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Interaction of Low-Frequency Electric and

Magnetic Fields with the Human Body

MARIA A. STUCHLY, FELLOW, IEEE, AND TREVOR W. DAWSON, SENIOR MEMBER, IEEE

Interactions of electric and magnetic fields at power line fre-quencies (50 and 60 Hz) in humans have been the subject of inten-sive scientific inquiry and considerable public concern during thelast two decades. As a part of the scientific effort, extensive eval-uations of induced electric field and current density in the humanbody have been performed. Realistic, heterogeneous, high-resolu-tion models of the body have been analyzed using various numer-ical methods. Exposures to uniform and nonuniform electric andmagnetic fields are considered, thus accounting for typical envi-ronmental and occupational scenarios. Numerical values of the av-erage and maximum induced electric field and current density aregiven for various organs and tissues. Effects on the dosimetric mea-

sures of changes in the tissue conductivity, model resolution andorgan modeling in situ, and isolation are discussed. It is shown thatresults from various laboratories agree reasonably well. It is alsoshown how the macroscopic numerical evaluation of induced fieldscan be further extended to model more refined cellular system. Thisis demonstrated for gap junction connected cells.

KeywordsHuman dosimetry, induced electric field, numericalmodeling, power line.

I. INTRODUCTION

Human exposure to low-frequency electric and magneticfields at power-line frequencies (50 or 60 Hz) has been wide-spread for more than a century. It is mostly associated withtransmission and distribution of electricity and the use of var-ious electrical and electronic devices at home and at work.The hazard of shocks and burns resulting from contact withenergized electric conductors or ungrounded large metallicobjects in strong electric fields has been well known nearlyfrom the beginning of the use of electricity. Also, it has beenwell recognized and exploited in medicinethat strong electricfields cause stimulation of muscle and neural tissue, as wellas cardiac fibrillation. However, over the last several years,concerns about possible health effects of weaker fields havebeen expressed. Following an early epidemiological study[1] showing a correlation of childhood leukemia with prox-

imity to high current distribution lines, inconsistent results

Manuscript received August 17, 1999; revised January 14, 2000.This work was supported by the NSERC/BCHydro/TransAlta IndustrialResearch Chair and by the EPRI.

The authors are with the Department of Electrical and Computer Engi-neering, University of Victoria, Victoria, BC, V8W 3P6 Canada.

Publisher Item Identifier S 0018-9219(00)04566-7.

frominitial series of other epidemiological studies fueled fur-ther public concern, as well as scientific interest in the sub-

ject. As a result, a few governments around the world andthe electric utility industry allocated substantial funds for re-search in academic and other research laboratories. Broad-based research has been conducted in such areas as humanexposure assessment, computations of induced fields in thebody, epidemiology, animal studies, cellular studies, interac-tion mechanisms, and risk assessment. Two comprehensivereviews by groups of experts have recently been published

[2], [3]. International groups of experts also have participatedin more specialized workshops, and summaries of the stateof knowledge in epidemiology, in vivo and in vitro studieshave been published [4][6]. A review of the cancer issue isalso given in [7].

Epidemiological investigations of childhood leukemiahave not reported consistent findings. Even the most recentwell-performed studies have not reduced the uncertaintybecause of some of them have found an increased risk whileothers have found none [8][10]. There is also limited butnot convincing and consistent evidence of chronic lymphaticleukemia in some occupational exposure studies [3], [5],[11]. The suggestions from epidemiological studies have

not been confirmed by animal studies [2][7]. The onlyequivocal findings relate to the animal breast model, wherethere are two studies: one showing an increased rates oftumors and the other, larger study not showing any increase[3], [6], [7].

In addition to cancer, concerns have been expressed aboutother possible detrimental effects. There is no evidence inanimal experiments of detrimental effects on the immunesystem, blood system, and reproduction and development.While behavioral and neuroendoctrine responses to strongfields have been observed in animals, there is no evidence foradverse effects. These mostly negative findings from animalstudies are also reflected in the outcomes of epidemiologicalstudies.

A recent epidemiological study (not considered in pre-vious reviews) refers to a possible risk of certain types ofcardiovascular disease (arrhythmia and acute myocardial in-farction) due to exposure to a low-frequency field [12]. Thisis a particularly noteworthy epidemiological finding, as itfollows from clinical investigations and is hypothesis-based.

00189219/00$10.00 2000 IEEE

PROCEEDINGS OF THE IEEE, VOL. 88, NO. 5, MAY 2000 643
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Clinical studies of humans provide some evidence of changesin heart-rate variability [13]. Other clinical studies also showweak evidence of sleep disturbance, or suppression of mela-tonin. Inconsistent results for melatonin suppression havebeen observed in animals [2], [3]. There is convincing ev-idence that low-frequency fields are associated with bonehealing [2], [3], [6], with induced electric field strengths onthe order of 0.11 mV/m.

In vitro studies, i.e., studies of cellular preparations, areusually conducted to identify and understand interaction

mechanisms. Physical interaction mechanisms can alsobe determined from such studies; however, in the case ofelectric and magnetic fields at power-line frequencies, thereis a paucity of relevant studies. This is due, in part, to thedifficulties in reproducing many of the positive findings,and partly due to the insufficient amount of experimentationin the case of more robust findings. The interactions areoften transient or cell-specific, and of low magnitude. Onthe whole, the data indicate that these fields can interactwith some biological processes [2], [3]. In most cases,interactions have only been reported by one laboratory. Thethreshold for some effects has been expressed in terms oftissue-induced electric fields, typically of 0.11 mV/m. The

magnetic field density showing interaction in most studiesis 0.1 mtorr or greater [3].

The most recent assessment of health effects of power-linefields was given in the 1999 NIEHS report to the U.S. Con-gress [14]. The main conclusion is that the scientific evi-dence suggesting that ELF-EMF exposures pose a health riskis weak.

As a part of the general effort to understand under whatconditions electric and magnetic fields cause biological ef-fects and which effects become harmful to human health andat what level, research in computation of induced electricfields and current density has been undertaken by severalgroups. Such research has recently become more quantita-

tive because of two factors. First, the availability of mag-netic resonance imaging (MRI) and computerized tomog-raphy (CT) has facilitated development of computer compat-ible heterogeneous models of the human body. These modelshave important tissues and even small organs such as thyroidor prostate identified, and their resolution is on the order of afew millimeters. Thus proper electrical properties can be al-located to tissues and used in solving Maxwells equations.The second factor is recent progress in numerical methodsand computers, allowing for the solution of large problemsinvolving millions of variables on workstations or small clus-ters of PCs.

It has been recognized that induced fields and currents

in tissues might not be the parameters that account forsome reported laboratory observations. On the other hand,the well-known interaction mechanisms such as tissueexcitation depend on the spatial distribution of the electricfield in tissue. Many reported biological effects have beenquantified in terms of the induced electric field strength[2], [6]. Furthermore, guidelines developed by variousorganizations express human exposure limits in terms ofthe external electric and magnetic field strength, but theselimits are derived on the basis of threshold tissue current

density [15], [16]. It should be noted that the rationale forselection of a given threshold and its translation into externalfield levels are not well supported in the guideline [16] bybiophysical and engineering data.

During the last five years, a few research laboratories haveperformed extensive computations of induced electric fieldand current density in heterogeneous models of the humanbody in uniform and nonuniform electric or magnetic fieldsat 50 or 60 Hz. There is convergence of the results obtainedby various groups and agreement with measurements where

such measurements are available [6], [17]. The results ofthese computations, as well as their extension to more de-tailed and sophisticated tissue models, are important for sev-eral reasons. The induced fields and their distribution insidethe tissue are related to well-understood interaction mecha-nisms for strong fields (excitable tissue stimulation, visualphosphenes). It is reasonable to expect that cells and tis-sues respond to the field strength in their immediate prox-imity rather than those outside the body. Different tissues,cells, and their components have vastly different complexpermittivity (i.e., dielectric constant and conductivity). Theseproperties are indicative of their interaction with the electricfield. To the contrary, the magnetic permeability of tissues,

with the exception of very small inclusions, is the same asof air, and the magnetic field in tissue at low frequencies isthe same as the local external field. A significant number ofinvestigated biological effects, though not all, indicate doseresponse in terms of the induced electric field (current den-sity) [2], [3]. Interactions on a subcellular level due to forcesacting on charged parts of cell membrane, potential differ-ences across parts of cell assemblies, or even nonlinear in-teractions with cell or tissue complexes all ultimately requireknowledge of the local induced electric fields and currentdensities. These parameters are required to establish plau-sible interaction mechanisms that are reasonably completeand consistent with biological knowledge and effects. Evalu-

ation of the field induced on the organ and tissue level at mil-limeter scale resolution is only a first step. From a more prag-matic point of view, if exposure standards are developed andbecome compulsory in the electric utility industry, humandosimetry in terms of the induced field and current densitywill become critical in establishing safe and rational expo-sure limits.

In this paper, a comprehensive review is given of more re-cent research aimed at the numerical evaluation of the in-duced electric field and current density under various expo-sure conditions. While most of the results and all of the illus-trations are based on the authors work, they are supportedby results obtained by other groups and by an extensive set

of references to significant journal publications. To place thenumerical modeling in a broader context, other issues cov-ered are 1) essential data on human exposure in various en-vironments and 2) a brief review of interaction mechanisms.

II. EXPOSURE FIELDS IN VARIOUS ENVIRONMENTS

At extremely low frequencies (ELFs), e.g., 60 Hz, ex-posure is characterized by the electric field strength ( ) orelectric flux density (also called electric displacement) ( ),

644 PROCEEDINGS OF THE IEEE, VOL. 88, NO. 5, MAY 2000
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and the magnetic field strength ( ) or magnetic flux density(also called magnetic induction) ( ). All these parametersare vectors. The flux density is related to the field strengthby the properties of the medium in a given location as

(1)

where is the permittivity and is the permeability. For bi-ological media, , where is the permeability of free

space (air). At ELF, the electric and magnetic fields are notcoupled. To determine exposure in a given location, both theelectric field and magnetic field have to be separately com-puted or measured. Typically, electric fields are defined interms of their strength in V/m and the magnetic fields interms of their flux density in T (Tesla) in the SI system. Mag-netic flux density is often also expressed in G (Gauss).1

Comprehensive data on exposure in various environmentsare given in [2], and more recent data for occupational ex-posures in electric utilities in [18]. Only a brief overviewfollows. Exposure to electric fields in the home and work-place has not been well characterized. This is due to theperturbation of the field by the human body and other ob-

jects, which make the field usually quite nonuniform anddifficult to measure. Typically, electric fields in the home oroffice are between 120 V/m. Fields in the close proximityof various electrical appliances and some electronic devicesmay be much higher (up to about 300 V/m), but they de-crease rapidly with distance from the device. Strong elec-tric fields, on the order of 110 kV/m, are present just underhigh-voltage transmission lines. They decrease to values ofless than 10 V/m at a distance of 100 m from the center ofthe right of way [19]. Workers in some occupations and worklocations may be exposed to high electric fields, e.g., substa-tion fields of 110 kV/m are common.

Exposure to magnetic fields has been well characterizedby surveys of various locations and body-mounted dosime-ters worn by people in residences and workplaces. Compre-hensive summary data can be found for general populationexposure [2]. Typical background levels in homes and officesare 0.050.3 T, with levels in most homes below 0.1 T.Household appliances may produce stronger localized fields,ranging up to 150 T (e.g., can openers) at a distance of 0.15m. More typical values are 0.550 T at 0.15 m. These fieldsdecrease significantly with distance away from the device.Similarly, some office electrical and electronic devices mayproduce strong local fields. Overall, typical exposure of mostpeople is similar at home and at work. This certainly does not

apply to some occupations.High-voltage transmission lines produce magnetic fluxdensity below 10 T under the line within the right of way.These fields decrease to less than 0.15 T 100-m away [19].Some means of transportation such as commuter trains havefields on the average of 0.36 T in their passenger com-partments [2]. Overall, exposure data gathered from locationsurveys agree very well with those obtained from personal

1G = 0 : 1 mtorr.

dosimetry with body-worn monitors of the magnetic fluxdensity. Another observation that can be made is that typical(50%) exposures at homes are 0.060.13 T with a meanvalue of 0.2 T, and the lowest 5% of 0.04 T and 95% of0.5 T [2].

A recent report [18] identifies some of the highest ex-posures in various workplaces within the utility industry.The facilities that are identified as producing high exposurelevels associated with at least short-term work tasks includehydroelectric generation, thermal generation, and transmis-

sion substations, distribution substations, and distributionnetwork vaults. Fields as high as 0.58 mtorr have beenmeasured in one hydroelectric generating facility close tothe isophase bus. However, the mean exposure of monitoredworkers has not exceeded a value of 8.4 T. In all cases,the highest exposures are to nonuniform magnetic fieldsassociated with complex configurations of current-carryingconductors. Surveys of such fields are invariably tediousbecause of the large spatial field variations in both mag-nitude and direction. Personal dosimeters also suffer fromserious limitations, particularly when a worker remainsfor a longer period of time in one position, and, e.g., thehead is in the highest field while the dosimeter is worn on

the waist. For nonuniform exposures, computation of thesource field based on proper modeling of a given conductorarrangement is more reliable. With respect to the fieldsinduced in the body, the same conclusions apply; namely,that numerical modeling provides a much more accurate andreliable means.

III. EVIDENCE OF INTERACTIONS AND MECHANISMS

Electric and magnetic fields at ELF, including 50 and 60Hz, are well known to cause stimulation of some tissues suchas nerves, muscles, and the heart, once the electric field inthe tissue exceeds a threshold value. Membranes surrounding

nerve and muscle cells can be excited once a membrane po-tential threshold is reached. The threshold action potential(the potential across a membrane that initiates propagationalong the nerve or muscle cell) depends on the type and di-mensions of the cell, and the frequency and waveform of theimposed signal. Cell excitation and action potential propa-gation are complex nonlinear processes [20][22]. However,the behavior prior to the onset of excitation can be describedby a cable equation. For a neuron (myelinated or nonmyeli-nated), the stimulation threshold resulting from an inducedelectric field in tissue, the cable equation takes form [22],[23]

(2)

whereinduced membrane potential;resting membrane potential;neural space constant;neural time constant;longitudinal position assuming a straightneuron along the direction;

STUCHLY AND DAWSON: LOW-FREQUENCY ELECTRIC AND MAGNETIC FIELDS 645
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activating function with being the electricfield component along .

Since neurons are mostly not straight, a more general ac-tivating function can be defined as where is thearc-contour along the neuron [24]. Thus, even in a spatiallyuniform electric field in tissue, an excitation can occur, and itdepends on the neuron shape. Furthermore, stimulation oftenoccurs at neuron terminus (dendrites). The membrane con-stants and depend on the cell type and dimensions. Thethreshold depends on the signal frequency, duration, and

waveform (e.g., monopolar pulse, bipolar pulse, sinusoid,single pulse, or repeated pulses). Typical is 20 mV forthe optimal pulse shape and duration, and a proper polarity(causing depolarization) [23], [25].

Despite the fact that it is the change of the electric fieldalong the neuron contour that is responsible for the onset ofneural stimulation, most of the available experimental dataare in terms of the electric field or current density [20][22].The internal (induced) electric field ( ) and conduction cur-rent density ( ) are related through Ohms law

(3)

where is the bulk tissue conductivity, and may be a tensorin anisotropic tissues. The vast majority of available data onstimulation thresholds have been obtained with electrodesof limited dimensions and given in terms of current or cur-rent density [22]. It is also apparent that a current densitythreshold of 10 mA/m , used as a benchmark for limiting ex-posure to electric and magnetic fields by a recent guideline[16], is based on generalization of the data and further ap-proximations. It does not appear to be supported by carefulanalyses of actual experimental data on neural stimulation.Furthermore, when most of these data were obtained, numer-ical analysis and computers were not sufficiently advanced toperform accurate evaluation of spatial distributions of fieldsand currents in tissue beyond simple in vitro preparations. Toinduce neural or cardiac stimulation by 50 or 60 Hz fields,very strong external electric or magnetic fields are required,as the reported thresholds are well above 100 mA/m and 1A/m (with local electrodes) for neural and cardiac stimu-lation, respectively. Models of the human body and numer-ical tools available today enable more exact evaluation of thethresholds for humans even with existing experimental dataon neural and cardiac excitation thresholds. Further studyof only a selected part of the human body or an organ cangive better understanding of stimulation. A perfect exampleof how productive such approaches are is in the bidomain

modeling of cardiac tissue [26].Experimental evidence and thresholds have been deter-mined for stimulation of the visual system [27], [28]. Thelowest threshold magnetic field has been found equal to10 mtorr (in darkness) at 20 Hz. The threshold is some-what higher when illumination increases, and it increasesfor higher frequencies. Visual stimulation resulting inphosphenes has also been obtained with current applied byelectrodes placed on the head. Again, the highest sensitivityhas been observed for 20 Hz, and the threshold increases for

higher and lower frequencies. Thus, the authors concludedthat the effect is a result of retina stimulation by the inducedelectric field and current density. From the data presented,this appears to be a conclusion well based in science. Theauthors, however, have estimated the induced current densityfor the magnetic stimulation by applying Faradays lawonly to the eyeball. This assumption is not correct, as largercurrent loops are induced even for nonuniform fields, as inthe case of the experimental arrangement described in [27].The authors estimate is 1 mA/m at 20 Hz. Scaled to 20

Hz, the result from the recent numerical modeling gives,for a uniform field of 10 mtorr of the same direction, theaverage current density in the eye equal to 27 mA/m andthe maximum approximately 70 mA/m [29]. Furthermore,numerical data also indicate the importance of modelingorgans within the whole body, not in isolation [30].

There is substantive evidence that low-frequency fields ac-celerate bone healing [2]. The physical interactions are re-lated to induced electric fields on the order of 30 mV/m at themost effective frequencies of 1030 Hz. These frequenciesare associated with those observed in live animals. Weakerfields of 0.11 mV/m elicit transient changes in bone cellpreparations [2]. Detailed biophysical mechanisms are only

partly understood.There is evidence that low-frequency fields affect

signal-transduction systems in cellular preparations (thisdoes not by itself indicate adverse effects). However, theinteraction mechanisms are very incompletely understood.There are several reasons behind the lack of well-estab-lished interaction mechanisms. The main reasons are thecomplexity of the living systems and the lack of suffi-ciently focused research. Biological processes involve manysimultaneous interactions, nonlinear dynamic processes,amplifications, and cooperative phenomena. Some areas ofbiology are only now beginning to be better understood.

Because much of the scientific evidence on interactionsof electromagnetic fields with biological systems has beenscattered and inconsistent, there really has not been enougheffort to explain some of the better documented laboratoryfindings through rigorous development of plausible mecha-nisms of action. Such mechanisms have to include the initialphysical stimulus, i.e., parameters of exposure responsiblefor the effect, through biophysical interaction to biologicalcascade of events. All of the phenomena ideally should bequantifiable, and the hypotheses have to be testable. Thishas not been accomplished yet. A brief overview of variousincomplete theories follows.

Attempts have been made, as summarized in [3], to eval-

uate the plausibility of biological effects at low field intensi-ties by comparisons to externally induced field effects withthose naturally occurring. Such comparisons have been madeconsidering forces and torques on ions and molecules, totalsurface charge induction energy of the field compared to thatof chemical reactions, endogenous fields associated with thebrain and heart action, thermal, shot, and 1/ noise, and com-peting thermal effects. Some of the physical interactions suchas forces, torques, and surface charges have been so far com-puted only for overly simplified cell structures. Their com-

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Table 1Main characteristics of the MRI-derived models of the human body

putations can be now also done for more realistic models,but their interpretation in terms of biological interactions ismore difficult. Various other comparisons involve so manyassumptions regarding values of parameters that are assignedthat their utility is rather limited. There have been interac-tion mechanisms proposed that evoke resonant interactionswith ions due to a static magnetic field (Earths field) andtime-varying magnetic field. Some experimental data alsosupport such interaction [3], [4]. However, there are prob-lems related to their importance in terms of effects on thewhole organism. Human brain tissue has minute amountsof magnetite, which is directly affected by magnetic fieldforces. Because of the small volume and number of mag-netite particles, the interactions by moderate intensity fieldsappear to be extremely small, and therefore too small to beof biological consequence. A well-established effect of mag-netic fields on free-radical reactions requires a field strengthat least on the order of 1 mtorr for cellular preparations, and

likely higher for the whole organism.

IV. ANATOMICAL MODELS OF THE HUMAN BODY

Until the last few years,the human body wasapproximatedby relatively simple models such as spheroids, ellipsoids,circular cylinders, or at best as composites of a few cylin-ders with a body-like shape with a few major organs rep-resented in a similarly simple fashion. Currently, a numberof laboratories have developed heterogeneous models of thehuman body with an anatomical shape and numerous tis-sues identified. Most of these models have been developedby computer segmentation of data from MRI and allocation

of proper tissue type [31][34]. Special care has been takento make these models anatomically realistic. The Univer-sity of Utah [31] collaborated with their MRI Laboratory atthe School of Medicine, and the University of Victoria [31]with the Radiology Department at the Yale Medical School[33]. Table 1 summarizes essential characteristics of thesemodels. More detail can be found elsewhere (e.g., [31], [32],[34][36]). In these three models, more than 30 distinct or-gans and tissues are identified. To illustrate the quality ofsuch models, Fig. 1 shows the external view, the skeleton,

the main blood vessels and some organs, and two cross-sec-tions of one such model [32], [36]. Another type of advancedmodel has been developed in France [37], [38]. The modelhas been constructed from several geometrical bodies of rev-olution. It is symmetric and contained about 100 000 ele-ments to represent only the major organs. In all the models,various conductivity values are allocated to tissues based onthe data either reported recently [39] or previously publishedin various articles.

V. COMPUTATIONAL METHODS

Various computational methods have been used to eval-uate induced electric fields in these high-resolution modelsfor exposures to the externally applied electric and magneticfields. Because of the low frequency of interest (50 or 60 Hz),exposures to the two fields should be considered separatelyand the induced vector fields added, if needed [40]. Expo-sure fields at power-line frequencies are not related by theplane-wave impedance, but can be directly computed fromcurrents and charges on conductors. In many cases, humanexposure (e.g., in cases of the general population except forappliance use) is far away from the field sources. As a con-sequence, the source fields can be considered uniform. Inmost computations and numerical codes developed for eval-uation of induced fields in the human body, advantage hasbeen taken of the quasi-static approximation, thus simpli-fying the computations without loss of accuracy. An addi-tional advantage is provided by the fact that at these frequen-cies, the induced conduction current is two to four ordersof magnitude higher than the displacement current. There-

fore, in most cases, it suffices to consider tissue conductivityvalues, and their permittivity values do not enter into compu-tations. All the computations relate to linear and macroscopic(bulk) properties of tissues.

Computations of exposure to electric fields are generallymore difficult, since the human body significantly perturbsthe exposure field. This necessitates a significant increase ofthe computational space in some method, e.g., in finite-dif-ference frequency-domain method. This increase is typicallythree times the external body dimension in each direction.

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(a)

Fig. 1. Model of the human body. (a) External view, skeleton, major blood vessels and organs.

The increase is not trivial if a high-resolution grid is requiredinside the model of the human body and the same grid is usedoutside. Often as a result, available computer resources maybe exceeded even for a modest grid size (e.g., 1 cm).

Suitable numerical methods are limited by the highlyheterogeneous electrical properties of the human bodyand equally complex external and organ shapes. Thus, themethods that have been successfully used so far for high-res-olution dosimetry are as follows. For the magnetic fieldexposure, different implementations of the finite-difference(FD) method have been used. In this case, the computationalspace is limited either to a box just around the body modelor to the body volume only. For the electric field, the FD

method in frequency domain and time domain (FDTD) hasbeen used. The finite-element method has been used forexposure to electric or magnetic field. Each method and itsimplementation offer some advantages and have limitations,as further elaborated.

For magnetic field induction, initially the impedancemethod (IM) has been used [31], [41], [42]. In this method,a three-dimensional impedance mesh (resistance for thepresent calculations) represents all voxels. For each faceof each body voxel, Kirchhoff voltages are equated to theelectromotive force (emf) produced by the rate of changeof magnetic field flux normal to the loop surface. Thesystem of equations for loop currents is solved using the

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(b)

Fig. 1. (Continued.) Model of the human body. (a) External view,skeleton, major blood vessels and organs.

successive overrelaxation (SOR) method. For each loop,the line currents or current density in the direction ofthe three coordinates are computed. More recently, the

scalar potential finite-difference (SPFD) technique hasbeen introduced [29], [43]. The equations for the electricfield components in each voxel are directly derived fromMaxwells equations, and the resultant set of equations issolved using the conjugate gradient method. The electricfield components ( ) are defined at voxel centersby averaging the three sets of four parallel edge components.This code has been extensively verified [43], [44]. The maindifference between the two methods is in their computationalefficiency. The impedance method is a vector method, whilethe SPFD is scalar. The impedance method leads to a matrixwith 13 nonzero diagonals, while the SPFD gives a matrixwith seven nonzero diagonals. Furthermore, the numerical

implementation limits the computational space to the modelvolume. More detailed information on both methods andtheir verification can be found in the previous publications.The efficiency comparison between the two methods hasbeen performed for three orientations of magnetic field[45]. It indicates that 540 Mbytes of memory is requiredfor the impedance method and 475 Mbytes for the SPFD.The computation times for SPFD are between 1.511 timesshorter. The greatest time saving is for the problem thatrequired the longest computing time. Both IM and SPFDalso can be used for nonuniform magnetic fields.

Accuracy evaluation has been performed in the SPFDmethod [46]. The analysis is based on comparisons of the

numerical results with analytic solutions for homogeneous,layered, and circumferentially stratified spheres, and homo-geneous ellipsoids of conductive tissue-like materials. Theerrors in the average induced field and current density valuesare on the order of 1% for a grid resolution of 3.6 mm.There is an inherent error on the order of 25% in maximumvalues for a 3.6-mm grid associated with representation ofsmooth surface conducting bodies by cubic voxels. Thislarge error is caused by the alteration of the current flow inthe staircased body in the vicinity of inner corners, where the

currents are concentrated. This error always results in highervalues of the maximum current density in some inner cornervoxels than would appear in a conformal grid. This error isthe greatest at the interface with air, and is smaller when thetissue conductivity gradient is less. The overall estimateduncertainty in the computed average and maximum currentdensities in the voxel model of the human body is 3% and25% (for organs not bordering with air), respectively. Whenthe conductivity contrast is lower, the uncertainty in themaximum current density is smaller, and it ranges from

4% for a contrast of 1 : 2 to 15% for 1 : 5. Numerical codescan reduce this error quite dramatically by smooth surfacerepresentation [47]. However, voxel models of the bodyare their staircase representations; thus this representationwould need to be changed to surface representation. TheIM method suffers from the same limitations in accuracyassociated with the staircasing.

For the electric field induction, the FDTD [48] and its newquasi-static formulation [49] have been used. A more nat-ural method used previously for grossly simplified models[50], such as the surface integral equation method, is not ef-ficient and difficult to apply to models consisting of tens ofmillions of computational variables.

The FD method has been used despite the problems oflarge computational space [51]. However, several consecu-tive computations are performed, starting with a very coarsegrid and then using the computed fields on the surface of asmaller volume box as sources for more refined grid com-putations. The steps in grid refinement are gradual to ensureaccuracy, as fields on the surface need to be interpolated forconsecutive computations.

The FDTD method has been used by one group at 10 MHz,and the results were scaled to 60 Hz [31], [52]. Computationswere made for a plane wave with wave impedance of 377 .Another group used the quasi-static FDTD formulation [49],either by itself for 7.2-mm resolution or hybridized with the

SPFD for 3.6-mm resolution to allow for these computationsto be run on a workstation [53]. All computations were per-formed at 60 Hz. Exposures were to the vertically orienteduniform electric field. Both groups used a recently developedabsorbingboundary conditionto terminate the computationalspace with minimal reflection [54]. For nonuniform electricfield exposures resulting from line sources, the quasi-staticmethod was further extended and used [47], [55].

It appears that the hybrid method [53] can provide the bestcomputational accuracy with the most efficient way. It hasbeen extensively verified using analytic solutions for a ho-mogeneous and layered sphere [46], [47]. Errors in averagevalues of the induced field and current density are small,

ranging from 2% for 7.2-mm resolution to 1% for 3.6-mmresolution. Large errors on the order of 50% for the currentdensity and 100% for the electric field occur in the maximumvalues. The location of the maximum values is at the outerlayer of the model bordering on air. Various computer codesproduce very similar errors. There are at least two factorsthat cause the problem. First, staircasing introduces singu-larities in charge density at voxel vertices bordering on freespace. Second, leakage of the large external electric fieldinto internal voxels occurs across the air-conductor boundary

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(a) (b)

Fig. 2. Layer-averaged magnitude of:(a) the electric fields in V/mand (b)current density in A/mfor exposure to uniform magnetic flux density of 1-

T 60-Hz oriented front-to-back. Two curves oneach graph correspond to different sets of tissue conductivity.

(infinite conductivity contrast). This problem arises from thestaircaseapproximation of smoothsurfaces andis dueto non-collocated field components (they are defined at voxel edgesrather than vertices) combined with the requirement of conti-nuity of tangential electric fields across material boundaries.The problem can be partly corrected and errors significantlyreduced by proper postprocessing of results [47]. However,

this correction has not been introduced in any data publishedso far. On the other hand, the errors in the maximum inducedvalues are much smaller in organs that border on other tissuesfor which the conductivity contrast is smaller. For contrast of1 : 5 and 1 : 2, the errors in the maximum current density areabout 20 and 10%, respectively, for a resolution of 14.4 mm[46]. The errors in this case decrease with decrease in thevoxel size.

The finite-element method (FEM) has been used forcomputations with the lower resolution model by the French

group [37], [38] and for cellular-level computation [56],[57]. In both cases general, general-purpose numericalcodes have been used. This method offers the advantagesof nonuniform and more conformal meshes. On the otherhand, there are no sufficiently detailed models of the humanbody available at present that can be directly introduced tothe computational codes. Additionally, only in the last few

years efficient absorbing boundaries are being developedthat can be placed close to the scattering object. The FEMshould prove in the future very useful for some problems indosimetry on the cellular or subcellular level.

VI. EXPOSURE TO MAGNETIC FIELDS

As mentioned earlier, at least four laboratories have per-formed computations of the induced electric field and cur-rent density for heterogeneous models of the human body

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Table 2Selected conductivity values ( ) used in modeling in S/m

in uniform magnetic fields. Typically, three orientations ofmagnetic flux density vector are considered: front-to-back,side-to-side, and head-to-feet (or in reverse, as the field

is alternating). Typical data reported are tissue-layer aver-aged values of the induced electric field or current densityin horizontal body cross-sections and average, root meansquare (rms), and maximum values of these parametersin various organs and tissues [29], [36][38], [45], [58].Effects of the tissue assigned conductivity [29], includingmuscle anisotropy [58] and model resolution [36], [45]have also been investigated. Fig. 2 illustrates changes ofthe tissue-layer averaged induced electric field and currentdensity for front-to-back 1- T 60-Hz exposure when twosets of conductivity values are used [29]. One set usuallyis taken from the most recent data [39] and the other fromthe earlier published data [29]. Both are shown in Table 2.

The effect of muscle anisotropy is illustrated in Fig. 3 [58].In this case, a simplified arrangement of muscle fibers hasbeen investigated. Conductivity values vary from 0.2 to0.7 S/m, and either the vertical or the horizontal directionis assigned the higher value. This is a highly simplifiedmodel, as muscle fibers are not vertically or horizontallydirected in the body (with rare exceptions). However, thissimplified model allows for some insight into the range ofchange of dosimetric parameters if muscle anisotropy isrepresented.

Representative values of the induced electric field for a3.6-mm model and the recent conductivity data are givenin Fig. 4 [29]. These data are for isotropic muscle. Corre-

sponding current density values can be obtained by multi-plying the data by conductivity given in Table 2. Fig. 5 il-lustrates the induced current density pattern in one of thebody cross-sections. Table 3 shows how the human body res-olution (3.6 compared with 7.2 mm) affects the computedvalues for selected organs. Since the low-resolution model isderived from the original model (3.6 mm), the volume ratioof each organ/tissue is given. Ideally, it should be equal toeight. It can clearly be seen that some organs are not wellrepresented by the coarse model. These are the organs thathave at least one dimension small compared with 7.2 mm.When the volume ratio is close to eight, differences in theaverage electric field for the two resolutions are due to the

overall shape changes. The maximum electric field is higherfor the finer resolution. This was also reported by anothergroup [45]. The maximum values are overestimated, as indi-cated in the description of the computational methods. Themaximum value for the whole body is for skin. Thus, it re-flects the highest conductivity contrast (infinity) between theskin and air.

Finally, since the data quoted are from our laboratory, it isworthwhile to compare them to values obtained by other re-searchers. When possible, such comparisons have been made

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(a) (b)

Fig. 3. Illustration of the muscle anisotropy. Layer averaged: (a) electric field in

V/m; two curvesshow the lowest and highest values and (b) current density in A/m ; two extreme curves show thelowestand highestvalues, andthe centercurveis forisotropicmuscle. Exposure to uniformflux densityof 1 T, 60 Hz oriented front-to-back.

Fig. 4. Dosimetric data for a few organs: induced average and maximum electric field for exposureto uniform magnetic flux density of 1 mtorr, 60 Hz of three orthogonal orientations.

[17]. Tables 4 and 5 give representative data for the compar-isons. The differences are reasonably small, given the differ-

ences in the models (Table 1), allocated conductivity values,and differences in resolution [17].

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Table 3Induced electric field, average (E ) and maximum ( E ), for two resolutions of the same bodymodel exposed to 1- T 60-Hz uniform field oriented front-to-back

a second large electrode. This creates highly nonuniformelectric field due to the current spread; thus current densitycomputed by dividing the total current by the area of thesmall electrode is a parameter only indirectly related to theactivating function given by (2).

Numerical computations have also underscored how theinduced quantities vary depending on the human body sizeand shape, tissue conductivity and its anisotropy, and reso-lution of body models used. Scaling with body size appearsreasonable, and the differences due to the shape and organsize differences can be approximately estimated, or com-puted accurately applying the existing methodology. Theimportance of tissue conductivity is clearly underscored.The conductivity values change the computed inducedelectric fields less than the induced current densities, aslong as the conductivity variations are relatively small.This is apparent from Fig. 2, and further shown in [36].Even more evident is this effect when muscle anisotropyis considered (Fig. 3). Various assumptions of the muscleconductivity (from 0.20.7 S/m) in vertical and horizontaldirections are reflected in the induced electric fields andcurrent densities also in other tissues [58]. The effects on the

average electric field vary from negligibly small 1%2% (inbrain and CSF for head-to-toe exposure field) to 50%70%(for bone marrow and exposure side-to-side and prostate,spinal cord, and testis for front-to-back exposure, and forthyroid in head-to-foot exposure). The difference for muscleis only 7%11% in the average electric field depending onthe orientation of the exposure field. On the other hand,the average current density in the muscle varies between200%300%.

Highest exposures to magnetic fields occur in occupa-tional settings in the vicinity of current-carrying conductors.Furthermore, the conductors generally carry three-phase

currents. In this case, the SPFD method can be used. How-ever, expressions have had to be derived for the magneticvector potential of the infinite conductors [60], [61], aswell as semi-infinite and finite conductor sections [62],as needed to model specific configurations, some of themshown in Fig. 6. For three-phase currents, all field quantitiesare represented as complex spatial vector fields. The in-duced quantities become elliptically polarized and are thencharacterized by local minimum, maximum, and rms fieldamplitudes at the voxel center over one time period. Global

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Table 4Comparison of the Induced Average Electric Field ( E ) in ( V/m) in Human Models. Exposure to60 Hz, B = 1 T, Front-to-Back

Table 5Comparison of Maximum Values of Current Density ( A/m ) in the Body for Various Orientationsof the Magnetic Field (all Values Normalized to 1 T)

field measures such as average and rms and variance can becomputed from the temporal rms amplitudes in each voxelof the organ [61], [62].

The two exposure scenarios shown in Fig. 6(a) and (b)represent quite typical situations associated with live-line

work. The worker wears a metallic-shielding suit, so thereis no exposure to the electric field. Typical current for thefour-conductor bundle is 250 A in each conductor. The cur-rents are in-phase, and the conductor bundles carrying theother two phases are sufficiently far away so that their fieldsare negligible compared with those from the conductors inclose body proximity. The conductors can be consideredas infinite straight lines in this case. These configurationsare representative of North American 500-kV high-voltagetransmission lines. Other configurations of infinite conduc-

tors have also been modeled [37], [60], [61]. Fig. 6(c)shows maintenance in a vault of bus bars of three-phaseconductors, each carrying 500 A. Inspection of isophasebuses of a 700-MW generator is shown in Fig. 6(d). Theconductors carry three-phase currents with 20 kA per con-

ductor. In the latter two cases, the conductors need to bemodeled as finite or semi-finite [62]. Approximate mod-eling of conductors shown in Fig. 6(c) leads to significantoverestimation of exposure [62]. To gain some perspectiveon how the magnitude of typical occupational exposurescompares to that of most people, Table 6 gives the inducedelectric fields (mV/m) in a few organs for exposure sce-narios shown in Fig. 6. In the case of three-phase currents,the values are for the temporal average exposure fields.They are the highest for the generator inspection [Fig. 6(d)].

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Fig. 6. Representative occupationalexposure scenarios:(a) and (b)live-linework on a 500-kV powerline, (c) vault, and (d) generator station.

However, a typical duration of exposure is short. Com-paring occupational exposures to typical environmental ex-posures of 0.11 T, it can be easily noted that occupationalexposures result in induced electric fields typically higherby 1000 or more times. Only in a few situations, e.g., di-rectly under a power line or very close to some appliances,are environmental exposures to high magnetic flux densi-ties. Even those higher environmental exposures are signif-

icantly lower than high occupational exposures illustratedin Fig. 6 and Table 6.

VII. EXPOSURE TO ELECTRIC FIELDS

The human body significantly perturbs a low-frequencyelectric source field. In most practical cases, the field is ver-tical (with respect to the ground). Since the body is a good


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Table 6Induced Electric Fields for Occupational Scenarios Shown in Fig. 6

conductor, the electric field is nearly normal to its surface.The electric field inside the body is many orders of magni-tude smaller than the external field. Nonuniform charges are

induced on the surface of the body, and the current direc-tion inside the body is mostly vertical, as illustrated in Fig. 7.Shown are the surface charge density and electric field linesfor human body in free space and in contact through the feetwith a perfectlyconducting ground. Also shown is thecurrentdensity and current streamlines in a vertical cross-section oftheupright body. A significant enhancement of thefield at thehead (and feet for the body in free space) can be observed.Total current flowing through the body when in free space,0.014 m above perfect ground, and in contact with ground,is shown in Fig. 8. These data agree well with measurements[19]. The conductivity values are given in Table 2 [53]. Av-erage and maximum electric fields (in mV/m) in a few organs

for the three separations from the ground are given for expo-sure to 1 kV/m 60 Hz. The induced values are clearly two tothree orders of magnitude below the external field. Inducedcurrent density values can be obtained from Fig. 8 in con-

junction with Table 2. Investigations of the effect of tissueconductivity on the current density yield similar results tothose for the magnetic field. On the contrary, the effect onthe induced electric fields is very small because the electricfield inside the body is to a large extent determined by itssize and shape (in addition) to the exposure field parameters.

For the two sets of conductivity values (Table 2), the electricfield remains within 15% for all tissues [53].

A comparison of the data presented here with data from

another laboratory is shown in Table 7 [17]. The data are for6-mm model and plane wave at 10 MHz used by Furse andGandhi [52] and for 7.2-mm model used by Dawson et al.[53]. Since Dawson et al. [53] considered exposures to eitherthe electric or magnetic fields, summation of induced valuesfrom separate computations is used [17]. Quite different con-ductivity values are used in the two models; with relative dif-ference exceeding 15% for some organs [17]. Also, an organsuch as theeye is poorly represented with theresolution used.Overall, the differences between the electric field values ob-tained by the two groups can be accounted for, as discussedin [17].

In some relatively rare occupational situations, a workermay be close enough to a charged conductor so that the ex-posure field cannot be adequately represented as uniform.The same exposure electric field 1 m above ground for a linesource 4 m above the ground and a human body under theline induces greater electric fields in all organs than thoseinduced by the same uniform field [47], [55]. Table 8 com-pares the induced electric fields for the two exposures for agrounded model of the body (resolution 7.2 mm) at 60 Hz in1-kV/m field 1 m above the ground.

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Fig. 7. Human bodyin theuniform electric field 1 kV/m at 60 Hz:surface charge densityand externalelectric field for the body: (a) in free space, (b) standing on a perfect conductor, and (c) current densitymap and current flow lines in a vertical body cross-section.

Fig. 8. Average and maximum induced electric field in mV/m for exposure to 1 kV/m, 60 Hz for thebody in free space, 0.014 m above perfect ground, and grounded by the feet.

VIII. COMPARISON OF EXPOSURES TO ELECTRIC ANDMAGNETIC FIELDS

The main difference between interactions with biologicaltissue between the electric and magnetic field at power-line

frequencies is that the exposure electric field is perturbedby human and other conducting bodies, while the magneticfield remains unchanged in free space as well as in the body.Both fields induce electric fields and currents; therefore, ifthese quantities are responsible for biological interactions,


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Table 7Comparison of the Calculated Organ-Averaged Induced Electric Fields E (mV/m) in the HumanBody Models in Contact with a Perfect Ground. Exposure to 60-Hz Uniform Fields E = 1 0kV/m (vertical),

B = 3 3

T Horizontal, Sideto-side

both fields produce similar effects. This is the case for ex-citable tissue stimulation, visual phosphenes, and some othereffects (e.g., bone healing). Spatial patterns of the inducedfields inside the body are different for the two fields (Figs.5 and 7), and these differences have to be considered whenevaluating their interactions. The magnitudes of the inducedfields are certainly also of importance. Therefore, it is inter-esting to compare the two types of exposure considering themagnitudes of induced electric fields in various organs andthe corresponding levels of the two exposure fields. Table 9

shows the external field levels required to induce 1-mV/maverage and maximum electric field in various organs. Moredata are given elsewhere [63].

IX. INDUCED FIELD ON SUBCELLULAR LEVEL

Macroscopic dosimetry that gives induced electric fieldsin various organs and tissues needs to be extended to morespatially refined models of subcellular structures to quanti-tatively predict and understand biophysical interactions. Thesimplest subcellular modeling that considers linear systemsrequires evaluation of induced fields in various parts of a cell.Such models, for instance, have been developed to under-

stand neural stimulation [20][24]. Also, in the past, simpli-fied models of cells consisting of a membrane, cytoplasm,and nucleus and suspended in conductive medium have beenconsidered [64]. The membrane potential has been computedfor spherical [65], ellipsoidal [66], and spheroidal cells [67]suspended in a lossy medium. Computations are availableas a function of the applied electric field and its frequency.Because cell membranes have high resistivity and capaci-tance (nearly constant for all mammalian cells and equal to1 F/cm ), high fields are produced at the two extremities

(a)

(b)

Fig. 9. Equivalent circuit representation of (a) two biological cellsconnected by gap junctions and (b) the gap junction.

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Table 8Induced Electric Fields (mV/m) in the Grounded Human Body for a 60-Hz Line Source 4 m Abovethe Ground (1 kV/m 1 m Above the Ground) and for a Uniform Vertical 1 kV/m Electric Field

of the membrane. The field is nearly zero fields inside thecell, as long as the frequency of the applied field is below themembrane relaxation frequency. The total membrane resis-tance and capacitance define this frequency; thus, it dependson the cell size (total membrane surface). The larger the cell,

the higher the induced membrane potential for the same ap-plied field. However, the larger the cell, the lower the mem-brane relaxation frequency.

Gap junctions connect most cells. A gap junction is anaqueous pore or channel through which neighboring cellmembranes are connected. Thus, cells can exchange ions,for example, providing local intercellular communication[68]. Certain cancer promoters inhibit gap communicationand allow the cells to multiply uncontrollably. It has been hy-pothesized with support from some suggestive experimentalresults that low-frequency electric and magnetic fields mayaffect intercellular communication. Gap-connected cellshave previously been modeled as long cables [69]. Also,

very simplified models have been used, in which gap-con-nected cells are represented by large cells of the size ofthe gap-connected cell assemblies [70]. With such models,relatively large membrane potentials can be expected, evenfor moderate applied fields.

To evaluate whether this model is correct, a numericalanalysis has been performed to compute membrane poten-tials in more realistic models [56], [57], [59]. Various as-semblies of cells connected by gap-junctions have been mod-eled with cell and gap-junction dimensions and conductivity

values representative of mammalian cells. The FEM tech-nique has been used, as it facilitates modeling of geome-tries with parts having vastly different dimensions and al-lows for computational grids reasonably conformal to sur-faces of bodies of revolution (sphere, cylinder). Such types

of geometry are typical representations of cells connected bygap junctions.A series of numerical simulations indicates that simplified

models such as a single cell or leaky cable can only be usedfor some specific situations. However, even in those cases,equivalent cells have to be constructed, in which cytoplasmproperties are modified to account for the properties of gap

junctions. These models predict reasonable results for smallassemblies of cells of certain shapes and at very low frequen-cies (practically only forstatic fields [56]). On the other hand,numerical analysis can predict correctly the induced mem-brane potential as well as the relaxation frequency [57], [59].

From the biological interaction perspective, the numerical

modeling indicates that as the size of the cell assemblyincreases, the membrane potential even at dc does notincrease linearly with dimensions, as it does for very shortelongated assemblies. There is a characteristic length forelongated assemblies beyond which the membrane potentialdoes not increase significantly. There is also limited increasefor the membrane potential for assemblies of other shapes.Even more importantly, as the assembly size (volume) in-creases, the relaxation frequency decreases (at the relaxationfrequency the induced membrane potential is 0.5 of that

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Table 9Electric (Grounded Model) or Magnetic Field (front-to-back) to Induce Average ( E )and Maximum ( E ) Electric Field of 1 mV/m

at dc). An approximate equivalent circuit representing twogap-connected cells is shown in Fig. 9.

Considering the macroscopic dosimetry and linear model

of gap-connected cells, it can be concluded that at 60 Hz,an induced membrane potential of 0.1 mV is not attained inany organ of the human body exposed to a uniform magneticflux density of up to 1 mtorr or to an electric field of approxi-mately 10 kV/m or less. These exposure values are estimatedon the basis of the numerically evaluated internal electricfields in the organs [29], [53] and the cellular modeling ofmembrane potential and relaxation frequency for gap-con-nected cells [56], [57], [59].

X. CONCLUSION

In the last decade, research on health effects of electric and

magnetic fields at 50 and 60 Hz culminated in several reportsby expert panels. While all panels agreed that the fields arenot a major health problem, lingering unresolved issues re-main. These relate to the possible association between ex-posure to relatively weak fields and childhood leukemia, andbetween stronger field exposures in occupational settings andadult leukemia. There appears also to be an agreement thatexposures producing 110 mV/m in tissue interact with cellsand elicit biological effects that are not necessarily harmful.On the other hand, it is well known and agreed upon that

strong fields cause harmful effects when their magnitude ex-ceeds stimulation thresholds for neural tissue (central ner-vous system and brain), muscle, and heart. However, these

thresholds are mostly expressed in terms of current densi-ties associated with electrodes producing highly nonuniformfields around them. It is well known that neural excitationis defined by activation function: the vector derivative ofthe electric field along the neuron. This translates for bendand terminal neurons to the electric field strength, with theneuron parameters such as size and shape playing a very sig-nificant role.

As a part of the increased research effort, a few laborato-ries have performed extensive evaluation of induced electricfields and current density. Highly realistic heterogeneousmodels of the human body have been used with typically30 tissues and organs identified and assigned different

conductivity values based on measurements. The modelsare based on segmentation of magnetic resonance imagesand have a resolution of 24 mm. Numerical methodsranging from various implementations of the finite-differ-ence method, classical FDTD and quasi-static FDTD, thefinite-element method, and to hybridization of the FD withquasi-static FDTD have been used. Exposures to uniformand nonuniform electric and magnetic fields have been eval-uated. Data for the most part are given in terms of averageand maximum electric field and current density values in

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various organs and tissues. Effects have been investigatedof various parameters, mainly allocated tissue conductivity,muscle anisotropy, body-model resolution, and organ (heart)placement outside the body and in situ. For occupationalexposures, several representative work scenarios have beenmodeled. Whenever possible, comparisons have been madewith experimental results, and good agreement observed.Also, results from three different laboratories have beencompared, and reasonable agreement has been found, withdifferences well accounted for.

These extensive modeling results, as well as the method-ology, facilitate several research venues that could help tounderstand the mechanisms of interaction of low-frequencyfields of moderate intensities and to develop rational safetyguidelines against tissue excitation and visual phosphenes.As illustrated by evaluation of the membrane potential incells connected by gap junctions in the human body in anelectric or magnetic field, data for organ dosimetry togetherwith numerical evaluation of subcellular structures can an-swer relevant biological questions.

Further extension of numerical modeling is needed to thecellular and subcellular level, coupled with an existing database of dosimetric measures on the organ/tissue level. The

same numerical methods can be used with boundary (source)data taken from macroscopic dosimetry. This approach is rel-atively straightforward once tissue and cell models are con-structed. It is directly applicable to linear systems and ex-tendible to nonlinear systems.

One relatively straightforward but very important appli-cation of the recently available numerical dosimetric datais their proper introduction into the health protection guide-lines. However, it needs to be emphasized that current den-sity is not the proper measure to be used, but rather tissue-induced electrical field. This change requires reevaluationof some experimental data on tissue and cell stimulation.Some literature data are also reported in terms of the electricfield strength. Reasonable, anatomically based models of ex-citable tissue (e.g., typical nerve curvature) will also have tobe considered in evaluating induced electric fields and theirspatial derivatives.

ACKNOWLEDGMENT

The authors would like to thank their associates, K. Ca-puta, E. Fear, and M. Potter, for research contributions to thedosimetry research and D. Shannon for her editorial assis-tance.

REFERENCES

[1] N. Wertheimer and E. Leeper, Electrical wiring configurations andchildhoodcancer,Amer. J. Epidemiol., vol. 109,pp. 273284,1979.

[2] National Research Council, Possible Health Effects of Exposure to Residential Electric and Magnetic Fields. Washington, DC: Na-tional Academy Press, 1997.

[3] National Institute of Environmental Health Sciences (NIEHS), As-sessment of health effects from exposure to power-line frequencyelectric and magnetic fields,, Brooklyn Park, MN, 1998.

[4] , Reports for theoretical mechanisms and in vitro researchfindings,, Durham, NC, Mar. 2427, 1998.

[5] , Reports for epidemiological research findings,, San An-tonio, TX, Jan. 1224, 1998.

[6] , Reports for clinical and in vivo laboratory findings,,Phoenix, AZ, 98-4400, Apr. 69, 1998.

[7] J. E. Moulder, Power-frequency fields and cancer, Crit. Rev.Biomed. Eng., vol. 26, pp. 1116, 1998.

[8] M. L. McBride, R. P. Gallagher, G. Theriault, B. G. Armstrong, S.Tamaro, J. J. Spinelli, J. E. Deadman, B. Fincham, D. Robson, andW. Chaoi, Power-frequency electric and magnetic fields and riskof childhood leukemia in Canada, Am. J. Epidemiol., vol. 149, pp.831842, 1999.

[9] L. M. Green, A. B. Miller, P. J. Villeneuve, D. A. Agnew, M. L.Greenberg, J. Li, and K. E. Donnelly, A case-control study of child-hood leukemia in southern Ontario, Canada and exposure to mag-

netic fieldsin residences,Int. J.Cancer, vol. 82,pp. 171170,1999.[10] L. M. Green, A. B. Miller, D. A. Agnew, M. L. Greenberg, J. Li, P.

J. Villeneuve, and R. Tibshirani, Childhood leukemia and personalmonitoring of residential exposures to electric and magnetic fieldsin Ontario, Canada, Cancer Causes Control, vol. 10, pp. 233243,1999.

[11] A. B. Miller, T. To, and D. A. Agnew et al., Leukemia followingoccupational exposure to 60-Hz electric and magnetic fields amongOntario electric utility workers, Amer. J. Epidemiol., vol. 144, pp.150160, 1996.

[12] D. A. Savitz, D. Liao, A. Sastre, R. C. Kleckner, and R. Kavet,Magnetic field exposure and cardiovascular disease mortalityamong electric utility workers, Amer. J. Epidemiol., vol. 149, pp.135142, 1999.

[13] A. Sastre, M. R. Cook, and C. Graham, Nocturnal exposure to in-termittent 60 Hz magnetic fields alter human cardiac rhythm, Bio-electromagnetics, vol. 19, pp. 98106, 1998.

[14] National Institute of Environmental Health Sciences (NIEHS),Health effects from exposure to power-line frequency electric andmagnetic fields,, Durham, NC, NIH Pub. 99-4493, May 1999.

[15] W. H. Bailey, S. H. Su, T. D. Bracken, and R. Kavet, Summaryand evaluation of guidelines for occupational exposure to powerfrequency electric and magnetic fields, Health Phys., vol. 73, pp.433453, 1997.

[16] International Commission on Non-Ionizing Radiation Protection(ICNIRP), Guidelines for limiting exposure to time-varyingelectric, magnetic and electromagnetic fields (up to 300 GHz),

Health Phys., vol. 74, pp. 494522, 1998.[17] M. A. Stuchly and O. P. Gandhi, Inter-laboratory comparison of

numerical dosimetry for human exposure to 60 Hz electric and mag-netic fields, Bioelectromagnetics, vol. 21, pp. 167174, 2000.

[18] Electric Power Research Institute (EPRI), Evaluation of occu-pational magnetic field exposure guidelines,, Palo Alto, CA,TR-111501, 1998.

[19] D. W. Deno and L. E. Zaffanell, Field effects of overhead transmis-

sion lines and stations Chapter 8, in Transmission Line ReferenceBook: 345 kV and Above, 2nd ed. Palo Alto, CA: EPRI, 1982, pp.329419.

[20] R. Plonsey and R. C. Barr, Bioelectricity, A Quantitative Ap-proach. New York: Plenum, 1988.

[21] J.Malmivuoand R.Plonsey,Bioelectromagnetism. New York:Ox-ford Press, 1995.

[22] J. P. Reilly, Electrical Stimulation and Electropathology. NewYork: Cambridge Univ. Press, 1992.

[23] P. J. Basser and B. J. Roth, Stimulation of a myelinated nerve axonby electromagnetic induction,Med.Biol. Eng.Comput., vol.29, pp.261268, 1991.

[24] M. A. Abdeen and M. A. Stuchly, Modeling of magnetic field stim-ulation of bent neurons, IEEE Trans. Biomed. Eng., vol. 41, pp.10921095, 1994.

[25] M. A. Stuchly and K. P. Esselle, Factors affecting neural stimula-tion with magnetic fields, Bioelectromagnetics Supp., vol. 1, pp.191204, 1992.

[26] B. J. Rothand J. J. P. Wikswo,The effect of externally appliedelec-trical fieldson myocardial tissue, Proc. IEEE, vol.84, pp.379391,1996.

[27] P. Lvsund, Biological Effects of Alternating Magnetic Fields withSpecial Reference to the Visual System. Linkping, Sweden: Uni-versity of Linkping, Dept. of Biomedical Eng. & Ophthalmology,1980.

[28] P. Lvsund, P. A. berg, and S. E. G. Nilsson, Magneto-and elec-tophosphenes: A comparative study, Med. Biol. Eng. Computing,vol. 18, pp. 758764, 1980.

[29] T. W. Dawson and M. A. Stuchly, High resolution organ dosimetryfor human exposure to low frequency magnetic fields, IEEE Trans.

Magn., vol. 34, pp. 111, 1998.


8/6/2019 #1 Stuchly, 2000

21/22

[30] T. W. Dawson, K. Caputa,and M. A. Stuchly, Magnetic induction at60 Hz in the human heart: A comparison between the in-situ and iso-lated scenarios, Bioelectromagnetics, vol. 20, pp. 233243, 1999.

[31] O. P. Gandhi and J.-Y. Chen, Numerical dosimetry at power linefrequencies using anatomically based models, Bioelectromagn. J.Supp., vol. 1, pp. 4360, 1992.

[32] T. W. Dawson, J. DeMoerloose, and M. A. Stuchly, Comparison ofmagnetically induced ELF fields in humans computed by FDTD andscalarpotential FD codes,Appl. Comput. Electromag. Soc. (ACES),vol. 11, pp. 6371, 1996.

[33] I. G. Zubal, C. R. Harrell, E. O. Smith, Z. Rattner, G. R. Gindi, andP. H. Hoffer, Computerized three-dimensional segmented humananatomy, Med. Phys. Biol., vol. 21, pp. 299302, 1994.

[34] P. J. Dimbylow, FDTD calculations of the whole-body averaged

SAR in an anatomically realistic voxel model of the human bodyfrom 1 MHz to 1 GHz, Phys. Med. Biol., vol. 42, pp. 479490,1997.

[35] O. P. Gandhi, Some numerical methods for dosimetry: Extremelylow frequencies to microwave frequencies, Radio Sci., vol. 30, pp.161177, 1995.

[36] T. W. Dawson, K. Caputa, and M. A. Stuchly, Influence of humanmodel resolution of computed currents induced in organs by 60 Hzmagnetic fields, Bioelectromagnetics, vol. 18, pp. 478490, 1997.

[37] P. Baraton, J. Cahouet, and B. Hutzler, Three-dimensional compu-tation of the electric fields induced in a human body by magneticfields, Electricit de France, Tech. Rep.93NV00013, 1993.

[38] B. Hutzler, P. Baraton, J. L. Vicente, J. C. Antoine, M. Roux, and J.P. Urbain, Exposure to 50 Hz magnetic fields during live work, inProc. CIGRE, 1994, pp. 19.

[39] S. Gabriel, R. W. Lau, and C. Gabriel, The dielectric properties of

biological tissues: III Parametric models of the dielectric spectrumof tissues, Phys. Med. Biol., vol. 41, pp. 22712293, 1996.[40] R. G. Olsen, Power-transmission electromagnetics, IEEE An-

tennas Propagat. Mag., vol. 35, pp. 716, 1994.[41] O. P. Gandhi and J. F. D. Ford, Calculation of EM power deposi-

tion for operator exposure to RF introduction heaters, IEEE Trans.Electromagn. Compat., vol. 30, pp. 6368, 1988.

[42] W. Xi, M. A. Stuchly, and O. P. Gandhi, Induced electric currentsin models of man and rodents from 60 Hz magnetic fields, IEEETrans. Biomed. Eng., vol. 41, pp. 10181023, 1994.

[43] T. W. Dawson and M. A. Stuchly, Analytic validation of a three-di-mensional scalar-potential finite-difference code for low-frequencymagnetic induction, Appl. Comput. Electromag. Soc. (ACES), vol.11, pp. 7281, 1996.

[44] , An analytic solution for verification of computer modelsfor low-frequency magnetic induction, Radio Sci., vol. 32, pp.343367, 1997.

[45] P. J. Dimbylow, Induced current densities fromlow-frequency mag-netic fields in a 2 mm resolution, anatomically realistic model of thebody, Phys. Med. Biol., vol. 43, pp. 221230, 1998.

[46] Electric Power Research Institute (EPRI), Validation of computa-tional methods for evaluation of electric fields and currents inducedin humans exposed to electric and magnetic fields, EPRI, Palo Alto,CA, Rep.TR-111 768, 1998.

[47] M. E. Potter, M. Okoniewski, and M. A. Stuchly, Low frequencyfinitedifference timedomain(FDTD) formodeling of inducedfieldsin humans close to line-sources, to be published.

[48] A. Taflove, Computational Electrodynamics: The Finite-DifferenceTime-Domain Method. Norwood, MA: Artech House, 1995.

[49] J. De Moerloose, T. W. Dawson, and M. A. Stuchly, Application ofthe finite-difference time-domain algorithm to quasistatic field anal-ysis, Radio Sci., vol. 32, pp. 329341, 1997.

[50] K.-M. Chen, H.-R. Chuang,and C.-J.Lin, Quantification of interac-

tionbetween ELF-LFelectricfields andhuman bodies,IEEE Trans.Biomed. Eng., vol. BME-33, pp. 12731276, 1986.[51] P. J. Dimbylow, Current densities in a 2mm resolution anatomically

realistic model of thebody inducedby lowfrequency electric fields,Phys. Med. Biol., vol. 45, 2000, to be published.

[52] C. M. Furse and O. P. Gandhi, Calculation of electric fields andcurrents induced in a mm-resolution human model at 60 Hz usingthe FDTD model,Bioelectromagnetics, vol. 19, pp.293299, 1998.

[53] T. W. Dawson, J. De Moerloose, and M. A. Stuchly, Hybridfinite-difference method for high-resolution modeling of low-fre-quency electric induction in humans, Computat. Phys., vol. 136,pp. 640653, 1997.

[54] J.-P. Berenger, Perfectly matched layer for the FDTD solution ofwave-structure interaction problems, IEEE Trans. Antennas Prop-agat., vol. 44, pp. 110117, 1996.

[55] M. E. Potter, M. Okoniewski, and M. A. Stuchly, Extension of theFDTD method to nonuniform excitation, Electron. Lett., vol. 3, pp.22162217, 1998.

[56] E. C. Fear and M. A. Stuchly, Biological cells with gap junctions inlow-frequency electric fields, IEEE Trans. Biomed. Eng., vol. 45,pp. 856866, 1998.

[57] , Modeling assemblies of biological cells exposed to electricfields, IEEE Trans. Biomed. Eng., vol. 45, pp. 12591271, 1998.

[58] T. W. Dawson, K. Caputa, and M. A. Stuchly, Effects of skeletalmuscle anisotropy on human organ dosimetry under 60 Hz uniform

magnetic field exposure, Phys. Med. Biol., vol. 43, pp. 116, 1998.[59] E. C. Fear and M. A. Stuchly, A novel equivalent circuit model

for gap-connected cells, Phys. Med. Biol., vol. 43, pp. 14391448,1998.

[60] T. W. Dawson, K. Caputa, and M. A. Stuchly, High-resolution mag-netic field numerical dosimetry for live-line workers, IEEE Trans.

Magn., vol. 35, pp. 11311134, 1999.[61] , Organ dosimetry for human exposure to nonuniform 60

Hz magnetic fields, IEEE Trans. Power Delivery, vol. 14, pp.12341239, 1999.

[62] , Numerical evaluation of 60 Hz magnetic induction in thehuman body in complex occupational environments, Phys. Med.

Biol., vol. 44, pp. 10251040, 1999.[63] , A comparison of 60 Hz uniform magnetic and electric induc-

tion in the human body, Phys. Med. Biol., vol. 42, pp. 23192329,1997.

[64] K. R. Foster and H. P. Schwan, Dielectric properties of tissues andbiological materials: A critical review, Crit. Rev. Biomed. Eng., vol.17, pp. 24104, 1989.

[65] , Dielectric Properties of TissuesChapter 1, in Handbookof Biological Effects of Electromagnetic Fields, 2nd ed, C. Polk andE. Postow, Eds. New York: CRC, 1996.

[66] J. Bernhardt and H. Pauly, On the generation of potential differ-ences acrossthe membranesof ellipsoidalcellsin an alternatingelec-trical field, Biophysik, vol. 10, pp. 8998, 1973.

[67] R. A. Jerry, A. S. Popel, and W. E. Brownell, Potential distributionfor a spheroidal cell having a conductive membrane in an electricfield, IEEE Trans. Biomed. Eng., vol. 43, pp. 970972, 1996.

[68] J. W. Holder, E. Elmore, and J. C. Barrett, Gap junction functionand cancer, Cancer Res., vol. 53, pp. 34753485, 1993.

[69] M. Cooper, Gap junctions increase the sensitivity of tissue cells toexogenous electric fields, J. Theor. Biol., vol. 111, pp. 123130,1984.

[70] C. Polk, Dosimetry of extremely-low-frequency magnetic fields,Bioelectromagn. Supp., vol. 1, pp. 209235, 1992.

Maria A. Stuchly (M71SM76F91) receivedthe M.Sc. degree from WarsawTechnical Univer-sity, Poland, in 1962 and the Ph.D. degree fromthePolishAcademy of Sciences, Poland,in 1970,both in electrical engineering.

Between 1962 and 1970, she was with theWarsaw Technical University and the Institute ofPolish Academy of Sciences. After immigratingto Canada during 1970, she was with theUniversity of Manitoba, Canada. In 1976, she

joined the Bureau of Radiation and MedicalDevices in Health and Welfare Canada as a Research Scientist. During1978, she was also associated with the Electrical Engineering Departmentat the University of Ottawa as an Adjunct Professor, and in 19901991as a Funding Director of the Institute of Medical Engineering. In 1992,she joined the University of Victoria as a Visiting Professor with theDepartment of Electrical and Computer Engineering, and since January1994 she has been a Professor and Industrial Research Chairholder fundedby the Natural Sciences and Engineering Research Council of Canada,BC Hydro, and Trans Alta Utilities. Her current research interests are innumerical modeling of interaction of electromagnetic fields with the humanbody and design of wireless communication antennas.


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Trevor W. Dawson (M95SM98) received theB.Sc. degree in physics and applied mathematics(honors) and the Ph.D. degree in geophysics(electromagnetic induction) from the Universityof Victoria, Toronto, Ont., Canada, in 1976 and1979, respectively.

His research interests are in the application ofanalytical andnumericalmethods to themodelingof physical phenomena. His graduate work expe-rience includes work into modeling of populationgrowths using nonlinear and time-delayed differ-

ential equations and the applicationof finitedifference methodsto modelingof electromagnetic induction in the Earth. In 1979, he became a Defence

Scientist at the Defence Research Establishment Pacific (DREP), joiningthe Fluid Dynamics Group. His work involved theoretical and computermodeling studies of the generation of internal and surface waves by sub-merged moving bodies; theoretical, experimental, and numerical studies ofinteractions between naturally occurring internal waves and surface waves;and the remote sensing of internal wave surface signatures by syntheticaperture radar and by radar and infrared laser scatterometers. In 1985, hemoved to the DREP Arctic Modeling and Signal Processing Group. There,his work involved theoretical and numerical studies concerning applicationof Boundary integral equation methods, in part combined with scatteringmatrix methods, for the accurate modeling of acoustic propagation and scat-tering in the presence of boundary roughness, with emphasis on the ArcticOcean. Later research was involved with extensions to BIEM and otheracousticpropagation modeling methods, with emphasis on the incorporationof coupled seismoacoustic propagation in the ocean floor and ice canopy.He became a Research Scientist under the NSERC/BC Hydro/TransAltaIndustrial Research Chair. His current research is focused on the applica-

tion of boundary element, finite-difference, and finite-difference time-do-main methods for modeling power-frequency-induced fields in biologicalsystems and in the application of analytical methods for the verification ofcomputer codes.

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