Mathematical modelling of response of polymer gel dosimeters to brachytherapy radiation

A dynamic partial differential equation (PDE) model is used to simulate effects of a single Ir192 brachytherapy seed on the amount and composition of polymer formed during polyacrylamide gel (PAG) dosimetry. Simulations are conducted for a point-source brachytherapy seed placed at the center of a 6%T 50% C anoxic PAG phantom. The seed is removed after one minute, but polymerization is simulated up to a final time of 24 hours. Simulation results indicate that changes occur in both the mass of polymer formed per unit dose and in the crosslink density as a function of the radial distance from the brachytherapy seed. For example, at a distance of 5 mm from the seed, 41 mg of polymer form per Gy of radiation absorbed (after 24 hours), whereas at a larger distance of 5 cm from the seed 75 mg of polymer form per Gy. The polymer that forms near the seed is predicted to have a higher level of crosslinking than the polymer that forms further away. These results suggest potential calibration problems that may occur during brachytherapy dosimetry using polymer gels.