Radiation Field Strengths Near Cylindrical Volume Sources Via Point-source Correction Factors

Due to the ease with which the radiation field strength is determined for a point source, the field strength emanating from radiopharmaceutical therapy patients is sometimes estimated by using the point source approximation with a correction factor. It is inevitable that the correction factor will occasionally be used under conditions that do not precisely match those for which the factor was originally derived. The difficulty is that the boundary of the correction factor's domain of acceptability is usually unclear. The purpose of this paper is to address this issue. The patient is modeled as a cylinder containing the radionuclide administered to the patient. From first principles, the expression for converting the radiation field strength of an unshielded point source to that of the extended cylindrical volume source is derived. This expression is analytically separated into the component depicting geometric dispersion of the source material into the volume and the component depicting self-absorption (absorption characteristics of I in water are used). These components, along with their composite, are presented showing their dependence on patient size, distance from the patient, and various dispersion patterns of the source material within the patient. Correlation of theory and measurement is demonstrated, and a conceptual grasp is conveyed regarding field strength variations around volume sources with changes in shape, size, distance, and other parameters. Using data presented, the radiation field strength emanating from a radiopharmaceutical therapy patient can be estimated from the point source approximation and customized for patient size and presumed internal radionuclide distribution.