Variability in EMF Permittivity Values: Implications for SAR Calculations

Transcription

1 396 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 47, NO. 3, MARCH 2000 Variability in EMF Permittivity Values: Implications for SAR Calculations William D. Hurt*, Senior Member, IEEE, John M. Ziriax, and Patrick A. Mason Abstract Digital anatomical models of man and animals are available for use in numerical calculations to predict electromagnetic field (EMF)-induced specific absorption rate (SAR) values. To use these models, permittivity values are assigned to the various tissues for the EMF frequencies of interest. There is, as yet, no consensus on what are the best permittivity data. This study analyzed the variability in published permittivity data and investigated the effects of permittivity values that are proportional on SAR calculations. Whole-sphere averaged and localized SAR values along the diameter of a 4-cm sphere are calculated for EMF exposures in the radio frequency range of 1 MHz to 1 GHz. When the dimensions of a sphere are small compared to the wavelength (i.e., wavelength inside the material is greater than ten times the dimensions of the object), the whole-sphere averaged SAR is inversely proportional to the permittivity of the material composing the sphere. However, the localized SAR values generally do not have the same relation and, as a matter of fact, vary greatly depending on the location within the sphere. These results indicate that care must be taken in choosing the permittivity values used in calculating SAR values and some estimate of the dependence of the calculated SAR values on variability in permittivity should be determined. Index Terms Conductivity, dielectric values, dosimetry, finitedifference time-domain (FD-TD), Mie, radio frequency radiation. I. INTRODUCTION HIGH-RESOLUTION digital anatomical models of man and animals based on medical imaging data are frequently used in electromagnetic field (EMF) dosimetry calculations. The application of such models requires that permittivity values be allocated to the various tissues for the EMF frequencies of interest. There is, as yet, no consensus as to what permittivity data should be used. The most recent and comprehensive permittivity data have been measured by Gabriel [1] on more than 20 tissue types for the frequency range 10 Hz to 20 GHz and on more than ten others from 1 MHz to 20 GHz. Variability in permittivity values result from the heterogeneous nature of biological tissues, the use of tissues from different species (as well as from different animals of the same species), the age of the samples when used, the tissue preparation procedure, whether the tissue is anisotropic, the Manuscript received December 15, 1998; revised September 30, This work was supported in part by the U.S. Air Force under Contract F C-9009 and in part by the Naval Health Research Center Detachment under Work Unit N MRO Asterisk indicates corresponding author *W. D. Hurt is with the Air Force Research Laboratory, Directed Energy Bioeffects Division, Building 1184, 8308 Hawks Road, Brooks AFB, TX USA ( william.hurt@brooks.af.mil). J. M. Ziriax is with the Naval Health Research Center Detachment, Brooks AFB, TX USA. P. A. Mason is with Veridian Engineering, Inc., San Antonio, TX USA. Publisher Item Identifier S (00) temperature of the sample, and systematic errors associated with the measurement technique used. In the present research, new and historical data in the Gabriel [1] report are analyzed so that a sense of the appropriate level of confidence in the permittivity value of various tissue types can be achieved. It is well know that specific absorption rates (SAR s) are dependent on permittivity values, however no systematic evaluation exploring this relationship has been published. Permittivity values, such as those published by Gabriel [1], are widely used in the calculation of SAR distributions by finite-difference timedomain (FD-TD), finite element, and other numerical methods. We used the Mie procedure [2] as a first examination of the effect of variations in permittivity on SAR values. The Mie procedure generates exact values of the electric -field distribution in a sphere. The results of the Mie technique have implications for the more sophisticated methods mentioned above and indicate that in future EMF dosimetry research, some estimate of the dependence of calculated SAR on variability in permittivity values should be determined. II. VARIABILITY OF PERMITTIVITY VALUES Permittivity is the complex quantity that describes both the reactive (real part) and the resistive (imaginary part) properties of a linear material as a function of frequency where is the imaginary unit. The relative dielectric value represents the real part of the relative permittivity where is the permittivity of free space ( F/m). Ramo et al. [3] gives the conductivity as the product of the angular frequency and the imaginary part of the permittivity. Muscle data are used for our first comparison of permittivity values. Hurt [4] fit multiterm Debye dispersion relations to permittivity values published by researchers who used samples from many different species. The five term Deby-type expression, that was fit to the published data by Hurt [4], gave values that agreed within 10% for more than half of the data points. Gabriel [1] reported that the spread of values for her measurements ranged from about 5% for frequencies above 100 MHz and to 15% for the lower frequencies. Gabriel's muscle data consist of a single set of measurements on ovine paravertebral muscle and was fit with a four-cole-cole model which describes the frequency dependence of the permittivity properties. The resulting fits reported by Hurt [4] and Gabriel [1] for, when the -field is transverse to the muscle fibers, are plotted in Fig. 1(a). In Fig. 1(b), the ratio of these two curves is plotted. For low frequencies ( 10 MHz) the ratio deviates substantially from unity. This may be attributed to /00$ IEEE

2 HURT et al.: VARIABILITY IN EMF PERMITTIVITY VALUES: IMPLICATIONS FOR SAR CALCULATIONS 397 TABLE I MAXIMUM AND MINIMUM OF CURVES GENERATED BY NORMALIZING DATA (" AND ) REPORTED BY HURT [4] OR BAO ET AL. [5] TO DATA REPORTED BY GABRIEL [1] FOR FREQUENCIES BETWEEN 10 MHz AND 100 GHz. THE FREQUENCY WHERE THE MAXIMUM OR MINIMUM OCCURS IS ALSO INCLUDED TABLE II PERCENT OF DATA REPORTED BY OTHER RESEARCHERS, BY TISSUE TYPE, THAT DEVIATES SUBSTANTIALLY FROM DATA REPORTED BY GABRIEL [1] Fig. 1. (a) Relative dielectric values for muscle reported by Hurt [4] and Gabriel [1]. (b) Ratio of dielectric values for muscle reported by Hurt [4] and Gabriel [1]. (c) Distribution of historical relative dielectric values and conductivity values normalized to data reported by Gabriel [1]. the fact that, unlike earlier investigators, Gabriel accounted for errors contributed by electrode polarization and lead inductance. However, for frequencies above 10 MHz, where EMF dosimetry modeling is primarily being done, the agreement is much better. A comparison of conductivity values produced similar results. Recently, Bao et al. [5] published the permittivity values of rat brain for the frequency range from 45 MHz to 26.5 GHz. They reported standard deviations that ranged from 4% to 16% for the twelve samples measured. The data were fit to a two-cole-cole model. We normalized Bao's values for gray matter to those from Gabriel for ovine brain. The ratio is close to unity despite species and other methodological differences. The results of a similar procedure for white matter also gave good agreement. Table I contains the maximum and minimum values of these ratios and the corresponding frequency where they occurred. Gabriel [1] included in her report much of the permittivity data published by other researchers. Fig. 1(c) is a histogram of the resulting normalization of this historical data to that of Gabriel [1]. The center bins are 10% wide while those farther out are larger, giving a skewed perception of the distribution. The majority of the ratios are near unity. None of the ratios for four tissue types (vitreous humor, stomach, cornea, and colon) deviated substantially from unity and many others had less than 10% of the data published for them deviate substantially from those of Gabriel. Data that deviate substantially (ratio either 0.5 or 2) are presented in Table II. More than 50% of the published data for inflated lung deviate substantially from Gabriel's data, which is not unexpected due to the difficulty in measuring inflated lung tissue. However, most ratios did cluster around unity for the published data. Some data we consider as extreme outliers (ratio either 0.1 or 10) in Table II are described in more detail in Table III. Bone marrow, breast fat, and fat are the source of 16 of the 22

3 398 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 47, NO. 3, MARCH 2000 TABLE III SPECIAL INFORMATION ON EXTREME OUTLIERS (RATIO OF <0.1 or >10) TAKEN FROM TABLE II outliers. Three of the other outliers are for muscle at the relatively low frequency of 100 Hz. Outliers are generally a consequence of the great inhomogeneity of these tissue types and the difficulty associated with sample preparation for the measurement procedure. III. DEPENDENCE OF SAR ON PERMITTIVITY A first approximation for objects small compared to the wavelength (i.e., wavelength inside material is greater than ten times the dimensions of the object) is given by Jackson [6] as Fig. 2. Calculated average SAR values in a prolate spheroidal model of an average man, as a function of frequency and several permittivity values (" = permittivity of muscle) in [7, Fig. 5.7]). TABLE IV FREQUENCY, SAR RATIO, AND PROLATE SPHEROID LENGTH FOR POINTS IN FIG. 2 Therefore, since and then for the special condition where permittivity values are proportional This suggests that for permittivity values that are proportional, SAR should be inversely proportional to permittivity for a given incident EMF frequency. Durney et al. [7] calculated the whole-body averaged SAR values for a homogeneous prolate spheroidal model of an average man for three different permittivities (Fig. 2). The procedure used was the Extended-Boundary-Condition Method which is a matrix formulation based on an integral equation and expansion of the EMF in spherical harmonics. It is exact within the limits of numerical computation capability. The SAR values for the highest permittivity ( where is the permittivity of (1) muscle) are slightly less than those for the lower permittivities ( and ). This trend is consistent with that predicted by (1), but while the ratio of the highest to lowest permittivity is 8, the ratio of the corresponding SAR values is much less. The reason these SAR values are not in good agreement with those predicted by (1) is because the length of the prolate spheroid is large compared to the wavelength. Table IV gives the frequencies, SAR ratios, and prolate spheroid length expressed in units of wavelength for the points plotted in Fig. 2. However, note that as the frequency decreases, the SAR ratio does increase. Next we investigated the dependence of the SAR distribution in a 4-cm diameter sphere on permittivity. This sphere is a reasonable representation of a rhesus monkey brain which we have occasion to study. The Mie procedure was used to calculate SAR values in the sphere for permittivity values equal to,

4 HURT et al.: VARIABILITY IN EMF PERMITTIVITY VALUES: IMPLICATIONS FOR SAR CALCULATIONS 399 (a) Fig. 3. (b) (a) Whole-sphere averaged SAR values for a 4-cm diameter sphere with permittivity values of " =3; 2" =3, and 4" =3. (b) Ratio of whole-sphere averaged SAR values for a 4-cm diameter sphere with permittivity values of " =3 and 4" =3 to SAR values for a sphere with permittivity value of 2" =3 where " = permittivity of muscle. Horizontal lines represent the values predicted by (1). and that of muscle [see Fig. 3(a)]. For frequencies from 1 to 200 MHz, the whole-sphere averaged SAR values are inversely proportional to as predicted by (1) [see curves in Fig. 3(b)]. This is demonstrated by the fact that the SAR ratio curves are relatively flat up to 200 MHz. The deviations for frequencies greater than 200 MHz are due to the fact that the wavelength is no longer large compared to the dimensions of the sphere. The effects of three different permittivity values on local SAR s are plotted in Fig. 4(a) (c). These localized SAR values, along the diameter that runs from the front to the back of the sphere, are plotted for the frequency range from 50 MHz to 1 GHz. Although the whole-sphere averaged SAR ratio values conform to (1) for 200 MHz and below [Fig. 3(b)], the localized SAR ratio values differ greatly [Fig. 5(a) and (b), solid lines]. The SAR s for these frequencies at the front of the sphere, where the EMF is incident, vary only slightly for the different permittivity values, so do not agree with (1). As we approach the rear of the sphere, SAR s are more dependent on permittivity. Thus, as we proceed through the sphere, dependence on permittivity increases. In Fig. 5(a), the ratios increase for points deep in the sphere. In Fig. 5(b), the ratios Fig. 4. Localized SAR values for a 4-cm-diameter sphere with permittivity values of: (a) " =3; (b) 2" =3; (c) 4" =3. Values plotted were those along the diameter, parallel to the direction of propagation of the EMF. In all figures, frequency ranges from 50 to 1000 MHz where " = permittivity of muscle. Dashed lines are for frequencies >200 MHz and solid lines are for frequencies 200 MHz. decrease until we approach the rear surface. The overall result is that the average SAR is approximately that predicted by (1), which is consistent with the SAR results for the whole-sphere average case as show in Fig. 3(b). For frequencies above 200 MHz (dashed lines in Fig. 5), where the whole-sphere SAR ratios do not conform to (1), the localized SAR ratios are dramatically different from (1). This may be due, in part, to the fact that the wavelength inside the sphere is smaller for higher values of permittivity. This would result in the spheres with the higher values of permittivity failing

5 400 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 47, NO. 3, MARCH 2000 Fig. 5. Ratio of localized SAR values for a 4-cm diameter sphere with permittivity values of: (a) " =3 and 2" =3; (b) 4" =3 and 2" =3. Values plotted were those along the diameter, parallel to the direction of propagation of the EMF. In both figures, frequency ranges from 50 to 1000 MHz where " = permittivity of muscle. Dashed lines are for frequencies >200 MHz and solid lines are for frequencies 200 MHz. Horizontal lines represent the values predicted by (1). to comply with the sphere being small compared to wavelength criteria for lower frequencies than for spheres with lower permittivity values. The fact that the conductivity rapidly increases with frequency may also complicate the picture. IV. CONCLUSION The relationship between permittivity and SAR was investigated for a 4-cm diameter sphere. For EMF s with wavelengths large compared to the dimensions of the sphere, the wholesphere averaged SAR is inversely proportional to the permittivity of the material comprising the sphere as predicted by (1). However, the localized SAR values generally do not have the same relation and, as a matter of fact, vary greatly depending upon the location within the sphere. This suggests that local SAR could vary greatly with the permittivity values used for the tissues that comprise the models, even when whole-body average SAR values are not sensitive. Therefore, care must be taken in choosing the permittivity values used, especially in the case of outliers (see Table II). Dosimetry modeling results are generally presented without any estimate of error, yet as we have shown the empirical errors that occur when the permittivity values were originally measured can greatly influence the modeling results. Worse yet, this error is not random with respect to tissue type, some tissues are associated with more error than others (see Table II). Nor is the error random with respect to wavelength, as wavelength in tissue becomes smaller relative to the dimensions of the object being modeled, the effect of errors in permittivity values on whole-sphere average SAR becomes greater [see Fig. 3(b)]. These relatively shorter wavelengths also produced more variability in the localized results, especially as the microwaves move deeper into the sphere [see Fig. 5(a) and (b)]. There are also conditions under which variations in permittivity values do not produce large errors. Under these conditions, when the value of the ratios in Figs. 3(b) and 5 approximated one, doubling or halving the permittivity had little effect on SAR. For example, it appears that near the surface, where the microwaves are incident, variations in permittivity have little effect [see Fig. 5(a) and (b)]. Under these conditions, a rough approximation of permittivity is likely to produce an accurate estimate of SAR. Addressing the problem of the effects of variations in permittivity values on calculated SAR s is the same for methods that provide exact solutions such as the Mie or for methods which provide approximate solutions such as the FD-TD and finite element methods. These results suggest that in future EMF dosimetry studies, some estimate of the dependence of the calculated SAR values on variability in permittivity should be determined. These estimates would lead to increased confidence in the validity of the numerical calculations and will become increasingly important as EMF dosimetry modeling becomes more widely used. This document is approved for public release, distribution unlimited. ACKNOWLEDGMENT The views, opinions and/or findings contained in this report are those of the authors and should not be construed as an official Departments of the Navy and Air Force position, policy, or decision unless so designated by other documentation. Trade names of materials and/or products of commercial or nongovernment organizations are cited as needed for precision. These citations do not constitute official endorsement or approval of the use of such commercial materials and/or products. REFERENCES [1] C. Gabriel, Compilation of the Dielectric Properties of Body Tissues at RF and Microwave Frequencies, Occupational and Environmental Health Directorate, Brooks AFB, TX, Rep. AL/OE-TR , [2] E. L. Bell, D. K. Cohoon, and J. W. Penn, Mie: A Fortran Program for Computing Power Deposition in Spherical Dielectrics Through Application of Mie Theory, USAF School of Aerospace Medicine, Brooks AFB, TX, Rep. SAM-TR-77-11, [3] S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics. New York: Wiley, [4] W. D. Hurt, Multiterm Debye dispersion relations for permittivity of muscle, IEEE Trans. Biomed. Eng., vol. BME-32, pp , Jan

6 HURT et al.: VARIABILITY IN EMF PERMITTIVITY VALUES: IMPLICATIONS FOR SAR CALCULATIONS 401 [5] J. Z. Bao, S. T. Lu, and W. D. Hurt, Complex dielectric measurements and analysis of brain tissues in the radio and microwave frequencies, IEEE Trans. Microwave Theory Tech., vol. 45, pp , Oct [6] J. D. Jackson, Classical Electrodynamic, 2nd ed. New York: Wiley, [7] C. H. Durney, H. Massoudi, and M. F. Iskander, Radiofrequency Radiation Dosimetry Handbook, USAF School of Aerospace Medicine, Brooks AFB, TX, Rep. SAM-TR-85-73, [8] S. R. Smith and K. R. Foster, Dielectric properties of low-water-content tissues, Phys. Med. Biol., vol. 30, pp , [9] A. M. Campbell and D. V. Land, Dielectric properties of female human breast tissue measured in vitro at 3.2 GHz, Phys. Med. Biol., vol. 37, pp , [10] G. M. Hahn, P. Kernahan, A. Martinez, D. Pounds, S. Prionas, T. Anderson, and G. Justice, Some heat transfer problems associated with heating by ultrasound, microwaves or radio frequency, Ann. NY Acad. Sci., vol. 335, pp , [11] J. Kyber, H. Hangsen, and F. Piquett, Dielectric properties of biological tissue at low temperatures demonstrated on fatty tissue, Phys. Med. Biol., vol. 37, pp , [12] Electrical Properties Measured with Alternating Currents; Body Tissues, Handbook of Biological Data, W. S. Spector, Ed., Sauders, Philadelphia, PA, [13] B. R. Epstein and K. R. Foster, Anisotropy in the dielectric properties of skeletal muscle, Med. Biol. Eng. Comput., vol. 21, pp , [14] T. Yamamoto and Y. Yamamoto, Electrical properties of the epidermal stratum corneum, Med. Biol. Eng., vol. 14, pp , John M. Ziriax received the B.S. degree in psychology from Arizona State University, Tempe, in 1974 and the M.S. degree in experimental and social psychology and the Ph.D. degree in experimental psychology from American University, Washington, DC, in 1977 and 1981, respectively. He worked as a Psychologist at National Institutes of Health from 1979 to 1981studying the neural correlates of thermal stimuli. From 1981 to 1983, as a National Research Council Research Associate at the Health Effects Research Laboratory of the Environmental Protection Agency, he performed research on the effects of microwaves and pesticides on circadian rhythms and schedule controlled behavior. From 1983 to 1990, he studied the neurotoxicology of mercury and manganese at the University of Rochester's Department of Biophysics, Rochester, NY. For Operational Technologies Corporation, he examined the behavioral effects of microwave exposure from 1990 to 1995 at the U.S. Air Force's Armstrong Laboratory. Since 1995, he has studied the behavioral effects of microwave exposure and microwave dosimetry for the Naval Health Research Center Detachment at Brooks A.F.B., TX. Dr. Ziriax is a member of the Bioelectromagnetics Society, the Behavioral Toxicology Society and the American Psychological Society. He is on the Program Management Committee and Editorial Board for the International EMF Dosimetry Project. William D. Hurt (SM'78) was born in Georgetown, TX, on March 16, He received the B.S. and the M.S. degrees in physics from St. Mary's University, San Antonio, TX, in 1964 and 1971, respectively, and the M.S. degree in engineering from the University of Texas at Austin, in He is a Research Physicist at the Air Force Research Laboratory, Brooks Air Force Base, San Antonio, TX. Mr. Hurt is a member of the IEEE Standards Coordinating Committee 28, Subcommittee I, Techniques, Procedures, and Instrumentation and serves as the chair of the Engineering Radio Frequency Radiation Literature Evaluation Working Group, IEEE SCC-28, SC-IV, Standard for Safety Levels with Respect to Human Exposure to Radio Frequency Electromagnetic Fields, 3 khz to 300 GHz. He is also on the Program Management Committee and Editorial Board for the International EMF Dosimetry Project. Patrick A. Mason was born in San Diego, CA, in He received the B.A. degree in biology and the B.A. degree in psychology from University of California at San Diego, La Jolla, in 1980 and the Ph.D. degree in physiological psychology from McGill University, Montreal, PQ, Canada, in From 1984 to 1990, he conducted research in the Department of Clinical Pharmacology at the University Colorado Health Science Center, Denver. He has been at Brooks Air Force Base, TX, since 1990 where he has conducted research on the bioeffects of electromagnetic field exposure. Dr. Mason is a member of the Bioelectromagnetics Society and the Society for Neuroscience. He is on the Program Management Committee and Editorial Board for the International EMF Dosimetry Project.