Absorbed fractions for electrons in ellipsoidal volumes

We applied a Monte Carlo simulation in Geant4 in order to calculate the absorbed fractions for monoenergetic electrons in the energy interval between 10 keV and 2 MeV, uniformly distributed in ellipsoids made from soft tissue. For each volume, we simulated a spherical shape, four oblate and four prolate ellipsoids, and one scalene shape. For each energy and for every geometrical configuration, an analytical relationship between the absorbed fraction and a 'generalized radius' was found, and the dependence of the fit parameters from electron energy is discussed and fitted by proper parametric functions. With the proposed formulation, the absorbed fraction for electrons in the 10-2000 keV energy range can be calculated for all volumes and for every ellipsoidal shape of practical interest. This method can be directly applied to evaluation of the absorbed fraction from the radionuclide emission of monoenergetic electrons, such as Auger or conversion electrons. The average deposited energy per disintegration in the case of extended beta spectra can be evaluated through integration. Two examples of application to a pure beta emitter such as Y-90 and to I-131, whose emission include monoenergetic and beta electrons plus gamma photons, are presented. This approach represent a generalization of our previous studies, allowing a comprehensive treatment of absorbed fractions from electron and photon sources uniformly distributed in ellipsoidal volumes of any ellipticity and volume, in the whole range of practical interest for internal dosimetry in nuclear medicine applications, as well as in radiological protection estimations of doses from an internal contamination.