Rheology modifiers in Fricke – gelatin dosimeters

Fricke gel dosimeters, while very sensitive and versatile, continue to suffer from one major issue – the diffusion of the dose signal. To tackle that problem, here we present the use of inert, linear polymers with very high molecular weights as rheology modifiers that can slow the diffusion in weak gels, based on 4% gelatin. At 0.2% loading of polyacrylamide (with mol. wt. 5×106 Da), a moderate, 20% decrease of the diffusion coefficient was achieved. This effect is compared to that of adding a crosslinker, such as glyoxal or increasing the concentration of gelatin by 1%.


Introduction
The development of new ferrous hydrogels dosimeters (Fricke gels) continues to be an active area of research (e.g.[1]) due to their relative ease of preparation, high sensitivity, and versatile applications in the three-dimensional dosimetry of ionizing radiation.Upon irradiation in an acidified aqueous medium, ferrous ions (Fe 2+ ) are oxidized to ferric ions (Fe 3+ ); the resulting dose signal can be read by either magnetic resonance imaging or, in the presence of an appropriate metal indicator, as a color change by optical computed tomography.One unresolved issue with Fricke gels is the tendency of the dose signal to dissipate over time due to the diffusion of the ferric ions in the hydrogel.To counteract this effect a variety of approaches have been proposed, such as the introduction of chelating agents and other ligands [1][2][3], changing the gelling agent [4][5][6], chemical functionalization of the gelling agent [5], and introduction of heterogeneous inclusions [7].Each approach comes with its own set of benefits and drawbacks such as high background signal, lower sensitivity, fast auto-oxidation, etc.What we propose here is to act on the liquid phase of the gel by addition of high molecular weight rheology modifiers -polymers that increase the viscosity of solution at very low concentrations.Similar work has been reported in the past [8], showing that introduction of low molecular weight rheology modifiers such as glycerol and saccharides limits the signal diffusion in Fricke gels.However, the glycerol and saccharides were too reactive and required too high concentrations to be of a practical use.By contrast, herein we demonstrate the use of two nearly inert, linear polymers, poly(ethylene oxide) (PEO) and polyacrylamide (PAM), with a very high molecular weight of ca.5×10 6 Da, and concentrations not higher than 0.2%, tested within a ferrous -methylthymol bluegelatin gel dosimeter, based on our earlier work [9].

Experimental
Gelatin (Gl) (Type A, bovine, 300 Bloom) was obtained from Rousellot (USA), methylthymol blue (MTB) from TCI America (USA); ferrous ammonium sulfate (FAS), ferric ammonium sulfate (F III AS), 2.00N sulfuric acid (SA), 40% glyoxal (Gx), polyacrylamide (PAM) (product no.178042500), and polyethylene oxide (PEO) (product no.A1553636) were obtained from Fisher Scientific (USA).PAM and PEO were dissolved to 1% solutions by dispersion in ice-cold deionized water and mixing at room temperature for a day, gelatin was dissolved with gentle heating, the rest of the chemicals were first dissolved in 100 mM SA immediately prior to their use.The order of addition of the individual components is important: to 2N sulfuric acid was added the PEO or PAM stock solution and mixed thoroughly, followed by addition of acidified solutions of MTB and FAS, and finally Gx, and deionized water.After homogenization of the other components, the gelatin solution, at around 30 °C, was added last.For all formulations, the concentrations of SA, FAS and MTB were kept constant at 35 mM, 0.1 mM and 0.1 mM, respectively.In the preliminary studies, gelatin was used at 4% and in the follow-up studies at 4 and 5%.The concentrations of the additives are given separately in each study.
For dosimetric evaluation, the gels were poured into 4-mL polymethylmethacrylate cuvettes, capped with polypropylene caps.Irradiations were performed on a Co-60 source (Eldorado 6, Atomic Energy of Canada Ltd.) to doses of 2.5, 5.0, and 10.0 Gy.The auto-oxidation was evaluated for 14 days, as unirradiated samples aged in the fridge.Optical readout was performed on a GENESYS 10S spectrophotometer (Thermo Scientific).For preliminary diffusion estimation, individual samples were semi-shielded with a led block and irradiated to 10.0 Gy, but for statistical purposes and to create sharp gradients, for each studied formulation a triplicate of cuvettes were prepared by first pouring into each cuvette 1.5 mL of gel without FAS or MTB, followed by setting at fridge temperature for 1-2 hours, addition of ~2 mL of gel prepared with F III AS instead of FAS, and setting in the fridge for another 2 hours.Once a diffusion gradient was formed by either approach, the gels were brought to room temperature and scanned on a flatbed scanner Expression 12000XL (Epson) every 20 to 30 minutes for 2-4 hours.Image analysis was performed in the red channel using ImageJ ver.1.53n [10], while curve fitting and statistical analysis were done in SigmaPlot ver.11 (SPSS Inc.).The diffusion profiles were fitted to the complementary error function to determine the 'curvature parameters' n (mm 2 ), which were fitted vs time to determine the diffusion coefficients D (mm 2 /h), according to [11], as shown in Figure 1.

Results and discussion
A preliminary set of experiments (data not shown) using 4% gelatin gels revealed that paradoxically at concentrations below 0.1% the presence of either PEO or PAM caused increased diffusivity relative to the control.This effect was most pronounced at PEO, which at 0.05% caused a 40% increase of diffusivity.Above 0.1% the rheology modifiers decreased the diffusivity, more pronounced in the case of PAM which at 0.2% loading caused approximately 20% reduction of the diffusion coefficient.At low concentrations, the additives likely disrupt the native gelatin matrix, increasing the disorder in the system (entropy) and therefore increasing the diffusivity of the ferric complex.At higher polymer concentration, more "free" water is bound to its chain, overcoming the entropic factor, and decreasing the diffusivity.Further, PEO is a polymer with no side groups, while PAM has the relatively bulky Cformylamide side group (-C(=O)NH2) which can form strong hydrogen bonding with the Fe III -MTB chelate, decreasing diffusion on a molecular level.In the follow-up study at 4% gelatin, the following formulations were evaluated: 0 or 0.2% PAM, and 0 or 10 mM Gx, plus 35 mM SA, 0.1 mM FAs and 0.1 mM MTB, against a control with 5% gelatin.
The optical attenuation in the control formulation (4% Gl) is given in Figure 2A, showing a maximum of the dose sensitivity at 620 nm, as can be expected for ferrous-MTB gels.The behavior of the other formulations is similar and only their background attenuation is given here (Figure 2B): all additives increase the background attenuation, but a more careful evaluation of that effect (Figure 2B, insert) shows that the scatter at 620 nm in a gel with 4%Gl and 0.2% PAM is not higher than that a 5%Gl gel at 585 nm -which is typical for ferrous -xylenol orange gel dosimeters.Therefore, the PAM-containing gels likely have acceptable level of optical scatter.
Figure 3 provides a visual representation of properties of the different formulations.Addition of 0.2% PAM provided an approximately 20% decrease in diffusivity, practically identical to the effect of the addition of 10 mM Gx or increasing the gelatin concentration from 4% to 5%; there was no synergistic effect on the diffusion between PAM and Gx.Among the formulations with decreased diffusivity, the background attenuation (optical scatter) was highest in those that contained PAM, as discussed above; however, the auto-oxidation rate is lowest, signifying potentially extended storage period for these gels.Another possible advantage to using PAM or Gx in a 4% gelatin gel is that the resulting gels have relatively low total suspended solids loading, which will likely accelerate the kinetics of the signal-forming reaction and therefore minimize any dose rate effects in the dosimeter, as we have shown in [9].

Conclusions
We have successfully demonstrated the use of very high molecular weight of (5×10 6 Da), generally inert, linear polymers such as poly(ethylene oxide) (PEO) and polyacrylamide (PAM) can be used as rheology modifiers in Fricke gels to slow the diffusion of the ferric ions.A moderate decrease of 20% of the diffusion coefficient was seen in weak, gelatin-based gels.The only drawback of using such polymers appears to be increased optical scatter, which is still manageable.Future work may evaluate the practical applications of these findings in large samples, particularly for small-beam irradiations and prescriptions with variable dose rates.The wider implications of the current study can be found in the rheological modification of other gel dosimeter chemistries, where decreased total suspended solids loading may be warranted.

Figure 1 .
Figure 1.Example calculations of the diffusion coefficient for a 4% gelatin control sample.The image from the flatbed scanner is analyzed in ImageJ (left panel) and analyzed in SigmaPlot (right panel).

Figure 2 .Figure 3 .
Figure 2. Optical attenuation, dose sensitivity and scatter in the studied formulations.