Bronchial Dosimeter for Radon Progeny

Transcription

1 Bronchial Dosimeter for Radon Progeny T.K. Cheung 1, K.N. Yu 1, D. Nikezic 1, A.K.M.M. Haque 1 and D. Vucic 2 1 Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong 2 Faculty of Technology, University of Nis, Lescovac, Yugoslavia ABSTRACT Traditionally, assessments of the bronchial dose from radon progeny were carried out by measuring the unattached fraction (f p ) of potential alpha energy concentration (PAEC), the total PAEC, activity median diameters (AMDs) and equilibrium factor, and then using dosimetric lung models. A breakthrough was proposed by Hopke et al. (1990) to use multiple metal wire screens to mimic the deposition properties of radon progeny in the nasal (N) and tracheobronchial (T-B) regions directly. In particular, they were successful in using four layers of 400-mesh wire screens with a face velocity of 12 cm/s for the simulation of radon progeny deposition in the T-B region. Oberstedt and Vanmarcke (1995) carried out precise calibrations for the system, and named the system as the bronchial dosimeter. Based on these, Yu and Guan (1998) proposed a portable bronchial dosimeter similar to a normal measurement system for radon progeny or PAEC and consisted of only a single sampler and employed only one 400-mesh wire screen and one filter. However, all these bronchial dosimeters in fact only determined the fraction of potential alpha energy from radon progeny deposited in the T-B region, which required certain assumptions and calculations to further give the final bronchial dose. In the present work, a true bronchial dosimeter was designed, which consisted of four 400-mesh wire screens and a filter paper. With a face velocity of 3.3 cm/s for home exposure and 4.6 cm/s for mine exposure, the deposition pattern on the wire screens were found to satisfactorily match the variation of the dose conversion factor (in the unit of msv/wlm) with the size of radon progeny from 1 to 1000 nm. In this way, this bronchial dosimeter directly gave the bronchial dose from the alpha counts recorded on the wire-screens and the filter paper. Calculations on the dose conversion coefficient (DCC) using the proposed bronchial dosimeter and the lung dosimetric model were performed for typical aerosol characteristics, and values obtained from the bronchial dosimeter gave overestimation on the DCC of 11.1% and 2.4% for typical home and mine conditions, respectively. With the development of this bronchial dosimeter, the present practice of dose estimation from largescale radon surveys can be replaced by large-scale dose surveys in the future. INTRODUCTION During the past decades, considerable attention has been directed towards the potential hazard of exposure of the general population at working places and in homes to radon ( 222 Rn) and its decay products (or progeny). It is now established that inhalation of airborne short-lived radon progeny in the indoor and outdoor environment yields the greatest amount of the natural radiation exposure to the human public. The major health concern comes from the deposition of its progeny onto the epithelium cells of the bronchial airways in the respiratory tract (1). To access the corresponding bronchial dose, the use of dosimetric lung models is necessary. Under this method, information on several important parameters such as the unattached fraction (f p ), the potential alpha energy concentration (PAEC) of radon progeny and the equilibrium factor (F) are required. The measurements of the unattached fraction were only partially successful on the basis of wire screen methods (2). The collection efficiency versus particle diameter characteristics of wire screens did not permit a distinct separation of the unattached and attached fractions. Hopke et al. (3) suggested that the deposition characteristics of short-lived progeny in the nasal (N) and tracheobronchial (T-B) regions be simulated and the deposited activity measured directly. They provided the theoretical concept of such a measurement system in detail and proposed to use multiple wire screens to simulate the collection characteristics of the N and T-B regions. According to these specifications, Oberstedt and Vanmarcke (4) built and calibrated a measurement system called the bronchial dosimeter consisting of three sampling heads. The difficulties in measuring the activity median diameter (AMD) and the unattached fraction could thus be removed by using this first generation bronchial dosimeter. To improve on the portability of this dosimeter, Yu and Guan (5) proposed a new bronchial dosimeter as a model for a portable one, which consisted of a single sampler housing one 400-mesh metal wire screen and one filter paper only. In fact, these bronchial dosimeters all gave the fractional deposition of PAEC in the T-B region only. For determining the bronchial dose, further assumptions and calculations were needed. Therefore, it is beneficial to find ways to obtain the bronchial dose directly from a measurement system. This paper outlines the conceptual procedures for developing such a dosimeter based on the collection efficiencies of wire screens. 1

2 METHODOLOGY Dosimetric lung model The traditional approach to calculate the radiation dose from inhalation of airborne short-lived radon progeny is the use of dosimetric modeling of the respiratory tract. The first step is to depict the structure of the lung. For purposes of modeling deposition and movement of the inhaled aerosols, the descriptive features of the T-B tree must be formalized into distinct quantities, which can appear in mathematical functions. In the present work, the ICRP lung morphometric model (6) was employed, which recommended a dichotomous branching scheme in a symmetric tree in which the daughter generation branched with relatively little irregularity. Each generation of the lung divided its passageways into two identical subpassages, which in turn aggregated the next generation. A typical airway was represented by a cylindrical tube of appropriate wall thickness with fixed dimensions. The dimensions of the airway branches gradually changed as they penetrated deeper into the lung. In general, the average diameter and length of the tubes decreased with increasing orders of generations. The T-B tree was considered as comprising the bronchial (BB) and bronchiolar (bb) regions. In addition, it was necessary to identify the sensitive targets, which led to respiratory tract cancers likely to result from radiation exposure. The nuclei of secretory and basal cells were considered to be the sensitive targets in the BB region while only secretory cells were considered in the bb region. Equal radio-sensitivities were assumed for these two types of cells. Radiation doses to tissues and cells of the respiratory tract were functions of the air flow rate through the lung passages. There was a large amount of variability in the breathing characteristics and respiratory parameters. Therefore, average values for normal and healthy people were used. To predict radiation doses for different types of population groups, different breathing rates were intended for the particular environmental conditions. Reference values of breathing rates for mine workers (Mines) and members of the public (Homes) were chosen as 1.2 m 3 /hr and 0.78 m 3 /hr respectively (7). Having specified the physical characteristics of the lung and having recommended values for physiological parameters to be used in calculating radiation doses from the inhalation of radon progeny, the next step was to estimate the fractions of inhaled progeny deposited in each anatomical region. Several processes contribute to the aerosol deposition. The most important mechanisms included Brownian diffusion, inertial impaction and sedimentation. The relative contributions from these three main processes depended upon the size distribution of the inhaled aerosols. Therefore, the model was required to estimate regional deposition for a wide range of particle sizes. To provide a straightforward model, an empirical mathematical approach was applied to describe the regional deposition in the extrathoracic and thoracic airways from the literature (6, 8, 9). The inhalation process continuously deposits radon progeny in different generations of the lung. The deposited progeny are assumed to distribute uniformly on the surfaces, and are cleared by mucociliary transport or absorption into blood with an assumed transit time of 10 hours for the slow transfer process (7). To sum the regional doses for the respiratory tract, they must be adjusted for their relative radiation sensitivities. The total lung dose was calculated by introducing equally weighted apportionment factors between BB, bb and alveolar (AI) regions as 0.333:0.333: The weighting factor of 0.12 specified for lungs was also applied to the total dose calculated for the thoracic region, together with the quality factor of 20 for alpha particles, to obtain the effective dose. Dividing by the exposure, the dose conversion factor (DCF) in unit of msv/wlm was obtained. Based on the definition of an occupational working month as 170 hours and the occupancy factor, a factor for effective dose rate (EDF) having a unit of msv/s/wl or msv/y/wl could be derived from the DCF. Once the PAEC is known for a particular environment, the corresponding EDF can be determined. To fit the DCF distribution (with progeny size), the EDF distribution was normalized using a normalizing factor (n-factor) to obtain the distribution of normalized effective dose rate (). On knowing or assuming the progeny size distribution of an environment in interest, the effective dose per unit exposure to radon progeny (dose conversion coefficient, DCC) could be computed for that situation. Fitting the DCF distribution The particle-size dependent diffusion coefficient is commonly estimated by the Einstein equation modified with the Cunningham correction factor. Based on the fan model filtration theory (10, 11), a semiempirical equation of particle penetration through wire screens was employed. The penetration for a wire screen, with solid volume fraction α, wire thickness w and diameter d f, is given by 4α w P = exp π ( 1 α ) d f (1) where is the single fiber collection efficiency expressed as a sum of the efficiencies for several deposition processes including diffusion d, interception in, impaction im, and diffusional interception id. In fact, the 2

3 diffusion process dominates the overall collection efficiency for particle diameters below 100 nm. The interception and impaction processes become significant after few µm. The efficiency for diffusional interception is insignificant compared to that for diffusion until after 1 µm. The mathematical presentations for the four deposition efficiencies can be found elsewhere (12). The wire screen collection efficiency is simply equal to (1 penetration). For using N wire screens with the same wire factor WF in series, the exponent in eqn (1) should be multiplied by N to give obtain the gross penetration. The value of WF characterizes a particular wire screen through WF 2 3 [ cm ] = α w 5 3 ( 1 α ) d f (2) and by incorporating the sampling face velocity U, the wire-velocity parameter KVF is defined as 2 [ cm /s] U KVF = (3) [ WF] 1.5 Each wire screen has its own WF. The collection efficiencies, except the one for interception, change according to U. Hence, varying U is a way to shift the distribution curve with the progeny particle diameter (Fig. 1). The curve can also be changed by using different combinations of wire screens (Fig. 2). Both techniques did not produce satisfactorily fits to the response at large particle sizes ranging from around tens of nm to 1 µm, which corresponded to the attached mode of radon progeny. A factor (called k-factor in this paper), employing the residual efficiency of a filter paper for collecting radon progeny after their passing through the combination of wire screens, was introduced to compensate for the discrepancies (Fig. 3). Denoting the collection efficiencies for a combination of wire screens as wire, the overall collection efficiency for the sampling system system is expressed as system where k is the k-factor mentioned before. wire ( 1 ) = k (4) wire cm/s 3.3 cm/s 6.0 cm/s Collection Efficiency Figure 1. The collection characteristics of four 400-mesh wire screens for various sampling face velocities U. The corresponding flow rate for 2.0, 3.3 and 6.0 cm/s were 1.5, 2.5 and 4.5 L/min, respectively. Also shown is the calculated value for members of the public. 3

4 10 0 4x400mesh 5x400mesh 4x250mesh Collection Efficiency Figure 2. The collection efficiencies of various series of wire screens at sampling face velocity of 3.3 cm/s. Two types of wire screens were employed for comparison. Also shown is the value of for members of the public Collection Efficiency 10-1 Collection for 4x400mesh k x Penetration through 4x400mesh Overall collection 10-2 Figure 3. The collection efficiency of the proposed sampling system including the application of the k-factor. The sampling face velocity was 3.3 cm/s and the k-factor was In fact, the penetration for mesh was equivalently the collection on the filter paper. The for members of the public with the n-factor of msv/s/wl is also shown. Bronchial Dosimeter It is now possible to design a sampling system that can measure airborne radioactivity from which the DCC can be estimated. The schematic diagram of such a sampler is shown in Fig. 4. It consists of two sampling heads, A and B. The sample head A houses only one filter paper and collects all radon progeny passing through it. On the other hand, the sample head B houses a series of stainless steel wire screens on top of a filter paper. The combination of the screen series is chosen according to the dosimetric lung model being used. For example, four 400-mesh screens with a sampling face velocity of 3.3 cm/s was selected to simulate the distribution 4

5 Filter Flowmeter A Series of wire screens B To PUMP Figure 4. Schematic diagram of the sampling system of the proposed bronchial dosimeter for radon progeny. Two sampling heads are included. The choice of the wire-screen configuration in head B depends on the employed dosimetric lung model. curve for home exposure. The collected activities on both filter papers are to be measured using either gross alpha or alpha spectroscopic systems. The required measurement techniques on acquiring the PAECs of the collected activities by the sampler have been presented elsewhere (5, 13). The collection efficiency of the wire screen series wire is obtained by wire PAEC PAEC PAEC A B = (5) A where PAEC A and PAEC B are the measured PAECs collected on the filer papers in the sampling heads A and B, respectively. By using eqn (4), the collection efficiency for the proposed system system can be determined based on wire and selected k-value. The PAEC collected by the proposed system is computed by the product of system and PAEC A. It is an integral count which has effectively considered the size distribution in the entire size range. When system fits satisfactorily to the distribution curve, the DCC is obtainable by multiplying the calculated PAEC with the normalizing factor. RESULTS AND DISCUSSION The functional form of DCF against particle size was determined according to the human respiratory tract model as proposed by ICRP (6). The DCF, and thus EDF and, had a strong dependence on the particle size (Fig. 5). The largest was obtained for radon progeny with diameters of a few nm corresponding to the unattached fraction. The then decreased until about 300 nm due to the decreasing diffusional deposition. After that, it slightly increased due to enhanced impactional and sedimental depositions for larger particles. The values for attached radon progeny were only 10-20% of those for the attached progeny. The calculated results for members of the public and for mine workers are also compared as shown in Fig. 5, which is effectively a comparison between different breathing rates; a higher breathing rate leads to an increase in the deposition of radon progeny. Also, the maximum value is shifted to a lower particle diameter for a larger breathing rate, as the one applies in Mine conditions. Notice that the n-factors for these two groups are different, so that the maximum values of both distributions are normalized to unity. For Home exposures, the n-factor is msv/s/wl, which transforms to an effective dose rate of msv/s for a nominal PAEC of 1 WL. For Mine exposures, the n-factor is msv/s/wl, which transforms to an effective dose rate of msv/s for 1 WL, which is higher than the corresponding value for the general public. Table 1. Summary of the measured parameters for the employed wire screens. Mesh number Screen diameter (cm) Mass of screen (g) Screen thickness (µm) Wire diameter (µm)

6 1 0.9 Home(0.78m3/hr) Mine (1.2m3/hr) Figure 5. The normalized effective dose rate () as a function of particle diameter for members of the public (Home) and for mine workers (Mine). The bracketed values represent the corresponding breathing rates for these two groups. The normalizing factors (n-factors) are and msv/s/wl, respectively. The functional forms of the distribution curves for both groups were simulated using various combinations of wire screens in series and using different sampling face velocities (corresponding to different sampling flow rates). Two types of wire screens, with different mesh numbers, were employed. Both were stainless steel metal wire screens with a specific density of 7.8 g/cm 3, and the other measured parameters are summarized in Table 1. The fits to the profiles are shown in Figs. 1 & 2. Since the sampled volume is a critical factor affecting the counting statistics, the sampling flow rate should not be too small. In practice, therefore, a practical flow rate was assumed at the beginning. Various multiple wire screens in series were then attempted to fit the curve. On identifying the combination with the best fit, different sampling flow rates were applied to this wire screen configuration. An increase in the flow rate in general led to a shift of the collection efficiency towards smaller particle sizes. It should also be noted that a larger sampling flow rate or face velocity will cause a decrease in the diffusion deposition of radon progeny onto the wire screen. Again, the flow rate with the best fit was ascertained. In this way, the best combination of wire screens as well as the best flow rate could be laid down. Nevertheless, in reality, similar fits could be obtained using different wire screen configurations and flow rates. The following discussion will be restricted to four 400-mesh wire screens with sampling face velocities of 3.3 cm/s and 4.6 cm/s for home and mine exposures, respectively. The attached fraction of PAEC is described by a log-normal distribution with an activity median diameter (AMD) of 200 nm for home condition and of 250 nm for mine condition (7). The geometric standard deviation (GSD) was defined by the ICRP formula (6). For these values, the analysis for the attached mode was restricted to particle sizes ranging from 50 nm to 1000 nm. The abundance at these two cutting points drops to less than one-third of the maximum. The discrepancies between the collection efficiencies and the values can be substantial at large particle sizes, ranging from several tens of nm up to µm-sized particles. This range corresponds to the attached fraction of radon progeny, which is the major portion (over 90%) of the total PAEC of progeny in almost all environmental situations (9). Accordingly, the unattached fraction of PAEC for underground mines only contributes to less than 8% of the DCC (14). Hence, the uncertainty brought from the sampler system simulating the curve can be greatly minimized if once the region of the attached mode is fitted satisfactorily. In the present study, a factor (called k-factor) is introduced as an attempt to improve the fit the characteristics for the attached mode. Here, the penetration through the wire-screen series is multiplied by the k- factor, which is to be subtracted from the collection efficiencies of the wire-screen series. The reduced collection efficiencies gave a much better match to the values for the attached mode (Fig. 3). The value of k-factor was determined by minimizing the χ 2 values computed at particle sizes from 50 nm up to 100 nm with steps of 10 nm and at particle sizes above 100nm with steps of 50nm. Before application of the k-factor, the error of the calculated DCC value from the attached mode was over 12% for typical home conditions and was nearly 20% 6

7 for typical mine conditions, and the gross error in the final DCC value was greater than 20% for both conditions. On introducing the k-factor, the error contributed by the attached mode became less than 1% for typical home conditions, and the gross error in the final DCC value was trimmed down to around 10%; the corresponding values for typical mine conditions were below 1% and around 2.5%, respectively. For Home exposure, the best configuration was four 400-mesh wire screens for a sampling flow rate of 2.5 L/min or equivalently a sampling face velocity of 3.3 cm/s. Close matches to the pattern could also be achieved by various wire-screen systems, such as five 400-mesh wire screens with a sampling face velocity of 4.6 cm/s or three 400-mesh wire screens with sampling face velocity of 2 cm/s. Even with the same sampling flow rate of 2.5 L/min, the configuration with six 250-mesh wire screens demonstrated a good fit. The possible wire-screen systems for fitting the pattern are presented in Table 2. For Mine conditions, four 400-mesh wire screens with sampling face velocity of 4.6 cm/s, five 400-mesh screens with 5.3 cm/s, and three 400-mesh screens with 2.7 cm/s were capable to provide adequately good match to the curve. The results are also summarized in Table 2. It is noted that, in the previous discussion, the collection efficiency of the proposed sampling system was always equal to unity for particle sizes below 3nm, which apparently overestimated the distribution. However, as discussed before, the contribution from the unattached progeny (with diameters between 0.5 nm to 5 nm) to the final DCC is less important compared to that from the attached mode. Taking into account the unattached fraction of PAEC of 8% and 1% in homes and in mines, respectively, the error from this mode is around 10% for homes and around 2% for mines. The discrepancies between the collection efficiency and the distribution within this region was therefore neglected in the previous discussion. Nonetheless, the discrepancies can be diminished through measurements made with an additional single 100-mesh wire screen (with wire diameter of 112 µm, screen thickness of 215 µm and solid volume fraction of 0.313) (15) and with a sampling face velocity of 3.3 cm/s (applicable for the discussions of the four 400-mesh wire-screen configuration with a sampling face velocity of 3.3 cm/s for home exposure). To remedy the overestimation mentioned in the preceding paragraph, the collection efficiency of this 100-mesh wire screen ( 100 ) was determined, multiplied by a factor f as presented in Fig. 6, and then subtracted from the collection efficiency of the four 400-mesh wire screens ( 400 ). A new n-factor for the is required to provide a good match with the resulting collection efficiency. Again, the k-factor is adopted to best fit the attached region by minimizing the corresponding χ 2 value. Hence, the overall collection efficiency of the system becomes system 400 k ( ) f 100 = (6) with k = 0.018, f = 0.4 and n-factor = msv/s/wl. The errors of the calculated DCC then decreased from 16% to 1% for the unattached mode and dropped from over 20% to less than 4% for the attached mode. In practice, the filter paper housed in the sampling head A in the original sampling system is now covered with an additional 100-mesh wire screen. For this configuration, the PAEC collected on the 100-mesh screen is required to be measured directly as PAEC 100. The total PACE in air PAEC T and the collection efficiencies of the wire screen, 100 and 400 are calculated as PAEC PAEC + PAEC T = (7) 100 A Table 2. Summary of the possible wire-screen systems providing good fits to the predicted distribution. Negative values in the estimated error represent underestimation while positive values represent overestimation. The wire parameters for the employed wire screens can be found in Table 1. Exposure condition Wire-screen system Sampling flow rate (L/min) k-factor Estimated error to DCC from the attached mode (bracketed values for those without taking the k-factor) Home mesh % (12.4%) mesh % (8.7%) mesh % (13.7%) mesh % (20.2%) mesh % (14.4%) Mine mesh % (19.3%) mesh % (34.6%) mesh % (23.0%) 7

8 10 0 Collection Efficiency 10-1 Collection for 4x400mesh k x Penetration through 4x400mesh f x Collection for 100mesh Overall collection 10-2 Figure 6. The collection efficiency of the proposed sampling system. The discrepancies in the unattached mode is diminished through measurements by an extra 100-mesh wire screen while the discrepancies in the attached mode is corrected by the k-factor. The sampling face velocity is 3.3 cm/s, the k-factor is and f is equal to 0.4. The for members of the public with n-factor of msv/s/wl is also shown. PAEC = (8) PAECT PAEC PAEC T B 400 = (9) PAECT where PAEC A and PAEC B are the PAEC values recorded by the filter papers housed in sampling heads A and B, respectively. The DCC is computed by multiplying the calculated PAEC on the overall system and the n-factor. CONCLUSION The design of a bronchial dosimeter which gives the bronchial dose from radon progeny by direct measurements has been proposed in this paper. The advantage of this dosimeter is the non-requirements of measurements on the size distribution of radon progeny. Extra assumptions on calculations are not required after measurements. The particle size dependence of the, which is normalized from the dose conversion factor, can be simulated by the collection efficiency of the proposed wire-screen sampling systems. In the present work, we further aim to minimize the discrepancies from the simulation in the particle size region corresponding to the attached mode of radon progeny, because the contribution from the attached mode towards the DCC is the major portion. Thus, a so-called k-factor was introduced and a good fit in the attached-mode region was successfully obtained. Various combinations of wire-screens in series were capable to give satisfactory fits to the pattern. Nevertheless, a four 400-mesh wire-screen configuration provided best fits for both home and mine exposures, with sampling flow rates of 2.5 and 3.5 L/min, respectively. After applying the k-factor, the estimated errors for the sampling systems in the DCC contributed from the attached mode decreased from over 12% to less than 1%. The values of k-factor were obtained as for home and for mine conditions. A pre-separator has previously been suggested to cut out part of the unattached radon progeny in order to provide a good fit for the unattached-mode region of the response (15). However, this pre-separator would screen out most of the unattached fraction of PAEC in air so that the resulting alpha counts on the succeeding wire screen will be very small. In the present paper, another method attempting to provide a good fit in the unattached-mode region was introduced. This required an extra 100-mesh wire screen and measurement of 8

9 the PAEC recorded on this screen. When the discrepancies in both the unattached and attached mode regions have been accounted for, the overall error in the DCC drops to around 3%. There are still uncertainties in the development on dosimetric lung models, and the dose conversion factors are yet to be changed in the future. However, the proposed sampling system (configuration and sampling face velocity) can easily be modified to suit the updated dosimetric lung models. The k-factor can always be used as a fine-tuning technique. ACKNOWLEDGMENT The present research was supported by the research grant CityU 1004/99P from the Research Grants Council (RGC) of Hong Kong (CityU project No ). REFERENCES 1. A.C.James, Dosimetric approaches to risk assessment for indoor exposure to radon daughters. Radiat. Prot. Dosim. 7, (1984). 2. M.Ramamurthi, P.K.Hopke, On improving the validity of wire screen unattached fraction Rn daughter measurements. Health Phys. 56, (1989). 3. P.K.Hopke, M.Ramamurthi, E.O.Knutson, A measurement system for radon decay product lung deposition based on respiratory models. Health Phys. 58, (1990). 4. S.Oberstedt, H.Vanmarcke, The bronchial dosemeter. Radiat. Prot. Dosim. 59, (1995). 5. K.N.Yu, Z.J.Guan, A portable dosemeter for radon progenies. Health Phys. 75, (1998). 6. International Commission on Radiological Protection, Human respiratory tract model for radiological protection. ICRP Publication 66. Pergamon Press, Oxford (1994). 7. C.Zock, J.Porstendörfer, A.Reineking, The influence of biological and aerosol parameters of inhaled shortlived radon decay products on human lung dose. Radiat. Prot. Dosim. 63, (1996). 8. A.C.James, W.Stahlhofen, G.Rudolf, M.J.Egan, W.Nixon, P.Gehr, J.K.Briant, The respiratory tract deposition model proposed by the ICRP Task Group. Radiat. Prot. Dosim. 38, (1991). 9. National Research Council, Comparative dosimetry of radon in mines and homes. National Academic Press, Washington, DC (1991). 10. A.Y.S.Cheng, H.C.Yeh, Theory of screen type diffusion battery. J. Aerosol Sci. 11, (1980). 11. A.Y.S.Cheng, J.A.Keating, G.M.Kanapilly, Theory and calibration of a screen-type diffusion battery. J. Aerosol Sci. 11, (1980). 12. J.Porstendörfer, Radon: measurements related to dose. Environ. Inter. 22, S564-S583 (1996). 13. K.N.Yu, Z.J.Guan, E.C.M.Young, M.J.Stokes, Active measurements of indoor concentrations of radon and thoron gas using charcoal canisters. Appl. Radiat. Isotopes. 49, (1998). 14. A.Birchall, A.C.James, Uncertainty analysis of the effective dose per unit exposure from radon progeny and implications for ICRP risk-weighting factors. Radiat. Prot. Dosim. 53, (1994). 15. S.B.Solomon, A radon progeny sampler for the determination of effective dose. Radiat. Prot. Dosim. 72, (1997). 9