Monte Carlo calculations of the dose backscatter factor for monoenergetic electrons

Recently, there has been growing interest in beta emitters for therapeutic uses, especially in connection with so-called endovascular (or intravascular) brachytherapy. Since accurate dose estimation is necessary for the success of such applications, some problems in beta-ray dosimetry need further study. Among these problems, we have investigated the effect of electron backscattering on dose, which has significance not only for accurate dose estimation but also for new source design. In this study, an empirical measure of electron backscattering, known as the dose backscatter factor, was calculated using EGS4 Monte Carlo calculations for monoenergetic electrons and various scattering materials. Electron energies were 0.1, 0.5, 1.0, 2.0 and 3.0 MeV in combination with Al (Z = 13), Ti (Z = 22), Sr (Z = 38), Ag (Z = 47) and Pt (Z = 78) scatterers. The dose backscatter factor ranged from 10% to 60%, depending on electron energy and material, and was found to increase with the atomic number Z by a log(Z + 1) relationship. A method is presented for calculating the beta-ray dose backscatter factors using the results of this study. To demonstrate the efficacy of this method, a dose backscatter factor depth profile for 32P near a water/aluminium interface was calculated and these calculated results were found to generally reproduce the depth profile obtained from direct EGS4 calculations using the 32P spectrum. The data presented in this study can be used to calculate dose backscatter factors for any combination of beta emitter/scatterer whose atomic number ranges from 13 to 78.