Giuseppe Battistoni; INFN, Milano
Stefan Roesler; CERN, Geneva
M. Pelliccioni, S. Roesler
Here the calculation conversion coefficients (fluence-to-effective dose and fluence-to-ambient dose equivalent) for radiological protection as calculated with FLUKA is presented. They are calclulated for photons, electrons, positrons, protons, neutrons, muons, charged pions and kaons, for incident energies up to 10 TeV.
ICRP (ICRP Publication 74 [1]) and ICRU (ICRU Report 57 [2]) recommended conversion coefficients for use in radiological protection for electrons and photons of energies up to 10 MeV and for neutrons up to 180 MeV. For various purposes conversion coefficients for higher energies and other kind of radiation are needed: for this reason sets of fluence-to-effective dose and fluence-to-ambient dose equivalent conversion coefficients for all kind of radiation (photons, electrons, positrons, protons, neutrons, muons, charged pions and kaons) and for incident energies (up to 10 TeV) of practical interest have been calculated in recent years using the FLUKA code [6]-[20].
All conversion coefficients have been calculated using the same methodology (same code, same geometry, same rules), they therefore constitute a coherent system of dosimetric data. The calculated conversion coefficients can be found on this web site (zip, tar.gz). In this documentation information can be found about the calculation methodology, the use of conversion coefficients and the papers to cite when using them for radiation protection calculation.
Definitions ::::::::::::There are two types of quantities defined for use in radiological protection: protection quantities (defined by the ICRP and used for assessing the exposure limits) and operational quantities (defined by the ICRU and intended to provide a reasonable estimate for the protection quantities).
The following is based on the set of protection quantities recommended in ICRP Publication 60 [3]: it includes the tissue or organ equivalent doses (HT ) and the effective dose (E). The equivalent dose HT in a tissue or organ T is given by:
|
HT = ∑R (wR · DT, R ) | (1) |
where DT, R is the average absorbed dose from radiation R, in tissue T, wR is the radiation weighting factor for radiation R and the sum is performed through all kind of radiation that constitue the radiation field considered. Table 1 gives the values of radiation weighting factors as recommended by ICRP. For radiation types and energies that are not included in table 1 an approximation to wR can be obtained by the calculation of the average quality factor, Q, at a depth of 10 mm in the ICRU sphere (for the definition of the ICRU sphere see section 3.2:
|
Q = 1/D ∫L Q(L) · D(L) · dL | (2) |
where D(L)dL is the absorbed dose at 10 mm between linear energy transfer values of L and L + dL and Q(L) is the corresponding quality factor. The relation between Q and L (recommended by ICRP 60) is shown in table 2.
Table 1: Values for radiation weighting factors recommended in ICRP Publication 60 [3].
| RADIATION | wR |
| Photons | 1 |
| Electrons and muons | 1 |
| Neutrons: | |
| E < 10 keV | 5 |
| 10 keV < E < 100 keV | 10 |
| 100 keV < E < 2 MeV | 20 |
| 2 MeV < E < 20 MeV | 10 |
| E > 20 MeV | 5 |
| Protons, other than recoil protons (E > 2 MeV) | 5 |
| α particles, fission fragments, heavy nuclei | 20 |
Table 2: Relation between L in water and the quality factor Q, as recommended by ICRP Publication 60 [3].
|
L in water keV / µm |
Q(L) (with L in keV / µm) |
| < 10 | 1 |
| 10 ÷ 100 | 0.32 · L – 2.2 |
| > 100 | 300 / √L |
The effective dose E is the sum of the weighted equivalent doses in all the tissues and organs of the body. It is given by the expression:
|
E = ∑T wT · HT | (3) |
where HT is the equivalent dose in tissue or organ T, wT is the weighting factor for tissue T and the sum is performed on all tissue and organs involved in irradiation. Table 3 gives the values of tissue weighting factors as recommended by ICRP.
Table 3: Tissue weighting factors recommended in ICRP Publication 60 [3].
| TISSUE or ORGAN | wT |
| Gonads | 0.20 |
| Red bone marrow, Colon, Lung, Stomach | 0.12 |
| Bladder, Breast, Liver, Oesophagus, Thyroid | 0.05 |
| Bone surface, Skin | 0.01 |
| Remainder | 0.05 |
The protection quantities HT and E are not directly measurable [4], but may be related by calculation to the radiation field if the condition or irradiation are known. The only way to estimate HT and E is to measure the radiation field outside the body and to convert it to HT and E using previously calculated conversion coefficients.
The mean absorbed dose DT, R is a quantity that cannot be evaluated experimentally, therefore operational quantities [5] (defined in terms of the quality factor Q) should be used. The operational quantities are intended to provide a reasonable estimate of the protection quantities, the goal is that the value of the appropriate protection quantity is less than that of the corresponding operational quantity.
For strongly penetrating radiation the appropriate operational quantity for area monitoring is ambient dose equivalent. The ambient dose equivalent H*(d) at a point in a radiation field is the dose equivalent that would be produced by the corresponding expanded and aligned field in the ICRU sphere at a depth d, on the radius opposing the direction of the aligned field. The recommended value of d for penetrating radiation is 10 mm. The dose equivalent at other depths may be considered when the dose equivalent at 10 mm provides an unacceptable underestimate of the effective dose.
All calculations were made using the FLUKA code (details can be found in papers [6]-[20]). In all cases the statistical uncertainties of calculation results were estimated by doing calculations in several batches and compunting the standard deviation of the mean. The number of histories considered was large enough to keep the standard deviation of conversion coefficients below a few percents.
Subsections:In computing effective dose an hermaphrodite mathematical model has been used. It was derived from the male phantom developed for MCNP by GSF-Forschungszentrum für Umwelt und Gesundheit (Germany) [21]. The MCNP phantom was translated in terms of bodies and regions appropriate for the combinatorial geometry of FLUKA. Then the female organs (breast, ovaries and uterus) were added. The various organs and tissues of human body have been represented by 68 regions. Internal organs have been considered to be homogenous in composition and density. The composition was limited to the 14 elements: H, C, N, O, Na, Mg, P, S, Cl, K, Ca, Fe, Zr and Pb. Different densities have been used for the lungs (0.296 g · cm3), bone (1.486 g · cm3), red marrow (1.028 g · cm3), soft tissue (0.987 g · cm3) and skin (1.105 g · cm3).
Calculations of effective dose have been carried out on the basis of equation 3 using the radiation weighting factors shown in table 1. For charged pions and kaons the approximation given by eq. 2 was used. If one is willing to adopt other wT values, the calculated data (fE calculated following eq. 4) should be scaled with respect to the wR used.
Concerning the tissue weighting factors wT, values shown in table 3 were used and the so called "remainder dose" has been evaluated from the doses to nine additional individual organs and tissues as arithmetic mean. In the present calculations, the dose to a given organ or tissue spread throughout the whole body and represented in the mathematical model by several regions (for instance skin, bone, red bone marrow, muscle...) has been determined as arithmetic mean of the doses received in the single constituent regions. According to ICRP Publication 67 the higher value of doses to the ovaries and testes was applied to the gonad weighting factor. The dose to muscles has been assumed as the arithmetic mean of the doses received by the part of the body volume which is not attributed to any other organ or tissue.
Calculations were performed for fully isotropic radiation incidence (obtained by the use of an inward-directed, biased cosine source on a spherical surface), from semi-isotropic (from the top) radiation source and with broad parallel beams with the following directions of incidence: antero-posterior, postero-anterior, right lateral, from the top and from the bottom. The medium between the source and the phantom was assumed to be vacuum.
The energy per primary incident particle deposited in the regions representing the various organs and tissues has been determined by use of MonteCarlo simulations.
Once the effective dose (E(ε)) as a function of particle energy for various kinds of radiation was computed, the fluence-to-effective dose conversion coefficients (fE(ε)) were calculated in terms of effective dose per unit of fluence (Sv · cm2):
|
f(E) = E(ε) / Φ(ε) | (4) |
where Φ(ε) is the fluence of primary particle of energy ε.
Calculation results are presented in section 4.
According to the definition of ambient dose equivalent, the geometry of the problem was very simple. A 30 cm diameter sphere of unit density tissue and composition as specified by ICRU (H, 10.1%; C, 11.1%; N, 2.6%; O, 76.2%; %-compositions are given by weight) was exposed to a parallel particle beam uniformely expanded over its front surface. The medium between the source and the ICRU sphere was assumed to be vacuum.
In order to obtain the depth-dose distributions along the principal axis of the sphere, the energy deposited has been scored as a function of the depth and radius in an R-Z binning cylindrical structure. Different grids have been selected according to the depth: 0.2 cm longitudinal bins have been considered up to 2 cm, and 1 cm longitudinal bins for larger depths. The radial bin was taken to be 1 cm.
The determination of the dose equivalents has been carried out taking the quality factor to be a function of linear energy transfer L, as shown in eq. 2. Therefore the energies deposited per unit mass have been directly multiplied by the quality factor appropriate to the linear energy transfer of the charged particle imparting energy to the matter.
The values of the ambient dose equivalent have been averaged over the depth 0.95-1.05 cm or 0.9-1.1 cm according to the incident energy.
Once the ambient dose equivalent (H*(ε)) as a function of particle energy for various kinds of radiation was computed, the fluence-to-ambient dose equivalent conversion coefficients (fH*(ε)) were calculated in terms of ambient dose equivalent per unit of fluence (Sv · cm2):
|
fH*(ε) = H*(ε) / Φ(ε) | (5) |
where Φ(ε) is the fluence of primary particle of energy ε.
Calculation results are presented in section 4.
The calculated sets of conversion coefficients can be found of the FLUKA web server in one compressed file (tar.gz or zip archive).
Each file contains three columns: energy GeV, conversion coefficients (Sv · cm2) and %-standard deviation.
The names of files with fluence-to-effective dose conversion coefficients are:
PHOTONS: eapph.dat ANTERO-POSTERIOR irradiation ebtph.dat from BOTTOM irradiation eisph.dat ISOTROPIC irradiation elaph.dat LATERAL irradiation epaph.dat POSTERO-ANTERIOR irradiation esiph.dat SEMI-ISOTROPIC irradiation etpph.dat from the TOP irradiation ELECTRONS: eapel.dat ANTERO-POSTERIOR eisel.dat ISOTROPIC elael.dat LATERAL epael.dat POSTERO-ANTERIOR esiel.dat SEMI-ISOTROPIC etpel.dat TOP POSITRONS: eispo.dat ISOTROPIC PROTONS: eappr.dat ANTERO-POSTERIOR eispr.dat ISOTROPIC elapr.dat LATERAL epapr.dat POSTERO-ANTERIOR esipr.dat SEMI-ISOTROPIC etppr.dat TOP NEUTRONS: eapne.dat ANTERO-POSTERIOR ebtne.dat BOTTOM eisne.dat ISOTROPIC elane.dat LATERAL epane.dat POSTERO-ANTERIOR esine.dat SEMI-ISOTROPIC etpne.dat TOP POSITIVE MUONS: eapmp.dat ANTERO-POSTERIOR eismp.dat ISOTROPIC elamp.dat LATERAL epamp.dat POSTERO-ANTERIOR esimp.dat SEMI-ISOTROPIC etpmp.dat TOP NEGATIVE MUONS: eapmm.dat ANTERO-POSTERIOR eismm.dat ISOTROPIC elamm.dat LATERAL epamm.dat POSTERO-ANTERIOR POSITIVE PIONS: eappp.dat ANTERO-POSTERIOR eispp.dat ISOTROPIC elapp.dat LATERAL epapp.dat POSTERO-ANTERIOR NEGATIVE PIONS: eappm.dat ANTERO-POSTERIOR eispm.dat ISOTROPIC elapm.dat LATERAL epapm.dat POSTERO-ANTERIOR POSITIVE KAONS: eapkp.dat ANTERO-POSTERIOR eiskp.dat ISOTROPIC NEGATIVE KAONS: eapkm.dat ANTERO-POSTERIOR eiskm.dat ISOTROPIC
The names of files with fluence-to-ambient dose equivalent conversion coefficients are:
adeel.dat ELECTRONS adekm.dat NEGATIVE KAONS adekp.dat POSITIVE KAONS ademm.dat NEGATIVE MUONS ademp.dat POSITIVE MUONS adene.dat NEUTRONS adeph.dat PHOTONS adepm.dat NEGATIVE PIONS adepp.dat POSITIVE PIONS adepo.dat POSITRONS adepr.dat PROTONS
The conversion coefficients are also implemented into a FLUKA user-routine which is distributed with the FLUKA package (file name: deq99c.f, subdirectory: flutil). Instructions for using and references can be found in the header of the file.
Use of conversion coefficients ::::::::::::Once the fluence spectrum Φ(ε) (cm–2) is known (by experimental measurements or through calculations) the effective dose E can be calculated using the following expression:
|
E = ∫ fE(ε) · Φ(ε) · d(ε) | (6) |
and the ambient dose equivalent can be calculated in a similar way:
|
H* = ∫ fH*(ε) · Φ(ε) · d(ε) | (7) |
When using these sets of conversion coefficients for calculations, you should cite paper [22].
Bibliography ::::::::::::