A simplified approach to beta dosimetry for small spheres labelled on the surface

We studied source spheres of radii 5 mu m-5 mm, labelled on the surface with beta emitters in order to simulate conditions of radioimmunotherapy for small tumours. We calculated, for different source sizes, the absorbed fraction of emitted energy and the mean dose rate in smaller concentric spherical targets simulating the nuclei of cells. A different approach allowed for calculation of dose rate as a function of the distance from the centre of the radiolabelled source sphere. Calculations were performed for monoenergetic emissions, which were then integrated over the beta spectra of various emitters (¹⁷⁷Lu, ⁶⁷Cu, ¹⁸⁶Re, ¹¹¹Ag, ¹³¹I, ¹⁵³Sm, ⁹⁰Y and ¹⁸⁸Re). For spheres with dimensions that are small compared to the mean particle range, the mean dose rate could be a misleading parameter since there is a large variation in dose rate with the distance to the source. Results agree well with different analytic approaches reported in the literature, but differ from those obtained using a Monte Carlo code. The computing features have been deliberately kept to a low level to allow for a simple introduction into hospital work.