Chemical radiation dosimetry in magnetic fields: characterization of a Fricke-type chemical detector in 6 MV photon beams and magnetic fields up to 1.42 T

The Fricke detector consists of a perfluoroalkoxy alkane (PFA) sample cup from AHF Analysetechnik filled to the top with Fricke solution (see figure 1). PFA was used as it is resistant against almost all chemical products, and because of its low surface tension, almost nothing adheres to this material. Therefore, the interaction of the Fricke solution with the vessel wall is small, lowering the self-oxidation processes of the Fricke solution. The sample cup has a diameter of 11.85 mm, a height of 36 mm and a wall thickness of approximately 0.21 mm. The sample cup is mounted on a holder during the irradiation as shown in figure 1(b).

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For the preparation of the Fricke solution, 112 ml concentrated sulfuric acid (96%, suprapur) was diluted in a 5 l volumetric flask to 0.4 mol l⁻¹ using ultrapure water from a Milli-Q Advantage A10 system. The concentration of the solution was verified by titration of 1 mol l⁻¹ NaOH. To eliminate non-linearity effects in the dose response curve, two drops of H₂O₂ (4%, suprapur) were added and neutralized with KMnO₄ solution (1%, pro analysis) as described in Davies and Law (1963). The Fricke solution was then prepared with 1 mmol l⁻¹ ammonium iron(II) sulfate (NH₄)Fe(II)(SO₄)₂·6H₂O (pro analysis), 1 mmol l⁻¹ NaCl (suprapur) and 0.4 mol l⁻¹ sulfuric acid.

The Fricke solution was prepared freshly on the first measurement day and was used during the next 1–2 weeks. The solution was stored in PFA bottles (1 l) that were covered with aluminum foil to protect the solution from light and to lower the self-oxidation processes (ISO 51026 2015). The Fricke solution was transferred to two sample cups shortly before the photon irradiation (see section 2.3) using a PFA wash bottle that was filled each day with the stored solution. It was taken care that no air bubbles were inside the sample cup. One of the two sample cups was irradiated; the other one was kept near the UV-spectrophotometer at 20 °C and was used as control.

Details about the working principle of the Fricke detector can be found in e.g. Fricke and Hart (1966). Here, only the details are discussed, that are relevant for this study. The absorbed dose to the Fricke solution (${{D}_{F}}$) was determined as described in ISO 51026 (2015) using the following equation:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{D}_{F}}=\frac{\Delta A}{\rho \cdot l\cdot \varepsilon \cdot G}\nonumber \end{align} \tag{ 2 }$$

where $\Delta A$ is the absorbance change of the Fricke solution upon irradiation, $\rho$ is the density of the Fricke solution, $l$ is the path length through the photometric cell, $\varepsilon$ is the molar extinction coefficient of Fe³⁺ and $G$ is the radiation chemical yield. $\Delta A$ was determined with a Cary 6000i UV-spectrophotometer (Varian) at a wavelength of 304 nm, with a spectral bandwidth of 1.5 nm. The determined absorbance values are an average over 2 min. The used quartz photometric cell had a path length of 0.9986  ±  0.0005 cm, as calibrated by METAS. The molar extinction coefficient ($\varepsilon$) and the radiation chemical yield ($G$) are given in the ICRU Report 90 (2014) as a combined value of $\varepsilon \cdot G$  =  3.525 cm² J⁻¹. However, as only relative measurements were performed where detector readings in an applied magnetic field were compared to readings without a magnetic field, the absolute value of $\rho \cdot l\cdot \varepsilon \cdot G$ is not needed since it is the same for all measurements.

The temperature in the photometric cell was held constant at the reference temperature of 25 °C using a thermostat (Lauda Eco 420). The temperature during each irradiation was recorded and all $\Delta A$ values were corrected to the reference temperature of 25 °C ($=\Delta {{A}_{25\,{}^\circ {\rm C}}}$) using the correction given by DIN 6800-3 (1980), which we have experimentally verified.

To obtain the absorbed dose to water (${{D}_{W}}$), correction factors have to be applied to ${{D}_{F}}$, as described e.g. in deAlmeida et al (2014). These corrections include a dose conversion from the Fricke solution to water and a correction for the vessel wall. Since they are not influenced by the magnetic field and since only relative measurements were performed, these corrections were not applied in this study.

The photometric cells were filled with a Pasteur pipette and emptied with a suction tube. Before each absorbance measurement, the photometric cell was rinsed with solution at least 2 times. For each sample, a new Pasteur pipette was used which has been cleaned with chrome sulfuric acid and ultrapure water. To compensate absorbance effects of the sulfuric acid and the photometric cells in the probe and reference beams of the spectrophotometer, a solution with the same composition as the Fricke solution but without any iron (basic solution) was filled into both photometric cells and the absorbance was measured at the beginning of each measurement day. This absorbance value was stored in the spectrophotometer application and subtracted from all subsequent measurements. By measuring the absorbance of the basic solution periodically during the day, the absorbance drift of the spectrometer was determined. However, no correction for this drift was applied as the absorbance of the unirradiated sample and of the irradiated sample were measured only 10 min apart and the drift was negligible. The absorbance measurements were performed typically 5–10 min but never longer than 1.5 h after the irradiation in order to keep the self-oxidation of the solution as low as possible.

The irradiation was performed at the experimental facilities of the German metrology institute Physikalisch-Technische Bundesanstalt (PTB) in Brunswick. Recently, the irradiation setup was described by Schüller et al (2019). The irradiations were performed in a 6 MV photon beam of a linear accelerator (Elekta Precise Treatment System) using a dose rate of 2–3 Gy min⁻¹ and a pulse repetition frequency of 400 Hz. A magnetic field was generated between the pole shoes of a constant-current driven electromagnet (Bruker ER0173W), which was homogeneous within 1 µT over 1 cm³ region up to 1.42 T (Delfs et al 2018). The photon beam (directed in $z$) and the magnetic field (directed in $x$) crossed orthogonally in the water phantom, as shown in figure 2. The freshly prepared Fricke detectors (see section 2.1) were placed at 10 cm water equivalent depth inside a water phantom with dimensions 7 cm ($x$)  ×  21 cm ($y$)  ×  21 cm ($z$).

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Dose response curves (see section 3.1) were recorded in the presence of magnetic field strengths (B) of 0 T, 0.6 T and 1.2 T by irradiating the Fricke detectors in a 6 MV photon beam (5  ×  10 cm²) with approximately 1070 monitor units (MU) (≈6 Gy), 7100 MU (≈40 Gy), and 17 800 MU (≈100 Gy). For the determination of ${{k}_{B,M,Q}}$ and the output factors (see sections 3.2 and 3.3), the Fricke detectors were irradiated with approximately 7100 MU using different magnetic field strengths (0 T–1.42 T) and different radiation field sizes (3  ×  3 cm²–5  ×  10 cm²). The same number of monitor units were used for irradiation with the magnetic field switched on as for the irradiations without magnetic field. The independence of the internal monitor readings from the magnetic field has been confirmed within 0.15% (Delfs et al 2018). For the determination of the absorbed dose to water (${{D}_{W}}$ and $D_{W}^{B}$), the monitor of the accelerator was calibrated at B  =  0 T in a photon-beam size of 5  ×  10 cm², using an ionization chamber (IBA FC65-G or PTW 30013) with the appropriate correction factors for temperature, pressure, saturation and beam quality (Andreo et al 2006; DIN6800-2, 2008). Afterwards, the monitor readings at B  =  0 T in a photon-beam size of 5  ×  10 cm² were checked periodically each morning, noon and evening by comparing the monitor units with ${{D}_{W}}$ measured with the ionization chamber. A linear correction for the drift of the monitor readings was assumed.

For each setting, 3–4 Fricke detectors were irradiated and evaluated. Since the delivered absorbed dose to water changed slightly from irradiation to irradiation, the detector readings (see section 2.2) were normalized with the average value of ${{D}_{W}}$ so that the mean value of the detector readings for each setting could be determined.

In figure 3(a) the Fricke readings ($\Delta {{A}_{25\,{}^\circ {\rm C}}}$) versus the absorbed dose to water (${{D}_{W}}$) for a 6 MV photon beam applying magnetic field strengths of 0 T, 0.6 T and 1.2 T are shown. The points correspond to the average value of 3–4 measurements. The experimental standard deviation of each $\Delta {{A}_{25\,{}^\circ {\rm C}}}$ is approximately 0.3%. All dose response curves are linear with a slope ($\Delta {{A}_{25\,{}^\circ {\rm C}}}/{{D}_{W}}$) of about 0.00 356 Gy⁻¹, with a correlation coefficient of 1.000 00. In figure 3(b) the deviation of the measured $\Delta {{A}_{25\,{}^\circ {\rm C}}}$ values from the fitted slope are shown. The deviation is smaller than 0.4% for all data points, hardly exceeding the measurement uncertainties.

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Following the notation of van Asselen et al (2018), ${{k}_{B,M,Q}}$ is defined as the ratio of the detector readings without a magnetic field (${{M}_{Q}}$) to the readings in the magnetic field ($M_{Q}^{B}$), see equation (1). For the Fricke detector, the readings correspond to the absorbance change ($\Delta A$) upon irradiation. As described in section 2.2, the influence of the irradiation and readout temperatures on the Fricke readings were corrected.

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{k}_{B,M,Q}}=\frac{{{M}_{Q}}}{M_{Q}^{B}}=\frac{\Delta {{A}_{25\,{}^\circ {\rm C}}}}{\Delta A_{25\,{}^\circ {\rm C}}^{B}}.\nonumber \end{align} \tag{ 3 }$$

Figure 4 shows the determined ${{k}_{B,M,Q}}$ factors for the Fricke detector measured in a 5  ×  10 cm² 6 MV photon beam. The measurements for B  =  0.6 T and 1.2 T have been repeated several months later to verify the reproducibility of the results, which is discussed in section 4.1. The error bars correspond to the relative combined standard uncertainty (k  =  1), see table 1.

Table 1. Relative standard uncertainties $u({{X}_{i}})/{{X}_{i}}~$ for the calculation of ${{k}_{B,M,Q}}$ ($=\Delta {{A}_{25\,{}^\circ {\rm C}}}/\Delta A_{25\,{}^\circ {\rm C}}^{B}$).

Quantity ${{X}_{i}}$	$u({{X}_{i}})/{{X}_{i}}$
Fricke readings without magnetic field
Monitor calibration	0.317%
Stability of monitor calibration over a day	0.058%
Stability of spectrophotometer over 10 mina	0.013%
Repeatability of absorbancea	0.070%
Solution temperature during detector readout	0.014%
Change of temperature during irradiation	0.015%
Positioning of detector (depth in water)	0.039%
Fricke readings with magnetic field
Monitor calibration	0.317%
Stability of monitor calibration over a day	0.058%
Independence of monitor from B-fieldb	0.150%
Stability of spectrophotometer over 10 mina	0.013%
Repeatability of absorbancea	0.070%
Solution temperature during detector readout	0.014%
Change of temperature during irradiation	0.015%
Positioning of detector (depth in water)	0.039%
Relative combined standard uncertainty	0.494%
Expanded relative uncertainty	0.977%

^aThe relative uncertainty was determined for typically measured $\Delta {{A}_{25\,{}^\circ {\rm C}}}$ values. ^bSee Delfs et al (2018).

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The output factor is defined as the ratio of the dose at the position P in a phantom for a field size A, to the dose at the same position P in a 10  ×  10 cm² reference field (Podgorsak 2005). The largest possible field in our experimental setup was only 5  ×  10 cm² due to the limited spacing between the magnet poles. Hence, the output factors for the Fricke detector are normalized to this field size. Typically, the output factors are shown as a function of equivalent square fields with the assumption that the output for rectangular fields is equal to the output for the equivalent square field. The rectangular fields with sides a and b were recalculated to a square field with sides ${{a}_{eq}}$ using Day's rule (Podgorsak 2005).

Figure 5 shows the output factors for the Fricke detector in the presence of different magnetic fields. Note that for the 4  ×  10 cm², 3  ×  10 cm² and 2  ×  10 cm² fields only B  =  0 T and B  =  1.42 T were applied, whereas for the other fields also B  =  0.35 T, B  =  0.6 T and B  =  1.2 T were applied. Only small changes of the output factors due to the magnetic fields are observed for fields  >2  ×  2 cm² (<1%), see figure 6. Here, all output factors are smaller in the presence of a magnetic field compared to the measurements without an applied magnetic field.

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The experimental standard deviation of $\Delta {{A}_{25\,{}^\circ {\rm C}}}$ for measurements without an applied magnetic field in a 5  ×  10 cm² irradiation beam is approximately 0.3% in the range of absorbed dose to water between 6 Gy to 100 Gy, see table 2, which is in the same magnitude as reported by Moussous et al (2011) for their measurements between 5 Gy and 25 Gy. In table 2 also the experimental standard deviation of $\Delta {{A}_{25\,{}^\circ {\rm C}}}$ measured in the presence of different magnetic field strengths are shown. They are with up to 0.5% slightly higher than for B  =  0 T. The different magnetic field strengths were not always applied in the same sequence and dependent on that sequence slightly different $\Delta {{A}_{25\,{}^\circ {\rm C}}}$ values were measured. The largest changes were observed when B  =  1.42 T was applied directly after B  =  0 T. It seemed that the monitor of the accelerator, which was used as reference, was slightly influenced by the magnetic field dependent on the sequence of the applied magnetic field strengths.

Measurements of k_B,M,Q factors were performed several months apart. They agree within 0.5%, see the two measurement sets in figure 4.

Figure 3 demonstrates that the Fricke detector has a linear dose response between 6 Gy and 100 Gy. The linearity is not affected by the presence of a magnetic field. The measured dose response curves with a slope of approximately 0.003 56 Gy⁻¹ are comparable with the results Moussous et al (2011) obtained for 6 MV photon beams (0.0036 Gy⁻¹), although they used glass-walled bottle-shaped ampoules while we used PFA sample cups. For both measurements, it was assumed that the detectors are water equivalent and no corrections for the different materials were applied to convert D_F into D_W.

Although only relative measurements were performed in this study where Fricke readings with and without the presence of a magnetic field were compared, the plausibility of our Fricke measurements for B  =  0 T was verified by determining $\varepsilon \cdot G$ and comparing it to the literature. The slope of the dose response curve for B  =  0 T was converted to $\varepsilon \cdot G$, see equation (2), using the density of the Fricke solution ρ and the path length through the photometric cell l. A value of $\varepsilon \cdot G$  =  3.491 cm² J⁻¹ is obtained, which is 1% lower than the value recommended in the ICRU report 90 (2014) for 6–15 MeV electron beams. According to this reference, $\varepsilon \cdot G$ decreases for smaller beam energies, e.g. $\varepsilon \cdot G$ is 0.7% smaller for ⁶⁰Co beams. As the corrections to convert D_F into D_W were not applied in this study, a deviation from the recommended value is expected. For pyrex glass vials, a material which has approximately the same density as the used PFA, a correction of 0.62% for 6 MV beams is predicted (Ma et al 1993). Hence, the predicted correction is close to the observed deviation of 1%. Note that for the determination of k_B,M,Q and output factors, the ratio of two Fricke readings is calculated and therefore possible deviations cancel out.

Table 3 summarizes the k_B,M,Q factors measured in a 5  ×  10 cm² 6 MV photon beam (see also figure 4). The change induced by the magnetic field on the Fricke readings slightly increases with the magnetic field strength, but it is smaller than 0.95% for all measurements. This increase is expected, as the altered dose distribution, which is corrected with the dose conversion factor c_B, is more influence by larger magnetic field strengths (Delfs et al 2018). c_B factors for 0.35 T and 1.42 T, calculated for the same setup as used in this work, were published to be 0.47% and 0.75%, respectively (Delfs et al 2018). As shown in equation (1), k_B,Q is obtained by multiplying c_B with k_B,M,Q. The k_B,Q factors for the Fricke detector are listed in table 3. The correction due to the magnetic field is 0.52% and 0.20% for 0.35 T and 1.42 T, respectively. The measurement uncertainty of the k_B,M,Q factors are in the same magnitude, see table 1. Hence, no significant change of the Fricke response due to the magnetic field could be observed.

Moussous and Medjadj (2016) have shown that output factors measured with Fricke detectors for field sizes between 5  ×  5 cm² and 20  ×  20 cm² in a ⁶⁰Co beam agree within 0.5% with ionization chamber measurements (WDIC70#141), when no magnetic field is applied. Here, we have measured output factors in the presence of magnetic field strengths between 0 T and 1.42 T using Fricke detectors. As shown in figure 6, the output factors decrease slightly in the presence of a magnetic field for irradiation beam sizes  >2  ×  2 cm². This was expected since we have measured all output factors at the same position although the presence of magnetic fields shift the depth dose profiles. Additionally, the applied magnetic field leads to a skew of the lateral beam profiles. Both effects will decrease the local dose at the measured position. It is expected that for smaller irradiation field sizes, larger changes in the output factors will occur since the asymmetry of the lateral dose profiles will be more pronounced (O'Brien et al 2017). This was indeed observed with the Fricke detectors. As shown in figure 6, the changes for the 3  ×  3 cm² field are larger than for the 5  ×  5 cm² field.

The agreement of the Fricke output factors at 0 T with microDiamond (PTW 60019), diode (PTW 600012) or Semiflex 3D (PTW 31021) measurements is within 0.7% for field sizes  ⩾4  ×  4 cm². By comparing the Fricke results for 1.42 T with the microDiamond, diode and Semiflex 3D results for 1.5 T, the same findings as for 0 T were observed.