Absorbed dose to water standard for 192Ir HDR sources using Fricke Dosimetry

The Fricke solution is a chemical dosimeter that is based on the oxidation of ferrous ions to ferric ions in the solution after interaction with ionizing radiation. It is composed of 96 % water (by weight), and its density is thus remarkably similar to that of water. In addition, studies show that the Fricke dosimeter can be used as a primary dosimeter in the determination of the absorbed dose to water for high dose rate (HDR) 192Ir brachytherapy. The Radiological Sciences Laboratory of the University of Rio de Janeiro State (LCR/UERJ) has been investigating the use of the Fricke dosimeter in various applications for more than ten years, particularly in the area of radiotherapy. This review paper presents important improvements in recent years by the LCR/UERJ in the determination of the absorbed dose to water for 192Ir sources. This includes a newly designed irradiation vessel, a new reading device, a description of the need for careful temperature control during irradiation and reading, a more accurate calculation of the correction factors and the results of an intercomparison with the National Calibration Laboratory of Canada. Careful preparation of the Fricke solution is one of the most critical steps in the process. Over the years, the LCR/UERJ has tested different methods of preparing the solution and the final procedure is presented. Regarding the irradiation vessel, a molded double-walled, spherical flask for the Fricke solution was first constructed and used to measure the absorbed dose to water. However, as it was difficult to manipulate the spherical flask, a second design also made with PMMA was molded as a cylinder, with a central tube where the source was centrally positioned. Different methodologies have been reported in the determination of the G-value, a key parameter in Fricke dosimetry, and herein, two different methodologies used by the LCR are reviewed. 1 Laboratório de Ciências Radiológicas, LCR-DCR-UERJ, Rio de Janeiro, Brazil 2 Comissão Nacional de Energia Nuclear, DIAMP/CGMI/CNEN, Rio de Janeiro, Brazil Email: cea71@yahoo.com.br. Revista Investigaciones y Aplicaciones Nucleares, 4, 31-44, 2020 Received: April 15, 2020 Accepted: August 25, 2020 Published online: November 18, 2020 Doi: https://doi.org/10.32685/2590-7468/ invapnuclear.4.2020.565 © de Almeida, C. E., Salata, C. 2020. This work is licensed under a Creative Commons Attribution 4.0 International License REVISTA INVESTIGACIONES Y APLICACIONES NUCLEARES IAN Minenergía Revista Invest igaciones y Apl icaciones Nucleares 32 S er vic io Geológico C olombiano For the absorbed-dose-to-water determination for 192Ir sources, the overall combined uncertainty associated with the measurements is estimated to be less than 1 % for k = 1. Thus, the obtained uncertainties for the determination of the absorbed dose to water using Fricke dosimetry are lower than those obtained using the standard protocols. With respect to clinical practice, this could improve the accuracy in the calculation of the dose delivered to the patients. Overall, the results show that Fricke dosimetry is a reliable system to measure absorbed dose to water as a standard for HDR 192Ir.


Introduction
ricke dosimetry, also called ferrous sulfate dosimetry, has been in use for several decades for different types of radiation beams [1]- [5]. The Fricke solution response depends on the oxidation, by ionizing radiation, of ferrous ions (Fe 2+ ) to ferric ions (Fe 3+ ). The solution contains 96% water (by weight), therefore, its density is close to the density of water. It is used in a dose range of 20-400 Gy and dose rates of up to 10 6 Gy/s [6], exhibiting a good linear response over the range of 5-70 Gy and an accuracy better than 2% for a 2 Gy/min dose rate [7]. The major disadvantages of Fricke dosimetry are its high sensitivity to impurities, and its sensitivity to the presence of oxygen in the solution [5], [8], [9].
For more than 10 years, the Radiological Science Laboratory of the Rio de Janeiro State University (LCR/UERJ) in Brazil has been investigating the use of Fricke dosimetry for different applications [7], [10]- [17]. The applications of Fricke dosimetry to 192 Ir HDR sources are one of the very most recent subjects of study [14], [18].
High-dose-rate brachytherapy (HDR) using 192 Ir is a widely used option for cancer treatment and requires an accurate dosimetry standard. However, a dosimetry standard for the direct measurement of absolute absorbed dose for 192 Ir HDR sources is not yet available. The AAPM TG-43 Report [19], and its update [20], constitute the accepted protocol for dose-to-water determination based on an air kerma strength (S k ) measurement. The dose-to-water conversion is done via the dose rate constant Λ, which converts the air-kerma strength to dose-to-water and uses different correction factors to account for scatter, attenuation, and anisotropy of the dose distribution [20]. Efforts are being made to establish a reliable method with reduced uncertainties for the measurement of the absorbed dose to water, thus improving the clinical treatment of patients.
Several authors have reported different methodologies to determine a standard for absorbed dose to water for 192 Ir sources. Sarfehnia et al. [21] developed the first methodology using a water-based calorimeter with uncertainties lower than 5% (k = 1). Very recently [22] and [23] have reported a reduction in uncertainty to 1.9 % (k = 1). The second was developed by Austerlitz et al. [8] using Fricke dosimetry, with an overall uncertainty of 3.4 % (k = 1) and more recently de Almeida et al. [24], Salata et al. [14] and Malcolm et al. [18], [25] have reported consistent results using Fricke dosimetry as a standard.
This paper presents important improvements in the last years [12], [14], [24] by the LCR/UERJ in the determination of the absorbed dose to water for 192 Ir sources. This includes a newly designed irradiation vessel, a new reading device, a description of the need for careful temperature control during irradiation and reading, a more accurate calculation of the correction factors and the results of an intercomparison with the National Calibration Laboratory-NRC, Canada.

The Fricke system
Careful preparation of the Fricke solution is one of the most important parts of the process. Over the years, LCR/UERJ researchers have tested different methods of preparing the solution, and here the final result procedure is presented. The laboratory glassware is first cleaned with 5% diluted Extran (MERCK-KGaA, Darmstadt, Germany), rinsed at least 10 times, and then filled with sulfuric acid 96%, which remains in the glassware for at least 24 h. After this period, the glassware is rinsed at least 10 times and then dried in an oven. The Fricke solution is prepared using chemicals of high purity. The Fricke solution is prepared in a 1 L volumetric flask. First, 22 ml of sulfuric acid, 98% (MERCK-KGaA, Darmstadt, Germany), is diluted with 250 ml of high purity water (Millipore Milli-Q system). The water-acid mixture is preirradiated with 10 Gy, using a completely self-shielded X-ray irradiator for biological research (RS 2000X, Radsource, CA, USA). This preirradiation step is included in the preparation of the Fricke solution prepare to reduce the influence of trace impurities present in the sulfuric acid, as described by Palm and Mattson [26].  [16]. Daily readings of the optical density (OD) (absorbance), over a period of nine days using recently made solutions had no measurable differences compared to a month-old solution. Hence, a fading correction is not considered.

Irradiation vessel design
Different vessels have been tested over the years by the LCR/ UERJ to be used for the determination of the absorbed dose to water for HDR 192 Ir sources. The device used for the Fricke solution must have the following properties: the material should not react with the solution, or at least this reaction should stabilize over a short period of time; it must be possible to seal the vessel; it should be easy to transfer the solution from the vessel into the cuvette; and the volume of solution contained in the vessel must be sufficient to rinse and fill at least one cuvette. The first vessel developed by the LCR was a double-glass balloon, as shown in figure 1a The Fricke solution was kept between the two balloons and the source was conducted to the center of the vessel using a thin glass tube positioned in the center of the inside balloon. The disadvantages of this vessel were that glass is not water equivalent, it was impossible seal, and the solution was not homogeneously irradiated.
The second vessel designed by the LCR was a spherical PMMA vessel reported by de Almeida et al. [24]. A PMMA tube was fixed at the top of the flask to allow the center of the source inside the catheter to coincide with the geometrical center of the vessel, as shown in figure 1b. The irradiated solution volume was 8.0 cm 3 , which was only sufficient to rinse and fill one cuvette and obtain one reading for each irradiation. The vessel is described in [24]. The main advantages of this vessel were that the density of PMMA is very close to that of water and the solution could be homogeneously irradiated, as the vessel is spherical. Only a ring in the center of this sphere was filled with Fricke solution, and the source was positioned in the center of this ring. The same reaction, which reaches equilibrium after 48 h, was described by Morrison and Boyd [27] for organic esters, possibly due to acid hydrolysis of the ester groups of the PMMA This vessel had the advantage of spherical geometry, but its major disadvantage was the difficulty of inserting the solution into its ring-shape compartment without creating any bubbles, and it was very difficult to vert the solution from the vessel to the cuvette. Thus, an improved PMMA vessel was designed to reduce this disadvantage. It also allows the center of the source inside the catheter to coincide with the geometric center of the ring, which is filled with the Fricke solution, as shown in figure 1c. The irradiated solution volume is 18.4 cm 3 , which is sufficient to rinse and fill at least two cuvettes and obtain two readings for each irradiation.
The complete dimensions of this vessel can be seen at [14].
It is important to highlight that, in this cylindrical vessel, the distance from the center of the source to the center of the ring compartment where the Fricke solution is located during irradiation is 2.7 cm, so a Monte Carlo (MC) factor is required to convert the measurements to the standard reference position of 1 cm from the source in water, according to the TG-43 formalism [20]. This is the main disadvantage of this design.
At present the LCR is testing a new vessel, which is a small version of the cylindrical one, but the distance from the source  relationship, initially described by Fregene [29] and modified by Olszanski et al. [9] is given in (2): where OD i and OD c are the optical densities of the irradiated and control solutions, respectively, T i is the temperature in °C of the Fricke solution during irradiation, and T r is the temperature in °C of the Fricke solution during the spectrophotometer reading. The control solutions were the Fricke solution that remained inside the vessel for the same amount of time as the irradiated solutions without being irradiated. A thermal bath inside the spectrophotometer was used to stabilize the temperature during the readings, at 25 °C [24].
After the measurements with the spherical vessel, the cylindrical vessel was used and the measurements with this vessel were done at the National Research Council Canada (NRC), to compare the standards of absorbed dose to water using Fricke dosimetry at both laboratories, the Radiology Science Laboratory (LCR) and the NRC. It was also possible to investigate any systematic effect in either methodology [14]. The irradiation methodology was almost the same, except that the microSelectron V2 192 Ir source was used for irradiation and an NRC-modified Cary 400 Scan spectrophotometer was used for the readings. This system allows the reading of two cuvettes simultaneously, along with a standard absorbance filter and an empty optical path. The irradiation time was calculated to deliver nominal doses of approximately 14 Gy to the Fricke solution.

Irradiation and measurement procedures
The first irradiations with the 192 Ir source were performed with a spherical vessel. The center of the spherical vessel was filled with water, and the ring-shaped shell was filled with the Fricke solution. The whole flask was placed in the center of the 30 . 30 . 30 cm3 water phantom. The irradiated solutions were inserted and extracted using a small Pyrex graduated pipette and were subsequently transferred to a quartz cuvette. A Nucletron microSelectron irradiator was used with an alpha omega model 192Ir source through the catheter, allowing the source to be positioned in the center of the vessel. The irradiation time was calculated to deliver nominal doses ranging from 14 to 40 Gy. Due to temperature gradients during irradiation, a thermoprobe was used to monitor the temperature in the water phantom, and the irradiation started only after the temperature was stable.
Before each reading the cuvette was rinsed and filled with Milli-Q water and the absorbance was read to ensure that the cuvettes were clean. If the absorbance reading at 304 nm was as great as 0.0362 the cuvettes were considered clean, otherwise they were cleaned again, but using cotton swabs, with acetone and Milli-Q water, until the water reading was less than 0.0362. After that, the absorbances of the irradiated and control solutions were measured. The temperature measured during the irradiation is used to correct the dose-induced change in OD using a reference temperature of 25 °C.
During the spectrophotometer reading the temperature was stabilized at 25 °C due to the use of the thermal probe. This

Fricke solution
As discussed by Klassen et al. [5], the absorbed dose to the Fricke solution, D F , was obtained from equation 3: where ΔOD is defined as the increase in OD at 304 nm taking into account the temperature effect as defined by (1) cm -1 at 304 nm according to Cottens et al. [30]), G(Fe 3+ ) is the radiation chemical yield of ferric ions (equal to 1.555 ± 0.017 x10 -6 mol.J -1 ), which was obtained using the methods discussed in section f).
The quantity absorbed dose to water, D w , is derived from the absorbed dose to the Fricke solution as proposed by Klassen et al. [5] and is defined in (4): where D F is the absorbed dose in the Fricke solution, f is the dose conversion factor from Fricke solution to water, p wall is the PMMA wall correction factor, F h is the homogeneity correction due to the volume-averaging effect as described by Ochoa et al. [12] and k dd is the correction factor due to the nonuniformity of the dose profile over the solution volume.
In addition, in the case of irradiation with the cylindrical vessel, a K pos factor was included in this equation to convert the dose from 2.7 cm to the dose at 1 cm. The correction factors were calculated using the MC method, as described in the next section.

Monte Carlo Simulations
The microSelectron HDR 192 Ir Alpha Omega source was used in the simulations and measurements for the spherical vessel, and the microSelectron V2 was used in the simulations and measurements for the cylindrical vessel. The specifications of the simulations are described at [14], [24].
The Monte Carlo particle-transport simulation code PE-NELOPE [31], was used to assess the data and the required corrections. In all cases, several simulations were conducted with at least three different random number generators, and the mean value was taken. The simulations were performed using a cluster with 192 processors taking the bare spectra, as reported by Borg and Rogers [32].
To validate our calculation results, these values were compared to the Borg and Rogers [32], Ma and Nahum [33] and Ma et al. [34] values, who used similar materials and geometry. In all three cases very comparable results   The obtained value was: The same factors were calculated for the cylindrical vessel, as published in [14], also using the PENELOPE code.
The only different MC factor is K pos , which converts the dose from 2.7 cm to 1 cm. Table 1 shows the calculated MC factors for both vessels.

Determination of the G-value
Three different methodologies were used to determine the G-value [G(Fe 3+ )]. The first consisted of the estimation of the energy-weighted G-value from published values. A curve fitting was performed using the ionometric and calorimetric measurements reported by Fregene [29] and the calorimetric measurements reported by Klassen et al. [5]. It is important to highlight that the values obtained from Fregene [29] were reported in his paper without much experimental detail. A G-value was assigned for every 50 keV of energy in the energy interval from 1 to 900 keV. These values were weighted according to the photon fluence per MeV per 100 decays, as described in [24].
The G-value obtained from this methodology was 1.555 ± 0.017 x10 -6 mol.J -1 , which was the value used for calculations of the absorbed dose to water using the spherical vessel.
This value is comparable to the ionometric measurements data using dosimetry protocols reported by Franco et al.
[11], 1.578 ± 0.016 x10 -6 mol.J -1 . The selection of the mean energy was not a critical issue for the semilog plots used. The energy fluence for water was calculated using Monte Carlo methods by Borg and Rogers [32] and from this work. Figure   2 shows the plotted data from the literature used to calculate the G-value.   [5], the full squares are those reported by Fregene [29], and the full line is all the data fitted in [24]. Source: modified from [24].
In the second method, the G-value was calculated based on the primary products, as described in [24]. The radiation yield of ferric ions in a Fricke solution can be expressed in terms of the radiation yields of the primary products due to radiolysis of the solution. Thus, the G-values were calculated using a fit of the LET values shown in figure 3 for 80 keV and 60 Co, both published by the ICRU 16 [35], and for 137 Cs, published by Meesungnoen et al. [36]. If the data are fitted using a first-order polynomial regression, the estimated LET value for 192 Ir is 1.28 keV. µm -1 , and if they are fitted with a second-order polynomial, the value is 1.237 keV. µm -1 . These values were used in the empirical formalism proposed by Meesungnoen et al. [36] in equation 5, to calculate the G-value in molecules per 100 eV for a given energy x: where the coefficients α i (i = 0-4) are used to express the LET variations for radicals and for radiolysis of aqueous 0.4 M H 2 SO 4 at room temperature.   Since the Fricke solution is 96% water by weight, the primary products produced by the radiation were mostly those of water. This process, though considered approximate, was extensively discussed by Klassen et al. [5], where it was assumed that the G-values for a Fricke solution behave in the same way as those for water.
The G(Fe 3+ ) obtained from the empirical formalism proposed by Meesungnoen et al. [36], based on primary products and LET values, were found to be 15.123 mol/100 eV (1.567 x10 -6 mol.J -1 ) and 15.144 mol/100 eV (1.569 x10 -6 mol.J -1 ) for the first and second-degree fits, respectively. This is rather close (within 1%) to the G-value determined using the published values from the literature.
In the third methodology the G-value determination was based on the NRC method, using polyethylene bags [25]. Effective energy was used for all the X-ray qualities, but for Co-60, the mean energy was used. The error bars represent the Type A uncertainty

Measurements of absorbed dose to water
The results shown in figure 5   The results presented here are consequences of careful improvements in several aspects over 10 years, as follows: Regarding the overall dimension of the irradiating vessel (by increasing the radial distance between the source and the solution, the uncertainty due to mechanical tolerances and the dose gradient across the solution were reduced); » The use of a thermal bath and a calibrated thermistor in the spectrophotometer; » The use of PMMA made the construction of the vessel easier and, as discussed earlier, has no measurable effect on the solutions; » The cylindrical vessel is an improvement from the spherical vessel, making it easier to clean and fill with Fricke solution without creating bubbles. In addition, it allows two measurements for one irradiation, decreasing uncertainties as well.

Traceability to the international network of metrology validation
The results for both the G-value and the absorbed dose to water, using the Fricke dosimetry system of the two institutions, NRC and LCR, were comparable and published [14]. irradiation. The main advantage of the NRC holder is that the D w measurement is already measured at the recommended distance, 1 cm [20], while for the LCR vessel this distance is 2.7 cm, which requires an MC calculated factor to convert this measurement to 1 cm. This comparison was made at the NRC laboratory using an 192 Ir source. The NRC group has established a method to determine the G(Fe 3+ ) for 192 Ir based on an interpolation between G-values obtained at 60 Co and 250 kVp X-rays [18]. This measurement was repeated using the LCR Fricke solution to investigate possible systematic uncertainties. G(Fe 3+ ) for 60 Co and 250 kVp X-rays.
Using the LCR Fricke system, an agreement was found with the NRC values within 0.5% and 1% for 60 Co and 250 kVp X-rays respectively. The standard uncertainty in the determination of G(Fe 3+ ) for 192 Ir was estimated to be 0.6%. For the comparison of absorbed dose measurements at the reference point for 192 Ir (1 cm depth in water, perpendicular to the seed long-axis), the ratio D w (NRC)/D w (LCR) was found to be 1.011 with a combined standard uncertainty of 1.7%.

Uncertainty budget
For the nominal dose of 20 Gy, Table 3 [24] lists all the sources of uncertainties involved in the experimental procedure using Fricke dosimetry to measure absorbed dose to water.
In general, the uncertainties are conservative, corresponding to the upper limits. The uncertainties in all quantities and correction factors in (4) are indicated. As a result, the overall combined uncertainty, as described in detail in Table 3, were significantly reduced to 1.4% for k = 1 compared to those reported earlier by Austerlitz et al. [8] The type B uncertainties for the MC calculations were the most difficult cases to estimate and they are still unclear in several papers [36]- [44]. In a recent work Wulff et al. [42] have specifically treated this issue, taking into account the various contributions related to the systematic uncertainties that also exist in the present work, such as stopping powers, spectrum, photon cross sections and transport parameters.
For this case the geometry sensitivity was also evaluated, and the differences were negligible. Although we have not performed a specific analysis for our geometry, the final value of 0.2% reported by Wulff et al. [42] was adopted here.  The obtained uncertainties for the determination of the absorbed dose to water using the Fricke dosimetry are lower Table 3. Uncertainty budget in the determination of D w using the Fricke solution [24].

Conclusion
Chemical dosimetry using a standard FeSO 4 solution is an interesting and reliable option as a standard for the quantity absorbed dose to water generated by HDR 192 Ir sources.
The overall uncertainties involving the vessel dimensions, wall thicknesses, dose calculation, wall attenuation, UV light band, source anisotropy, G-value and source transit time were estimated to be less than 1.4% for k = 1.
Some characteristics of the device used for the Fricke solution must be considered: the wall material should be water equivalent and should not chemically react with the solution; it must be sealed, but easy to vert the solution from the vessel into a cuvette to be read by the spectrophotometer.
LCR has been working on an adequate vessel during the past 10 years. The first vessel developed was water equivalent and the solution volume was irradiated only at the central ring resulting in a homogeneously irradiated solution. However, than those obtained using the standard protocols, the AAPM TG-43 Report [19], and its update [20]. This can be reflected in clinical practice, as the calculation of the dose delivered to the patients can be more accurate.
Beside the application of Fricke dosimetry for 192 Ir sources dosimetry, there are other studies using Fricke solution that have been developed by the LCR. One is the use of Fricke dosimetry for 137 Cs blood irradiator dosimetry using a specific phantom that was constructed and patented by the authors to perform these measurements [47], [48]. The other study tests the Fricke dosimeter properties as a potential system to be used in a postal dosimetry project for research irradiators [49]. In addition, the application of Fricke dosimetry for the determination of the absorbed dose to water for medium-energy X-ray beams was also studied and compared to the standard protocol TG 61 [50]. A new study also in progress concerns the use of Fricke dosimetry for the determination of the absorbed dose to water at linear accelerators. This work compares two different methods to determine the absorbed dose to water using Fricke dosimetry, opening up the possibility of using one of them as postal dosimetry [51].