Model-based evaluation of point-source approximation error for extended radionuclide sources in nuclear medicine

Accurate estimation of external radiation exposure is essential in nuclear medicine (NM) for occupational safety and regulatory compliance. Point-source models are widely used because they are simple and require limited input data; however, their accuracy can degrade when radioactive material is distributed over extended line, surface, or volume geometries. This study evaluates point-source approximation error across a range of extended-source models, beginning with non-attenuating line and disc geometries and extending to attenuating finite-thickness slab and laterally viewed cylindrical volume sources. Absolute dose-rate examples were calculated using a Tc-99 m gamma constant, while relative error and correction-factor results were expressed using geometry- and attenuation-dependent parameters. For non-attenuating line and disc sources, point-source approximations can overestimate exposure by up to approximately 100% when source dimensions exceed the exposure distance. A practical threshold was identified: when the source dimension-to-distance ratio is less than one, point-source errors remain below 5%; above a ratio of 1, line or disc models should be considered or the point-source estimate corrected using the factors provided. For attenuating finite-thickness slab sources, an analytical correction factor was derived that separates into a lateral-extent term governed by the source diameter-to-distance ratio, and an attenuation-thickness term governed by. Together, these two dimensionless parameters allow point-source error to be mapped across combinations of source size, distance, attenuation coefficient and slab thickness. For laterally viewed cylindrical sources, kernel-based volume integration showed that point-source error depended jointly on,and, whereis the surface-to-point distance. The 20% error region narrowed markedly as, indicating that patient-scale attenuating cylinders cannot be assessed from distance alone. Representative Tc-99 m examples showed modest error for a 5 ml syringe-scale cylinder at 1 m, but substantial overestimation for a patient-torso-scale cylinder. Comparison with published measured patient dose-rate studies showed that the patient-torso cylindrical model produced values of a similar order of magnitude to measured 1 m patient dose rates, whereas point-source estimates were generally higher. This paper provides practical correction factors, error-threshold maps and model-selection guidance to support more appropriate selection of source models in NM exposure assessments.