Dosimetry of inhaled 219Rn progeny

Abstract During prostate cancer treatment with 223Ra. 219Rn (actinon) occurs and may be exhaled by the patient. Nurses and other hospital employees may inhale this radionuclide and its decay products. The alpha-emitting decay products of actinon deposited within a body will irradiate tissues and organs. Therefore. it is necessary to evaluate organ doses of actinon progeny. The purpose of this study is to set up a dosimetric method to assess dose coefficients for actinon progeny. The effective dose coefficients were calculated separately for three modes. The unattached mode which concerned the activity median thermodynamic diameter (AMTD) of 1 nm. and the nucleation and accumulation modes which are represented by activity median aerodynamic diameters (AMAD) of 60 and 500 nm respectively. The recent biokinetic models of actinon progeny developed in the Occupational Intakes of Radionuclides (OIR) publications series of the International Commission of Radiological Protection (ICRP) were implemented on BIOKMOD (Biokinetic Modeling) to calculate the number of nuclear transformations per activity intake of actinon progeny. The organ equivalent and effective dose coefficients were determined using the dosimetric approach of the ICRP. The inhalation dose coefficients of actinon progeny are dominated by the contribution of lung dose. The calculated dose coefficients of 211Pb and 211Bi are 5.78 × 10−8 and 4.84 × 10−9 Sv.Bq−1 for unattached particles (AMTD = 1 nm). and 1.4 × 10−8 and 3.55 × 10−9 Sv.Bq−1 for attached particles (AMAD = 60 nm). and 7.37 × 10−9 and 1.91 × 10−9 Sv.Bq−1 for attached particles (AMAD = 500 nm). These values are much closer to those of the recently published ICRP 137.


INTRODUCTION
Actinon ( 219 Rn) is a radioactive noble gas and a decay product of 223 Ra in the 235 U decay chain. 219 Rn decays through the short-lived progeny 215 Po. 211 Pb. 211 Bi and 207 Tl to the stable nuclide 207 Pb (Fig. 1). In contrast to radon ( 222 Rn) and thoron ( 220 Rn) which leave the soil and building materials and enter into the atmosphere. 219 Rn due to its very short half-life (3.96 s) is generally less able to emanate from mineral matrices. Because of typically very low concentrations in the ambient air. exposure to 219 Rn and its progeny are usually neglected. Thus. the measurement of 219 Rn has not been described in standards such as ICRP 137 or ICRU 88 [1,3]. Recently. in hospitals cancer treatment with 223 Ra (Xofigo) was introduced [4,5]. 223 Ra is injected into patients to fight against bone metastasis of prostate cancer. In the decay chain. 219 Rn occurs which may be exhaled by the patient. Secondary exposure of care-takers in the hospital and at home may happen by inhalation of actinon and its decay products.
Whereas many papers have been published on dosimetric studies of radon. thoron and their decay products. the International Commission on Radiological Protection (ICRP) has published inhalation dose coefficients of decay products of actinon ( 211 Pb and 211 Bi) using the size characteristics of radon progeny [1].
There are several pieces of software for internal dose assessment. However. most of them are commercialized. In the present work. the models for inhalation of actinon progeny have been mathematically implemented using a freely available package ICRP130Models on the recent version of BIOKMOD (version 5.4). and a dosimetric method is established to evaluate inhalation dose of actinon progeny using Microsoft excel. To make it effective. the effective doses and the organ equivalent doses in lung and in other organs of inhaled 219 Rn progeny such as 211 Pb and 211 Bi were determined separately as a function of particle size distribution of three modes. using the human respiratory tract model (HRTM). the human alimentary tract model (HATM) and systemic models developed by ICRP [1,6,7]. The aim of this study is to determine the inhalation dose coefficients of actinon decay products. This approach could be used to also determine the dose conversion • 226 Fig. 1. Decay chain of 223 Ra with half-lives and decay-energy types [1,2]. coefficient of actinon progeny for a real situation of secondary exposures of nurses at hospitals or the members of public at home.

MATERIAL AND METHODS
In this section the internal dose calculations of actinon progeny are introduced. First the deposition fractions in the different regions of HRTM are presented. Then the biokinetic models describing dissolution. absorption and elimination of deposited material in the human body were implemented. and the activities occurring within the organs or tissues were calculated. Finally. the dosimetric model was applied to assess organ equivalent dose and effective dose coefficients with the calculation of radiation weighted S coefficient values. denoted S w . or specified source and target organs which were derived from the new ICRP voxel computational phantoms for a reference adult [8].

Aerosol fractional deposition in human respiratory tract
Up to now there is no activity size measurement of actinon progeny. Due to its short half-life. 219 Rn will probably not be able to escape from the point where it is formed. Therefore. 219 Rn and its progeny are very

Biokinetic models of actinon progeny
The behavior of inhaled radioactive particles in the respiratory tract is described in the HRTM and some changes have been made in ICRP 130 [6,7]. The systemic models for actinon progeny ( 211 Pb and 211 Bi) and the HATM are described respectively by ICRP 137 and ICRP 100 [1,9]. The biokinetic models describing inhalation of each actinon progeny are represented in Fig. 2 for 211 Pb and Fig. 3 for 211 Bi. The dissolution and absorption parameter values of inhaled 211 Pb were applied to 211 Bi formed in the respiratory tract [7,10]. The systemic model for bismuth as progeny of lead (bismuth formed within the body) is described in ICRP 137 [1]. The biokinetic model parameters. i.e. transfer rate. absorption parameter values of the actinon progeny between organs or tissues in the HRTM. HATM and systemic models were taken from ICRP publications [1,7].
The dynamic behavior of decay products of actinon in the organism can be represented by a number of interconnected compartments with transfer coefficients describing the exchange of material. The transfer of inhaled actinon progeny between compartments can be modelled as systems of coupled. first-order differential equations. These systems have been implemented and solved in BIOKMOD; a computer tool developed by Sanchez using the Wolfram Mathematica programming language [11][12][13]. The general form of the rate of change of the radionuclide concentration i. can be written as in [14].
where A i is the retention in compartment i. k i.j is the transfer coefficient of material from compartment i to compartment j (the first term represents the inputs to the compartment i from the rest of compartments  r =i and the second term represents the outputs from the compartment i to others compartments j =i). λ is the physical decay constant and b i (t) is the input from outside. The initial conditions were determined by using the deposition fractions ( Table 1). The number of nuclear transformations occurring in source region r S during the commitment period (18250 days for adults) denoted where 18 250 (50 years) represents the number of days which is the commitment period for an adult. The summation in the equation above is over the association of kinetic compartments i forming source regions r s . These numbers of nuclear transformations for actinon progeny were calculated by using Wolfram Mathematica software. The number of nuclear transformations per activity intake in the source region r s is given in the following equation [8]: where A i (0) represents the initial deposition fraction in each compartment i.

Dosimetric models
This section presents the method used to calculate the radiationweighting S coefficient. committed equivalent doses in each organ/tissue within the body and effective dose after inhalation of actinon decay products.

Radiation weighted S coefficient
The radiation weighted S coefficient S w (r T ← r s ) represents the time-dependent equivalent dose rate in the target tissue r T per unit activity present in source tissue r S . S w (r T ← r s ) was calculated for each radiation type emitted by the actinon progeny. The general form of the S w coefficient is given by [8].
where w R is the radiation weighting factor for radiation type R. E Ri is the energy of the i th radiation of type R emitted in the nuclear transformations of the radionuclide in joules ( J); Y Ri is the yield of the i th radiation of type R per nuclear transformations (Bq.s −1 ); φ(r T ← r S .E Ri ) is the specific absorbed fraction denoted as SAF which is defined as the fraction of energy E Ri of radiation type R emitted within the source tissue/organ r s that is absorbed per mass in the target tissue r T (kg −1 ). 211 Pb decays to the nuclide 211 Bi through beta particle emission. In this case the spectral data are used in the calculation of S w instead of mean energy value [8]. S w for beta radiation is given by: where P(E) is proportional to the probability that the beta particle will be emitted with kinetic energy between E and E + dE. E represents the beta energy. P(E) and E are taken from DECDATA software [16]. The calculation of integral over the beta particle spectrum is made by numerical methods. However. 211 Bi decays to the nuclide of 207 Tl through alpha particle emission and to 211 Po through beta emission. The form of S w (r T ← r s ) of alpha emission is given by: w α.β.γ values (radiation weighting factor) are taken form ICRP publication 103 [17]. The specific absorbed fractions values are taken from the electronic data of ICRP 133 [8]. The linear interpolation was done on Microsoft excel to find each corresponding value of φ(r T ← r S .E Ri ) to E Ri .For the compartment called other soft tissue in the biokinetic models. including several source regions r s . the specific absorbed fraction φ(r T ← r S ) was calculated as [8]: Committed equivalent dose and committed effective dose The committed equivalent dose h (r T ) in the target region was calculated for reference adult male h M (r T ) and reference adult female h F (r T ) as [8]: where S M W (r T ← r S ) and S F W (r T ← r S ) are the S coefficients for male and female respectively. There is an exception for target regions consisting of several target tissues: extrathoracic region. lung. colon and lymphatic nodes. For each target region in those tissues there is an associated fractional weighting factor. The committed equivalent dose for those particular regions was calculated as: where f (r T .T) is the fractional weight. the values are taken from ICRP 133 [8]. The committed effective dose coefficient was calculated as [17]: where w T is the weighting factor for tissue T taken from the ICRP publication [17]. Microsoft Excel was used to calculate the radiation weighting S coefficient. the committed equivalent dose coefficient and the committed effective dose coefficient after inhalation of the actinon progeny. Fig. 3. Inhalation biokinetic compartmental model for bismuth. It combines the HATM [9]. The systemic model of bismuth [1] and the HRTM [6,7]. Extrathoracic region: ET 1 = anterior nose, ET 2 =posterior nasal passages, larynx, pharynx and mouth. LN ET = lymph nodes. Thoracic region: BB = bronchial, bb = bronchiolar, AI = alveolar-interstitial, LN TH = lymph nodes [15].

RESULTS AND DISCUSSION
The calculated committed equivalent dose coefficients (male and female) from 211 Pb and 211 Bi for each target organ/tissue are shown in the Appendix (Tables A1 and A2). In general. the equivalent dose coefficients in the lung and extrathoracic tissues were relatively larger than in other organs for the three particles sizes (radon and thoron progeny as well). For the progeny of 211 Pb. the equivalent doses in bronchi basal cells. bronchiole basal cells and ET 1 basal cells were the highest for each mode: unattached. nucleation and accumulation respectively. However. for the progeny of 211 Bi the ET 2 basal cells. bronchiole basal cells and ET 2 basal cells were the target regions where the equivalent dose coefficient was the highest for unattached (1 nm). nucleation (60 nm) and accumulation (500 nm) modes. respectively. The committed equivalent dose in each tissue/organ for actinon progeny in unattached and attached modes are given in Table 2. For both actinon progeny the lung equivalent dose was the highest for unattached and nucleation modes. However. the ET airways (extrathoracic region) equivalent dose was the highest for accumulation mode. The lung dose strongly depends on the percentage of the deposition fraction within the bronchial and bronchiolar tissues. The organs and effective doses (dose coefficients) after inhalation actinon ( 219 Rn) progeny. 211 Pb and 211 Bi in unattached and attached (nucleation and accumulation) modes are given in Table 2. The dose coefficient of short-lived actinon progeny was the highest for unattached mode (1 nm).
In this study. the lung equivalent dose for 211 Pb (4.65 × 10 −7 Sv.Bq  Table 3 effective dose coefficients of actinon progeny calculated in this study were compared to those of ICRP 137 and the differences were found to be in the range −36 to 0.4% for 211 Pb and 0.8-260% for 211 Bi. The calculations were made using assumptions of the Occupational Intakes of Radionuclides (OIR) publications series. The differences found between the dose coefficients would come from the calculation pattern (the numerical integration of equation (5). the calculation of specific absorbed fractions φ(r T ← Other) for the compartments denoted other soft tissues and the linear interpolation of specific absorbed fractions) and some details about the treatment of decay products formed in the respiratory tract. Apart of 211 Bi. all other progeny radionuclides formed in the respiratory tract ( 207 Tl and 211 Po) after inhalation of 211 Pb were neglected. In addition. the bound parameter values (transfer rate from the bound-state compartments to the body fluids as shown in Fig. 2) were also neglected for bismuth formed in the respiratory tract. Inhalation dose coefficients for actinon progeny were also calculated by Stabin and Siegel [19]. The dose coefficients were 3.46 × 10 −11 and 1.76 × 10 −9 Sv.Bq −1 for 211 Pb and 211 Bi. respectively [18]. One should note that Stabin and Siegel assessed the dose coefficients for one particles size mode (AMAD 5 μm) with the aerosol type 'M' in a particular situation of exposure. The dose coefficients (inhalation) of actinon progeny of tissues other than the lungs are ∼5% of the total effective dose in the unattached and nucleation modes. while for the accumulation mode the coefficient is ∼15% of the total effective dose. Overall the effective dose of inhaled actinon progeny was dominated by the lung equivalent dose. The extrathoracic equivalent dose was of the same order of magnititude or lower than that to the lungs. However its contribution to the effective dose was quite low, because it is one of the 13 remainder organs (equivalent dose of remainder tissues is the arithmetic mean of the 13 equivalent doses of the remainder tissues) [17].

CONCLUSION
This work presents internal dose calculations of inhaled actinon progeny. The effective dose coefficients were calculated separately for three modes. using biokinetic and dosimetric models developed in the recent OIR publications series of ICRP. The biokinetic models of 211 Pb and 211 Bi have been implemented and solved in BIOKMOD using the approach developed by Sanchez is described in references [11,12]. The inhalation actinon progeny provided the highest dose to the lungs and ET airways. The calculations indicated that the most exposed region of the lung tissues for 211 Pb was the bronchial tissue for the unattached and attached fractions respectively for particle sizes of 1 nm and 500 nm and the bronchiolar tissue for the attached fraction of 60 nm. However. the most exposed region of the lung tissues for 211 Bi was the bronchiolar tissue for unattached fraction (1 nm) and bronchioles for attached fractions (60 nm and 500 nm particles size). The inhalation dose coefficients of actinon progeny found in this work were much closer to those of ICRP 137. Furthermore. in order to work out the dose conversion coefficient for actinon ( 219 Rn) decay products. a study of activity size distributions and measurement of activity concentration of actinon progeny is recommended to be conducted in hospitals during the treatment of prostate cancer metastasis with 223 Ra. Table A1. Committed equivalent dose coefficients (Sv.Bq −1 ) for target region after inhalation 211 Pb as decay product of actinon (reference adult male and female). f (r T, T) M h(r T ) and f (r T, T) F h(r T ) are committed equivalent dose coefficients for adult male and female respectively

Target tissue a
Unattached Nucleation Accumulation