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Electric Fields in the Human Body due to Electrostatic Discharges

Article in IEEE transactions on bio-medical engineering · September 2004

DOI: 10.1109/TBME.2004.828047 · Source: PubMed

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1460 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 8, AUGUST 2004

Electric Fields in the Human Body

due to Electrostatic Discharges
T. W. Dawson, Senior Member, IEEE, M. A. Stuchly*, Fellow, IEEE, and R. Kavet

Abstract—Electrostatic discharges (ESDs) occur when two responsible for health effects, most notably childhood leukemia
objects at different electric potentials come close enough to arc [3]. Numerical modeling indicates that the electric fields in
(spark) across the gap between them. Such discharges may be human tissue resulting from typical contact currents are much
either single-event or repetitive (e.g., 60 Hz). Some studies have
indicated that ESDs may be a causative factor for health effects in greater than those induced from typical exposures to electric
electric utility workers. Moreover, a hypothesis has recently been and magnetic fields at power line frequencies [4].
forwarded imperceptible contact currents in the human body may An ESD consists of two phases: a relatively slow build-up
be responsible for health effects, most notably childhood leukemia. of charges on objects (resulting in a voltage differential) and a
Numerical modeling indicates that the electric fields in human
rapid transfer of the charges due to the breakdown of air. In the
tissue resulting from typical contact currents are much greater
than those induced from typical exposures to electric and magnetic case of 50 or 60 Hz, the build up of charges of opposite po-
fields at power line frequencies. Numerical modeling is used here larity occurs every half cycle; e.g., 100 or 120 times per second.
to compute representative spark-discharge dosimetry in a realistic In alternating (ac) fields, ESD is described in terms of the cur-
human adult model. The frequency-domain scalar potential finite rent peak value, wave shape (frequency spectrum), and repeti-
difference method is applied in conjunction with the Fourier
transform to assess electric fields in selected regions and tissues of
tion rate [5]. These parameters depend on many factors and can
interest in the body. Electric fields in such tissues as subcutaneous vary widely. However, typical discharges and relevant character-
fat (where peripheral nerves may be excited), muscle and bone istics of the human body have been agreed upon in testing im-
marrow are of the order of kilovolts per meter in the lower arm. munity of electronic equipment. An equivalent circuit consisting
The pulses, however, are of short duration ( 100 ns). of resistances and capacitances leading to ground represents the
Index Terms—Dosimetry, electrostatic spark discharges, human characteristics of the human body. This circuit and the charac-
body, modeling, tissue electric field. teristics of the spark determine the waveform of ESD events.
A specific waveform has been agreed upon in the compatibility
I. INTRODUCTION test standards [6]–[8], and is shown in Fig. 1 for a potential dif-
ference of 2 kV. For other potential differences the current scales
E LECTROSTATIC discharges (ESDs) occur when two
objects at different electric potentials come close enough
to arc (spark) in the gap between the objects. In electric utilities
linearly, while the rise time of the pulse remains approximately
0.7–1 ns. The spectrum of a typical ESD discharge extends up
to about 1 GHz.
or under high-voltage transmission lines, spark discharges
While numerous simulations and measurements have been
occur between an ungrounded person and an isolated con-
performed on ESD interactions with various electronic devices,
ducting object in the electric (or magnetic) field, or vice versa.
Discharges associated with a static field (as in the case of only relatively limited research is available on interactions with
walking on a carpet) are usually nonrepetitive phenomena human tissue. Reilly [9] discusses the characteristics of ESD
(self-extinguishing). On the other hand, for time-varying fields interactions with humans and relevant experimental results.
(50 or 60 Hz), the discharges can be repetitive due to the The most advanced numerical modeling to date involved a
recharging of the bodies (provided that the gap between the human model consisting of 11 interconnected spheres repre-
bodies is maintained sufficiently small). Previous laboratory senting basic anatomical parts (head, upper and lower torso,
studies and analyzes of blood samples from electric power and upper and lower limbs) [10]. A diakoptic method was
employees have suggested that chromosomal anomalies may used to compute capacitances to ground of the body parts,
result from exposure to spark discharges [1], [2]. Recently, a equivalent circuit components of the body parts, and currents
hypothesis has been forwarded that imperceptible currents in at the junctions of the body parts. The analysis showed that
the human body due to contact with charged objects may be high-frequency components of the pulse were short-circuited
by the capacitances between the lower arm and ground.
In this contribution, electric fields resulting from a single typ-
Manuscript received June 17, 2003; revised January 2, 2004. This project was
supported by an EPRI contract and by an NSERC/BC Hydro/Bell Mobility/Al- ical ESD event are computed in the human body. The analysis
taLink industrial research chair. Asterisk indicates corresponding author. is limited to frequencies of the pulse below 40 MHz, as the
T. W. Dawson, deceased, was with the Department of Electrical and Computer spectral power density decreases with frequency, as shown in
Engineering, University of Victoria, Victoria, BC V8W 3P6, Canada.
*M. A. Stuchly is with the Department of Electrical and Computer En- Fig. 1(b). A heterogeneous, anatomically representative model
gineering, University of Victoria, Victoria, BC V8W 3P6, Canada (e-mail: of the human body is used. Computations are performed with the
mstuchly@ece.uvic.ca). scalar potential finite difference (SPFD) code, which assumes
R. Kavet is with the EPRI—Electric Power Research Institute, Palo Alto, CA
94304-1344 USA. quasistatic conditions [4]. At frequencies below 1 MHz, the dis-
Digital Object Identifier 10.1109/TBME.2004.828047 placement currents are less than a small fraction of one percent.
0018-9294/04$20.00 © 2004 IEEE
DAWSON et al.: ELECTRIC FIELDS IN THE HUMAN BODY DUE TO ESDs 1461

and, hence, its spectral content. The most critical factors include
impedances between the human body and the ground (strongly
dependent on the posture), and characteristics of the contact
impedance between the current entry area and the charged ob-
ject. Therefore, the data can be considered as representative but
do not encompass all possible ESD events. The data cannot be
used directly to evaluate biological effects reported in [1], [2].
However, the results presented are useful in comparing elec-
tric fields in tissue due to ESD with those resulting from other
events. Should animal experiments be designed to test chromo-
somal aberrations due to spark discharges, the data presented in
this paper may be of assistance.

II. METHODS
A. Numerical Method and Model
The computations are based on the quasistatic frequency-do-
main SPFD method [4]. In the absence of any magnetic fields,
the electric field at position within the body and at
harmonic frequency may be defined in terms of a scalar po-
tential as

(1)
Fig. 1. Top: typical ESD pulse for 2-kV potential difference (dashed line), its
40-MHz bandwidth content (solid line), and reconstruction of the latter from Under the quasistatic approximation, the internal current density
the 42 point subsampled band-limited spectrum (circles): Middle: Real (solid)
and imaginary (dashed) parts of the spectrum of the full ESD pulse, showing is conserved, so that
part of a slowly decaying tail which extends to over 500 MHz and is associated
with the discharge spike. Bottom: real (solid) and imaginary (dashed) parts of (2)
the spectrum filtered to 40 MHz. The crosses on the real part and circles on the
imaginary part indicate the 42 nonuniformly spaced frequency samples used to Hence, the heart of the SPFD method is the solution of the equa-
represent this spectrum. The inverse DFT of these spectral points give the curve
indicated by the circles in the top panel. tion

(3)
Above 10 MHz, the errors due to neglecting displacement cur-
rents are of the order of a few percent. Thus, only conduction This is subject to the mixed boundary conditions of conservation
currents are computed. While each human tissue is represented of total current
solely by its conductivity, capacitances between the body parts
and ground are incorporated via the waveform of the applied (4)
ESD current pulse. Effects due to contact capacitance and non-
at any surface point(s) with local outward normal through
linear effects of the skin [9] on the total impedance are not di-
which external applied current enters the body, or the
rectly incorporated in the modeling.
condition
Complete dosimetry data are obtained for several tissues of
interest, namely bone marrow, heart, muscle, and fat. For these (5)
tissues, the electric-field magnitude is given in the time domain.
The waveforms are illustrated and the summary data, such as at any grounded surface points. Thus, for each fixed frequency,
the averages in various body parts and tissues, and the 99th per- the problem is essentially one of harmonic contact currents [4].
centile electric fields (i.e., the values not exceeded in 99% of the The SPFD method assigns potentials at the nodes, and elec-
volume of the tissue), are given. The results for ESD are com- tric-field vectors at the edge centers. The second-order partial
pared to the fields in tissue reported for contact currents [4]. differential equation (3) governing the scalar potential leads to
The selection of tissues of interest is based on the possible in- a seven-point computational star and consequently a heptadiag-
teraction mechanisms, namely the hypothesized leukemia link onal matrix representing the underlying mixed boundary-value
to strong electric fields in bone marrow [3], and the established problem. Solution is efficiently obtained using the conjugate
interaction with excitable tissue, namely heart, muscle and fat gradient method, as explained in [4].
(where peripheral nerves are located). The brain is not explic- The human body model used in the present modeling is the
itly considered, as the associated electric fields due to ESD in- same as in [4], and is illustrated therein (see also Fig. 5). It con-
volving limb-to-limb paths are very low. sists of approximately cubic voxels. Each voxel is ho-
The data presented have several limitations. The waveforms mogeneous (of constant conductivity), with 3.6-mm edges. Ap-
and numerical results are limited to a single representative pulse, proximately 80 tissues and organs are segmented in the whole
as defined and shown in Fig. 1. As discussed by numerous au- body. The body is grounded via the soles of both feet. At each
thors ([5]–[9]), various factors can change the shape of the pulse frequency, the ESD event is modeled as a contact current en-
1462 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 8, AUGUST 2004

tering the palm of the right hand via an electrode representing a

single voxel facet (i.e., via four nodes at the vertices of a square
with 3.6-mm edges).

B. Model of Low-Frequency ESD Pulse

The SPFD is a frequency-domain method, and tissue con-
ductivity is frequency-dependent. Hence, the ESD pulse is rep-
resented by its spectral components obtained from the Fourier
transform (FT), using the convention

(6)

After computation of the fields in tissues on a suitable subset

of spectral sample points, the inverse FT is used to synthesize
the corresponding time-domain response. This process is carried
out for each Cartesian component of the electric field and cur- Fig. 2. Conductivity of muscle (solid lines) from 10 Hz to 40 MHz. The
rent density spectra, and the field magnitudes are subsequently crosses represent the spectral sample points used.
computed in the time domain.
The model for the low-frequency part of an ESD pulse is . Fig. 2 shows, as an example, conductivity of muscle
based on the CENELEC ESD standard described by Angeli tissue with the crosses depicting the chosen frequency sample
and Cardelli [8]. The full-spectrum pulse is indicated in Fig. 1 points. The need to properly subsample the conductivity curves
(top) as the solid line with the 7.5-A discharge peak. This pulse partially dictated the choice (7) of frequency sample points. The
may be viewed as the sum of two Gaussians in the time do- conductivity values are based on those of Gabriel et al., [13],
main, one narrow and the other broad. Thus, the spectral con- [14], but with several adjustments. For example, conductivi-
tent may also be considered as a sum of two Gaussians. The ties of some (e.g., cortical and cancellous bone and infiltrated
Filon–Trapezoidal method [11] is well suited for nonuniformly and noninfiltrated bone marrow) tissues were averaged, with
spaced sample points and is used for the numerical spectral anal- weights chosen to fit values previously used in modeling 60-Hz
ysis. This rule is outlined in the Appendix. The narrow time-do- interactions [15]. In addition, the recent data reported by Raicu
main discharge pulse obtained with this method has the expected et al. for wet skin were used [16]. Representative conductivity
high frequency content (in excess of 500 MHz). A portion of this values are given in Table I.
full spectrum is illustrated in Fig. 1 (middle). The low ampli-
tude at higher frequencies, and the main spectral content having C. ESD at 60 Hz
a much narrower bandwidth are clearly visible. The lower fre- The low-frequency pulse was band-limited to 40 MHz
quency portion of the spectrum is associated with the broader and had a corresponding width of the order of 100 ns. For ESDs
part of the time-domain pulse. A corresponding filtered pulse in a 60-Hz harmonic field, this single pulse is repeated at 120 Hz
spectrum (real and imaginary parts), band-limited to 40 MHz with alternating polarity, at intervals of 8.33 ms. For a bipolar
by use of a Hanning–Blackman [12] window, is shown in Fig. 1 ESD pulse of period
(bottom). Only the positive half of the spectrum is shown, since
the real part is even and the imaginary part is odd. The Fourier (8)
inverse of a high-resolution pair of these curves yields the model
low-frequency ESD pulse shown as the solid line with circles in its Fourier series representation is
Fig. 1 (top). The band-limited spectrum pulse is sampled at 42
points evenly spaced in logarithm over two separate bands, i.e., (9)
(7)
where
where the terms in braces have the form .
The crosses and circles superimposed on the spectral curves in (10)
Fig. 1 (bottom) indicate these sample points. To verify this ap-
proach, the low-resolution set of points was inverted, to get the
Since the original single-pulse duration is measured in nanosec-
pulse represented by the circles in Fig. 1 (top). Finally, the model
onds, corresponding sampling frequencies are in gigahertz.
pulse was normalized to a peak amplitude of 1 A, for ease of
Defining the frequency-sampling interval as
scaling to other desired peak values.
As mentioned earlier, the wide frequency range necessitated
consideration of the frequency dependence of the conductivity (11)
DAWSON et al.: ELECTRIC FIELDS IN THE HUMAN BODY DUE TO ESDs 1463

TABLE I
TISSUE CONDUCTIVITIES (S/m) AT REPRESENTATIVE FREQUENCIES

it can be noted that for 60 Hz,

MHz. This leads to an extremely fine sampling
of the single-pulse spectrum. For the pulse band-limited to
40 MHz, approximately Fourier coefficients
are needed. Clearly, this is an unwieldy numerical problem.
However, it is easily seen from (6)–(9) that the Fourier series
representation is simply an (extremely good) approximation to
the Fourier integral for a single pulse. Hence, 60-Hz bipolar
ESD can be considered as a series of independent events
repeated with a frequency of 60 Hz.

III. RESULTS AND DISCUSSIONS

A. Typical ESD Waveforms in Tissue
Typical electric field and current density pulses are presented
in Fig. 3. The data are for the distal right arm (where the pulse
enters the body). The four panels each contain waveforms in the
fat, muscle, and bone marrow. They depict the average [Fig. 3(a)
and (c)] and 99th percentile [Fig. 3(b) and (d)] traces (taken over
all voxels in the indicated region and tissue) for the electric field
[Fig. 3(a) and (b)] and current density [Fig. 3(c) and (d)]. The Fig. 3. Time-domain fields in fat (dotted), bone marrow (dashed), and muscle
(solid) in the lower right arm (the ESD contact is via a right hand): (a) lower-
99th percentile data here are defined as the pulse(s) whose am- arm average electric field; (b) 99th percentile electric field; (c) average current
plitude is exceeded in 1% of the voxels of the tissue and region density; and (d) 99th percentile current density. These curves are for a 1-A
under consideration. This measure is used as an effective max- temporal peak ESD current pulse.
imum to minimize the staircasing overestimates inherent in a
voxel-based model [17]. Since the modeling represents the body to a few megahertz), the effects of the conductivity of the human
conductivity as a frequency-domain filter, an appropriate time body as a low-pass filter, and the limitation in the asymp-
shift was also introduced to produce a causal output [12]. Also, totic decay of the pulse spectrum in the Filon–Trapezoidal DFT
to obtain the data in Fig. 3, an asymmetrical Hanning–Blackman algorithm [see (15) in the Appendix].
window was applied to the raw data from the inverse FT. This Muscle conductivity is the highest (ranging from 0.27–
procedure removed artifacts resulting from the quasistatic ap- 0.67 Sm over the 40-MHz bandwidth). Fat has the lowest con-
proximation up to 40 MHz (which is valid in the strict sense only ductivity (0.040–0.064 Sm ), while bone marrow (0.049–0.082
1464 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 8, AUGUST 2004

Fig. 4. Average (solid) and 99th percentile (dashed) electric fields in fat in the
distal limbs: (a) right arm; (b) left arm; (c) right leg; and (d) left leg. Note that
the side lobes in (b) are a result of numerical round-off error in the solution, as Fig. 5. Cross-sectional average electric-field amplitudes in the right arm and
the fields in the lower left arm are negligible. both legs as a function of height above the soles of the feet. The data are for
tissue conductivities at a single frequency, namely 10 kHz.

Sm ) has a similar but slightly higher value. Thus, the current

density in muscle [Fig. 3(c) and (d)] has the highest values for current event [4], and the fields in Fig. 5 correspond to a 1-A
both the average and 99th percentile measures. Bone marrow contact current. The maximum is 18.7 (4.3) kVm in the arm
and fat have significantly lower, but similar average values. The (legs). Results at other frequencies would be similar, but with
reversed ordering in the average and 99th percentile current the field levels decreasing with frequency as the tissue conduc-
densities in these tissues is dictated by their distribution relative tivities increase. The results in Fig. 5 are for tissue conductivities
to the ESD contact patch. Similarly, fat has the highest electric at 10 kHz.
fields [Fig. 3(a) and (b)], while muscle has the lowest average
electric field [Fig. 3(a)]. The 99th percentile electric-field B. Quantitative Dosimetry Measures
measure [Fig. 3(b)] shows the bone marrow and fat rankings Table II presents an overview of dosimetry for the electric
reversed from expectations, again due to the tissue spatial field and current density. The first two columns indicate the
distribution. The waveform in all cases closely resembles that body region and tissue. The limb nomenclature used here con-
of the applied pulse. A slight broadening of the pulses in tissue sists of three-digit abbreviations taken from the pattern
occurs due to the increase of conductivity with frequency (the
tissue acting as a low-pass filter with a low Q).
(12)
To indicate the current flow through the body, Fig. 4 depicts
the 99th percentile and average electric fields in fat in the distal
arms [Fig. 4(a) and (b)] and legs [Fig. 4(c) and (d)]. Note that For example, the character sequence “LUR” denotes Leg,
the electric-field peaks values are measured in kVm for the Upper, Right. Data are also reported for certain organs in the
right arm (ESD contact) and both legs (paths to ground), but whole body (brain and spinal cord) and in the torso (fat, heart,
in mVm in the left arm, which does form part of the main and muscle).
current path. The electric fields in the lower legs are similar in To characterize pulses over whole organs in various body
amplitude [Fig. 4(c) and (d)], with the 99th percentile electric regions, several measures are used. These measures are deter-
field slightly higher in the lower left leg [Fig. 4(d)]. mined after the pulse is time shifted to start at zero and the long
To further illustrate the field distribution in the body, Fig. 5 tail is filtered by an asymmetric Hanning–Blackman window,
shows the layer-averaged electric-field amplitudes at a single as outlined in Section III-A. Fig. 6 illustrates the definitions
frequency in the lower right arm and both legs (the averages for a single voxel pulse. With denoting either of or , the
in the legs separately were found to be almost identical). The quantity denotes the temporal maximum of the pulse in a
traces are superimposed on a surface view of the body model. particular voxel. In addition, various fractions of the maximum
The current entry point on the palm is clearly visible, as are the and the associated pulse widths at values of interest are shown.
effects of current spreading into the fingers. Elevated values at Thus, , for example, denotes the field level at 71% (as an
the wrist, elbow, knees and ankles are consistent with the higher rms estimate) of maximum, i.e., % . The associ-
impedance of these regions [9]. Fields within the torso are low ated pulse temporal width at that amplitude is denoted by .
due to the associated low impedance [9]. It may be noted that Finally, the area under the pulse over this time interval is de-
at a single frequency, the modeling is essentially of a contact noted as . Having defined single voxel measures, body-part
DAWSON et al.: ELECTRIC FIELDS IN THE HUMAN BODY DUE TO ESDs 1465

TABLE II
GLOBAL MEASURES OF PULSES OVER ALL VOXELS OF THE INDICATED TISSUES AND REGIONS. THE ESD PULSE IS NORMALIZED TO 1 A PEAK IN TIME

99th percentile electric field. Columns 6–8 of Table II present

the analogous data for the current density. All values are
normalized to a 1-A peak ESD pulse. As might be expected,
the highest electric fields occur in the right arm, with 99th
percentile values ranging from 2.8 to 25 kVm in the tissues
of the lower portion, to 0.38 to 1.7 kVm in those of the upper
portion. High field values also occur in fat in the lower legs
(1.6 and 1.9 kVm ) and torso (1.1 kVm ). As expected, the
lowest fields occur in the lower left arm. The brain also has low
(3.3 Vm ) electric-field values.
Field values in the upper right arm and the heart are of the
order of tens of volts per meter. The remaining tissues and re-
gions reported in Table II generally experience values of the
order of hundreds of volts per meter. Average electric fields
(Table II, column 3) are lower, and only in the lower right arm
fat does the average peak field exceed one kVm . Average
values in the remaining tissues forming the main current path
Fig. 6. Various parameters used to characterize a single voxel electric field or
current density pulse.
(upper right arm, torso, legs) range from 36.8 Vm (heart) to
342 Vm (lower left leg fat). The numbers in Table II would be
multiplied by a factor of four for the low-frequency ESD pulse
data are based on volumetric analyses using the individual voxel of Fig. 1.
data. In particular, the volume average (“Avg”) and maximum Table III contains several measures of the electric field, based
(“Max”) are reported. They are computed over all voxels of the on data taken at 71% of the temporal peak value within each
particular tissue and body region. voxel. Spatial statistics are computed over the whole organ and
Columns 3–5 of Table II report the average region, as explained above.
and maximum values of the maximum electric The columns headed and give
field, as well as the maximum value of the the spatial average and maximum pulse width at 71% of the
1466 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 8, AUGUST 2004

TABLE III
MEASURES OF ELECTRIC FIELD PULSES TAKEN AT 71% OF THE MAXIMUM VALUE, FOR A 1-A PEAK ESD PULSE

TABLE IV
MEASURES OF CURRENT DENSITY PULSES TAKEN AT 71% OF THE MAXIMUM VALUE, FOR A 1 A PEAK ESD PULSE

temporal peak. The next pair of columns gives the average Two general observations apply to these dosimetric measures
and maximum field values at for the electric fields and current density in tissue resulting from
these levels. The final pair of columns gives the area under ESD. First, very high field and current density occur in some
the pulses at the 71%-of-maximum level for the average field locations where excitable cells are located, namely in subcuta-
and maximum field . Table IV neous fat where peripheral nerves are located, and in muscle.
presents the analogous data for the current density pulses. All Also, bone marrow fields and current densities are high. Second,
values correspond to a 1-A peak ESD pulse. It can be noted that the duration over which the tissue experiences these strong
the time-integrals of the current density pulses have the units of fields is short ( ns) compared to the duration of typical
a surface charge density, i.e., nC/m . The pulse duration at the cell time constants (e.g., 0.1–3 ms for excitable cells [9]).
71%-of-peak level is about to 45 to 50 ns for the electric fields,
and slightly shorter for the current density. C. Comparison With Contact Current Dosimetry
Table V contains similar data to those in Table IV, but taken A previous numerical investigation into the effects of 60-Hz
at 50% of the per-voxel peak. This table reports the average and contact currents considered adult and child human models,
maximum electric-field pulse widths and values in columns 3–6. with a particular emphasis on bone marrow electric fields [4].
The final two columns report the time-integral of the current One scenario involved contact current flowing from the left
density pulse. The pulse duration at the 50%-of-maximum level hand to ground through both feet. This scenario is similar
is about 65–75 ns. to the ESD model, (except for the surface area and arm of
DAWSON et al.: ELECTRIC FIELDS IN THE HUMAN BODY DUE TO ESDs 1467

TABLE V
MEASURES OF ELECTRIC FIELD AND CURRENT DENSITY PULSES TAKEN AT 50% OF THE MAXIMUM VALUE FOR A 1-A PEAK ESD PULSE

TABLE VI to those due to contact currents, when the ESD values are
ELECTRIC FIELDS IN BONE MARROW PRODUCED BY 60-Hz CONTACT normalized (reduced) according to their short duration.
CURRENTS AND ESD. THE FIELDS, DUE TO CONTACT CURRENT, ARE 99TH
PERCENTILE VALUES FOR 0.1 mA. THE ESD VALUES ARE THE AVERAGE AND
99TH PERCENTILE PER PULSE AT 71% PEAK IN COLUMNS 3 AND 4, WHILE
COLUMNS 5 AND 6 CONTAIN THE AVERAGES OF THE ESD PULSES OVER IV. CONCLUSION
A 120-Hz (BIPOLAR) REPETITION RATE. THE ESD VALUES CORRESPOND
TO THE 4-A PEAK LEVEL SHOWN IN Fig. 1(d) Typical ESD through a human body has peak currents of the
order of a few to several tens of amperes and a relatively short
duration of the order of 100 ns. Most of the ESD pulse energy is
contained at frequencies below 40 MHz. At these low frequen-
cies, quasistatic approximation can be used to evaluate the elec-
tric fields in human tissue. Numerical evaluation of the electric
field and current density from ESD has been performed for a het-
erogeneous model of the human body. The computations have
used the FT to obtain the spectrum of the ESD part, which is
the band-limited to 40 MHz. Thus, the frequency-domain SPFD
code and inverse FT permitted computation of the fields in var-
ious tissues.
Waveforms computed in selected tissues indicate that ESD
contact). Table VI gives a comparison of electric fields in produces the highest fields in the lower part of the arm when
bone marrow between ESD and contact currents. The second ESD occurs via a small area of the hand. The computations in-
column contains the temporal rms 99th percentile fields in dicate electric fields of about 25-kV/m and 100-ns duration in
the contact arm and the right leg bone marrow. The con- subcutaneous fat, where peripheral nerves may be stimulated.
tact current level is set at 0.1 mA for easy normalization to Also relatively high fields occur in muscle and bone marrow.
other levels. The resulting electric fields range from about Electric fields in the heart and spinal cord are lower (of the order
30–460 mV/m. The table also contains the ESD time-averaged of hundreds of volts per meter), and in the brain are very low.
electric fields over the 71%-of-maximum levels. Specifically, Electric fields in human tissue from ESD are much higher
the values given are (column 3) and than those associated with other environmental or occupational
(column 4) from Table III. The final exposures, such as contact currents, or electric and magnetic
two columns give the time average values for a 120-Hz bipolar fields at power line frequencies (50 or 60 Hz). However, the ESD
repetition rate. All data in this table correspond to the 4-A level fields are of very short duration. In the case of repetitive ESD
of the low-frequency ESD pulse model in Fig. 1. events, which may occur in power-line environments(mostly in
Contact currents vary considerably in residential settings. occupational settings), time-averaged fields are comparable to
Typical imperceptible currents are of the order of tens of those resulting from contact currents.
microamperes [4]. However, up to between 0.5 and 5 mA are Biological significance of the computed tissue electric fields
the limits recommended in safety standards [4], [18]. Contact needs to be evaluated. Interactions such as stimulation of ex-
currents up to about 1 mA may occur also under high voltage citable tissue are an obvious phenomenon that may be expected.
transmission lines (in 10 kV/m) [4]. Thus, the electric fields in Possible effects on cells can be evaluated by applying the elec-
bone marrow produced by 60-Hz ESD currents are comparable tric-field waveforms in a tissue into its cells.
1468 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 8, AUGUST 2004

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(16)
T. W. Dawson (M’95–SM’98), deceased, photograph and biography not avail-
able at the time of publication.
where .

ACKNOWLEDGMENT
M. A. Stuchly (M’71–SM’76–F’91), photograph and biography not available
This paper is dedicated to the Memory of Dr. Trevor Dawson, at the time of publication.
who passed away suddenly in December 2003. The authors
thank Dr. K. Caputa, from the University of Victoria, and
Dr. M. Okoniewski, from University of Calgary, for helpful
discussions related to signal processing. R. Kavet, photograph and biography not available at the time of publication.

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