Answer to Question #3132 Submitted to "Ask the Experts"

After discussions with several medical physicists and a review of some of the better-noted physics references listed below (Bureau of Rad Health 1970; Johns and Cunningham 1983), I believe that the theoretical derivation for the radiation exposure from an x-ray machine does not exist. The basis for this statement is outlined below.

When accelerated electrons produced in the x-ray tube interact with the target, there are four typical interactions (electron scattering, electron capture, characteristic x-ray production, and bremsstralung production), of which three produce x rays or photons. In order to determine radiation exposure, one would first have to determine the number or intensity of x rays produced. This is possible using first principles and assuming that the target is "thin," that is, no electron suffers more than one collision on average when passing through the target. Since the typical target is "thick," the calculation would assume that the target is then made up of a number of thin targets and the spectra of x-ray energies for each individual thin target calculation could be superimposed on one another to give a theoretical spectrum of x-ray intensities.

The problem is that this calculation is for an unfiltered x-ray beam. It does not take into account beam filtration from the x-ray tube housing and any other inherent or added filtration that the beam passes through. When these factors are considered, a kV specific curve of photon intensities can be generated that starts at zero intensity for some maximum kVp value, rises to a maximum, and finally drops off due to the attenuation of the filtering materials.

These energy output curves may vary from one x-ray tube to the next due to variations in any of the parameters listed above, or from other factors such as the absorption of the produced radiation within the target itself and the complexity of the path in the thick target of each individual electron. X-ray production will also vary over time due to wear on the anode or target. As the anode is bombarded by electrons, over time the target it will become pitted and can harden and crack. All these factors will result in less x-ray production. Since x-ray production will vary over time, it would be extremely difficult to calculate the actual output for the same x-ray tube without knowing the exact conversion efficiency of input electrons to output x-rays at any given time.

From a practical standpoint, the intensity of the x-ray emissions is related to the following parameters: (1) Intensity is directly proportional to the atomic number (Z) of the target, (2) Intensity is directly proportional to current (mA), (3) Intensity is directly proportional to the voltage to the power of 2 to 3, and (4) Beam quality or hardness will increase with added filtration in the beam.

Fortunately, there are measured outputs for x-ray production using the parameters listed in the previous paragraph. One such source for this information is the Radiological Health Handbook (Bureau of Rad Health 1970), pages 158-160, which provides tables for average mR/mAs at 12 inches for various kVp settings and filtration for dental and nondental x-ray tubes. Also, two graphs indicate exposure as mR/mAs versus focal spot distance for various kVp settings, and mR/mAs versus filtration for various kVp settings.

Ken "Duke" Lovins, CHP

Bureau of Radiological Health, US Dept. of Health, Education and Welfare, Radiological Health Handbook, Revised Edition, US Government Printing Office, Washington, DC; 1970.

Johns HE, Cunningham JR. The physics of radiology. 4th ed. Springfield, IL: Charles C. Thomas; 1983.

Editor's Note: An additional source for x-ray equipment output can be found in the National Council of Radiation Protection and Measurements Report 102, "Medical X-Ray, Electron Beam and Gamma-Ray Protection for Energies Up to 50 MeV (Equipment Design, Performance and Use)," 1989.