Physical mechanism of the Schwarzschild effect in film dosimetry—theoretical model and comparison with experiments

In consideration of the importance of film dosimetry for the dosimetric verification of IMRT treatment plans, the Schwarzschild effect or failure of the reciprocity law, i.e. the reduction of the net optical density under 'protraction' or 'fractionation' conditions at constant dose, has been experimentally studied for Kodak XOMAT-V (Martens et al 2002 Phys. Med. Biol. 47 2221-34) and EDR 2 dosimetry films (Djouguela et al 2005 Phys. Med. Biol. 50 N317-N321). It is known that this effect results from the competition between two solid-state physics reactions involved in the latent-image formation of the AgBr crystals, the aggregation of two Ag atoms freshly formed from Ag(+) ions near radiation-induced occupied electron traps and the spontaneous decomposition of the Ag atoms. In this paper, we are developing a mathematical model of this mechanism which shows that the interplay of the mean lifetime tau of the Ag atoms with the time pattern of the irradiation determines the magnitude of the observed effects of the temporal dose distribution on the net optical density. By comparing this theory with our previous protraction experiments and recent fractionation experiments in which the duration of the pause between fractions was varied, a value of the time constant tau of roughly 10 s at room temperature has been determined for EDR 2. The numerical magnitude of the Schwarzschild effect in dosimetry films under the conditions generally met in radiotherapy amounts to only a few per cent of the net optical density (net OD), so that it can frequently be neglected from the viewpoint of clinical applications. But knowledge of the solid-state physical mechanism and a description in terms of a mathematical model involving a typical time constant of about 10 s are now available to estimate the magnitude of the effect should the necessity arise, i.e. in cases of large fluctuations of the temporal pattern of film exposure.