Calculating the absorbed dose from radioactive patients: the line-source versus point-source model

In calculations of absorbed doses from radioactive patients, the activity distribution in such patients is generally assumed to be an unattenuated point source and the dose to exposed individuals at a given distance is therefore calculated using the inverse square law. In many nuclear medicine patients, the activity distribution is widely dispersed and does not simulate a point source. In these cases, a line-source model is proposed to more accurately reflect this extended activity distribution.

Calculations of dose rate per unit activity were performed for a point source and for line sources of lengths of 20, 50, 70, 100, and 174 cm, and the ratios of line-source values to point-source values were calculated. In addition, radionuclide-independent conversion factors, to convert exposure rate constants to dose rates per unit activity, for these line-source lengths at various distances were determined.

The calculated values, substantiated by published data, indicate that the inverse square law approximation is not valid for a line source until a certain distance is reached, dependent on the length of the line source. For the 20-, 50-, 70-, 100-, and 174-cm line sources, the dose rate values estimated by the inverse square law approximation are within approximately 10% of the values estimated using the line-source approach at distances of 20, 45, 60, 85, and 145 cm, respectively. At closer distances, use of the point-source model for a patient with an extended activity distribution will overestimate the radiation absorbed dose to exposed individuals, sometimes by a very significant amount.

The line-source model is a more realistic and practical approach than the traditional point-source model for determining the dose to individuals exposed to radioactive patients with widespread activity distributions.