
Radiofrequency Radiation Dosimetry Handbook
(Fourth Edition)

Chapter 9. Dosimetry In The VeryLowFrequency And
MediumFrequency Ranges
In the frequency range from 10 kHz to 3 MHz, which
includes the very lowfrequency (VLF) and mediumfrequency
(MF) bands, other dosimetric data may be more important than
the SARs given in Chapters 6 and 8. Exposure fields (even
relatively intense ones) at the low frequencies produce
relatively inconsequential amounts of absorbed energy but may
cause electric shocks and RF burns. Since the shocks and
burns are more directly related to current density and total
current, these quantities are probably more useful dosimetric
data than SARs in the VLFMF ranges.
Dosimetry in the VLFMF bands thus consists primarily of
relating current densities in the exposed bodies to the
exposure fields. Important factors in this relationship are
the presence of nearby objects, especially conducting objects
such as automobiles, and the exposed person's contact with
the objects. The impedance between the exposed person and
ground is useful in relating the current densities to the
exposure field. This section contains information about
methods of calculating and measuring impedances and current
densities, and summaries of such data. Most of the
information was obtained from work reported under USAFSAM
contracts with Guy and Chou (1982) and Gandhi and Chatterjee
(1982).
Most objects of interest are small compared to a
wavelength in the VLFMF ranges, so quasistatic analyses are
useful for obtaining dosimetric information. In the
quasistatic approximation, the calculated results at one
frequency are directly applicable to all frequencies for
which the approximation is valid. Fortunately this includes
the 60Hz range, where a great deal of theoretical and
experimental dosimetry has been done. All of these 60Hz
results can be applied to the VLFMF bands. The basic reason
is explained by Kaune and Gillis (1981), among many others.
They showed, from the quasistatic approximation to Maxwell's
equations, that the field internal to a living subject is
very small compared to the external field, which means that
the perturbed external field and the induced surfacecharge
density are independent of the permittivity of the body tissues. The
induced surface charge causes internal currents that depend
directly on the electrical properties of the body tissue, but
the total conduction current passing through any section of
the body is independent of the tissue characteristics (Kaune
and Gillis, 1981; Deno, 1977). This also means that the total
induced volume charge in the body is negligible compared to
the total induced surface charge. The induced current in the
body is directly proportional to frequency.
Several approaches have been used to calculate induced
currents and energy absorption, but experimental measurements
have proved to be more accurate. The methods described here
consist of calculating currents, current densities, potential
distributions, resistances, and local and average SARs from
measured impedances and fields. The only polarization
considered here is the one that causes the greatest
absorption; as indicated in Chapters 6 and 8, that is the
polarization in which E is parallel to the long
dimension of the body.
9.1.1. Calculation of Current
In the quasistatic approximation, the total charge, q,
on an object close to ground is given by
(Equation 9.1)
where E is the Efield magnitude in the
absence of the object, h is the effective height of the
object, and is the capacitance between the object and
ground. The current, induced on the object by E
when the object is shortcircuited to ground is given by
(Equation 9.2)
where corresponds to the time derivative in
the sinusoidal steadystate case, and is the radian
frequency of E. Writing as
(Equation 9.3)
where S is an effective surface area and is
the permittivity of free space,and combining Equations 9.1,
9.2, and 9.3 gives for the magnitude of ,
(Equation 9.4)
An approximate value for S may be obtained from
the geometrical relation shown in Figure 9.1. Using this
calculated value for S gives
(Equation 9.5)
where h is the height in meters, E is the
Efield magnitude in kilovolts per meter, f is the frequency
in kilohertz, and is in milliamperes.
Deno (1977) measured the shortcircuit current and the
distribution of current at 60 Hz in a metallized mannequin
consisting of insulated material covered with copper foil.
Breaks in the copper foil were used to measure current
distribution. By measuring shortcircuit currents near
powerful VLFMF transmitting stations, Guy and Chou (1982)
showed that the determination of currents at 60 Hz is
applicable to the VLFMF band.
Gandhi and Chatterjee (1982) used a Norton's equivalent
circuit to represent the body and from it calculated the
total current in the human body to be
(Equation 9.6)
where is leakage resistance of the body to
ground, and and are equivalent body resistance and
capacitance respectively. Combining Equations 9.6 and 9.4
gives the current in a person exposed to an electric field,
E.
Figure 9.1.
Relationship between effective area and
shortcircuit current () for exposed human figure (Guy
and Chou, 1982).
9.1.2. Measurement of Body Potential and
Dimensions
In baboons the equipotential planes occur perpendicular
to the long axis of the body when the incident Efield
is parallel to the long axis (Frazier et al. , 1978; Bridges
and Frazier, 1979), so the potential distribution inside the
body can be predicted from the surface potential. While
applying a harmless lowlevel VLF current through volunteers'
bodies, Guy and Chou (1982) measured the surface potential
distribution. They measured the circumference and maximum
dimensions of the subject's body and limbs as a function of
position every 5 cm from the feet to the head, and then
assumed an elliptical cross section to determine the crosssectional area. The
sum of the volumes of those elliptical cylinders was compared
to the body volume to check the accuracy of the measurements.
The body volume was calculated from body weight by assuming a
specific gravity of 1.06.
9.1.3. Calculation of Body Resistance and SAR
From the information obtained in the body potential
measurements described above, Guy and Chou (1982) calculated
the electrical conductivity and the resistance per unit
length for various regions of the body. The resistance
between two equipotential planes perpendicular to the axis of
the body or body member is given by
(Equation 9.7)
where is the measured potential difference,
I is the applied current, is the incremental distance, and
R(i) is the resistance per unit length of the length. The
conductivity of a particular region of the body is related to
R(i) by
(Equation 9.8)
where A(i) is the crosssectional area of the
ith section. Combining Equations 9.8 and 9.7 and solving for
gives
(Equation 9.9)
where is the effective conductivity in the
region between the equipotential planes where V_{nm} is
measured. Once a has been determined, the potential
distribution [V(k)], the current density [J(i)], and the
local SAR [SAR(i)] may be obtained for any known current
distribution [I(i)] from the following equations:
(Equation 9.10)
J(i)=I(i)/A(i) (Equaiton 9.11)
(Equation 9.12)
where is the density of the tissue (usually
assumed to be equal to unity). Regional and wholebody power
absorption can be found from
(Equation 9.13)
9.2. CALCULATED AND MEASURED DATA
Figures 9.29.4 show Guy and Chou's (1982) plots of
Deno's measured distributions of surface currents on
copperfoilcovered mannequins. In the data shown in Figures
9.2 and 9.3, Deno had not measured the current distribution
in the arm but reported it as 14% of the shortcircuit
current. Guy and Chou assumed a cosine distribution for their
plots. In Figure 9.2, the maximum current occurs at the feet,
with a value given by Equation 9.5. From Figure 9.3, the
maximum current for a man exposed in free space is given
by
(Equation 9.14)
(same units as Equation 9.5), and from Figure
9.4, with feet insulated but a hand grounded, by
(Equation 9.15)
Figure 9.2.
Relative surfacecurrent distribution in
grounded man exposed to VLFMF fields [after Deno, 1977 (Guy
and Chou, 1982)].
Figure 9.3.
Relative surfacecurrent distribution in man
exposed in free space to VLFMF electric fields [after Deno,
1977 (Guy and Chou, 1982)].
Figure 9.4.
Relative surfacecurrent distribution in man
exposed to VLFMF electric fields with feet insulated and
hand grounded [after Deno, 1977 (Guy and Chou, 1982)].
Tables 9.1 and 9.2 summarize, respectively, the effects
of currents on humans and some values specified in safety
standards. Table 9.3 gives currents in various parts of the
body, based on 60Hz work by Kaune (1980). Table 9.4 gives
shortcircuit currents for various objects exposed to VLFMF
fields, based on 60Hz work. Tables 9.59.7 show data
measured in VLFMF fields. The plot of these data in Figure
9.5 compares very well with values calculated from Equation
9.5
Table 9.1.
Summary Of ElectricCurrent Effects On Humans (Guy and Chou, 1982)
Table 9.2.
Maximum 60Hz Currents Allowed To Human Body By National Electrical Code (mA) And Equivalent Levels At Other Frequencies (Guy and Chou, 1982)
Table 9.3.
Current And Current Density In Man Exposed To VLFMF [f(kHz)] 1kV/m Electric Fields (based on Kaune, 1980)
(Guy and Ghou, 1982)
Table 9.4.
ShortCircuit Currents For Objects Exposed To VLFMF [f(kHz)] 1kV/m Electric Fields (Guy and Chou, 1982)
Table 9.5.
Comparison Of Measured And Theoretical
ShortCircuit Body Current For Man Exposed To VLFMF Electric Fields With Feet Grounded (Guy and Chou, 1982)
Table 9.6.
Measured Body Currents [mA/(kv/m)] To Ground For Subjects Exposed Under Different Conditions To 24.8kHz VLF Electric Fields [Washington VLF (Guy and Chou, 1982)]
Table 9.7.
Comparison Of Measured And Theoretical
PersonToVehicleCurrent Resulting From VLFMF ElectricField Exposure (Guy and Chou, 1982)
Figure 9.5.
Comparison of theoretical and measured
shortcircuit body current of grounded man exposed to VLFIAF
electric field that is parallel to body axis (Guy and Chou,1982).
Figures 9.69.8 show results by Gandhi and Chatterjee
(1982) of human body resistance, threshold perception and
letgo currents and corresponding unperturbed incident
Efields that would produce these threshold currents for
various conditions. Perception current is defined as the
smallest current at which a person feels a tingling or
pricking sensation due to nerve stimulation. Letgo current
is defined as the maximum current at which a human is still
capable of releasing an energized conductor using muscles
directly stimulated by that current. Tables 9.89.10 show
values of threshold perception measured with an experimental
setup like the one illustrated in Figure 9.9. Either a
copperdisk or a brassrod electrode was used in the
measurements. Table 9.11 gives calculated values of currents
through the wrist and finger for a maximum SAR of 8 W/kg.
Table 9.12 shows the body dimensions calculated by Guy
and Chou for one person. Figures 9.109.17 show their
calculated current distributions for the current
distributions of Figures 9.29.4. The data in Figures
9.109.17 are for exposure of a subject with feet
electrically grounded, in free space, with feet insulated but
hands grounded, and with feet grounded but one hand
contacting a large object such as a vehicle. To calculate
values of current, current density, and potential in a
subject contacting one of the specific objects in Table 9.4,
multiply the values in Figures 9.109.17 by the shortcircuit
object currents in Table 9.4. Calculations for objects not
given in Table 9.4 can be made by looking up methods for
calculating the effective surface area, S, in the literature
(for example, Deno, 1977; TransmissionLine Reference Book,
1979) using Equation 9.5 to calculate , and proceeding as
described above.
Figure 9.6.
Average values of the human body resistance,
R_{h}, (see Equation 9.6) assumed for the range 10 kHz to 20 MHz
(Gandhi and Chatterjee, 1982).
Figure 9.7.
Perception and letgo currents for finger
contact for a 50th percentile human as a function of
frequency assumed for the calculations (Gandhi and
Chatterjee, 1982). [These were obtained as a composite of the
experimental data of Dalziel and Mansfield (1950), Dalziel
and Lee (1969), and Rogers (1981).]
Figure 9.8.
Unperturbed incident Efield
required to create threshold perception and letgo currents in a human for conductive
finger contact with various metallic objects, as a function of frequency (Gandhi and
Chatterjee, 1982)
Table 9.8.
Threshold Currents For Perception When In Contact With The CopperPlate Electrode And Threshold Incident Electric Fields For Perception When In
Contact With Various Metal Objects (Gandhi et al., 1984)
Table 9.9.
Statistical Analysis Of Measured Data On
Threshold Currents For Perception With Subjects Barefoot And With The Wristband (Gandhi et al., 1984)
Table 9.10.
Threshold Currents For Perception When In Grasping Contact With The BrassRod Electrode And Threshold External Electric Fields For Perception When In Contact With A Compact Car (Cg = 800 pF) (Gandhi et al., 1984)
Figure 9.9.
Experimental arrangement for measuring
threshold currents for perception and letgo (Gandhi and Chatterjee,
1982).
Table 9.11.
Currents Through The Wrist And Finger For Maximum SAR = 8 W/kg. (Crosssectional areas are for nonbony regions of respective parts of the body.) (Gandhi et al., 1984)
Table 9.12.
Dimensions Of Body Used For VLFMF Exposure Model (Guy and Chou, 1982)
Figure 9.10.
Calculated current distributions as a function of a position in man exposed to 1kV/m VLFMF
fields with feet grounded (Guy and Chou, 1982)
Figure 9.11.
Calculated current density flowing through one arm. The exposure is the same as that of Figure 9.10 (Guy and Chou, 1982).
Figure 9.12.
Calculated current distribution as a function of position in
man exposed to 1kv/m VLFMF fields in free space (Guy and Chou, 1982).
Figure 9.13.
Calculated current density flowing through one arm. The exposure condition is the same as
for Figure 9.12 (Guy and Chou, 1982).
Figure 9.14.
Calculated current distribution as a function of position in
man exposed to 1kv/m VLFMF fields with feet insulated but hands grounded (Guy and Chou, 1982).
Figure 9.15.
Calculated current density flowing through one arm. The exposure condition is the same as
for Figure 9.14 (Guy and Chou, 1982).
Figure 9.16.
Calculated current distribution as a function of position in man with hand contacting a large object and with feet grounded. A 1mA current is assumed to floating throughb the arm, thorax, and legs of the subject to the ground, F=60 Hz (Guy and Chou, 1982).
Figure 9.17.
Calculated current density flowing through one arm. The exposure condition is the same as for Figure 9.16 (Guy and Chou, 1982).
Table 9.13 gives regional and average SARs for various
exposure conditions. Figure 9.18 shows measured values of the
imaginary component of the permittivity (Tables 9.14 and
9.15; see Section 3.2.6 for the relationships of
permittivity, conductivity, and loss factor) along with
values of the real and imaginary components given in the
first edition of this handbook. Figures 9.19 and 9.20 show
average SARs of Table 9.13 compared with theoretical values.
Further power absorption calculations are given in Table
9.16.
Figure 9.21 shows the maximum electricfield strength
below levels of 1000 V/m that would violate any of the
following conditions:
 The maximum current through any body member contacting
ground or an object should not exceed levels equivalent to
those allowed by the National Electric Safety Code in the
frequency range where shock hazards may occur.
 Total possible current entering the body should not
exceed 200 mA, for prevention of RF burns.
 The 0.4W/kg average and 8W/kg maximum SAR
recommended by the ANSI C95.11982 Standard shall not be
exceeded.
According to the calculated data of Guy and Chou (1982),
none of the conditions would be violated for exposure of
persons isolated in free space at Efield strengths of 1 kV/m
or below. Other conditions are shown in Figure 9.21.
Table 9.13.
Distribution Of Power Absorption (Watts)In Man Exposed To VLFMF Fields: 1kV/m Exposure, EField
Parallel Long Axis, 1mACurrent Assumed For Contact With Object (Guy and Chou, 1982)
Figure 9.18.
Real part, ', and imaginary part,",
of the dielectric constant for highwatercontent tissue. The
dashed line is measured values (Guy and Chou, 1982) The
other lines are values given in the first edition of this
handbook
Table 9.14.
Average Apparent Conductivity Of Man Based On WholeBody In Vivo Measurements(S/m) (Guy and Chou, 1982)
Table 9.15.
Average Apparent Loss Factor Of Man Based On WholeBody In Vivo Measurements (Guy and Chou, 1982)
Figure 9.19.
Comparison of calculated average SAR
(obtained from VLF analysis) with average SAR (reported in
the first edition of this handbook) of average absorbed power
in an ellipsoidal model of an average man (Guy and Chou,
1982).
Figure 9.20.
Comparison of theoretical and experimentally
measured wholebody average SAR for realistic man models
exposed at various frequencies. The experimental curve is
measured results in scaled humanshaped models at simulated
VLF frequencies (Guy and Chou, 1982).
Table 9.16.
Distribution Of Power Absorption (Watts) In Man, With Feet Grounded, Exposed To 1kV/m VLFMF Fields While In Contact With Vehicle (Guy and Chou, 1982)
Figure 9.21.
Required restrictions of VLFMF
electricfield strength to prevent biological hazards related to shock, RF
burns, and SAR exceeding ANSI C95.1 criteria (Guy and Chou,
1982).
Go to Chapter 10.
Return to Table of Contents.
Last modified: June 14, 1997
© October 1986, USAF School of Aerospace Medicine,
Aerospace Medical Division (AFSC), Brooks Air Force Base,
TX 782355301