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Radiofrequency Radiation
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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:(Equation 2.1 )
(Equation 2.2)
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(Equation 2.3)
(Equation 2.4 )
(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
E | H | |||
110-g rat | 0.36 W/kg | 0.25 W/kg | ||
320-g 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 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.
Last modified: November 12, 1996
© October 1986, USAF School of Aerospace Medicine, Aerospace Medical Division (AFSC), Brooks Air Force Base, TX 78235-5301