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, including non-attenuating line and disc geometries, an attenuating finite-thickness slab approximation and a laterally viewed cylindrical volume source. Absolute dose-rate examples were calculated using a Tc-99m 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. Errors generally remained below 5% when the source dimension-to-distance ratio was less than one. For attenuating finite-thickness slab sources, an analytical correction factor was derived using the source diameter-to-distance ratio D/d and attenuation-thickness product μt. For laterally viewed cylindrical sources, point-source error depended jointly on L/d, D/d and μd. Representative Tc-99m 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 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 for NM exposure assessments.