Multiple-site fast exchange model for spin-lattice relaxation in the Fricke-gelatin dosimeter

The ferrous sulfate-doped gel dosimeters have been developed for three-dimensional magnetic resonance imaging of radiation dose distributions. When the gel dosimeter is irradiated, ferrous ions are converted to ferric ions and the nuclear magnetic spin relaxation of the dosimeter varies with dose. In this paper, a model is presented for the dose dependence of the spin-lattice relaxation rate R1 of the ferrous sulfate doped-gelatin dosimeter. The model is based on three basic physical quantities: the ferric ion yield and the ferrous and ferric ion relaxivities, r2+ and r3+, respectively. These relaxivities specify the ability of the ions to enhance the spin-lattice relaxation of water protons. The effects of gelatin and sulfuric acid concentration on the ferric ion yield and ion relaxivities are presented. The measured r2+ values agree with those predicted by a model in which the measured spin relaxation is considered the result of the fast exchange of water hydrating the ferrous ion with water in the bulk. The r3+ values are lower than predicted by the fast exchange model. The discrepancies in the measured and predicted r3+ values are shown to result from the complexing of ferric ions arising from pH variation caused by changes in gelatin or sulfuric acid concentrations. A modified version of the R1-dose response model accounting for ferric ion complexing is presented and tested spectrophotometrically.