Impact of new ICRU Report 90 recommendations on calculated correction factors for reference dosimetry

In 2016 the ICRU published a new report dealing with key data for ionizing radiation dosimetry (ICRU Report 90). New recommendations have been made for the mean excitation energies I for air, graphite and liquid water as well as for the graphite density to use when evaluating the density effect. In addition, the ICRU Report 90 discusses renormalized photoelectric cross sections, but refuses to give a recommendation on the use of renormalization factors. However, the Consultative Committee for Ionizing Radiation recommends to use renormalized photoeffect cross sections. Goal of the present work is to evaluate the impact of these new recommendations on clinical reference dosimetry for high energy photon and electron beams. The beam quality correction factor kQ was calculated by Monte Carlo simulations for compact and parallel plate ionization chambers. In case of photons seven phase space files from clinical accelerators and twelve spectra taken from literature from 4 MV to 24 MV and additionally a 60Co source were applied. As electron source thirteen electron spectra available in literature were used in the range of 4 MeV–21 MeV. The new ICRU recommendations have a small impact on Monte Carlo calculated kQ values for the chosen ionization chambers in the range of 0.1%–0.35% only—the difference increases for higher photon energies. The impact of the ICRU Report 90 recommendations on Monte Carlo calculated stopping power ratios sw,a, perturbation factors p and beam quality correction factors kQ was investigated and confirmed a decrese of sw,a by a fraction of a percent for photon and electron beams. This study indicates that the impact of the new ICRU recommendation is within 0.35%. The determined deviations should be taken into account, when widely published Monte Carlo calculated values are examined.

test. The accuracy of the geometry model depends on the quality of the available data of the ionization chamber. However the cross-section data also have a significant influence on the results of a Monte Carlo simulation.
In this respect, the ICRU Report 37 (Berger et al 1984) recommends values for the mean excitation energy I and the density of elements and compounds. Based on newer measurements, recommendations for the I values for graphite I g and water I w have been revised in the recent published ICRU Report 90 (Seltzer et al 2014), i.e. I g = 81 eV and I w = 78 eV. Moreover, the ICRU Report 90 recommends using the grain density of graphite in the evaluation of the density effect. A recent study (Andreo et al 2013) investigated the impact of the increase of the I w value from 75 eV (ICRU 37) to 78 eV (ICRU 90) on stopping-power ratios water to air for photon, electron and proton beams by Monte Carlo simulations. Moreover, potential changes in dosimetric quantities for the Farmertype ionization chamber NE2571 in a 60 Co radiation source due to the new I values for water and graphite were discussed. A recent publication (Gomà et al 2016) investigated the impact of the new I values for water and graphite on the beam quality correction factor for a wide range of ionization chambers in monoenergetic proton beams.
Apart from the recommendations on the I value and density, the ICRU Report 90 discusses the use of renormalized photoelectric cross sections. Based on a review of this discussion in the ICRU Report 90, the Consultative Committee for Ionizing Radiation (CCRI) recommends the use of renormalized photoelectric cross sections (McEwen et al 2017).
According to the investigations published by Andreo et al (2013), the impact of these new key data for clinical reference dosimetry was evaluated. Following the results of Andreo et al (2013), stopping-power ratios water to air for high energy photon and electron beams were calculated according to the recommendations of the ICRU Report 37 (Berger et al 1984) and 90 (Seltzer et al 2014). Extending the investigation of Andreo et al (2013), the impact on the beam quality correction factor k Q according to the IAEA dosimetry protocol TRS-398 (Andreo et al 2001) due to adoption of the new I values and using the grain density of graphite to evaluate density correction, was investigated by Monte Carlo simulations for high energy photon and electron beams. In addition to that, the impact on the perturbation factor p for the ionization chamber NE2571 was investigated for high energy photon fields. Thereby the present work expanded the study of Andreo et al (2013) to high energy photon beams and also includes the impact of the new recommendations on the k Q values of two widely used parallel-plate ioniz ation chambers in high energy electron beams.

Calculation of the beam quality correction factor
The ratio between absorbed dose to water D w and absorbed dose to air of the sensitive volume D det of an ionization chamber is related to the Spencer-Attix stopping power ratio water to air s w,a and a perturbation factor p, which takes the fluence perturbation of non-ideal Spencer-Attix cavities occurring in real ionization chambers into account.
Based on equation (1) the beam quality correction factor k Q can by calculated theoretically as shown by Andreo (1992) where the indices Q and 60 Co represent the considered beam quality and the reference radiation field of a 60 Co γ-ray beam, respectively. W air is the mean energy to create an ion pair in air at the beam qualities Q and 60 Co. For electron and photon radiation fields W air can be assumed to be independent from energy . The aim of this work was to compare Monte Carlo calculated k Q values according to the recommendations of the new ICRU Report 90 (Seltzer et al 2014) and the ICRU Report 37 (Berger et al 1984). For this purpose the ratio of Monte Carlo calculated k Q values according to the ICRU Report 90 and 37 were determined. For shorter notation this ratio is symbolized by a Δ throughout this work, as can be seen in equation (3) for the restricted water-to-air mass collision stopping power ratio s w,a .
The applied reference conditions to determine the absorbed dose in 60 Co and high-energy photon and electron beams were chosen according to the recommendations of the TRS-398 dosimetry report (see table 1).
It should be noted that the water density ρ in the ICRU Report 90 is provided with more decimals, so that the influence of the temperature under atmospheric pressure on the density of water is noticeable. Therefore, the calculated values according to ICRU Report 37 and 90 refer to the same water depth d but not to the same radiological depth dρ. However, the difference in radiological depth between the simulations according to ICRU-90 and ICRU-37 is only 0.018 g cm −2 and should therefore not influence the results calculated according to the ICRU Report 90 for photon beams. For this reason, the reference depth of 10 cm was used also for calculations according to ICRU Report 90. The beam quality correction factor TPR 20 10 for calculations according to ICRU Report 90 was also calculated from the dose ratio in 20 cm and 10 cm water depth. The depth R 50 for electron beams was determined from calculated depth-dose curves according to ICRU Report 37 and 90.

Monte Carlo simulation
This Monte Carlo study is documented according to the recommendations of the report No. 268 of the AAPM T 268 (Sechopoulos et al 2017). Monte Carlo simulations of photon and electron radiation fields have been performed with the EGSnrc code system (Version 2017) .

Radiation source and geometry definition
The radiation fields of photon and electron beams were generated by a collimated isotropic radiation source. The spectral energy distributions of the electron beams are taken from Ding et al (1995). The published spectral energy distributions from Sheikh-Bagheri and Rogers (2002) and Mohan et al (1985) were used for the simulations of the megavoltage photon beams. The spectrum of the 60 Co beam was taken from Han et al (1987). Moreover, seven linear accelerator (linac) head models generated with the BEAMnrc user code have been used to simulate a radiation field as comprehensive as possible. The BEAMnrc linac head models have already been used in several publications (Czarnecki et al 2012, Czarnecki and Zink 2013, Horst et al 2015 to calculate dosimetric quantities. The absorbed dose to water D w and absorbed dose to air of the sensitive volume D det of the ionization chamber NE2571, NACP-02 and Roos were calculated in a 30 × 30 × 30 cm 3 water phantom with the egs_chamber user code (Wulff et al 2008b). The absorbed dose to water D w was calculated in a small cylindrical water voxel of 0.25 cm radius and 0.1 cm height. The cylinder was positioned symmetrical around the point of measurement. The dose D det was calculated in detailed models of the investigated ionization chambers using the egs++ class library . The detailed geometry of the NE2571 Farmer-type chamber was adopted from Andreo et al (2013). All chambers did pass the Fano cavity test (see appendix A). The geometry of the NACP-02 and Roos chamber was taken from a previous work .
The variance reduction techniques implemented in the user code egs_chamber were used to improve the efficiency of the Monte Carlo simulations (Wulff et al 2008b). The following variance reduction techniques have been used: intermediate phase space storage; photon cross-section enhancement (XCSE) volume with an XCSE factor of 256 (only for photon beams) and the Russian Roulette range rejection technique with a survival probability of 1/512.
In addition to the k Q calculations, the restricted water-to-air mass collision stopping-power ratio s w,a was calculated with the user code SPRRZnrc in a small cylindrical volume of 0.25 cm radius and 0.1 cm height for reference conditions. The perturbation factor p was determined from the calculated dose ratio D det /D w and the stopping power ratio s w,a according to equation (1).

Radiation transport parameters
A transport and particle production threshold energy of ECUT = AE = 512 keV for electrons and PCUT = AP = 1 keV for photons was used to calculate D w and D det . To calculate s w,a the ECUT and PCUT values were set to 521 keV and 10 keV, respectively.
All Monte Carlo calculations were performed with two different sets of the materials, water and graphite, following the recommendations of the ICRU Report 37 and 90. Table 2 shows the different material properties of the two sets. The I value of air has remained at 85.7 eV but the uncertainty has been reduced to 1.2 eV in the new ICRU Report 90.
The ICRU Report 37 notes that the available density effect theory provides no indication as to which assumed density value would provide the best approximation. However, the ICRU Report 37 prefers to use a value equal Source to surface distance 100 cm 100 cm 100 cm Field size at surface 10 × 10 cm 2 10 × 10 cm 2 10 × 10 cm 2 to or close to the bulk density of graphite (1.7 g cm −3 ) to calculate the density correction factor. For this reason the density of 1.7 g cm −3 was chosen for evaluating the density effect correction according to ICRU Report 37, although the density of the graphite used in the chamber was 1.8 g cm −3 . Beside the new I values, the ICRU Report 90 recommends to use the grain density of graphite (2.265 g cm −3 ) to evaluate the density effect correction. Further transport parameter settings used in all Monte Carlo simulations with the EGSnrc code system are summarized in table 3.

Results
In the recent published ICRU Report 90, new recommendations were made on I values and density of water (see table 2). The impact of these recommendations on the calculation of the beam quality specifier TPR 20 10 and R 50 is presented in figure 1.
The difference between TPR 20 10 values calculated according to the ICRU Report 37 and 90 is below 0.24%. This difference is within the statistical uncertainty (2 σ) of the calculated data. However, a change of 0.24% has a negligible effect on the k Q value. A change in TPR 20 10 of 0.25% would cause a change in k Q value of approximately 0.015% and 0.05% for lower photon energies (TPR 20 10 ≈ 0.65) and high photon energies (TPR 20 10 ≈ 0.75), respectively. The difference between the water depths R 50 as well as z ref according to ICRU Report 37 and 90 increases with the energy of the electron radiation field, but is still in the submillimeter range.
In the following figures all determined ratios between values calculated according to ICRU Report 37 and 90 are presented as a function of beam quality specifiers calculated according to ICRU Report 37. The ratio between s w,a with density-effect correction and I value according to the recommendations of the ICRU Report 37 and 90 (see table 1) are shown in figure 2 for electron and photon beams. The filled symbols show the ratio of s w,a using collimated spectra as particle source, whereby the open symbols represent the ratio of s w,a using a full linac treatment head simulation as particle source.
The ratio of the Monte Carlo calculated perturbation factors p between the ICRU Report 90 and 37 recommendations is given in figure 3 for the cylindrical ionization chamber NE2571 in photon fields and the two parallel plate ionization chambers NACP-02 and Roos in electron fields. The ratio ∆p is shown as a function of the beam quality specifier TPR 20 10 and R 50 for photon and electron beams, respectively. In the 60 Co radiation field the Density for evaluation of 1.00 g cm −3 1.7 g cm −3 0.9982 g cm −3 2.265 g cm −3 Density effect correction  (1)) for the used ion chambers is given in figure 4. In the 60 Co radiation field the ratio ∆ (s w,a p) for the NACP-02 and Roos ionization chamber was ∆ (s w,a p) = 0.9955 ± 0.0006 and ∆ (s w,a p) = 0.9972 ± 0.0005 , respectively.
The resulting k Q factors according to ICRU Report 37 and 90 for the NE2571 thimble chamber are given in figure 5. The left panel of figure 5 presents Monte Carlo calculated k Q values with clinical spectra (circles) and Monte Carlo simulations through the linac treatment head as a radiation source. A closer look on the data in the left panel of figures 5 and B1 reveals, that the k Q values differ systematically for the two different source models. This difference is caused by the different radial dose distributions of the source models as shown in appendix B. The k Q values are compared to the data given by the IAEA dosimetry protocol TRS-398 and polynomial fits through experimental data and Monte Carlo calculated data determined by Andreo et al (2013). The ratios ∆k Q are shown in the right panel of figure 5.

Stopping power ratios and perturbation factors
The s w,a values for photon beams vary between −0.6% ( 60 Co beam) and −0.3% (high energy photon beams) between the ICRU 37 and the new ICRU 90 recommendation-the s w,a values for electron beams vary −0.3% and −0.2%. The calculated ∆s w,a values are in good agreement with the results published by Andreo et al (2013) which are also given in the ICRU Report 90 (Seltzer et al 2014).
The perturbation factor of the NE2571 increased between 0.1% and 0.3% when the new ICRU Report 90 (Seltzer et   The new recommendations had a small impact on the parallel plate ionization chambers in an electron field. The impact on the perturbation factor p of the NACP-02 chamber was smaller than −0.2%. The p values of the Roos chamber vary between 0% and −0.1%. The small impact on the p value of the Roos chamber may be due to the small amount of graphite in the ionization chamber.

Beam quality correction factor
For all chambers the factor (s w,a p) decreased when the new recommendations were applied. For the NE2571 chamber in photon fields a difference between −0.15% and −0.4% was observed, primarily due to the change in mass-stopping power ratio s w,a . Looking at the results for 60 Co beam, Andreo et al (2013)   with the findings presented in this publication. Using the new recommendations to calculate (s w,a p) for the parallel plate ionization chambers NACP-02 and Roos in clinical electron beams would change the values by around −0.3% compared to the recommendations in the ICRU Report 37. In contrast to photon fields, (s w,a p) was energy independent for electron fields. As a result, k Q was also energy independent. Using the data from figure 4 and applying the change of the 60 Co value of ∆ (s w,a p) = 0.9955 and ∆ (s w,a p) = 0.9972 for the NACP-02 and Roos chamber a change of the k Q values for these chambers due to the new ICRU recommendation is in the range of 0.16%. The k Q values for the NE2571 calculated in this work are in good agreement with the fit through Monte Carlo calculated data given by Andreo et al (2013)-the root-mean-square deviation is 0.0014. However, as can be seen in figure 5 there is a discrepancy between Monte Carlo calculated and experimentally determined k Q values. Even with recently renewed I values, the discrepancy cannot be explained. However, Monte Carlo calculated k Q values according to the new recommendations of the ICRU Report 90 resulted in an increase of the k Q values of up to 0.35% for high photon energies.

Renormalized photoelectric cross sections
Furthermore, within the framework of this study the developer version of EGSnrc was used to investigate the impact of using multiconfiguration Dirac-Fock (MCDF) renormalization factors for photoelectric cross sections to calculate k Q values. As expected, renormalized photoelectric cross sections did not effect the k Q values since the photonelectric effect in the used materials is only dominant at very low photon energies (<100 keV). It has to be mentioned that applying MCDF renormalization factors to cross sections for the photoelectric effect was only discussed, but not recommended in the ICRU Report 90.

Uncertainties of I values
Besides new I values for the materials water and graphite, the ICRU Report 90 also includes new data on the uncertainties of the I values for these materials and also for air. The impact of these new type-B-uncertainties on resulting k Q values can be estimated by the method applied in one of our previous publications (Wulff et al 2010).
In this paper the I value of different materials was varied, i.e. new cross section data were calculated and the k Q value for the NE2571 chamber was recalculated with the new cross section data. This was done for the highest available photon energy (24 MV, TPR 20 10 = 0.806) as the impact of changed I values is largest for high energy photon beams. From these calculations a sensitivity coefficient ∂ (∆k Q /k Q ) /∂x i for every material or I value x i was calculated. Applying these coefficients to the type-B-uncertainties given in ICRU Report 37 and ICRU Report 90, respectively, the standard uncertainties given in table 4 are resulting. The data show that the standard uncertainty of the Monte Carlo based k Q factor of the NE2571 chamber is halved, especially due to the strong decrease of ∆I for the material graphite. According to Wulff et al (2010), the uncertainty of the I values is by far the largest contribution to the total uncertainty of Monte Carlo based k Q values. Beyond this background the new ICRU recommendation regarding the ∆I values is of great importance for the direct comparison of future Monte Carlo based and experimental based k Q determinations.

Conclusion
The impact of the new ICRU Report 90 recommendations on Monte Carlo calculated dosimetric quantities was investigated, confirming the decrease of s w,a by a fraction of a percent for photon and electron beams. The study showed good agreements with the work published by Andreo et al (2013) and extended the investigation to clinical linear accelerators. However, in this work only three ionization chambers were investigated; the results may vary for other ionization chamber types, but the results should be comparable. According to the results, the impact of the new recommendations of the ICRU Report 90 on k Q values is within 0.35%. This deviation should be taken into account when widely published Monte Carlo calculated values are examined. In addition, data based on Monte Carlo simulations in the current dosimetry protocols should be revised with regard to the recommendations of the ICRU Report 90.

Appendix B. Volume perturbation
Monte Carlo calculated k Q values for the NE2571 chamber using a full linac treatment head simulation as particle source differ systematically from k Q values calculated using collimated isotropic radiation source with spectral energy distributions of the respective linac, as can be seen in figure 5 and left panel of figure B1. The k Q values calculated using a full treatment head are systematically below the k Q values when using collimated isotropic spectra as a particle sources. These are caused primarily by the different radial dose distributions of the two particle sources. Using only spectra as particle source results in concave radial dose distributions with a volume perturbation factor p vol 1. On the other hand, full treatment head simulations of conventional linac with flattening filter generate radial dose distributions with a tendency to be convex, resulting in a volume perturbation p vol 1. Dividing k Q values by p vol eliminated the deviation between k Q values from different source models (see figure B1).   Figure B1. The left panel shows Monte Carlo calculated beam quality correction factor kQ as a function of TPR 20 10 for the ionization chamber NE2571 using full linac head simulations (open symbols) and spectra (filled symbols) as a particle source of the Varian Clinac 6 MV, 10 MV and 18 MV. Inside the left panel the corresponding lateral profiles in 10 cm water depth are presented. Right panel provides the beam quality correction factors shown in the left panel divided by the perturbation factor p vol (calculated accordingly to Bouchard et al (2009)). The error bars represent the Monte Carlo statistical uncertainty (1 σ). The Monte Carlo statistical uncertainty of the calculated dose profiles are not shown for the sake of clarity and are within 0.12%.