
Radiofrequency Radiation Dosimetry Handbook
(Fourth Edition)

Chapter 2. How To Use Dosimetric Data
In This Handbook
The material in this section is intended to help the
reader interpret and use the quantitative dosimetric
information contained in this handbook. Readers not familiar
with some of the concepts or terms used in this chapter may
wish to read Chapter 3 (background and qualitative
information about dosimetry) in conjunction with this
material.
Although the dosimetry data are given in terms of SAR,
the internal Efield can be obtained directly from the SAR by
solving for the internal Efield from Equation 3.49 (Section
3.3.6):
(Equation 2.1 )
For a given frequency, the internal fields in irradiated
objects are a strong function of the size of the object (see
Chapters 6 and 8). In extrapolating results obtained from an
experimental animal of one size to an animal of another size
or from an experimental animal to a man, it is often
important to determine what incident fields would produce the
same (or approximately the same) internal fields in these
differentsize animals. For example, a person studying
biological effects in rats irradiated at 2450 MHz may want to
relate those to effects expected to occur in humans exposed
to the same radiation. Since the rat and man are very
different in size, exposing them to the same incident fields
would result in quite different internal fields. Therefore,
if their internal fields are to be similar, the incident
fields irradiating each must be different. We have two
general ways to adjust the incident fields to get similar
internal fields:
 Change the power density of the incident radiation.
 Change the frequency of the incident radiation.
The first might be called power extrapolation; the
second, frequency extrapolation. Under either condition, the internalfield
patterns in the two cases would differ even if the average
SARs were the same. The internal distributions can be made
similar in a very approximate sense, however, by relating the
wavelength of the incident radiation to the length of the
object.
When biological effects are due to heat generated by the
radiation, combined power and frequency extrapolation is
probably the better course; it makes the average SARs nearly
the same and results in a similar distribution of internal fields, which depends strongly on the
relationship of absorber size to wavelength. For studying
effects that might be strongly frequency dependent, such as a
molecular resonance of some kind, frequency extrapolation
would not be appropriate.
The following examples will illustrate both kinds of
extrapolation and generally how the dosimetric data in this
handbook might be used.
EXAMPLE 1
Suppose that in a study of RFinduced biological effects
a 320g rat is being exposed to Epolarized RF radiation at
2450 MHz with an incidentpower density of 20 mW/cm ^{2}.
The researcher desires to know what exposure conditions would
cause approximately the same average SAR and internalfield
distribution in an average man that the 20 mW/cm^{2} at
2450 MHz produces in the rat. Since the physiological
characteristics of rats differ significantly in many respects
from those of people, any interpretation of the rat's
biological responses in terms of possible human responses
must be made with great care. By this example we are not
implying that any such interpretation would be at all
meaningful; that must be left to the judgment of the
researcher for a particular experiment. On the other hand,
knowing exposure conditions that would produce similar
average SARs and internalfield distributions in rats and
people is desirable for many experiments. The following
information is provided for such cases.
First, because the rat is much smaller than a man, at
2450 MHz their internal field patterns will differ
considerably. One indication of this difference can be
obtained from Equation 3.46 (Section 3.3.4). The skin depth
() at 2450 MHz is about 2 cm. From Tables 5.2 and 5.4,
the values of the semiminor axis (b) for prolate spheroidal
models of an average man and a 320g rat are 13.8 and 2.76 cm
respectively; thus the ratio /b for an average man is
0.14; for the rat, 0.72. These ratios indicate that any RF
heating would be like surface heating for the man but more
like wholebody heating for the rat. Consequently, comparing RF effects in humans and
smaller animals may not be meaningful at 2450 MHz. Comparison
might be more meaningful at a lower frequency, where the
internal field patterns in the man and the rat would be more
similar. A simple way to choose an approximate frequency for
human exposure is to make /2a, the ratio of the
freespace wavelength to length, the same for both the man
and the rat. This approximation neglects the change in
permittivity with frequency, which is acceptable for these
approximate calculations. (more precise methods that include
the dependence of permittivity are described in Section
7.2.6.) Since = c/f (Equation 3.29, Section 3.2.8),
requiring 2af to be the same for the rat and the man would be
equivalent. Thus, we can calculate the frequency for the
human exposure to be:
(Equation 2.2)
(Equation 2.3)
where subscripts h and r stand for human and rat
respectively. This result shows that we should choose a
frequency in the range 200400 MHz for human exposure to
compare with the rat exposure at 2450 MHz. Permittivity
changes with frequency, so the /2a ratio does not
correspond to the /b ratio; however, since both ratios
are approximations and the /2a ratio is easier to calculate,
it seems just as well to use it. Another point regarding
frequency extrapolation is that meaningful comparisons can
probably be made when the frequency for both absorbers is
below resonance; but if the frequency for one absorber is far
above resonance and the frequency for the other absorber is
below resonance, comparisons of SAR will not be
meaningful.
Now that we have completed the frequency extrapolation,
we can calculate the incidentpower density required at 280
MHz to provide the same average SAR in an average man that is
produced in a 320g rat at 2450 MHz with 20mW/cm^{2} incidentpower density. The average SAR in the rat for 1mw/cm^{2} incidentpower density is 0.22 W/kg (Figure 6.16); thus the average SAR in the rat for 20mw/cm^{2} incidentpower density is 4.4 W/kg. The average SAR in the average man at 280 MHz is 0.041 W/kg for 1 mW/cm^{2} (Figure 6.3); thus to produce an average SAR of 4.4 W/kg in the average man would require an incidentpower density of (4.4/0.041)(1 mW/cm^{2}), or 107 mW/cm^{2}).
Our frequency extrapolation resulted in similar relative
positions with respect to resonance on the SAR curves for the
rat and the man. Yet because the SAR curve for the rat is
generally higher than that for man, equivalent exposure of
man requires considerably higher incidentpower density. The
generally higher level of the SAR curve in the rat is due to
the combination of size and variation of permittivity with
frequency.
EXAMPLE 2
An average man is exposed to an electromagnetic planewave
with a power density of 10 mW/cm^{2} at 70 MHz with E
polarization. What radiation frequency would produce the same
average SAR in a small rat as was produced in the man?
Here, as in the previous example, comparing SARs may be
meaningful only at frequencies for which the /2a ratios
are similar. From the relation developed in the last example,
we find that
(Equation 2.4 )
Since 70 MHz is approximately the resonant frequency for
man (Figure 6.3) and 875 MHz is close to the resonant
frequency (900 MHz) for the small rat (Figure 6.15), let's
use 900 MHz for the rat. At 70 MHz the average SAR for the
average man exposed to 10 mW/cm^{2} is 2.4 W/kg (Figure
6.3). For the small rat, the average SAR for 1 mW/cm2
at 900 MHz is 1.1 W/kg. Hence at 900 MHz, the incident power
density for the rat should be (2.4/1.1)(1 mW/cm^{2} ), or
2. 18 mW/cm^{2}.
EXAMPLE 3
A 420g rat (22.5 cm long) is irradiated with an incident
planewave power density of 25 mW/cm ^{2} at a frequency
of 400 MHz with E polarization. What incident planewave power
density and frequency would be expected to produce a similar
internalfield distribution and average SAR in an average
man?
Again, frequency extrapolation should be used because 400
MHz is above resonance for the man and below resonance for
the rat. The approximate equivalent exposure frequency for
man is
(Equation 2.5)
Since a curve for a 420g rat is not included in the
dosimetric data, we will calculate the average SAR for the
rat by using the empirical formula given in Equation 5.1. The
first step is to calculate b for the rat. Since 2a = 22.5 cm
and the volume of the rat is 420 cm^{3} (assuming a
density of 1 g/cm^{3}), we can solve for b from the
relation for the volume of a prolate spheroid:
(Equation 2.6)
(Equation 2.7)
Now, substituting a=0.1125 m and b = 0.0299 m into
Equations 5.2 through 5.6 gives us
f_{o} = 567 MHz
f_{o1} = 860 MHz
f_{o2} = 1579 MHz
A_{1}= 717
A_{2}= 1226
Since f_{ol }and
f_{o2} are both larger than 400 MHz, we need not calculate A_{3}, A_{4}, and A_{5} because
u (f  f_{ol} ) = u(f  f_{o2} ) = 0. Substituting into Equation 5.1 results in SAR = 0.44 W/kg for the rat exposed to 1
mW/cm^{2}at 400 MHz. The average SAR for the rat exposed to 25 mW/cm^{2} at 400 MHz is 11.0 W/kg. For the average man at 51 MHz for 1mW/cm^{2} incidentpower
density, the average SAR is 0.11 W/kg (Figure 6.3); hence, to
produce 11 W/kg in the man would require 11/0.11
mW/cm^{2}, or 100 mW/cm^{2}
EXAMPLE 4
With E polarization, what incidentpower density at
resonance would produce in a small rat an average SAR equal
to twice the resting metabolic rate? Compare this with the
incidentpower density at resonance that would produce in an
average man an average SAR equal to twice the resting
metabolic rate.
For a small rat the resting metabolic rate is
8.51 W/kg (Table 10.4), and the average SAR at resonance is
1.1 W/kg for 1mW/cm^{2} incidentpower density (Figure
6.15). The incidentpower density to produce an average SAR
of 2 x 8.51 W/kg is therefore 17.02/1.1 mW per cm^{2}, or 15.5
mW/cm^{2}. For an average man the resting metabolic rate is 1.26
W/kg (Table 10.2), and the average SAR at resonance is 0.24
W/kg for 1mW/cm ^{2} incidentpower density (Figure
6.3). The incidentpower density required to produce an
average SAR equal to twice the resting metabolic rate is
therefore 2.52/0.24 mW per cm^{2}, or 10.5 mW/cm^{2}.
Even though the resting metabolic rate for the rat is nearly
7 times larger than that for the man, the incidentpower
density required for the rat is only 1.5 times that required
for the man because the average SAR for the rat is higher
than for the man. In general, since smaller animals have
higher metabolic rates and also higher values of average SAR
at resonance, the ratio of resting metabolic rate to average
SAR at resonance probably does not vary by more than an order
of magnitude for most animal sizes.
EXAMPLE 5
Suppose that experiments were conducted in which a 200g
rat (16 cm long) was irradiated with an incident planewave
power density of 10 W/cm^{2} at a frequency of 2375
MHz, with experimental conditions similar to those of
Shandala et al. (1977). Since the incident E and H field vectors were parallel to a horizontal plane in which the rat was free to move, the rat was irradiated with a random combination of E and H
polarizations. What incidentpower density would produce a
similar average SAR and internalfield distribution in an
average man at 70 MHz, for E polarization?
Even though the internalfield pattern may be quite
different in the man at 70 MHz than in the rat at 2375 MHz,
let's calculate the incidentpower density required to
produce the same average SAR in man at 70 MHz, since that is
the resonant frequency. Dosimetric data are not given for a
200g rat and the empirical relation is given only for E
polarization, so we will interpolate between the values for a
110 and 320g rat. From Figures 6.15 and 6.16, we find the
following values of average SAR for an incidentpower density
at 1 mw/cm^{2}:
  E
  H

110g rat   0.36 W/kg   0.25 W/kg 
320g rat   0.225 W/kg   0.185 W/kg 
By assuming that the SAR varies approximately linearly
with weight and by using linear interpolation for E
polarization in a 200g rat, we get
(Equation 2.8)
and for H polarization,
(Equation 2.9)
Averaging these two values to account for the random polarization gives us 0.26 W/kg for the rat for 1mW/cm^{2} incidentpower density, and 0.0026 W/kg for 10 W/cm2 incidentpower density. The average SAR for an average man irradiated at 70 MHz with 1 mW/cm^{2} is
0.24 W/kg (Figure 6.3); hence the incident power density required to produce an average SAR of 0.0026 W/kg in the man is 0.0026/0.24 mW/cm^{2} , or 11 W/cm^{2}.
Go to Chapter 3.1.
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Last modified: November 12, 1996
© October 1986, USAF School of Aerospace Medicine, Aerospace Medical Division (AFSC), Brooks Air Force Base, TX 782355301