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The modeling of voltage and current sources as either added or replaced sources in FDTD simulations is described and their differences discussed in terms of a transmission line analogy. An infinitesimal current element (ICE) is used to illustrate the validation of added source modeling and to study the errors involved with modeling an infinitesimal element within the finite-sized FDTD grid. This model is also used to illustrate the behavior of radiation boundary conditions as their near-field position with respect to the source is varied. We characterize the errors due to modeling and boundary conditions and give guidelines for obtaining acceptable accuracy in simulations. >

The finite-difference-time-domain (FDTD) method is extended to include distributed electromagnetic systems with lumped elements (a hybrid system) and voltage and current sources. FDTD equations that include nonlinear elements like diodes and transistors are derived. Calculation of driving-point impedance is described. Comparison of FDTD calculated results with analytical results for several two-dimensional transmission-line configurations illustrates the accuracy of the method. FDTD results for a transistor model and a diode are compared with SPICE calculations. The extended FDTD method should prove useful in the design and analysis of complicated distributed systems with various active, passive, linear, and nonlinear lumped electrical components. >

In analytical studies, we investigated induced-field patterns and SAR distributions in a lossy, dispersive, homogeneous, dielectric sphere typical of muscle tissue as irradiated by a plane-wave pulse train consisting of a pulse-modulated sinusoidal carrier wave. Calculations were made for carrier frequencies of 1, 3, and 15 GHz, pulse widths of 0.333, 2.0 and 4 ns, and pulse repetition rates of 1.11 x 10(6), 100 x 10(6), and 181.18 x 10(6) pps. The classical Mie solution was modified for a train of incident pulses that was represented by a Fourier series, and the fast-Fourier transform was used to sum the series. Computationally, the technique proved to be feasible and less expensive than we expected. The calculated field patterns show that the sphere's physical dimensions and the internal wavelength of the carrier greatly influence the nature of pulse-train propagation in the sphere. Harmonics having internal wavelengths nearly equal to the radius of the sphere produce most of the absorption; other harmonics produce little absorption. An intense hot spot is observed in spheres with radii that match the carriers' wavelengths.

Microwave irradiation at 960-MHz CW of isolated poikilothermic hearts in Ringer's solution causes bradycardia. Tachycardia is usually produced by generalized heating, suggesting the possibility of a different mechanism in this case. The effect occurs only over a narrow power range of approximately 2-10 mW/g absorbed by the heart. It is hypothesized that microwave radiation causes neurotransmitter release either by excitation of the nerve remnants in the heart, or by some other mechanism, producing bradycardia over a restricted range of power absorption. Drugs which can change the response of the heart to transmitter substances have been used, and the results support a neurotransmitter release hypothesis. A generalized heating effect, causing tachycardia, is predominant at higher levels of absorbed power.

Numerical calculations of absorbed energy deposition have been made for a block model of man that is defined with careful attention given to the biometric and anatomical features of a human being. CalcuIated post-resonant absorption and distribution of energy deposition through the body have better agreement with experimental results than previous calculations made using less realistic models.

Strong dielectric-constant anisotropy exists in muscle tissue at the lower microwave frequencies. Based on a model derived from tissue measurements, an analysis is carried out for single and multiple tissue layers. Calculated effects of tissue anisotropy on microwave fields and power absorption in the tissues are presented.

A previously developed long-wavelength analysis is applied to ellipsoidal models of humans and experimental animals to obtain the distribution of tissue power absorption and average power absorption for different frequencies and orientations of the model with respect to the field vectors. Curves showing the distribution of absorbed power inside the model, and the average absorbed power versus frequency are presented for several species. Comparisons of calculated data with preliminary experimental data on monkeys are given. The theoretical results show that the power absorption in the ellipsoidal model is a strong function of frequency and orientation with respect to the incident plane wave field vectors. The quantitative data presented here are valuable for estimating tissue electromagnetic (EM) power absorption in experimental animals and humans. These data may also be used in extrapolating EM induced effects measured in animals to those expected in humans.

The electric fields and power deposition patterns generated in two-dimensional inhomogenous models exposed to the axially directed uniform magnetic fields of an infinitely long solenoid are calculated numerically. The fields are calculated using the method of moments (Galerkin procedure) with linear basis and weighting functions. This low-frequency analysis is useful for studying the power deposition patterns attributable to solenoidal inductive applicators operated at frequencies up to 13.56 MHz. For the models we have studied, the ratio of power per volume deposited into the tumor to power per volume deposited into the immediately surrounding tissue is largest for tumors in the lung, although the power per volume deposited into the outermost layer is still much larger than the power per volume deposited into the tumor; it may be possible, however, to cool this region adequately from the body surface. When the complex permittivity of the tumor model is similar to that of the region in which it is embedded, the currents in the torso and tumor circulate primarily around the center of the body, as has been previously calculated for concentric cylinders. When the complex permittivity of the tumor is much greater than the region in which it is embedded, the currents in the tumor circulate primarily around the center of the tumor.

Analysis of the near-field irradiation of prolate spheroidal models of humans and animals by a short electrical dipole is described. The method of solution involves an integral equation formulation of the problem in terms of the transverse dyadic Green's function and expanding the fields irradiated by a short dipole in terms of the vector spherical harmonics. The extended boundary condition method (EBCM) is employed to solve the integral equations. The power distribution and the average specific absorption rate (SAR) are calculated and plotted as a function of the separation distance. It is shown that for a dipole placed along the major axis of the spheroidal (k-polarization), and for a very short separation distance, d= 0.15 lambda, the relative power values at both ends of the spheroid are about 40 compared with the ratio of 15 in the planewave exposure case. Furthermore, the calculated average SAR values as a function of the separation distance were found to oscillate around the constant value obtained from the planewave irradiation case. Differences between the near-and far-field exposure cases occurred only at separation distances shorter than 0.5 lambda where the magnitudes of the electric and magnetic energy densities are higher than the time-average radiation power density.

Block models of man which consist of a limited number of cubical cells are commonly used to predict the internal electromagnetic (EM) fields and specific absorption rate (SAR) distributions inside the human body. Numerical results, for these models, are obtained based on moment-method solutions of the electric-field integral equation (EFIE) with a pulse function being used as the basis for expanding the unknown internal field. In this paper, we first examine the adequacy of the moment-method procedure, with pulse basis functions, to determine SAR distributions in homogeneous models. Calculated results for the SAR distributions in some block models are presented, and the stability of the solutions is discussed. It is shown that, while the moment-method, using pulse basis functions, gives good values for whole-body average SAR, the convergence of the solutions for SAR distributions is questionable. A new technique for improving the spatial resolution of SAR distribution calculations using a different EFIE and Galerkin's method with linear basis functions and polyhedral mathematical cells is also described.

Expressions are derived for the induced eletric fields in an ellipsoidal model of man, and experimental animals irradiated by an electromagnetic (EM) plane wave when the wavelength is long compared to the dimensions of the ellipsoid. Calculations of the power absorbed by an ellipsoidal model of man are given for six different orientations of the ellipsoid with respect to the incident plane wave field vectors. The results show that the induced fields and the absorbed power in the ellipsoid are strong functions of frequency, size, and orientation with respect to the incident EM field vectors. The results for the ellipsoidal model of man are also compared with those of the prolate spheroidal model.

The power absorption characteristics of the prolate spheroidal model of an average man have been studied when the model is exposed to the near fields of an arbitrarily located small loop antenna. An integral equation is formulated and the fields radiated by the loop are expanded in terms of the vector spherical harmonics. This equation is then solved using the extended boundary condition method (EBCM,). For three different loop-spheroid configurations, the power distribution and the average SAR have been calculated as a function of the frequency and the separation distance. It is shown that the results obtained for separation distances larger than lambda /2 agree well with those obtained from the plane wave exposure case. Furthermore, the average SAR value calculated as a function of separation distance for the case where the magnetic dipole moment is aligned parallel to the major axis of the spheroid are found to oscillate around the constant value obtained from the H-polarized plane wave exposure case. On the other hand, the average SAR values for the E-polarization case (magnetic dipole is parallel to the spheroidal minor axis) are found to increase monotonically with the decrease in separation distance. It is also shown that despite the complicated nature of the near fields, the absorption characteristics can still be explained in terms of the variations of the incident radiation. These loop results, together with those obtained from other simple soures, can be used as building blocks in arriving at a qualitative understanding of the near-field absorption characteristics for more general exposure cases.

The absorption characteristics of multilayered cylindrical models of man irradiated by a normally incident electromagnetic plane wave are investigated. Numerical calculations for a specific skin-fat-muscle cylindrical model of man predict a layering resonance at 1.2 GHz with an average specific absorption rate (SAR) about double that calculated for the corresponding homogeneous model. The layering resonance frequency is found to be the same for incident waves polarized parallel and perpendicular to the cylinder axis. The effects of layers on whole-body absorption by man are determined by averaging the effects obtained for many combinations of skin and fat thicknesses. Absorption effects due to clothing are also investigated.

A moment method for calculating the internal field distributions of arbitrarily shaped, inhomogeneous dielectric bodies is presented. A free-space Green's function integral equation is used with 3-D linear basis functions to describe the field variation within cells. Polyhedral volume elements are used to model the scatterer's curvature realistically without an excessive number of unknowns. A new testing procednre, called the modified Galerkin's method, is developed and used to obtain the matrix equations with less CPU time but greater accuracy. Calculated internal field distributions of dielectric spheres, spheroids, and a composite model of a rat are compared with other calculations and experimental data. The agreement is generally good.

A previously developed electromagnetic (EM) field perturbation analysis is used to calculate the electric fields in tissue prolate spheroids irradiated by plane waves with long wavelength compared to the spheroid dimensions. This theory is applied to prolate spheroid models of man and animals to obtain internal electric field strength, absorbed power distribution, and total absorbed power. These data are of value in estimating tissue EM power absorption in experimental animals and man. The theory may be used to help extrapolate animal biological effects data to man, and as a guide to establishing an EM radiation safety standard.

A surface integral equation (SIE) method is used to calculate the specific absorption rate (SAR) in spherically capped cylindrical models irradiated by an axially incident electromagnetic plane wave (K polarization) in a frequency range for which calculations previously have not been available (80-400 MHz for man models). In the SIE method, the electromagnetic (EM) field relations are formulated in terms of electric and magnetic currents on the surface of the model. The average SAR is calculated from the far scattered EM fields by means of the forward scattering theorem. SAR data calculated by the SIE method agree with data calculated by the extended boundary condition method (EBCM) for frequencies up to 80 MHz (the upper frequency limit of the EBCM) for man models. For rat models exposed to 1-3 GHz radiation, reasonable agreement was also obtained with the limited experimental data available.

The recently developed iterative extended boundary condition method (IEBCM) has been used to compute the internal fields induced in homogeneous, axisymmetric, lossy dielectric objects of large aspect ratios when exposed to incident planewave radiation. Calculations were made for both the E- and k-polarization cases. The computed results for a prolate spheroidal model of an average man are found to be accurate for frequencies up to 300 MHz, while the use of the popular EBCM [1] was found to be essentially restricted to frequencies less than 70 MHz for these models and exposure conditions. The applicability of the IEBCM to composite bodies has also been examined by studying the irradiation of a capped cylindrical object. This composite object was first partitioned into several overlapping spherical subregions, and, alternatively, into two spherical subregions overlapping with a central cylindrical subregion. Spherical harmonics were used to represent the internal fields in the spherical subregions, while cylindrical expansions were utilized in the cylindrical subregions. It is shown that the second partitioning scheme is more computationally efficient and thereby suggests that the basis functions used to represent the subregional fields should be compatible with the subregional geometry. The new IEBCM, therefore, is a very valuable procedure which provides the opportunity of using the mixed basis functions in the solution.

In this paper, we describe a new approach to continuous, noninvasive monitoring of changes in lung-water content based on radiometry. It is shown theoretically, as based on a planar model of the lung, that a one-percent change in lung-water content corresponds to a 0.260-K change in brightness temperature, which is within the detection sensitively of available radiometers. Practicably, taking into account reflections at the tissue interfaces and attenuation in the chest wall, it is estimated that it is possible to detect a three to four-percent change in lung-water content. Initial experimental measurements at 1 GHz also have shown promising results. Some of the basic problems associated with the adaptability of the radiometric technique for clinical use have been identified and are discussed along with suggested solutions.

Continuous 960-MHz microwave irradiation of isolated poikilothermic hearts in Ringer's solution causes bradycardia, in contrast to the tachycardia usually produced by generalized heating. The effect appears to occur only over a narrow power range in the neighborhood of an estimated 3 mW absorbed by the heart. It is hypothesized that the bradycardia is produced by stimulation of the nerve remnants in the heart.

Irradiation of prolate spheroidal models of biological models by the near fields of electrically small apertures is analyzed. The solution procedure involves the replacement of the aperture source by an equivalent configuration of electric and magnetic dipoles. The specific absorption rate (SAR) induced in the irradiated object is then calculated using the extended boundary condition method (EBCM). Numerical results are presented for the exposure case where the incident electric field at the spheroid location is parallel to the major axis of the model. This polarization is associated with the maximum low-frequency absorption in biological models and, hence, is the most important polarization case in microwave dosimetry.