Trevor W. Dawson

Application of the finite difference time domain algorithm to quasi‐static field analysis

In this paper, the use of the standard finite difference time domain (FDTD) algorithm is extended to quasi-static electromagnetic field problems. While straightforward application of the standard FDTD algorithm at very low frequencies leads to excessively long simulation times, we show that for linear structures this problem can be circumvented by using a ramp excitation function. The use of appropriate absorbing boundary conditions such as Berengers perfectly matched layer is also shown to be necessary. By combining two plane waves in opposite directions, a uniform electric or magnetic field can be created so that the electric and magnetic field solutions are decoupled, as required in quasi-static analysis. Calculations of the induced fields and currents in a human model exposed to power line frequency fields provide a realistic example of an application of this novel FDTD technique.

Numerical evaluation of 60 Hz magnetic induction in the human body in complex occupational environments.

Exposure to 60 Hz non-uniform magnetic fields is evaluated using realistic configurations of three-phase current-carrying conductors. Two specific scenarios are considered, one involving a seated worker performing cable maintenance in an underground vault with conductors carrying 500 A root-mean-square (rms) per phase, and the other involving a standing worker during inspection of a 700 MW generator with conductors carrying 20000 A (rms) per phase. Modelling is performed with a high-resolution (3.6 mm) voxel model of the human body using the scalar potential finite difference (SPFD) method. Very good correspondence is observed between various exposure-field measures, such as the maximum, average, rms and standard deviation values, and the associated induced field measures within the whole body and various organs. The exposure fields produced by the lower currents in the vault conductors result in correspondingly low current densities induced in human tissues. Average values are typically below 0.2 mA m(-2). On the other hand, the average exposure related to the inspection of the generator isophase buses is about 1.5 mT at a distance of 1.2 m from the conductors. This field induces organ average current densities in the range of 2-8 mA m(-2), and peak (maximum in voxel) values above 10 mA m(-2). A comparison with uniform field exposures indicates that induced fields in organs can be reasonably well estimated from the accurately computed exposure fields averaged over the organs and the organ dosimetric data for uniform magnetic fields. Furthermore, the non-uniform field exposures generally result in lower induced fields than those for the uniform fields of the same intensity.

Magnetic field exposures for UK live-line workers

Dosimetry is evaluated for live-line workers exposed to 50 Hz non-uniform magnetic fields from typical high-voltage transmission lines in the United Kingdom. The configurations involve twin-, triple- and quadruple-conductor transmission line bundles. Scenarios include three worker postures for the twin and triple bundles, and four postures for the quadruple bundle. The postures are selected to simulate worst case scenarios representative of work practices and result in highest values of dosimetric measures in critical organs. Only single-phase bundles are considered, as adjacent bundles of differing phase result only in a small reduction of the dosimetric measures. Reported data include various measures of the electric field and current density induced in tissues, as well as of the current density averaged over 1 cm2 areas normal to the current flow. A value of this latter quantity of 10 mA m(-2) is suggested as a threshold for neural tissue in the UK and international regulations. Critical tissues considered in this study include the retina, spinal cord, brain and cerebrospinal fluid. Some discussion is devoted to problems associated with the concept of current-density averaging, and two algorithms are considered. For a nominal load of 1 kA per subconductor, averaged current densities exceed the guideline bounds, only for a small number of postures and bundle configurations, in the brain, retina and cerebrospinal fluid. Non-averaged current densities in the cerebrospinal fluid exceed the suggested bound for all scenarios modelled, as well as in the retina for three postures involving a quadruple bundle.

Electric fields induced in humans and rodents by 60 Hz magnetic fields

Numerical computations are used to evaluate electric field dosimetry for high-resolution anatomically based inhomogeneous models of a human male child, and male and female rats and mice, under exposure to 60 Hz uniform magnetic field sources of three perpendicular orientations. The goal is to compare the child data to previously computed adult dosimetry and to evaluate the accuracy of linear scaling of organ dosimetry between species. It is expected that this work will aid in the design and interpretation of experiments involving rodents. It is found that child-to-adult and mouse-to-rat organ dosimetry shows the expected linear dependence on the geometric scale factor between models. The comparison between mice and the human child shows that postural and individual organ differences do have significant effects, and that care is required in scaling-based extrapolation of rodent experiment results to humans. However, for unrestrained animals, linear scaling appears to be a reasonable and conservative approach. Most of the rodent organ fields, for at least one field orientation, are greater than those expected from linear scaling.

Effects of skeletal muscle anisotropy on human organ dosimetry under 60 Hz uniform magnetic field exposure

The recent development of anatomically derived high-resolution voxel-based models of the human body suitable for electromagnetic modelling, and of effective methods for computing the associated induction, has resulted in numerical estimates of organ-specific dosimetry for human exposure to low-frequency magnetic fields. However, these estimates have used an isotropic conductivity model for all body components. More realistic estimates should account for the anisotropy of certain tissues, particularly skeletal muscle. In this work, high-resolution finite-difference computations of induced fields are used to estimate the effects of several extremal realizations of skeletal muscle anisotropy on field levels in various organs. It is shown that, under the present assumptions (anisotropy ratios up to 3.5:1), the resulting dosimetric values can vary by factors of between two or three for tissues other than muscle and up to 5.4 for muscle, despite the unchanged nature of the conductivity model used for all other body components.

Electric fields in the human body due to electrostatic discharges

Electrostatic discharges (ESDs) occur when two objects at different electric potentials come close enough to arc (spark) across the gap between them. Such discharges may be either single-event or repetitive (e.g., 60 Hz). Some studies have indicated that ESDs may be a causative factor for health effects in electric utility workers. Moreover, a hypothesis has recently been forwarded imperceptible contact currents in the human body may be responsible for health effects, most notably childhood leukemia. Numerical modeling indicates that the electric fields in human tissue resulting from typical contact currents are much greater than those induced from typical exposures to electric and magnetic fields at power line frequencies. Numerical modeling is used here to compute representative spark-discharge dosimetry in a realistic human adult model. The frequency-domain scalar potential finite difference method is applied in conjunction with the Fourier transform to assess electric fields in selected regions and tissues of interest in the body. Electric fields in such tissues as subcutaneous fat (where peripheral nerves may be excited), muscle and bone marrow are of the order of kilovolts per meter in the lower arm. The pulses, however, are of short duration (/spl sim/100 ns).

An analytic solution for verification of computer models for low-frequency magnetic induction

This paper considers the analytical solution to the problem of low-frequency induction by an applied axial uniform magnetic field, in an equatorially stratified sphere having the conductivity distribution σ (ϕ) = σ0e−λcos(pϕ), where p ∈ {1, 2} is a periodicity factor, λ > 0 is a conductivity contrast parameter, σ0 is a conductivity scale factor, and ϕ is the equatorial angle. The resulting induced electric and current density fields are fully three-dimensional. While of interest in its own right, the model should prove useful in the validation of low-frequency electromagnetic computer modeling codes. The development includes a full discussion of the underlying Greens function, which can also be used for modeling induction by alternative excitation fields.

MAGNETIC INDUCTION AT 60 HZ IN THE HUMAN HEART : A COMPARISON BETWEEN THE IN SITU AND ISOLATED SCENARIOS

Numerical modelling is used to estimate the electric fields and currents induced in the human heart and associated major blood vessels by 60 Hz external magnetic fields. The modelling is accomplished using a scalar-potential finite-difference code applied to a 3.6-mm resolution voxel-based model of the whole human body. The main goal of the present work is a comparison between the induced field levels in the heart located in situ and in isolation. This information is of value in assessing any health risks due to such fields, given that some existing protection standards consider the heart as an isolated conducting body. It is shown that the field levels differ significantly between these two scenarios. Consequently, data from more realistic and detailed numerical studies are required for the development of reliable standards.

Evaluation of Nonuniform 60-Hertz Magnetic-Field Exposures for Compliance with Guidelines

Magnetic-field exposures are considered in compliance with guidelines if they do not cause the induced electric field or current density to exceed basic restrictions that are based on possible adverse biological responses. Magnetic-field guidelines provide induction models for extrapolating from external field exposures to basic restrictions and vice versa. However, the uniform-field exposures used in these models do not reflect the nonuniform fields often encountered in actual high-field exposures. The purposes of this study were to investigate the relationships between external magnetic-field exposures and induced electric fields in nonuniform 60-hertz fields and to present a method for evaluating the compliance of such exposures with guidelines. Induction factors provide the induced electric field per unit of incident magnetic field. They represent a means of extrapolating from external field exposure to a peak induced electric field. Uniform and nonuniform field induction factors were computed for homogeneous ellipses and ellipsoids, and for an anatomically correct heterogeneous human model. Computations were carried out for three orthogonal uniform fields and for related nonuniform fields at varying distances from three line sources. Analytic expressions were used to compute induced peak electric fields for homogeneous models in uniform fields. A scalar-potential finite-difference method computed induced quantities for all models at 3.6-mm resolution in uniform and nonuniform fields. Equivalent uniform magnetic fields that produce the same peak electric field as a nonuniform field with a known maximum field were derived from the induction factors. To evaluate a nonuniform field exposure for compliance, the equivalent uniform field for the exposure is estimated based on the magnitude of the maximum surface field and the distance from the line source. Compliance is achieved if the equivalent uniform magnetic field is below the magnetic-field limit. Equivalent uniform magnetic-field exposures are computed for two actual electric utility tasks, as examples. *Deceased

Evaluation of interactions of electric fields due to electrostatic discharge with human tissue

Electrostatic discharges (ESDs) produce in the human tissue very strong electric fields of short duration. Possible biophysical interactions are evaluated by comparing the fields in subcutaneous fat/skin to the thresholds for peripheral nerve stimulation, and by computations of membrane potential and electric fields in cytoplasm of a typical cell in bone marrow. It is found that a 4-A peak ESD event is capable of stimulation of nerves located in subcutaneous fat of the lower arm of the hand eliciting a spark, with tens of kV/m and pulse duration of /spl sim/80 ns. For the same ESD event, the transmembrane potential (TMP) reaches 32 mV with a pulse duration of /spl sim/200 ns (half-width duration). The electric field in the cytoplasm of a bone marrow cell changes from about 8.8 kV/m to-2 kV/m in about 200 ns.