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This paper discusses the causes of and some solutions to the commonly observed problem of DC field offsets in finite-difference time-domain (FDTD) simulations. DC electric and magnetic field offsets are shown to be valid calculated responses of the modeled systems, resulting from interaction between the turn-on characteristics of the source and the properties of the models. The DC offsets may be avoided in the time domain by tailoring the source waveforms or in the frequency domain by post-processing the FDTD output.

Calculations are presented of the induced electric fields and current densities in the cartilage of the knee produced by a coil applicator developed for applying pulsed magnetic fields to osteoarthritic knees. This applicator produces a sawtooth-like magnetic field waveform composed of a series of 260-μs pulses with a peak to peak magnitude of approximately 0.12 mT in the cartilage region. The simulations were performed using a recently developed 3 dimensional finite difference frequency domain technique for solving Maxwell's equations with an equivalent circuit model. The tissue model was obtained from the anatomically segmented human body model of Gandhi. The temporal peak electric field magnitude was found to be −153 mV/m, averaged within the medial cartilage of the knee for the typical dB/dt excitation levels of this coil. The technique can be extended to analyze other excitation waveforms and applicator designs. Bioelectromagnetics 22:224–231, 2001. © 2001 Wiley-Liss, Inc.

Electric (E) fields induced near metal implants by MRI switched-gradient magnetic fields are calculated by a new equivalent-circuit numerical technique. Induced E-field results are found for a metallic spinal-fusion implant consisting of two thin wires connected to the metallic case of a current generator as well as for its subsections: a bare U-shaped wire, an insulated U-shaped wire, a cut insulated wire, and a generator. The presence of the metallic implants perturbs the E field significantly. Near the ends of the bare U-shaped wire, the E field is 89.7 times larger than in the absence of the wire. The greatest E field concentration occurs near the ends of the cut insulated wire, where the E field is 196.7 times greater than in the absence of the wire. In all cases, the perturbation of the induced E field by the implanted wire is highly localized within a few diameters of the wire.

A hyperthermia applicator design tool consisting of a finite-difference time-domain (FDTD) technique in combination with a graphical display of electric fields and normalized linear temperature rise is described. This technique calculates, rather than assumes, antenna current distributions; it includes mutual interactions between the body and the applicator, and it calculates driving-point impedance and power delivered to the applicator. Results show that the fundamental limitation of 2-D electric-type applicators is overheating of the fat by normal components of the electric field, which exist because of near fields and capacitive coupling with the muscle. Two factors which contribute to the capacitance are the muscle conductivity and the small antenna size in air. Two examples of applicators designed to avoid fat overheating are described: a 27-MHz segmented dipole for heating large tumors to 7 cm depth, and a 100-MHz dipole for small tumors to 5 cm depth. The first uses a water bolus, and the second uses a water bolus with low-permittivity strips to reduce normal fields at the antenna ends. The results of this study describe fundamental limitations of electric field applicators, and illustrate the use of a powerful applicator design tool that allows rapid evaluation of a wide range of ideas for applicators which would require months and years to test experimentally.

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.

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.

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.

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.

Our results demonstrate high-frequency electrical resonances in outer hair cells (OHCs) exhibiting features analogous to classical piezoelectric transducers. The fundamental (first) resonance frequency averaged f(n) approximately 13 kHz (Q approximately 1.7). Higher-order resonances were also observed. To obtain these results, OHCs were positioned in a custom microchamber and subjected to stimulating electric fields along the axis of the cell (1-100 kHz, 4-16 mV/80 microm). Electrodes embedded in the side walls of the microchamber were used in a voltage-divider configuration to estimate the electrical admittance of the top portion of the cell-loaded chamber (containing the electromotile lateral wall) relative to the lower portion (containing the basal plasma membrane). This ratio exhibited resonance-like electrical tuning. Resonance was also detected independently using a secondary 1-MHz radio-frequency interrogation signal applied transversely across the cell diameter. The radio-frequency interrogation revealed changes in the transverse electric impedance modulated by the axial stimulus. Modulation of the transverse electric impedance was particularly pronounced near the resonant frequencies. OHCs used in our study were isolated from the apical region of the guinea pig cochlea, a region that responds exclusively to low-frequency acoustic stimuli. In this sense, electrical resonances we observed in vitro were at least an order of magnitude higher (ultrasonic) than the best physiological frequency of the same OHCs under acoustic stimuli in vivo. These resonance data further support the piezoelectric theory of OHC function, and implicate piezoelectricity in the broad-band electromechanical behavior of OHCs underlying mammalian cochlear function.

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.

Expressions are derived for the induced internal electric fields and average specific absorption rate (s.a.r.) in prolate spheroidal models of man and experimental animals irradiated by electromagnetic (e.m.) fields having arbitrary orientation and arbitrary impedance. These expressions are of value in estimating the s.a.r. in man and test animals exposed to e.m. near fields when the wavelength is long compared to the dimensions of the body.