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 E-field can be obtained directly from the SAR by solving for the internal E-field 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 different-size 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:
  1. Change the power density of the incident radiation.
  2. Change the frequency of the incident radiation.
The first might be called power extrapolation; the second, frequency extrapolation. Under either condition, the internal-field 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 RF-induced biological effects a 320-g rat is being exposed to E-polarized RF radiation at 2450 MHz with an incident-power density of 20 mW/cm 2. The researcher desires to know what exposure conditions would cause approximately the same average SAR and internal-field distribution in an average man that the 20 mW/cm2 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 internal-field 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 320-g 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 whole-body 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 free-space 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 200-400 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 incident-power density required at 280 MHz to provide the same average SAR in an average man that is produced in a 320-g rat at 2450 MHz with 20-mW/cm2 incident-power density. The average SAR in the rat for 1-mw/cm2 incident-power density is 0.22 W/kg (Figure 6.16); thus the average SAR in the rat for 20-mw/cm2 incident-power density is 4.4 W/kg. The average SAR in the average man at 280 MHz is 0.041 W/kg for 1 mW/cm2 (Figure 6.3); thus to produce an average SAR of 4.4 W/kg in the average man would require an incident-power density of (4.4/0.041)(1 mW/cm2), or 107 mW/cm2).
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 incident-power 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/cm2 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/cm2 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/cm2 ), or 2. 18 mW/cm2.

EXAMPLE 3

A 420-g 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 internal-field 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 420-g 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 cm3 (assuming a density of 1 g/cm3), 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

fo = 567 MHz

fo1 = 860 MHz

fo2 = 1579 MHz

A1= 717

A2= 1226

Since fol and fo2 are both larger than 400 MHz, we need not calculate A3, A4, and A5 because
u (f - fol ) = u(f - fo2 ) = 0. Substituting into Equation 5.1 results in SAR = 0.44 W/kg for the rat exposed to 1 mW/cm2at 400 MHz. The average SAR for the rat exposed to 25 mW/cm2 at 400 MHz is 11.0 W/kg. For the average man at 51 MHz for 1-mW/cm2 incident-power 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/cm2, or 100 mW/cm2

EXAMPLE 4

With E polarization, what incident-power density at resonance would produce in a small rat an average SAR equal to twice the resting metabolic rate? Compare this with the incident-power 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 1-mW/cm2 incident-power density (Figure 6.15). The incident-power density to produce an average SAR of 2 x 8.51 W/kg is therefore 17.02/1.1 mW per cm2, or 15.5 mW/cm2. 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 1-mW/cm 2 incident-power density (Figure 6.3). The incident-power density required to produce an average SAR equal to twice the resting metabolic rate is therefore 2.52/0.24 mW per cm2, or 10.5 mW/cm2. Even though the resting metabolic rate for the rat is nearly 7 times larger than that for the man, the incident-power 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 200-g rat (16 cm long) was irradiated with an incident planewave power density of 10 W/cm2 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 incident-power density would produce a similar average SAR and internal-field distribution in an average man at 70 MHz, for E polarization?
Even though the internal-field pattern may be quite different in the man at 70 MHz than in the rat at 2375 MHz, let's calculate the incident-power 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 200-g rat and the empirical relation is given only for E polarization, so we will interpolate between the values for a 110- and 320-g rat. From Figures 6.15 and 6.16, we find the following values of average SAR for an incident-power density at 1 mw/cm2:

E
 H
110-g rat0.36 W/kg0.25 W/kg
320-g rat0.225 W/kg0.185 W/kg

By assuming that the SAR varies approximately linearly with weight and by using linear interpolation for E polarization in a 200-g 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 1-mW/cm2 incident-power density, and 0.0026 W/kg for 10 W/cm2 incident-power density. The average SAR for an average man irradiated at 70 MHz with 1 mW/cm2 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/cm2 , or 11 W/cm2.




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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 78235-5301