Answer to Question #5693 Submitted to "Ask the Experts"

I am working on an experiment to determine if radiation exposure affects our material. I need to determine the radiation dose for comparison purposes. Ultimately I would like to see the answer in mrems, but gray or rad would also be okay.

Estimations are okay. Also, I would like the calculation formula that can be used for future studies.

Available information:
70 kVp
8 mA
three-second exposure time (constant)
<1 cm distance from lens
0.5 g mass exposed (suspended in air)

Given the small mass of material (0.5 g) that you specify, and assuming a more or less spherical sample geometry and a relatively low atomic number for the sample material (for example similar to soft tissue or water), for estimative purposes we can neglect x-ray attenuation in the sample, in which case the air kerma can be converted to soft tissue kerma in units of mrads, rads (or centigray), milligray, or gray and, assuming a condition of secondary charged particle equilibrium (SCPE), the latter can be converted to dose equivalent rate in appropriate units—for example, mrem, rem, millisievert, or sievert. The conversion is done by simply multiplying the tissue kerma, assumed to be the same as tissue absorbed dose under SCPE, by the quality factor for x rays, which is taken as unity.

The output rate of the machine is best determined by making appropriate measurements with an appropriate instrument such as a calibrated ionization chamber. I am assuming that this technique is not available to you. The air kerma rate delivered by the x-ray machine depends, among other things, on the operating voltage of the machine, the current, the amount and type of filtration in the machine, the distance from the target focal spot to the sample being irradiated, and whether the machine is a single-phase or three-phase unit. You provide the values of kilovoltage and current but the other quantities are not specified.

I will assume that the machine has enough filtration to provide a half-value layer for the beam of about 2.5 mm aluminum, typical for diagnostic machines operating at the quoted voltage. The approximate output air kerma rate in the beam at 30 cm from the focal spot is 0.069 centigray (cGy equal to one rad) per milliamp (mA) per second for a three phase machine and 0.041 cGy per mA per second for a single phase machine. These values have been taken from NCRP Report No. 102 (National Council on Radiation Protection and Measurements, Medical X-Ray, Electron Beam and Gamma-Ray Protection for Energies up to 50 MeV).

For a machine current of 8 mA, the air kerma rate for a three-phase machine would then be (0.069 cGy/mA-s)(8 mA) = 0.552 cGy/second at 30 cm, and for a three-second exposure the air kerma would be (0.552 cGy/s)(3 s) = 1.656 cGy at 30 cm. You give a "distance from lens" of 1 cm. I assume the "lens" represents the x-ray window.

The specific distance from the target focal spot depends on the particular tube design characteristics, which you can likely obtain from the manufacturer (alternatively it is possible to determine the position of the focal spot by making a series of measurements at varying distances from the tube window and, by a graphical means, interpret the position of the focal spot by assuming an inverse square relationship between machine output rate and distance from the focal spot).

For our present purposes I will assume that the distance from the focal spot to the sample dose point is 7.0 cm. Then, by application of the inverse square law, the air kerma at 7 cm would be obtained from the 30 cm value as (1.656 cGy)(30 cm/7 cm)² = 30.4 cGy. This air kerma may be converted to soft tissue kerma by multiplying by the ratio of the mass energy absorption coefficient for the x rays in soft tissue compared to air. At the x-ray energies of interest here this ratio has a value close to unity, and we shall assume the same value for soft-tissue kerma as for air kerma. Since the quality factor for the x rays is also unity we can then convert the 30.4 cGy to 30.4 cSv, which is equal to 304 mSv or 30.4 rem (30,400 mrem). You will have to make adjustments to the calculation based on the information specific to your machine.

I hope this is helpful to you.

George Chabot, PhD, CHP