ratio of the wavelength squared to the antenna area, equation 4-4 reduces to P = kT D f (4-5) which is identical to equation (4-1). The requirement of a small D f results in emitted power levels that are extremely low. Figure 4-3 shows the power-temperature relati onship for an assumed measurement bandwidth of 300 MHz. Note that the emitted power is confined to the picowatt level for the entire range of biological temperatures. The d etection of signals of this magnitude requires an extremely sensitive, low-noise receiver as the basis of the radiometer.
71 Figure 4-3 Emitted Power vs. Temperature Over a 300 MHz Bandwi dth 4.3 Propagation ModelBefore we can begin to apply the radiometric princi ples discussed in section 4.2 to a biological system, we must first expand the princ iples of blackbody radiation to accommodate multiple materials and temperature grad ients as found in human physiology. Considerable theoretical work in the s tudy of thermal emissions from multilayered structures has already been performed , , ; the derivations presented here follow mainly from . From  we know that the effective input noise te mperature TIN of a noiseless device at physical input temperature T1 is related to the noise figure F by 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.34 300302304306308310312314316318320 Temperature (K)Power (Picowatts)
72 TIN = (F 1)T1. (4-6) For the passive materials such as those we will enc ounter in biological systems, the noise figure F is taken to be equal to the signal attenua tion L of the material , and equation 4-6 becomes TIN = (L 1)T1, (4-7) where L is related to the signal attenuation in dec ibels (dB) by10/10dBL-= (4-8) Now, assume that the noiseless device (or material layer, for this discussion) is at physical temperature TH. The temperature emitted from this layer (TE) is the sum of the material temperature TH and the input temperature given by equation 4-7, d ivided by the signal loss of the layer: ()1)1 1 T L T L TH E+ = (4-9) which simplifies to 11 1 T L L T TH E + = (4-10)
73 For a structure consisting of two passive material layers with losses corresponding to L1 and L2 (where layer 1 is adjacent to the heat source TH and TE is the emitted temperature of layer 2), equation 4-10 can be expan ded to TE = TH ¢ / L2 + T2 (1 1/ L2), (4-11) where TH ¢ is given by TH ¢ = TH / L1 + T1(1 1/ L1), (4-12) andTE represents the temperature emitted by the structure TH is the elevated temperature of the internal organ (T0 in Figure 4-3), and L1 and L2 are the losses introduced by layers 1 and 2, respe ctively. We are now ready to begin a first approximation ana lysis of the radiometric characteristics of simple biological structures.4.4 Biological ModelFigure 4-4 shows an illustration of the radiometry problem . An internal organ at elevated temperature (the heart, in this e xample) is separated from the radiometer antenna by several layers of biological tissue. Each layer is assumed to have its own temperature (T) and propagation loss (L) ch aracteristics. Further, the layers are
74 considered homogeneous in that the temperature and loss characteristics are not functions of position within the layer. Figure 4-4 Simplified Biological Model (Used with Permission) Signal propagation from the organ to the surface of the skin is influenced by factors such as the number of layers and the thickn ess, loss characteristics and temperature of each layer. Further, propagation is affected by reflections resulting from impedance changes at the boundaries between layers. As a first approximation to the physiology of the h uman body, consider a similar structure with parallel planar layers consisting of fat and skin. The organ whose temperature is to be measured lies directly below t he fat layer. The measurement is made
75 using radiometric emissions that have traveled vert ically through the fat and skin layers and emerged into the ambient air above the skin lay er. Since the material in each layer has its own complex permittivity, the attenuation, propagation and boundary reflection characteristics of the emission will change as the signal progresses ultimately to the ambient air. Additionally, each layer is assumed t o have its own unique temperature (T). Figure 4-5 illustrates this concept. Figure 4-5 Two-Layer Biological Structure Several assumptions are inherent in Figure 4-5. Fi rst, the boundary between the internal organ and the fat layer is assumed to be a t temperature T0 . Secondly, the thickness of the ambient air layer is assumed to be negligible. This implies a receiving antenna that is proximal to, but not necessarily in contact with, the skin layer. The internal organ at layer 0 emits electromagnetic radiation in accordance with equation 4-2 and corresponding to its elevated temp erature in relation to the remaining Organ at Elevated Temperature T0 Fat Layer e 1, g 1, h 1, T1 Skin Layer e 2, g 2, h 2, T2 Ambient Air h 3 G 23 G 12 G 01
76 layers. As this radiation propagates through the f at and skin layers and into ambient air, the signal is affected by the propagation constants g1 and g2, the boundary reflection coefficients G12 and G23, and the temperatures T1 and T2. Temperatures T1 and T2 are assigned values of 98.6 F and 80 F, and layer thicknesses L1 and L2 are 25 mm and 1 mm, respectively. Propagation through this structu re is modeled using equations 4-11 and 4-12. Losses L1 and L2 are implemented in the following manner. The prop agation constant g is a complex quantity with real and imaginary comp onents a and b, respectively. Attenuation per unit length is repre sented by a, while b yields similar information for phase. Figure 2-3 shows the bulk a ttenuation as a function of frequency for select biological materials expressed in dB per mm. From this figure we obtain the information shown in Table 4-1 for skin and fat at 1.4 GHz. Table 4-1 Propagation Constants for Skin and Fat at 1.4 GHz TissueAttenuation (a) Phase (b) Dry Skin0.2655 dB/mm0.1873 rad/mmInfiltrated Fat0.0731 dB/mm0.0983 rad/mm
77 The attenuation constants in Table 4-1 are converte d to linear units for computational purposes using 1010a-= Atten, (4-13) where a is the attenuation constant from Table 4-1 and is the thickness of the respective layer in millimeters. The magnitude of the layer loss L is then calculated using the linear magnitude of the attenuation as a dampin g factor. We also account for the reflection losses ( G12 and G23) caused by impedances changes at the tissue boundari es. A MathCAD implementation of this code is given in App endix F. 4.5 Results of AnalysisFigure 4-6 shows a plot of the calculated emitted s tructure temperature at 1.4 GHz, given a variable internal organ temperature. The internal temperature corresponds to a range of 98.3 to 103.7 F. The data shown in Figure 4-6 display linear characteristics similar to those of the power infor mation in Figure 4-3, and demonstrate the utility of equations 4.11 and 4.12 for detectin g diagnostically useful temperature changes within a biological structure.
78 Figure 4-6 Emitted vs. Internal Temperatures for a Biological Structure 4.6 VerificationWhile the previous analysis demonstrates the workin g principle of equations 4.11 and 4.12, a more complex structure is needed to res onably approximate a typical human physiology. We constructed a physical model that c ould be used to generate experimental data and analyzed using these equation s. This model consists of three layers: muscle, breast fat and skin in ascending or der. We selected material phantoms with electrical properties corresponding as closely as possible to those of the respective biological materials in each layer. The phantoms i ncluded a hydroxyethylcellulose (HEC) solution for muscle, RANDO simulation materia l  for breast fat, and 93% lean ground beef for skin. Table 4-2 shows a comparison of the electrical properties of each phantom with the respective biological material. 301.8 301.9 302.0 302.1 302.2 302.3 302.4310. 0 310. 4 310.8 311.2 311. 6 312. 0 312.4 312.8Internal Organ Temperature (K) Emitted temperature (K)
79 Table 4-2 Permittivity Comparison for Biological Material Pha ntoms at 1.4 GHz HEC1 Muscle2RANDO1 Breast Fat2 Beef1 Skin2e¢ 52.4159 54.11204.3950 5.3404 40.8768 39.7340 e¢¢ 18.4890 14.65720.5800 0.9136 13.4560 13.50881 Measured2 Calculated using ,  A Total Power Radiometer (TPR) was designed and ass embled to collect data from this construct. The TPR is based on informati on obtained from  and is described in Figure 4-7. Operation in the low GHz frequency range was determined to be suitable for this study; sensing depths would be on the order of 9 cm into adipose tissue and 2.4 cm into internal organs . The specific operating frequency of 1.4 GHz was chosen to coincide with a radioastronomical quiet portion of the electromagnetic spectrum, in order to minimize the effect of extern al RF signals.
80Component Descriptions:1.) Low-Noise RF Amplifier, Gain = 34 dB, Noise Figure (NF) = 0.74 dB at 1.4 GHz 2.) Band-Pass Filter, 0.91 to 3 GHz, NF = 1.97 dB at 1. 4 GHz 3.) Local Oscillator, Frequency = 1.1 GHz, Power = +8dB m 4.) Mixer, Conversion Loss = 7.5 dB, IF = 300 MHz 5.) Low-Noise IF Amplifier, Gain = 21 dB, NF = 0.8 dB a t 300 MHz 6.) DC Block 7.) Low-Pass Filter, DC to 490 MHz, NF = 0.67 dB at 300 MHz 8.) Low-Noise IF Amplifier, Gain = 21 dB, NF = 0.8 dB a t 300 MHz 9.) Diode Detector, 0.01 to 20 GHz, Sensitivity = 500 m V/mW 10.) DC Amplifier, DC to 17 MHz, Gain = 30 dB 11.) Low-Pass Filter, DC to 22 MHz 12.) Digital MillivoltmeterFigure 4-7 Total Power Radiometer Block Diagram The radiometer antenna, pictured to the left of the low noise RF amplifier in Figure 4-7, is a printed dipole designed for 1.4 GH z operation and has a practical bandwidth of approximately 300 MHz . The anten na, along with its SMA-series input connector, is shown in Figure 4-8; the antenn a frequency response curve is shown in Figure 4-9.4 1 6 58 7 3 2 9 1011 12
81 Figure 4-8 Total Power Radiometer Antenna 0 2 4 6 8 10 12 14 16 18 20 15 195 375 555 735 915 1095 1275 1455 1635 1815 1995 2175 2355 2535 2715 2895 Return Loss (dB)Frequency (MHz)Figure 4-9 TPR Antenna Frequency Response
82 In order to mathematically accommodate this three-l ayered biological model, equations 4.11 and 4.12 are expanded to include a s econd intermediate temperature, resulting in TE = TH ¢ ¢/ L3 + T3 (1 1/ L3), (4-14) where TH ¢¢ is given by TH ¢¢ = TH ¢ / L2 + T2(1 1/ L2), (4-15) TH ¢ is defined as TH ¢ = TH / L1 + T1(1 1/ L1), (4-16) and L1, L2 and L3 are the losses introduced by layers 1, 2 and 3, re spectively. Implementation of this set of equations follows tha t of the two-layered model described previously. An electrically quiet heat source is needed in orde r to establish a thermal gradient within the phantom construct, while emitting no RF noise outside that resulting from thermal emission. After some experimentation, we c hose a reservoir of pre-heated water
83 for this task. The water serves as the internal or gan at elevated temperature and provides initial temperature T0 for analysis. It is the water temperature that is ultimately sensed by the radiometer system. Rather than implementing a phantom construct whose physical dimensions would mimic those of an anatomical system, we constructed a model with dimensions that could be easily obtained and controlled using the phantom materials available. This decision was made in order to allow us to accurately analyze the test data and compare those results with those of our analyses. The layer thic knesses were: HEC (muscle) = 3 mmRANDO (fat) = 1 mmBeef (skin) = 10 mmFigure 4-10 shows a schematic diagram of the therma l test bed, including phantom layers and heat source.
84 Figure 4-10 TPR Test Bed Schematic The temperature at each phantom layer was monitored using a digital thermocouple. Additional temperatures monitored we re those of the antenna and the hot and cold thermal references. A TTL logic-controlle d switch installed between the antenna and the low noise RF amplifier determined t he input to the radiometer. At each reading, the hot and cold reference temperatures an d voltage levels were used to linearly interpolate the radiometric temperature correspondi ng to the antenna voltage. A schematic diagram of the switch configuration is sh own in Figure 4-11. Antenna Beef (10 mm) RANDO (1 mm) HEC (3 mm) www www wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww w wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww w wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww w wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww w wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww w Water (Heat Source)
85 Figure 4-11 Input TTL Switch Configuration We accounted for gain variations in the radiometer components by performing separate temperature calibrations at each data poin t, using the noise voltages emitted by the hot and cold references. The cold reference co nsisted of a 50 ohm resistor at a known temperature. The noise voltage corresponding to th is temperature (approximately ambient) established one data point for linear inte rpolation. The hot reference was comprised of a calibrated noise source followed by a 20 dB attenuator. The noise source voltage, attenuated by the 20 dB pad at known tempe rature, established the second data point for linear interpolation. Depending on the a ttenuator temperature, the hot noise source voltage corresponded to approximately 390K ( 472 F). Hot ReferenceCold ReferenceAntenna VHighVLowTo Radiometer
86 Temperature and voltage information were taken as t he pre-heated water cooled. Readings were taken at source temperature changes o f 5 Fahrenheit; this scale was chosen because of its smaller temperature divisions compared to those of the Celsius scale. The readings taken were:Water (organ) temperatureHEC (muscle) temperatureRANDO (fat) temperatureBeef (skin) temperatureAntenna temperatureCold reference voltageHot reference voltageAntenna (emission) voltageAdditionally, the physical temperatures of the hot and cold references were monitored throughout the data collection procedure. These da ta, in addition to those provided in Table 4-2 for the phantoms, were used by the MathCA D implementation of equations 414 through 4-16, as exemplified by the file shown i n Appendix F. A comparison of the test and analysis results is sh own in Figure 4-12. The curves show a relatively constant temperature difference o f 4K to 6K between the analysis and test results. This difference becomes more constant as the water temperature approaches
87 the values that may be encountered in a physiologic al application ( 310K to 313K). We attribute this phenomenon at least partly to the fa ct that the time rate of water cooling slows as the water temperature approaches that of i ts surroundings; this slower rate of cooling provides a more thermally stable phantom co nstruct and allows for more accurate data collection. The error bars attached to the solid curve (measure d data) show the results of a Monte Carlo analysis performed to account for non-h omogeneities in the skin phantom. Permittivity measurements taken at various points o n and within the beef sample showed a range of complex values between approximately (37 .2 j 7.4) and (53.2 j 23.4). A Monte Carlo simulation was executed in Advanced Des ign System (ADS) 2004A, in which the permittivity of the beef layer was allowe d to uniformly vary between these extremes for 10,000 iterations. The change in rece ived power was converted to temperature and represents the height of the error bars. This addition to Figure 4-10 allows us to show that the data agree within the li mits of the permittivity uncertainty. A fairly uniform offset exists between the curves, with the measured temperature being consistently lower than that calculated based on the propagation model. This offset may be attributed to a number of factors, including but not limited to antenna sidelobe effects, phantom non-homogeneity and the limitation of reflection effects (especially at the air-beef interface) to the first order. Howeve r, we are encouraged by the similarities in magnitude and average slope of the two curves, a nd offer these results as a
88 demonstration of the validity of our radiometric mo del for measuring internal body temperatures. Figure 4-12 Radiometric Temperature of a Biological Phantom Con struct (Measured Temperature Solid, Calculated Temperature Dashed) 4.7 Measurement SensitivityWhile the material data available from  provide a reasonable estimate of the properties of biological tissue, they cannot supply the user with an estimate of the possible variations from person to person, or withi n the same person over time. For example, interpersonal variations in skin layer pro perties may result from factors such as pigmentation, moisture content, thickness, etc. [62 ]. Additionally, space flight has the potential to induce changes in fat content, bone de nsity, muscle mass and other effects 280 285 290 295 300 305 310 315 320 330.4327.6324.8322319.3316.5313.7 Organ (Water) Temperature (K)Emitted Temperature (K)
89 within the same person during an extended mission [ 63]. A consideration of the effect these changes may have on the accuracy of radiometr ic measurements will provide insight into the ultimate utility of this technique to provide useful multi-personal data over extended periods of time. We examined several parameters from an analytical s tandpoint for their effect on the emitted radiometric temperature from the body. Skin permittivity could easily vary from person to person, therefore we investigated th e effect of permittivity changes on temperature emission. Table 4-2 lists typical comp lex skin permittivity at 1.4 GHz as approximately (40 j14). We varied this value fro m (30 j6) to (50 j16) and compared the results with those of an analytical model that used the nominal value. The results, shown in Figure 4-13, indicate a rather pronounced effect on emitted temperature throughout the biological temperature range of 310K to 313K (98.3 F to 103.7 F). These results indicate the need for sensor calibration fo r each user.
90 300.5 301.0 301.5 302.0 302.5 303.0 303.531 0 .0 3 1 0. 2 31 0. 4 31 0 .6 310. 8 31 1. 0 31 1 .2 311.4 3 1 1. 6 31 1 .8 31 2 .0 3 1 2. 2 31 2. 4 31 2 .6 312. 8 31 3. 0Internal Organ Temperature (K)Emitted temperature (K) e = 30 j6 e = 40 j13 e = 50 j16Figure 4-13 Effect of Skin Permittivity Variations on Emitted T emperature We also examined the effect that a change in fat co ntent might have on the measured temperature. For the purpose of our analy sis, we modeled a fat content change as a difference in fat layer thickness, as might de velop over time on an extended mission. Figure 4-14 shows the effect of a fat layer change on emitted temperature, as the layer thickness decreases from 25 mm to 5 mm. Normal bod y temperature (37 C, or 310.15K) is assumed in the model. The results show that, at elevated organ temperatures, a decrease in body fat thickness increases the sensit ivity of the radiometric measurement. These results highlight the need for periodic calib ration of the measuring system, to account for body parameter changes on extended miss ions.
91 301.7 301.8 301.9 302.0 302.1 302.2 302.3 302.4 302.5 302.6 3 10 0 310.2 3 10.4 3 10 6 3 1 0.8 3 11.0 3 11 2 3 1 1. 4 311.6 3 11 8 3 12 0 312.2 3 12.4 3 12 6 3 1 2.8 3 13.0 Internal Organ Temperature (K)Emitted temperature (K)Fat = 5 mm Fat = 25 mmFigure 4-14 Effect of Fat Thickness Variations on Emitted Tempe rature 4.8 Limitations of Present StudySeveral factors in the radiometer and model design and implementation contribute to the discrepancies noted between the measured and analytical temperatures in Figure 410. Some of the major limitations include:The radiometer sensitivity, which is limited by (am ong other things) component noise factors. The present radiometer is constructed usi ng commercial off-the-shelf (COTS) components that are not necessarily designed for ra diometric use. For example, the stability of our present output in millivolts is li mited to two decimal places. A timeaveraging algorithm, while slowing the measurement speed, would improve the stability of the readings.
92 The diode detector sensitivity, which is assumed to be linear (at least in the temperature range of 310K to 313K). Any non-linearity in the d iode response needs to be characterized, and our interpolation methods modifi ed to accommodate this characterization.The analytical model we are using, which does not a ccount for system effects such as antenna pattern, efficiency and sidelobes, and loss es within the measurement system. 4.9Future Work Much needs to be accomplished in order to fully dem onstrate the applicability of this technique to a clinical or mission environment The sensitivity of the radiometer must be increased to meet the goal of 0.02K measure ment resolution. This may be accomplished by implementing more spohisticated rad iometer designs, such as the Dicke radiometer . The noise characteristics of the radiometer system and the environment require more rigorous definition than in the presen t work. Phantom selection needs to be based more closely on the biological materials bein g simulated. Finally, clinical tests need to be devised and implemented in order to full y determine the effectiveness of this technology.
93 4.9 ConclusionAlthough research into the use of microwave radiome try for passive monitoring of internal conditions is in its relative infancy, this area nonetheless hold promises for multiple life-monitoring and potentially life-savin g functions. Continuous non-contact evaluation of astronaut internal temperatures has a lready been discussed. Other potential applications of this technology include bone densit y loss detection, muscle mass measurements, and monitoring of cardiac function [6 6]. These functions have significant implication for terrestrial uses, as well.
94 Chapter 5 Summary and Conclusion 5.1 SummaryIn this work we have investigated several potential new applications of microwave radiometry for the biomedical field. It may certainly be said that the basic technologies presented in the previous chapters are not new or original. The innovation lies in the context of the applications for which t hese techniques have been investigated and adapted. For example, we are unaware of any past or contempo rary research efforts being made toward the detection of blood oxygen resonance s near 60 GHz. The impetus for this direction was provided in no small part by our participation in the NSF IGERT SKINS fellowship at the University of South Florida which encouraged research into the nature of skin as an interface for internal physiol ogical phenomena. Our work on radiometric techniques for the measurem ent of internal body temperatures was inspired not only by the goals of the IGERT fellowship, but also by our fascination with and support of the exploration of space. It is our hope that this
95 innovative, continuous and non-invasive method of h ealth monitoring may contribute in some small way to mankinds continuation and expans ion, while at the same time adding to the quality of life here on Earth.5.2 ConclusionThe progress of mankind has for centuries been driv en in no small part by a need to explore its environment. Whether that environme nt is external, such as land, sea, air and space, or internal in the case of the human bod y and mind, the need for knowledge through exploration has and will continue to help d efine the species as it is. For the hope that this work may contribute in some small way to this spirit of exploration, we are extremely grateful.
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99 Cui, W., Ostrander, L.E. and Lee, B.Y., In Viv o Reflectance of Blood and Tissue as a Function of Light Wavelength IEEE Transaction s on Biomedical Engineering, June 1990, pp. 632-639. Berardesca, E., Elsner, P. and Maibach, H.I., e ds., Bioengineering of the Skin, Cutaneous Blood Flow and Erythema CRC Press, 1995, ch. 8, p. 123. Ulaby, F.T., Moore, R.K. and Fung, A.K., Micro wave Remote Sensing, Active and Passive Artech House, 1981, vol. 1, ch. 6, p. 345. Bigu del Bianco, J., Romero-Sierra, C. and Tann er, J.A., Some Theory and Experiments on Microwave Radiometry of Biological S ystems S-MTT Microwave Symposium Digest, June 1974, pp. 41-44. Bardati, F., Mongiardo, M., Solimini, D. and To gnolatti, P., Biological Temperature Retrieval by Scanning Radiometry IEEE MTT-S International Microwave Symposium Digest, June 1986, pp. 763-766. Carr, K.L., Microwave Radiometry: Its Importan ce to the Detection of Cancer IEEE Transactions on Microwave Theory and Technique s, December 1989, pp. 1862-1869. Carr, K.L., Radiometric Sensing IEEE Potentia ls, April/May 1997, pp. 21-25. Land, D.V., Medical Microwave Radiometry and i ts Clinical Applications IEE Colloquium on the Application of Microwaves in Medi cine, February 1995, pp. 2/1-2/5. Ulaby, F.T., Moore, R.K. and Fung, A.K., Micro wave Remote Sensing, Active and Passive Artech House, 1981, vol. 1, ch. 4, p. 192. Ulaby, F.T., Moore, R.K. and Fung, A.K., Micro wave Remote Sensing, Active and Passive Artech House, 1981, vol. 1, ch. 4, p. 198. Ulaby, F.T., Moore, R.K. and Fung, A.K., Micro wave Remote Sensing, Active and Passive Artech House, 1981, vol. 1, ch. 4, p. 200. Wilheit, T.T. Jr., Radiative Transfer in a Pla ne Stratified Dielectric IEEE Transactions on Geoscience Electronics, April 1978, pp. 138-143. Ulaby, F.T., Moore, R.K. and Fung, A.K., Micro wave Remote Sensing, Active and Passive Artech House, 1981, vol. 1, ch. 4, pp. 232-245.
100 Montreuil, J. and Nachman, M., Multiangle Meth od for Temperature Measurement of Biological Tissues by Microwave Radi ometry IEEE Transactions on Microwave Theory and Technoques, Ju ly 1991, pp. 1235-1239. Ulaby, F.T., Moore, R.K. and Fung, A.K., Micro wave Remote Sensing, Active and Passive Artech House, 1981, vol. 1, ch. 6, p. 349. Pozar, D.M., Microwave Engineering (3rd ed.) John Wiley and Sons, 2005, ch. 10, p. 494. Roeder, R., Raytheon Company, Simple Model e lectronic correspondence to T. Weller at University of South Florida, August 2006. Cheever, E.A. and Foster, K.R., Microwave Radi ometry in Living Tissue: What Does it Measure? IEEE Transactions on Biomedical Engineering, June 1992, pp. 563-568. The Phantom Laboratory, Salem NY, http://www.ph antomlab.com/rando.html Ulaby, F.T., Moore, R.K. and Fung, A.K., Micro wave Remote Sensing, Active and Passive Artech House, 1981, vol. 1, ch. 6, pp. 360-367. Bonds, Q., Weller, T., Maxwell, E., Ricard, T., Odu, E. and Roeder, R., The Design and Analysis of a Total Power Radiometer (TP R) for Non-Contact Biomedical Sensing Applications (unpublished manus cript) University of South Florida, February 2008. Vander Vorst, A., Rosen, A. and Kotsuka, Y., R F/Microwave Interaction with Biological Tissues IEEE Press/Wiley-Interscience, 2006, ch. 2, pp. 69-82. Roeder, B., Weller, T., and Harrow, J., Techni cal Proposal for Astronaut Health Monitoring Using a Microwave Free-Space Sensor (Pr eliminary) University of South Florida and Raytheon Company, December 2007, p. 13. Ulaby, F.T., Moore, R.K. and Fung, A.K., Micro wave Remote Sensing, Active and Passive Artech House, 1981, vol. 1, ch. 6, pp. 369-374. Roeder, B., Weller, T., and Harrow, J., Techni cal Proposal for Astronaut Health Monitoring Using a Microwave Free-Space Sensor (Pr eliminary) University of South Florida and Raytheon Company, December 2007, p. 14.
102 Appendix AElectrical Properties of Various Biologic al Materials The properties of complex permittivity, conductivit y, and attenuation are shown in Figures 2-1 through 2-3 for tissues and organs o f specific interest to this work. The corresponding properties of the following tissues a nd organs are contained in this Appendix, for reference and completeness:CartilageCortical BoneCancellous BoneInfiltrated Bone Marrow Cortical bone refers to the hard, outer portion of bony tissue. Cancellous bone indicates the relatively soft, spongy interior tiss ue which allows space for blood vessels and marrow. Infiltrated bone marrow refers to marr ow containing other related tissue, such as blood vessels.
103 Appendix A (Continued) Figure A-1 Complex Permittivity of Various Biological Material s Cartilage1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 234567891011 Log Frequency (10x = Hz)Relative Permittivity Real Imaginary Bone (Cortical)1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 234567891011 Log Frequency (10x = Hz)Relative Permittivity Real Imaginary Bone (Cancellous)1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 234567891011 Log Frequency (10x = Hz)Relative Permittivity Real Imaginary Bone (Marrow, Infiltrated)1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 234567891011 Log Frequency (10x = Hz)Relative Permittivity Real Imaginary
104 Appendix A (Continued) Figure A-2 Conductivity and Loss Tangent of Various Biological Materials Cartilage0.1 1 10 100 234567891011 Log Frequency (10x = Hz) Conductivity Loss Tangent Bone (Cortical)0.01 0.1 1 10 100 1000 234567891011 Log Frequency (10x = Hz) Conductivity Loss Tangent Bone (Cancellous)0.01 0.1 1 10 100 1000 234567891011 Log Frequency (10x = Hz) Conductivity Loss Tangent Bone (Marrow, Infiltrated)0.1 1 10 100 1000 234567891011 Log Frequency (10x = Hz) Conductivity Loss Tangent
105 Appendix A (Continued) Figure A-3 Attenuation and Phase Characteristics of Various Bi ological Materials Cartilage0.001 0.01 0.1 1 10 100 1000 10000 234567891011 Log Frequency (10x = Hz) Attenuation (n/m) Phase (rad/m) Bone (Cortical)0.001 0.01 0.1 1 10 100 1000 10000 234567891011 Log Frequency (10x = Hz) Attenuation (n/m) Phase (rad/m) Bone (Cancellous)0.001 0.01 0.1 1 10 100 1000 10000 234567891011 Log Frequency (10x = Hz) Attenuation (n/m) Phase (rad/m) Bone (Marrow, Infiltrated)0.001 0.01 0.1 1 10 100 1000 10000 234567891011 Log Frequency (10x = Hz) Attenuation (n/m) Phase (rad/m)
106 Appendix BMATLAB Code for Oxygen Resonance by Reduc ed Line Base Method %% Oxygen Attenuation Calculator%% Based on Brussard & Watson,% "Atmospheric Modelling and Millimetre Wave Prop agation" % and using the Reduced Line Base Model of Liebe%% Version 2, July 22, 2006% (Version 1 was lost due to hard drive failure)%% Spectral Line Coefficients:%% f = Spectral Line Frequency in GHz%f = [51.5034 52.0214 52.5424 53.0669 53.5957 54.130 0 54.6712 55.2214 ... 55.7838 56.2648 56.3634 56.9682 57.6125 58.3269 58.4466 59.1642 ... 59.5910 60.3061 60.4348 61.1506 61.8002 62.4112 62.4863 62.9980 ... 63.5685 64.1278 64.6789 65.2241 65.7648 66.3021 66.8368 67.3696 ... 67.9009];%% a1 = Spectral Line Strength Factor (*E-7 KHz pe r millibar) %a1 = [6.08 14.14 31.02 64.1 124.7 228.0 391.8 631.6 953.5 548.9 1344 ... 1763 2141 2386 1457 2404 2112 2124 2461 2504 22 98 1933 1517 1503 ... 1087 733.5 463.5 274.8 153.0 80.09 39.46 18.32 8.01]; %a1 = a1*10^(-7);%% a2 = Spectral Line Strength Temperature Depende ncy %a2 = [7.74 6.84 6.00 5.22 4.48 3.81 3.19 2.62 2.12 0.01 1.66 1.26 0.91 ... 0.62 0.08 0.39 0.21 0.21 0.39 0.62 0.91 1.26 0. 08 1.66 2.11 2.62 ... 3.19 3.81 4.48 5.22 6.00 6.84 7.74];%% a3 = Spectral Line Width Factor (*E-4 GHz per m illibar) %a3 = [8.90 9.20 9.40 9.70 10.00 10.20 10.50 10.79 1 1.10 16.46 11.44 ... 11.81 12.21 12.66 14.49 13.19 13.60 13.82 12.97 12.48 12.07 11.71 ... 14.68 11.39 11.08 10.78 10.50 10.20 10.00 9.70 9.40 9.20 8.90]; %a3 = a3*10^(-4);%
107 Appendix B (Continued)% a4 = Spectral Line Interference Factor (*E-4 pe r millibar) %a4 = [5.60 5.50 5.70 5.30 5.40 4.80 4.80 4.17 3.75 7.74 2.97 2.12 0.94 ... -0.55 5.97 -2.44 3.44 -4.13 1.32 -0.36 -1.59 -2 .66 -4.77 -3.34 ... -4.17 -4.48 -5.10 -5.10 -5.70 -5.50 -5.90 -5.60 -5.80]; %a4 = a4*10^(-4);%% a5 = Spectral Line Interference Temperature Dep endency %a5 = [1.8 1.8 1.8 1.9 1.8 2.0 1.9 2.1 2.1 0.9 2.3 2 .5 3.7 -3.1 0.8 0.1 ... 0.5 0.7 -1.0 5.8 2.9 2.3 0.9 2.2 2.0 2.0 1.8 1. 9 1.8 1.8 1.7 1.8 1.7]; %% Pressure and Temperature Parameters%% p = dry air pressure in millibars (1013.3 mbar = 1 atm.) % e = water vapor partial pressure in millibars% T = temperature in Kelvin% freq = computation frequency in GHz%p = 212.73 % Atmospheric pO2e = 9.45 % Value in AirT = 291.15 % Lab Air Tempt = 300/Tcount = 1;for freq = 50:0.0375:65;%% Wet Continuum%Nw = 1.18*10^(-8)*(p+30.3*e*t^6.2)*freq*e*t^3.0 + .. 2.3*10^(-10)*p*e^1.1*t^2*freq^1.5;%% Dry Continuum%d = 5.6*10^(-4)*(p+1.1*e)*t^0.8;%Nd = (freq*p*t^2)*(6.14*10^(-5)/(d*(1+(freq/d)^2)*( 1+(freq/60)^2)) + ... 1.4*10^(-11)*(1-1.2*10^(-5)*freq^1.5)*p*t^1.5);%% Spectral Line Interference%
108 Appendix B (Continued)s = a4.*p.*t.^(a5);%% Spectral Line Width%deltaf = a3*(p*t^0.8+1.1*e*t);%% Line Shape Factor%F = (freq./f).*((deltaf-s.*(f-freq))./((f-freq).*(f -freq)+deltaf.*deltaf) + ... (deltaf-s.*(f+freq))./((f+freq).*(f+freq)+delta f.*deltaf)); %% Line Strength%S = a1.*p*t^3.*exp(1).^(a2.*(1-t));%% Imaginary Part of Complex Refractivity%Ndoubleprime = sum(S.*F) + Nd + Nw;%% Gaseous Absorption Coefficient in dB per Kilome ter %alpha(count) = 0.1820*freq*Ndoubleprime;count = count + 1;end
109 Appendix C MATLAB Code for Oxygen Resonance by Th eory of Overlapping Lines %% Oxygen Attenuation Calculator%% Based on Ulaby, Moore & Fung,% "Microwave Remote Sensing, Active and Passive ( Volume 1)" % and using the Theory of Overlapping Lines of Ro senkrantz (1975) %% November 24, 2006%% Input Tabulated Parameters%% Rotational Quantum Numbers%N = [1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39]; %% Resonant Frequencies (GHz)%fNplus = [56.2648 58.4466 59.5910 60.4348 61.1506 6 1.8002 62.4112 ... 62.9980 63.5685 64.1278 64.6789 65.2241 65.7647 66.3020 66.8367 ... 67.3694 67.9007 68.4308 68.9601 69.4887];%fNminus = [118.7503 62.4863 60.3061 59.1642 58.3239 57.6125 56.9682 ... 56.3634 55.7838 55.2214 54.6711 54.1300 53.5957 53.0668 52.5422 ... 52.0212 51.5030 50.9873 50.4736 49.9618];%% Interference Coefficients (per millibar)%YNplus = [4.51 4.94 3.52 1.86 0.33 -1.03 -2.23 -3.3 2 -4.32 -5.26 ... -6.13 -6.99 -7.74 -8.61 -9.11 -10.3 -9.87 -13.2 -7.07 -25.8]; YNplus = YNplus*10^(-4);%YNminus = [-0.214 -3.78 -3.92 -2.68 -1.13 0.344 1.6 5 2.84 3.91 ... 4.93 5.84 6.76 7.55 8.47 9.01 10.3 9.86 13.3 7. 01 26.4]; YNminus = YNminus*10^(-4);%% Input Conditional Variables%count = 0;for f = 50:0.0375:65; % Frequency in GHz count = count + 1;P = 212.8 % Total pressure in millibars (1 atm = 1013 mb)
110 Appendix C (Continued)T = 291 % Temperature in degrees Kelvin (300 K = 80 F) %% Calculations%gammaN = 1.18*(P/1013)*(300/T)^0.85; % Resonant Line width Parameters gammab = 0.49*(P/1013)*(300/T)^0.89; % Nonresona nt Line width Parameters %% Spectral Line Amplitudes%dNplus = sqrt(N.*(2*N+3)./((N+1).*(2*N+1)));dNminus = sqrt((N+1).*(2*N-1)./(N.*(2*N+1)));%PhiN = 4.6*10^(-3)*(300/T)*(2*N+1).*exp((-6.89*10^( -3))*N.*(N+1)*(300/T)); %gNplus_of_plus_f = ((gammaN*dNplus.*dNplus)+ ... P*(f-fNplus).*YNplus)./((f-fNplus).*(f-fNplus)+ gammaN^2); gNplus_of_minus_f = ((gammaN*dNplus.*dNplus)+ ... P*(-f-fNplus).*YNplus)./((-f-fNplus).*(-f-fNplu s)+gammaN^2); %gNminus_of_plus_f = ((gammaN*dNminus.*dNminus)+ ... P*(f-fNminus).*YNminus)./((f-fNminus).*(f-fNmin us)+gammaN^2); gNminus_of_minus_f = ((gammaN*dNminus.*dNminus)+ .. P*(-f-fNminus).*YNminus)./((-f-fNminus).*(-f-fN minus)+gammaN^2); %% Absorption Spectrum Shape%Fprime = ((0.7*gammab)/(f^2+gammab^2))+ ... sum(PhiN.*(gNplus_of_plus_f+gNplus_of_minus_f+ ... gNminus_of_plus_f+gNminus_of_minus_f));%% Oxygen Absorption Coefficient%k(count) = 1.61*10^(-2)*f^2*(P/1013)*(300/T)^2*Fpri me; end
111 Appendix DBovine Blood Permittivity DataNovember 12, 2007 10:11 AMFrequency (Hz)e'e''50000000000. 11.3313 14.633250037500000. 11.3585 14.659350075000000. 11.3888 14.661350112500000. 11.4637 14.693950150000000. 11.5138 14.635650187500000. 11.5801 14.540650225000000. 11.6193 14.461850262500000. 11.6275 14.322450300000000. 11.4441 14.114350337500000. 11.3757 13.954550375000000. 11.2532 13.826050412500000. 11.1395 13.814550450000000. 11.0375 13.686450487500000. 10.9343 13.678850525000000. 10.8712 13.754050562500000. 10.7800 13.808150600000000. 10.7517 13.898650637500000. 10.7441 14.008550675000000. 10.7461 14.138550712500000. 10.7675 14.210850750000000. 10.8059 14.293250787500000. 10.8525 14.344450825000000. 10.9065 14.341650862500000. 10.9403 14.326350900000000. 11.0186 14.241750937500000. 11.0338 14.135950975000000. 11.0528 14.044951012500000. 10.9883 13.975751050000000. 10.9660 13.806851087500000. 10.8907 13.752351125000000. 10.7884 13.667051162500000. 10.7150 13.651551200000000. 10.6325 13.626951237500000. 10.5971 13.650051275000000. 10.5159 13.719651312500000. 10.4746 13.775251350000000. 10.4574 13.840251387500000. 10.4168 13.9480
112 Appendix D (Continued)51425000000. 10.4444 14.000751462500000. 10.4898 14.095351500000000. 10.5139 14.103751537500000. 10.5726 14.085551575000000. 10.6237 14.079851612500000. 10.6620 14.055451650000000. 10.6716 13.954451687500000. 10.6768 13.868551725000000. 10.6898 13.725851762500000. 10.6391 13.693551800000000. 10.5891 13.589551837500000. 10.5039 13.521051875000000. 10.4481 13.515051912500000. 10.3889 13.493351950000000. 10.2973 13.521151987500000. 10.2531 13.547052025000000. 10.2213 13.582552062500000. 10.1969 13.668152100000000. 10.1872 13.727052137500000. 10.2021 13.778452175000000. 10.2245 13.831452212500000. 10.2738 13.861752250000000. 10.2972 13.866052287500000. 10.3069 13.863852325000000. 10.3473 13.811552362500000. 10.3880 13.782052400000000. 10.3887 13.642352437500000. 10.3578 13.591252475000000. 10.3508 13.501852512500000. 10.2713 13.427852550000000. 10.2418 13.388052587500000. 10.1817 13.342752625000000. 10.1315 13.335352662500000. 10.0672 13.327052700000000. 10.0204 13.377852737500000. 9.9804 13.415952775000000. 9.9748 13.446752812500000. 9.9506 13.526252850000000. 9.9467 13.566652887500000. 9.9786 13.611152925000000. 10.0055 13.618452962500000. 10.0490 13.6318
113 Appendix D (Continued)53000000000. 10.0987 13.600653037500000. 10.1266 13.546853075000000. 10.1826 13.490253112500000. 10.1660 13.426053150000000. 10.1605 13.356453187500000. 10.1290 13.261653225000000. 10.0862 13.224753262500000. 10.0569 13.161453300000000. 10.0056 13.110053337500000. 9.9507 13.139953375000000. 9.9194 13.115553412500000. 9.8470 13.151953450000000. 9.8242 13.191653487500000. 9.8172 13.225553525000000. 9.7995 13.283053562500000. 9.8228 13.309353600000000. 9.8285 13.341353637500000. 9.8876 13.365153675000000. 9.8987 13.382353712500000. 9.9456 13.372853750000000. 9.9856 13.316653787500000. 10.0135 13.288553825000000. 10.0376 13.216053862500000. 10.0297 13.153553900000000. 9.9886 13.056753937500000. 9.9737 13.032053975000000. 9.9321 12.954654012500000. 9.8903 12.940354050000000. 9.8270 12.919454087500000. 9.7893 12.921854125000000. 9.7457 12.934754162500000. 9.7002 12.990654200000000. 9.6809 13.014354237500000. 9.6782 13.061654275000000. 9.6597 13.110154312500000. 9.6744 13.118854350000000. 9.7182 13.153954387500000. 9.7088 13.179254425000000. 9.7697 13.131354462500000. 9.7817 13.084054500000000. 9.8039 13.031054537500000. 9.8199 13.0020
114 Appendix D (Continued)54575000000. 9.8108 12.927254612500000. 9.7893 12.861154650000000. 9.7580 12.783154687500000. 9.7239 12.755754725000000. 9.6796 12.709554762500000. 9.6331 12.693854800000000. 9.5774 12.698554837500000. 9.5467 12.706654875000000. 9.5071 12.729654912500000. 9.5006 12.760754950000000. 9.4780 12.830354987500000. 9.4968 12.864555025000000. 9.4837 12.866955062500000. 9.4783 12.880255100000000. 9.5151 12.882055137500000. 9.5190 12.879555175000000. 9.5682 12.825355212500000. 9.6152 12.825555250000000. 9.7036 12.801955287500000. 9.7650 12.819955325000000. 9.7926 12.810555362500000. 9.7619 12.728955400000000. 9.6387 12.604855437500000. 9.4495 12.474455475000000. 9.3620 12.450355512500000. 9.3142 12.425655550000000. 9.3046 12.471155587500000. 9.2471 12.455755625000000. 9.2886 12.533355662500000. 9.2730 12.539755700000000. 9.2857 12.593955737500000. 9.3365 12.647155775000000. 9.3395 12.672855812500000. 9.4132 12.671855850000000. 9.3491 12.603455887500000. 9.5683 12.741955925000000. 9.5062 12.620955962500000. 9.5341 12.553056000000000. 9.5592 12.536656037500000. 9.5069 12.469156075000000. 9.4227 12.323556112500000. 9.3297 12.2506
115 Appendix D (Continued)56150000000. 9.2502 12.215756187500000. 9.1991 12.192056225000000. 9.1635 12.181756262500000. 9.1150 12.172056300000000. 9.0761 12.207156337500000. 9.0692 12.246756375000000. 9.0667 12.255556412500000. 9.0558 12.283356450000000. 9.0197 12.350156487500000. 9.0770 12.358156525000000. 9.1031 12.389256562500000. 9.1449 12.338856600000000. 9.1859 12.330056637500000. 9.1975 12.246056675000000. 9.1997 12.223756712500000. 9.2147 12.150656750000000. 9.1931 12.086756787500000. 9.1681 12.045056825000000. 9.1314 11.970256862500000. 9.0787 11.938056900000000. 9.0421 11.902256937500000. 9.0257 11.906556975000000. 8.9446 11.934957012500000. 8.8959 11.956457050000000. 8.8865 11.942257087500000. 8.8866 12.000757125000000. 8.8612 12.038757162500000. 8.8668 12.057457200000000. 8.8911 12.082457237500000. 8.9164 12.074757275000000. 8.9241 12.087357312500000. 8.9438 12.015657350000000. 8.9672 11.959757387500000. 8.9647 11.938057425000000. 8.9802 11.846157462500000. 8.9499 11.812957500000000. 8.9561 11.730657537500000. 8.8834 11.674757575000000. 8.8807 11.624357612500000. 8.8246 11.617157650000000. 8.7720 11.604657687500000. 8.7266 11.6254
116 Appendix D (Continued)57725000000. 8.6944 11.639057762500000. 8.6835 11.641157800000000. 8.6632 11.684657837500000. 8.6584 11.734157875000000. 8.6455 11.750357912500000. 8.6559 11.796957950000000. 8.7234 11.782657987500000. 8.7436 11.773458025000000. 8.7712 11.767958062500000. 8.8040 11.694158100000000. 8.8180 11.656658137500000. 8.8118 11.571358175000000. 8.8182 11.505358212500000. 8.8137 11.443258250000000. 8.7751 11.367658287500000. 8.7410 11.312258325000000. 8.6857 11.303358362500000. 8.6455 11.268858400000000. 8.5892 11.298558437500000. 8.5628 11.327458475000000. 8.5088 11.343358512500000. 8.5173 11.382258550000000. 8.4971 11.429258587500000. 8.4948 11.472858625000000. 8.5157 11.496658662500000. 8.5457 11.518658700000000. 8.5806 11.509158737500000. 8.6133 11.472858775000000. 8.6443 11.427058812500000. 8.6975 11.361458850000000. 8.7205 11.319158887500000. 8.7095 11.209758925000000. 8.7076 11.147758962500000. 8.6812 11.036259000000000. 8.6255 10.993859037500000. 8.6201 10.957259075000000. 8.5679 10.961659112500000. 8.5341 10.970559150000000. 8.4924 11.005459187500000. 8.4456 11.013159225000000. 8.4719 11.099159262500000. 8.3788 11.1206
117 Appendix D (Continued)59300000000. 8.3941 11.153559337500000. 8.4401 11.224959375000000. 8.5766 11.320659412500000. 8.6578 11.334259450000000. 8.7265 11.329359487500000. 8.6328 11.152459525000000. 8.7325 11.081759562500000. 8.9400 11.146459600000000. 8.8836 10.947259637500000. 8.7806 10.724759675000000. 8.7976 10.683759712500000. 8.7355 10.584359750000000. 8.8008 10.618059787500000. 8.6949 10.577059825000000. 8.5812 10.526559862500000. 8.4377 10.523559900000000. 8.3901 10.577959937500000. 8.3629 10.690959975000000. 8.3890 10.817460012500000. 8.3419 10.893360050000000. 8.3907 10.987360087500000. 8.4468 11.077860125000000. 8.4532 11.061560162500000. 8.5605 11.088560200000000. 8.6765 11.041460237500000. 8.8021 10.949060275000000. 8.9443 10.870860312500000. 8.9937 10.653660350000000. 9.0164 10.490760387500000. 9.0499 10.278860425000000. 8.8499 10.021960462500000. 8.7468 9.907560500000000. 8.7184 9.881160537500000. 8.5360 9.870560575000000. 8.4267 9.933660612500000. 8.2861 10.010260650000000. 8.1297 10.119960687500000. 8.0500 10.272260725000000. 7.9747 10.423860762500000. 7.9224 10.567460800000000. 7.9173 10.712460837500000. 7.9971 10.8317
118 Appendix D (Continued)60875000000. 8.1242 10.927360912500000. 8.3517 10.972660950000000. 8.6543 10.991960987500000. 9.0557 10.914661025000000. 9.4977 10.764961062500000. 9.9459 10.582861100000000. 10.3479 10.312561137500000. 10.5748 10.051361175000000. 10.6035 9.791661212500000. 10.4375 9.622361250000000. 10.1604 9.524861287500000. 9.8092 9.491361325000000. 9.3508 9.530861362500000. 8.9205 9.608161400000000. 8.4888 9.708961437500000. 8.1142 9.800761475000000. 7.7830 9.941661512500000. 7.5323 10.072861550000000. 7.3141 10.245561587500000. 7.1383 10.472061625000000. 6.9992 10.757661662500000. 6.8474 11.062061700000000. 6.7407 11.388361737500000. 6.6451 11.707261775000000. 6.6329 12.042661812500000. 6.6705 12.323261850000000. 6.8208 12.533361887500000. 7.0160 12.643061925000000. 7.3099 12.667561962500000. 7.5758 12.526762000000000. 7.8359 12.265062037500000. 8.0345 11.871362075000000. 8.1837 11.380062112500000. 8.2154 10.929962150000000. 8.1585 10.484062187500000. 8.0651 10.133762225000000. 7.9291 9.847862262500000. 7.7704 9.651562300000000. 7.6020 9.545962337500000. 7.4181 9.472162375000000. 7.2689 9.449362412500000. 7.0895 9.4584
119 Appendix D (Continued)62450000000. 6.9161 9.517562487500000. 6.7567 9.575962525000000. 6.5994 9.665562562500000. 6.4628 9.774962600000000. 6.3516 9.875362637500000. 6.3060 9.979562675000000. 6.3174 10.058462712500000. 6.4317 10.132862750000000. 6.5979 10.142262787500000. 6.8068 10.139362825000000. 7.0317 10.071462862500000. 7.2296 9.972062900000000. 7.4055 9.837962937500000. 7.5203 9.704862975000000. 7.5756 9.588763012500000. 7.6010 9.473863050000000. 7.5838 9.387963087500000. 7.5291 9.312963125000000. 7.4596 9.260063162500000. 7.3945 9.201763200000000. 7.3023 9.184163237500000. 7.2087 9.177363275000000. 7.1246 9.132863312500000. 7.1113 9.108463350000000. 7.0960 9.073663387500000. 7.0897 9.181663425000000. 7.0881 9.165563462500000. 7.1197 9.204163500000000. 7.2042 9.195863537500000. 7.2488 9.273463575000000. 7.3112 9.280563612500000. 7.3819 9.202663650000000. 7.4549 9.296563687500000. 7.4760 9.233263725000000. 7.5233 9.288663762500000. 7.4601 9.191763800000000. 7.5538 9.139163837500000. 7.4036 9.162163875000000. 7.3953 9.035863912500000. 7.4050 9.002563950000000. 7.2958 9.026363987500000. 7.3569 8.9422
120 Appendix D (Continued)64025000000. 7.3726 8.951364062500000. 7.2847 9.097964100000000. 7.2496 8.956364137500000. 7.2551 8.963664175000000. 7.3347 9.039864212500000. 7.2506 9.008564250000000. 7.2971 8.986264287500000. 7.3777 8.977064325000000. 7.4353 9.148864362500000. 7.3472 9.063764400000000. 7.4073 9.020764437500000. 7.5685 8.994964475000000. 7.4689 9.052164512500000. 7.3550 8.912064550000000. 7.3411 8.807364587500000. 7.4043 8.835864625000000. 7.3949 8.840564662500000. 7.1715 8.807164700000000. 7.1304 8.664164737500000. 7.3018 8.697164775000000. 7.2653 8.710164812500000. 7.0661 8.821464850000000. 7.0878 8.659564887500000. 7.2546 8.714064925000000. 7.1866 8.745564962500000. 7.2286 8.857365000000000. 7.0752 8.7682
121 Appendix EAgilent 37397 Vector Network Analyzer Spe cifications
122 Appendix FMathCAD Code for Planar Biological Struct ureDry skin propagation, dB per mm and radians per mm at frequency f a 10.0731 := b 10.098345573 := Fat layer propagation, dB per mm and radians per mm at frequency f g 1 a 1j b 1 + := Temp2300 := Dry skin temperature (300K = 80F) Temp1310.2 := Fat layer temperature (310.2K = 98.6F) Temp0310310.2 313 .. := Organ temperature (98.3F to 103.7F) TempR300 := Radiometer antenna noise temperature L21 := Thickness of skin layer in mm L125 := Thickness of fat layer in mm COHERENT MULTI-LAYER CALCULATOR (Layer 3 is atmosphere, layer 2 is dry skin, layer 1 is infiltrated fat, layer 0 is organ.) f1.4109 := For reference only not used in calculations B27106 := Bandwidth in Hertz e 2prime39.661173 := e 2doubleprime13.300211 := Dry skin complex permittivity at frequency f e 2 e 2primej e 2doubleprime := e 1prime11.15166 := e 1doubleprime1.9237886 := Fat layer complex permittivity at frequency f e 1 e 1primej e 1doubleprime := a 20.2655 := b 20.1872977 := g 2 a 2j b 2 + :=
123 Appendix F (Continued)TempFTemp0 () 95 Temp0 459.666 := Convert power level back to temperature TempEmittedTemp0 () TmeasTemp0 () kB := TmeasTemp0 ()TETemp0 () 1 G 23 ()2r n TR G 32 ()2 + := TETemp0 ()T0primeTemp0 ()10a 2L2 () 10 r n 1 G 23 ()2r n T2 + T210a 2L2 () 10 r n 1 G 23 ()2r n := T0primeTemp0 ()T0Temp0 ()10a 1L1 () 10 r n 1 G 12 ()2r n T1 + T110a 1L1 () 10 r n 1 G 12 ()2r n := Calculate effects ofattenuation and reflection T0Temp0 ()kTemp0 B := T1kTemp1 B := Convert temperatures into power levels T2kTemp2 B := TRkTempR B := Boltzmann's Constant k1.38065031023 - := Reflectance, air-to-skin G 32 G 23 := Reflectance, skin-to-air G 23 Z3Z2 () Z3Z2 + () := Reflectance, fat-to-skin G 12 Z2Z1 () Z2Z1 + () := Fat impedance Z1 Z3 e 1 := Dry skin impedance Z2 Z3 e 2 := Free-space impedance (layer 3 is free space) Z3376.73 :=
About the Author Thomas Armand Ricard began his engineering educatio n at Waterbury (CT) State Technical College (now part of Naugatuck Valley Com munity College), where he earned his ASEE degree with high honors in 1982. He compl eted his undergraduate studies at the University of Hartford, receiving his BSEE degr ee cum laude with mathematics minor in 1988. His graduate work began at Syracuse University as part of the General Electric Edison Engineering Program, where he earne d his MSEE degree in 1991. After devoting his efforts to industry for more than a de cade, he returned to academia and completed his doctoral requirements at the Universi ty of South Florida in 2008. Mr. Ricard is a member of Phi Kappa Phi, Tau Beta P i and Eta Kappa Nu honor societies and is a biographee in several Marquis Wh os Who publications. He lives in Tampa Florida with his wife Gina and their daughter s, Bernadette and Amanda.