Mathematical Modeling of Depth‐Dose Response of Polymer‐Gel Dosimeters

Abstract

A dynamic PDE model is developed to simulate the effects of radiation depth doses on polymer formation in polyacrylamide gel dosimeters. Depth doses are simulated using different types of radiation including Co60 γ and 6 and 15 MV X‐ray photon beams, along with 6, 9, 12, 16 and 20 MeV electron beams. Effects of monomer diffusion (edge enhancement) and temperature are studied. Diffusion results in excess polymer formation at the position of maximum dose (2.6% for Co60 γ‐radiation and less for other types of radiation studied). Temperature increases on the order of 2 °C increase the mass of polymer formed by ≈1.25%. The influence of dose‐rate dependence was also investigated. Results of this work provide insight for developing effective calibration curves using depth‐dose information.magnified image

Mathematical Modeling of the Response of Polymer Gel Dosimeters to HDR and LDR Brachytherapy Radiation

“…Previous partial differential equation (PDE) models, developed by Fuxman et al from our research group26, 27, 29 are extended and reformulated to account for brachytherapy irradiation instead of radiation by an external beam. The original models were expressed in Cartesian coordinates using the spatial variable x , whereas the current model uses the radial coordinate r to indicate the distance from the center of the radioactive seed (Figure 5).…”

“…Concentration data from the literature were not used for parameter estimation because of the lack of detailed information about storage conditions (such as the temperature and oxygen levels) that influence the monomer concentrations and polymerization rate 50–54. A complete list of all model parameters and their values is provided in a recent article by Chain et al29 who verified that the model can predict the qualitative trends in these monomer consumption data using the current parameter values. Note that there is considerable uncertainty in some of these parameter values.…”

“…The complete system of 31 PDEs was solved using the VLUGR2 solver in FORTRAN 55. Note that this PDE model could also be solved using the pdepe subroutine in Matlab, but simulation times are prohibitively long 29. The PDEs were solved to predict the mass and type of polymer formed as well as the temperature distribution as a function of time and radial distance from the brachytherapy seed.…”

“…Mathematical models have been developed to describe PAG dosimeters under spatially uniform19, 26 and non‐uniform27–29 radiation conditions. These models help gel dosimetry researchers to better understand the influence of chemical and physical phenomena that occur in PAG dosimeters during and after irradiation.…”

“…These models help gel dosimetry researchers to better understand the influence of chemical and physical phenomena that occur in PAG dosimeters during and after irradiation. The models have been used to simulate edge enhancement and temporal instability problems,27 as well as oxygen inhibition19 and the response of PAG dosimeters to radiation depth dose profiles 29…”