Mathematical Modeling of PAG‐ and NIPAM‐Based Polymer Gel Dosimeters Contaminated by Oxygen and Inhibitor

Abstract

A mathematical model for crosslinking copolymerization of acrylamide (or NIPAM) and N,N'‐methylenebisacrylamide is extended to account for contamination by oxygen and the inhibitor MEHQ. This model improves basic understanding of interactions among oxygen, MEHQ and polymerization reactions in gel dosimeters that are used to verify radiation doses delivered by cancer treatment equipment. Improved parameter estimates result in a good match between model predictions and data. The model predicts that a larger absorbed dose will be required to overcome the oxygen inhibition with increasing oxygen contamination, in agreement with experimental data. The model also predicts that MEHQ, in the absence of oxygen, has almost no influence on dosimeter response.magnified image

Model for a solid–liquid stirred tank two-phase partitioning bioscrubber for the treatment of BTEX

“…ter estimation in a variety of chemical [11][12][13][14][15][16][17] and biochemical [18][19][20] models. It selects parameters for estimation based on information about uncertainties in each of the initial parameter values, sensitivity of model predictions to the various parameters, and the quantity and quality of the dynamic experimental data.…”

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

“…The calibration curve in Figure 3(b)7 was obtained by uniformly irradiating a set of vials containing the polymer gel using different known doses [Figure 3(a)]. 19 Polymerization in PAG phantoms continues for several hours after irradiation ceases, so the vials are typically scanned 1 day after irradiation to ensure stable R 2 readings 6. Note that the polymer gel phantom in Figure 2 received a non‐uniform radiation dose that physicists delivered using a series of external radiation beams from different directions 18.…”

“… Construction of calibration curves for use in polymer gel dosimetry. (a) Photograph of PAG calibration vials that were uniformly irradiated using different doses ranging from 0 to 40 Gy19 and (b) Calibration curve constructed from magnetic resonance (MR) analysis of a different series of PAG calibration vials produced using the recipe in Table 1,7 used with permission. …”

“…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…”