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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.

A previous extension of the finite-difference time-domain (FDTD) method to include lumpedcircuit elements is further extended to model lumped-element circuits connected across multiple FDTD cells. This formulation is needed to model many kinds of circuits, like those with a transistor or other active device connected across a transmission line with more than one dielectric. The FDTD analysis of a shielded suspended microstrip transmission line excited by a current source in parallel with a resistance illustrates the usefulness of the formulation.

An elementary model consisting of one charged particle in a viscous medium exposed to weak ac-dc low-frequency magnetic fields is analyzed to identify and explain the fundamental characteristics of the physical mechanisms that result in a resonance response, which is similar to the familiar cyclotron resonance. The model predicts both frequency and amplitude windows, which are explained in terms of synchronization of the particle with electric fields. Although extrapolation of model results to biological systems is limited by the elementary nature of the model, the model results indicate that observed resonant responses by others of biological systems to ac-dc magnetic fields are probably not due to resonant response of ions in solution, since the model predicts that no resonant response is possible unless the viscous damping is very low, many orders of magnitude lower than the viscous damping of ions in solution.

Perturbation theory has been used to find the first-order internal electric field, the SAR (specific absorption rate), the spatial variations of the SAR, and the maximum SAR in prolate spheroidal and ellipsoidal models of man and experimental animals during irradiation by an electromagnetic plane wave when the wavelength is long as compared to the dimensions of the exposed body. In our “conductor” model of man, conductivity is written explicitly in the curl H equation as: ∇ × H = σE + jω∈ E. In what we call the “dielectric” model, the conductivity is contained implicitly in the complex permittivity, so that the curl H equation is ∇ × H=jω∈E. The two models give different results for first-order fields because the equations are expanded in a power series in k (k = ω√μ∈); in the conductor model σ enters into the zero-order equations but in the dielectric model it does not. Because of the nature of the zero-order equations, the expressions obtained from the conductor model are not valid as σ→0. We have found that the conductor model is valid only if ∈2 »ϵ1 where ϵ1 and ∈2, respectively, are the real and imaginary parts of the complex dielectric constant of the models. Consequently, some caution must be exercised in applying the results of perturbation theory as based on the conductor model. In this paper, the results of perturbation theory as applied to a lossy dielectric ellipsoidal model are described. The SAR in a dielectric ellipsoidal model of a rhesus monkey is calculated and compared with that of the conductor model. The SAR in the two models is found to be the same if the conduction current in the body is much larger than the displacement current. Although the conductor model is inaccurate for low values of conductivity, the equations are simpler than the ones for the dielectric model, and hence the conductor model is advantageous when valid.

Two new methods, termed "plane-wave correction" and "cylindrical-cell correction," are presented for improving the convergence of moment-method solutions in electromagnetics. Convergence is improved because the calculations include an approximation for the variation of the field within each cell.

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.

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.

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 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 Galerkin method with subsectional linear basis and weighting functions is used to calculate the low-frequency transverse electric fields in lossy dielectric cylinders. Arbitrarily shaped polygonal cells are employed to allow more accurate modeling of complex objects without excessive matrix sizes. To demonstrate the validity of the method, the analytical and numerical solutions are compared for triple-layered concentric cylinders. The calculated fields in a model of the human torso exposed to a solenoidal field are also presented. Among other applications, the method should be useful for evaluating electromagnetic (em) biohazards, and for analyzing and designing dielectric antennas and hyperthermia applicators at low frequencies.

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.

It is shown that the average specific absorption rates (SAR's) in a prolate spheroidal model of man are essentially the same as those for a block model of man irradiated by a short electric dipole at 27.12 MHz, even in the near fields. For purposes of average SAR, this allows use of the simpler and less expensive prolate spheroidal calculations.