Conversion coefficients from total air kerma to the newly proposed ICRU/ICRP operational quantities for radiation protection for photon reference radiation qualities

The International Commission on Radiation Units and Measurements (ICRU) has recently proposed a set of new operational quantities for radiation protection. ICRU supplied conversion coefficients for mono-energetic photons but not for photon reference radiation qualities defined by the International Organization for Standardization (ISO) in ISO 4037 and by the International Electrotechnical Commission (IEC) in IEC 61267. Therefore, in this work, conversion coefficients from total air kerma to the newly proposed operational quantities are averaged for photon reference radiation qualities. Also, parameters necessary to determine the influence of the air density on the conversion coefficients are determined. Finally, the impact of the newly proposed quantities upon the response of dosemeters is investigated.


Introduction
In its report number 57 on operational quantities used in radiological protection [1], the International Commission on Radiation Units and Measurements (ICRU) published conversion coefficients for those quantities for mono-energetic particles (photons, electrons, and neutrons). However, over the years, ICRU has developed new definitions of operational quantities in radiation protection and has published corresponding values of conversion coefficients from fluence to the newly proposed quantities for mono-energetic particles of several types (photons, electrons, neutrons, and others) as well as conversion coefficients from total air kerma to the new quantities for photons [2][3][4]. The corresponding report ICRU 95 has been jointly published by ICRU and ICRP (International Commission on Radiological Protection) in 2020 [5].
In this work, data for spectrum averaged conversion coefficients from total air kerma to the new quantities are calculated for the x-and gamma radiation qualities defined by the international standards ISO 4037 [6][7][8][9] and IEC 61267 [10], using the methods described earlier [11] to determine the corresponding conversion coefficients for the current operational quantities according to ICRU 57 [1]. Furthermore, the influence of the air density on the spectral distributions and consequently on the conversion coefficients is determined by applying the exponential attenuation law for photons to the spectra. Subsequently, the conversion coefficients are calculated for air densities from ρ = 0.96 kg m −3 to ρ = 1.32 kg m −3 (i.e. −20 % to +10 % from reference air density, ρ ref = 1.1974kg m −3 , covering the range of standard test conditions recommended by ISO [8]) to obtain the corresponding correction factors for the conversion coefficients that have been calculated [12].
As mentioned above, the same methods described in earlier publications of one of the authors are used and only the conversion coefficients for mono-energetic particles for the newly proposed operational quantities are applied instead of those according to ICRU 57. Therefore, several formulas and descriptions have been adopted from the author's previous publications [11,12].

Quantities considered
The new operational quantities are as follows [5]: • estimates of the effective dose for the protection against stochastic effects and, accordingly, in the unit Sv: * ambient dose, H * , and * personal dose, H p , depending on the direction of incidence, Ω; • estimates of the dose to the lens of the eye for the protection against the tissue effects (often deterministic) and, accordingly, in the unit Gy: The corresponding values of conversion coefficients from total air kerma, K a , to these quantities are denoted accordingly with small symbols instead of capital ones, i.e. h * K = H * /K a and h pK = H p /K a for example.
The numerical values of conversion coefficients for d' lensK and d p lensK are identical for the same particle type, energy and direction or angle of incidence. The symbol used is d lensK .
Accordingly, the numerical values of conversion coefficients for d' local skin K and d p local skin K , the latter for exposure of the slab phantom, are identical for the same particle type, energy and direction or angle of incidence. The symbol used is d local skin K .
For d local skin K , additional indices describe the calibration phantom considered: d local skin K slab , d local skin K pillar and d local skin K rod denote the quantity D p local skin on the slab, the pillar and the rod respectively.
Finally, table 1 shows an overview of all quantities for which values are determined in this work. All values presented in this paper are based on data calculated using the kerma-approximation method, i.e. during an irradiation charged particle equilibrium must be assured, e.g. by placing a sufficiently thick plate made of polymethyl methacrylate (PMMA) in front of the object to be irradiated. For details, see ISO 4037-3 [8].

Calculation of spectrum averaged conversion coefficients
Spectrum averaged values of the conversion coefficients, c K (E i ;α), from total air kerma to quantity C for radiation quality R are obtained by averaging the spectra with the corresponding conversion coefficients for msono-energetic photons. The spectra are available in binned form and the averaging is performed by a sum over all bins: where N is the number of energy channels of the spectrum, Φ(R;E i ) is the spectral fluence of the radiation quality R, at photon energy E i. c K (E i ;α) is the conversion coefficient from total air kerma to the operational quantity calculated using the kerma-approximation method at photon energy E i . k Φ (E i ) is the conversion coefficient from photon fluence to total air kerma for photon energy E i given by k Φ (E i ) = K a /Φ = (µ en /ρ)·E i /(1−g) with the energy absorption coefficient, (µ en /ρ), and fraction of radiative losses in air, g, for energy E i . The values for (µ en /ρ) are from the literature [14,15] with renormalized Scofield photoeffect cross sections from ICRU report 90 [13] and actual values for g [16]. These values for D' lens (α)/Ka = D p lens (α)/Ka Total air kerma to directional absorbed dose in the lens of the eye total air kerma to personal absorbed dose in the lens of the eye d local skin K (α) slab D' local skin (α)/Ka = D p local skin (α)/Ka Total air kerma to directional absorbed dose in local skin total air kerma to personal absorbed dose in local skin on the slab phantom d local skin K (α) pillar D p local skin (α)/Ka Total air kerma to personal absorbed dose in local skin on the pillar phantom d local skin K (α) rod D p local skin (α)/Ka Total air kerma to personal absorbed dose in local skin on the rod phantom kΦ Ka/Φ Fluence to total air kerma (1−g) One minus the fraction of radiative losses in air ( µen, not_renorm. µen,renorm. ) Energy absorption coefficient based on not renormalized photoeffect cross sections divided by energy absorption coefficient based on renormalized photoeffect cross sections (taken from ICRU 90 [13]) Table 2. Sources for the spectra used.
Type of radiation quality Radiation qualities and abbreviation a Source of spectra have different degrees of filtration with decreasing filter thickness from the L, N, W, H to the RQR series, see figure 4. Thus, the spectra of the L series are narrowest, i.e. similar to mono-energetic photons, while the spectra of the RQR series are broadest. The spectra of the S and R series are dominated by one or a few mono-energetic photon energies. Thus, as expected, the values for the L, S and R series lie almost on the lines for mono-energetic photons, while the values for the N, W, H and RQR series lie further below the lines the less filtration the series have, i.e. the broader the corresponding spectra are. The reason for this is, especially for broad spectra like the RQR series, that the conversion coefficients for mono-energetic photons from the left and right of the spectrum's mean energy contribute to the averaging according to equation (1) and lead to lower mean values, see e.g. the curve for α = 0 • in figure 1. If the values for mono-energetic photons are not strongly dependent on energy (see e.g. the curve for α = 0 • in figure 3), the averaging according to equation (1) does not lead to significantly lower values than for mono-energetic photons. Therefore, almost all symbols in figure 3 nearly match the lines. Thus, the corresponding conversion coefficient, in this case d local skin K (0 • ) rod , can be approximated by the value for the respective spectrum's mean energy. This is not the case if the values for mono-energetic photons strongly depend on the energy, see e.g. Figure 1.

Values for air kerma, K a , and conversion coefficients to the operational quantities, c K : ICRU 90 vs ISO 4037
To be clear: the values for air kerma, K a , the kerma coefficient, k Φ , and the conversion coefficients, c K , according to this work are based on total air kerma according to ICRU 90 [13], K a,ICRU90 , i.e., using renormalized cross sections for the mass energy absorption coefficients or air, (µ en /ρ). However, in the current version of ISO 4037-3 [8] all values are based on not renormalized cross sections and total air kerma, K a,total . What is even more different is that in the outdated but still often used version of ISO 4037-3 as of 1999, all values are based on collision air kerma, K a,col , and also on not renormalized cross sections.
To obtain K a,ISO2019 and c K, ISO2019 , alternative values which are compatible with the values in ISO 4037-3 [8], from the values for K a,ICRU90 and c K,ICRU90 stated in this work the following equations need to be used: K a,ISO2019 = K a,ICRU90 · k ISO2019,ICRU90 and c K,ISO2019 = c K,ICRU90 k ISO2019,ICRU90 with k ISO2019,ICRU90 = K a,total K a,ICRU90 = To obtain corresponding values which are compatible with the values in the outdated ISO 4037-3 as of 1999, the following equations need to be used: K a,ISO1999 = {K a,ICRU90 · k ISO2019,ICRU90 · (1 − g)} and c K,ISO1999 = c K,ICRU90 {k ISO2019,ICRU90 · (1 − g)} with g being the fraction of the kinetic energy transferred to charged particles that is subsequently lost on average in radiative processes (bremsstrahlung, in-flight annihilation, and fluorescence radiations) as the charged particles slow to rest in the material (air) [13].
Thus, of course, the values for the operational quantities, C, are independent of the scheme used, be it according to ICRU90, ISO1999 or ISO2019 as the corresponding corrections cancel each other out during the multiplication leading to the operational quantity: with C either being H or D.

Impact of the newly proposed quantities
The impact of the newly proposed quantities is investigated by the calculation of the ratio of the conversion coefficients for the newly proposed and the current operational quantities, see figure 5. This ratio represents the response of a dosemeter with respect to the newly proposed quantities while the dosemeter is assumed to have an ideal response of unity with respect to the current quantities.
From the top of figure 5 it is obvious that, for whole body and area dosemeters, a simple change of the calibration factor can be sufficient (depending on the dosemeter's response with respect to the current quantities) to fulfill at least the minimum performance requirements according to IEC 62387 [23] or IEC 61526 [24], i.e. a response within 0.71 and 1.67 between 80 keV and 1.25 MeV; possibly even between about 50 keV and 7 MeV. Conversion coefficients from total air kerma to personal dose for normal radiation incidence (α = 0 • , red upper curve) as well as for rotational incidence (ROT, blue lower curve) for mono-energetic values taken from ICRU [5], interpolated as described in the text, lines, as well as values averaged over radiation qualities, symbols.

Figure 2.
Conversion coefficients from total air kerma to directional and personal absorbed dose in the lens of the eye for normal radiation incidence (α = 0 • , red upper curve) as well as for rotational incidence (ROT, blue lower curve) for mono-energetic values taken from ICRU [5], interpolated as described in the text, lines, as well as values averaged over radiation qualities, symbols.

Figure 3.
Conversion coefficients from total air kerma to personal absorbed dose in local skin on the rod phantom for normal radiation incidence (α = 0 • , red upper curve) as well as for rotational incidence (ROT, blue lower curve) for mono-energetic values taken from ICRU [5], interpolated as described in the text, lines, as well as values averaged over radiation qualities, symbols. Comparison of spectra of the L, N, H, W and RQR series with 100 keV endpoint energy (only in the W series 100 keV endpoint energy is not available, therefore, 110 keV was chosen). The degree of filtration is largest for the L series and smallest for the RQR series [17,21].

Figure 5.
Ratio of conversion coefficients for the current operational quantities and the newly proposed for personal dose, top, absorbed dose in the lens of the eye, middle, and absorbed dose in local skin, bottom. On the left the quantities for individual monitoring and on the right the quantities for area monitoring are treated. This ratio represents the response of a dosemeter with respect to the newly proposed quantities while the dosemeter is assumed to have an ideal response of unity with respect to the current quantities. The data for the current quantities were taken from ISO [8] and, for very low energies, from the corresponding references in ISO [11,17]. Grey line: unity; dashed red lines: response limits according to IEC 62387 [23] or IEC 61526 [24] The middle part of figure 5 shows that, for eye lens dosemeters, above about 13 keV possibly no change of the calibration factor is required to fulfill the relevant IEC standard.
The bottom part of figure 5 reveals that, for local skin dosemeters, possibly no change is necessary at all. The strong difference between the graphs for h pK (0.07;α) rod /d local skin K (α) rod and h' K (0.07;α)/d local skin K (α) slab below about 20 keV have their reason in different interpolation methods used for h pK (0.07;α) rod and h' K (0.07;α), see the corresponding references given in ISO 4037-3 [8].
For all types of dosemeters, the following applies: if one wants to reach a more or less perfect response, i.e. unity, or one wants to fulfill the relevant IEC standard in a broader energy range, or the dosmeter's response with respect to the current quantities is rather disadvantageous, either the algorithm to determine the dose from the detector's signal(s) or, more likely, the detector's housing and/or filter material will need to be changed.

Method
The spectrum of low energy photon radiation qualities depends on the air density during an irradiation as, for example, a larger air density results in more absorption and scattering between the radiation source (usually an x-ray tube) and the point of test. Therefore, the spectra of all radiation qualities with a mean energy below 40 keV are calculated for air densities from ρ = 0.96 kg m −3 to ρ = 1.32 kg m −3 by applying the exponential attenuation law for photons. As a basis, the spectra at reference conditions, i.e. at ρ ref = 1.1974 kg m −3 , are used. From the resulting spectra at different air densities the conversion coefficients h(ρ) and d(ρ) have been calculated. The corresponding correction factor is given by where ρ is the considered air density, ρ ref is the reference air density, and h(ρ ref ) or d(ρ ref ) is the conversion coefficient calculated in the previous section, i.e. given in tables (A1)-(A7). The corresponding correction factor for the quantity total air kerma is The dependence of the conversion coefficients on the air density is approximately linear resulting in where m(d air ) is the slope for an air path d air between the source and the point of test. For the quantity total air kerma, K a , the following equation applies where d MC is the distance between the source and the monitor chamber to determine the total air kerma during an actual irradiation, see ISO 4037-2 [8].
The slope for both the total air kerma and the conversion coefficient m(d air ) depends approximately linearly on the distance d air where m(1.0 m) is the slope for d air = 1.0 m and m d is the slope of the slope m(d air ).
From the parameters m(1.0 m) and m d , a correction factor for the air density during an irradiation, ρ irr , finally results in (by inserting equation 6 into equation 5.1) for the conversion coefficients h or d, and to (by inserting equation 6 into equations 5.2 or 5.3) for the total air kerma K a . The approximation via the slopes m(1.0 m) and m d results in errors not larger than 1 % for the ranges of air densities specified in the tables of results (see below).
As the operational quantities are given by the product H = K a · h or D = K a · d, the corresponding correction factor is given by the product of the two contributions: The dose during an irradiation finally results from the dose under reference conditions in for total air kerma K a and in for the operational quantity H or D. Further details and examples for the calculation of the correction factors were outlined in a previous publication [12]. Reproduced from [12] by permission of Oxford University Press.

Results for the factors to account for air densities apart from the reference air density
Some typical values of the correction factors, k(ρ), are shown in figure 6. It can be seen that the correction of the influence of the ambient conditions is more important for the measurand air kerma, K a , than for the quantity personal dose, H p . This is due to the fact that the correction factor for the personal dose, k(ρ,H p ), results from the product of the correction factors for both, the quantity air kerma, k(ρ,K a ), and the conversion coefficient from air kerma to the personal dose, k(ρ,h pK ): k(ρ,H p ) = k(ρ,K a ) · k(ρ,h pK ). As can be seen from figure 6, these two correction factors compensate in part. Furthermore, the correction factor is closer to unity the larger the spectrum's mean energy as the absorption and scattering of photons decreases with rising energy. The parameters m(1.0 m) and m d to determine m(d air ) according to equation (4) are given for low energy photon reference radiation qualities in appendix C in tables (C1a)-(C7b) for the total air kerma, K a (R), the kerma coefficient, k Φ (R), and the conversion coefficients, c(R;α). The parameters are only given for those radiation qualities where the conversion coefficient itself is at least 0.0005 Sv Gy −1 or 0.0005 Gy Gy −1 , for h and d, respectively.

Summary
In this work, a complete data set necessary to perform accurate photon irradiations in terms of the newly proposed operational quantities in radiation protection is presented: • conversion coefficients as well as correction factors for other radiation field characteristics, e.g. the mean energy or the total air kerma, ready for adoption in ISO 4037-3 [8] and • correction factors for these conversion coefficients and radiation field characteristics to account for the actual air density during an irradiation, ready for adoption in ISO 4037-4 [9].
• Finally, the impact of the newly proposed quantities on the response of dosemeters is investigated for both individual and area monitoring as well as for normal and oblique radiation incidences.
All data are presented in the Appendices, see below. For convenience, the same data are available on the journal's website as supplementary data files in ASCII format compiled in a single zip file (available online at stacks.iop.org/JRP/42/011519/mmedia). Table A1 provides data for the fluence weighted mean energy, E(R), the kerma coefficient (i.e. total air kerma using the divided by photon fluence), k Φ (R), one minus radiative losses in air, (1−g)(R), and the ratio (µ en,not_renormalized /µ en,renormalized )(R) for reference radiation qualities R. Tables (A2)-(A7) provide data for the conversion coefficients, c K (R;α), for the coefficients listed in table 1.
All values presented are based on data calculated using the kerma-approximation method, i.e. during an irradiation, charged particle equilibrium must be assured. Appendix B. Tabulated results for a distance of 2.5 m between the radiation source and the point of test Table B1 provides data for the fluence weighted mean energy, E(R), the kerma coefficient, k Φ (R), one minus radiative losses in air, (1−g)(R), and the ratio (µ en,not_renormalized /µ en,renormalized )(R) for reference radiation qualities R. Tables (B2)-(B7) provide data for the conversion coefficients c K (R;α), for the coefficients listed in table 1. No data for the RQR radiation qualities are given for 2.5 m between the radiation source and the point of test as no corresponding spectra are available.
All values presented are based on data calculated using the kerma-approximation method, i.e. during an irradiation, charged particle equilibrium must be assured.
Appendix C. Tabulated parameters to determine the correction factors to account for air densities apart from reference air density Tables (C1a)-(C7a) provide values for m(1 m) and tables (C1b)-(C7b) provide values for m d for the determination of the air density correction, see equations (2) and following, as well as the corresponding text for details. Table A1. Fluence weighted mean energy, E(R), kerma coefficient, k Φ (R), one minus radiative losses in air, (1−g)(R), and the ratio (µ en,not_renormalized /µ en,renormalized )(R) for photon reference radiation qualities, R. The values are valid for a distance of 1.0 m between the radiation source and the point of test.      Table A3. Conversion coefficients for the maximum absorbed dose in the complete lens for left and right irradiations for different irradiation geometries, d lensK (R;α), for photon reference radiation qualities, R, in Gy/Gy. The values are valid for a distance of 1.0 m between the radiation source and the point of test. The standard uncertainties (k = 1) are in the order of 5·10 −4 or ± 2 %, whatever is larger.              Table B3. Conversion coefficients for the maximum absorbed dose in the complete lens for left and right irradiations for different irradiation geometries, d lensK (R;α), for photon reference radiation qualities, R, in Gy/Gy. The values are valid for a distance of 2.5 m between the radiation source and the point of test. The standard uncertainties (k = 1) are in the order of 5·10 −4 or ± 2 %, whatever is larger. Data are only given in case the deviation from the data for d air = 1.0 m is larger than 0.2 %.             Table B6. Conversion coefficients for the personal absorbed dose in local skin on the rod phantom for different irradiation geometries,    Table B7. Alternative conversion coefficients for the maximum absorbed dose in the sensitive cells of the lens for left and right irradiations for different irradiation geometries, d lens,sensK (R;α), for photon reference radiation qualities, R, in Gy/Gy. The values are valid for a distance of 2.5 m between the radiation source and the point of test. The standard uncertainties (k = 1) are in the order of 5·10 −4 or ± 2 %, whatever is larger. Data are only given in case the deviation from the data for d air = 1.0 m is larger than 0.2 %.       Table C2a.  Table C2b.  Table C3a.  Table C3b.  Table C4a.   Table C5a.  Table C5b.  Table C6a.  Table C6b.    Table C7a.  Table C7b.