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Effects of different lung morphometry models on the calculated dose conversion factor from Rn progeny
Journal of Environmental Radioactivity 47 (2000) 263}277
E!ects of di!erent lung morphometry models on the calculated dose conversion factor from Rn progeny D. NikezicH !,", K.N. Yu!,*, T.T.K. Cheung!, A.K.M.M. Haque!, D. Vuc\ icH # !Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Kowloon, Hong Kong "Faculty of Sciences, University of Kragujevac, 34000 Kragujevac, Yugoslavia #Faculty of Technology, University of Nis\ , Lescovac, Yugoslavia Received 9 November 1998; accepted 1 April 1999
Abstract To investigate the e!ect of di!erent morphometry models on the calculation of the dose conversion factor, three morphometry models were used, namely Yeh}Schum asymmetrical lung model, as well as Weibel and ICRP66 symmetrical models. The original Yeh}Schum model was scaled according to the volume of the standard man, and the results for both the scaled and unscaled models were presented. Dose conversion factors (in mGy WLM~1) were obtained as a function of particle diameter, breathing rate and generation number. Comparison among di!erent lung morphometry models showed that the Weibel and ICRP66 models gave larger dose conversion factors than the Yeh}Schum model, which was explained by the di!erence in their total surface areas of the tracheo-bronchial tree. The distribution of dose conversion factor in the "rst few generations was also found to be di!erent among the examined models. ( 1999 Elsevier Science Ltd. All rights reserved. Keywords: Lung model; Dosimetric model; Rn; Rn progeny
1. Introduction Inhaled Rn progeny are the most important source of irradiation of the human respiratory tract. Calculation of the dose delivered by short-lived Rn progeny to the * Corresponding author. Tel.: #852-2788-7812; fax: #852-2788-7830. E-mail address: [email protected] (K.N. Yu) 0265-931X/99/$ - see front matter ( 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 5 - 9 3 1 X ( 9 9 ) 0 0 0 4 4 - 2
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tracheo-bronchial (T-B) tree requires many models such as the deposition model, clearance model, dose calculation model and morphometry model of the T-B tree. However, all these models varied in di!erent investigations, and the results (e.g., the dose conversion factors, denoted by DCFs in the following) were di!erent from each other. It is di$cult to clarify the di!erence of models and estimate the e!ects of a model on the "nal results (e.g., from a particular morphometry model to another morphometry model). In the present work, we aimed to "nd out the e!ects of the di!erence of morphometry models on the DCFs for Rn progeny by "xing other parameters. These models were the Yeh}Schum asymmetrical model (Yeh & Schum, 1980), the Weibel symmetrical model (Weibel, 1963) and the ICRP66 symmetrical model (ICRP, 1994).
2. The calculation model Short-lived Rn progeny were usually taken to be homogeneously distributed in the mucous layer. The a particles emitted in the mucous layer lost their energy in the tissue of the bronchi epithelium. The amount of the energy deposited in the target cells depended on the stopping power of the a particles in the tissue. The stopping power of heavily charged particles in a medium was given by the Bethe}Bloch expression, and the formula for the non-relativistic case is dE z2e4 2m v2 ! " 1 NZ ln e , (1) dx 4pe2m v2 I 0 e where z is the atomic number of the projectile, e the electron charge, v the velocity of 1 the projectile, Z the e!ective atomic number of the stopping medium, N the number of atoms per unit volume, m the rest mass of electron and I"11.5 Z is the mean e ionizing potential of the medium The Bethe}Bloch (BB) theoretical treatment was based on the Born approximation applied to collisions between heavy particles and the atomic electrons. The use of the Born approximation required the criterion z e2/mvA1. This condition was well 1 satis"ed for high velocity and small charge of the incident particle. In the case of a particles stopping in tissue, this condition is not ful"lled in the low-energy region below 2 MeV. In addition, other physical processes took place such as capture and release of electrons by the projectile particle, so the BB formula was not applicable in this energy region. The reasonably adequate experimental information about slowing down of the a particles in tissue was given in ICRU49 (ICRU, 1993). The data given by ICRU49 were "tted by the seventh-order polynomial dE ! "c #c E#c E2#c E3#c E4#c E5#c E6#c E7, 1 2 3 4 5 6 7 8 dx
(2)
where c "332.201, c "11465.805, c "!34405.805, c "65160.750, c "!74817.644, 1 2 3 4 5 c "48668.099, c "!16413.770 and c "!2225.653. This polynomial was ap6 7 8 plied in the low-energy region below 2 MeV.
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In the higher energy region (above 2 MeV), the di!erences between the BB expression and the ICRU49 experimental data exceed 5%, so the BB formula was not again used in this region. In this region, another 6th-order polynomial "t was used with the parameters as c "3467.934, c "!1577.94579, c "459.644431, c "!81.19981, 1 2 3 4 c "8.44979, c "!0.47563 and c "0.01115. The di!erences between these data 5 6 7 and the experimental data were below 2% in energy region of 2}8 MeV. Therefore, Eq. (2) with two sets of the parameters were employed to determine the absorbed doses per unit exposure to Rn progeny in sensitive cells of the bronchial epithelium. This involved two phases. First, the absorbed dose per unit surface activity on the inner bronchi wall was determined. Here, the bronchi wall represented by the model of the Nuclear Research Council (NRC, 1991), and later adopted in ICRP66 was used. Monte Carlo simulations of propagation the a particle in tissue and air inside the bronchi were performed, which consisted of the following (usual) steps: (1) Sampling of starting points of a particles in the mucous layer (assuming a homogeneous distribution of a emitters in the mucous layer) and starting directions for propagation of a particles; (2) Calculation of the coordinates of entrance points where the a particles enter the layers of secretory and basal cells. The distance between starting and entrance points was calculated based on the obtained coordinates. The energy loss was then determined by the following equation.
P
P
X E0 E dE dx"X" , (3) dEdx 0 Ex where E (MeV) is the energy of an a particle, which has an initial energy E , after x 0 passing a distance X (lm) in the tissue. When the a particle crossed the lumen of the tube, the density di!erence of air and tissue was considered and X was given in cm in this case. The unknown quantity of E was determined by the iteration x procedure since the integral was not solvable analytically. (3) Determination of the energy deposited in the layers of secretory and basal cells as a di!erence between input and output energies. Steps (1)}(3), which created histories of a particles, were repeated a large number of times. The absorbed dose in the interested layers (basal and secretory cells) per one emitted a particle was then obtained as the average value for all particle histories. This quantity, called the conversion coe$cient (CC), was given in units of MeV per a particle. These simulation procedures, described above from steps (1) to (3), formed the basis of our "rst computer program called CCOEF (conversion coe$cient). The results obtained in the "rst phase of calculation were used in the second phase of calculation. There was a major di!erence in the second phase between the present model and the ICRP66 model which was a compartment model. In our model each airway tube in generations 1}15 was treated separately. The main objective in the second phase was to obtain the equilibrium activity and the number of emitted a particles N of Rn progeny in every airway tube for the exposure of 1 WLM. a
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The equilibrium activity is the activity of some Rn progeny in an airway in generation j, which is established as the balance between the processes which increase its activity (deposition # decay of the parent nuclide in the radioactive chain # activity cleaned and transported by mucus from generations 'j) and those processes which decrease its activity (decay, transfer to blood, cleaned and transported by mucus into generations (j). N was found in the present paper as the number of a particles per a WLM. The product of N ) CC gave the DCF (in mGy WLM1) for the sensitive cells. a The second program consisted of a few modules as follows. (1) Determination of air#ow distribution throughout the T-B tree; (2) Determination of deposited fraction in every airway tube; (3) Determination of activity deposited in some tube per one breath (by taking into account the "ltration in the previous airway system); (4) Determination of the number of atoms M of the ith Rn progeny in the jth ij generation using dM B i,j" ij#A #2j M !(j #j #j )M , (4) i~1,j c,j`1 i,j`1 i b c,j i,j dt j i where B is the activity of ith Rn progeny deposited in the jth generation per unit time ij (in Bq s~1m~2), A was equilibrium activity (in Bq m~2), j the decay constant of the ij i ith Rn progeny (in s~1), j the mucous clearance rate in the jth generation and j is cj b the transfer rate to blood (all j's in s~1). 2.1. Nasal xltration Nasal "ltration is important for small particles as well as for large particles. In the present work, the formulas for nasal deposition by James et al. (1991) were used g "1!e~kD0.5V~1@8 (5) 5) for thermodynamical deposition, with D as the di!usion coe$cient, k a constant and < the volumetric #ow rate, and 1 (6) g "1! ae 3]10~4d2 <#1 ae for aerodynamic deposition where d is the aerodynamic particle diameter calculated ae by iteration as described in ICRP66. Di!erent values of the constant k for Eq. (5) could be found in the literatures; ICRP66 recommended k"18, NRC took k"7.7 and Cheng, Su, Yeh and Swift (1993) obtained k"12.65. The value of 18 resulted in the largest "ltration of ultra"ne particles (unattached fraction), which considerably diminished the dose delivered by them. In the present work k"7.7 was adopted, so as to consider the most conservative case. Eqs. (5) and (6) gave the deposition in the entire extrathoracic (ET) region and additional formulas for deposition in the larynx and other extrathoracic organs
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were not used. In the case of mouth-breathing, the "ltration was smaller by a factor of 2, so that k"3.9 was used in the present paper. 2.2. Deposition in T-B tree Deposition in airway tubes in the T-B tree was determined as the competitive sum of three di!erent processes, namely, di!usional, impactional and sedimental deposition. Di!usional deposition in a tube was calculated using the equation from Ingham (1975): g "1!0.819e~14.63D!0.0976e~89.22D!10.0325e~228D!0.0509e~125.9D2@3, h (7) where D"(plD/4<), l is the length of the airway tube, D the di!usion coe$cient of particles and < is the #ow rate. The di!usion coe$cient was calculated di!erently during inspiration and expiration, i.e., D(x)"D#1.08ud for inspiration and D(x)"D#0.37ud for expiration, where D is the di!usion coe$cient calculated by Ck¹ D" , (8) 3pkd p where k is the Boltzman constant, ¹ the temperature in K, k the viscosity of air, d the p diameter of the particles, u the convective #ow velocity, d the diameter of an individual airway for the #ow being considered and C is the Cunningham slip factor. The Ingaham's equation should be corrected for turbulent #ow in the "rst 6 generations as given by ICRP66: 2 p )) . cor"1#100e~(-0'(100`[email protected]
(9)
Impactional deposition was calculated by g
"aSb, (10) imp where a and b are constants depending on the generation number, and S is the Stoke's number (see NRC 1991 for details). Sedimental deposition g was calculated by the sed formula given in Chang, Gri"th, Shyr, Yeh, Cuddihy, and Seiler (1991) as
A
B
4gCod2¸ cos U p g "1!exp ! , sed 9pR<
(11)
where ¸ and R are the length and the radius of the tube, respectively, o is density of the particles, g"9.81 m s ~2 and U is the inclination angle relative to gravity (U"0 for a horizontal tube). Furthermore, the transfer into the blood was characterized by the half time of ¹"600 min (NRC, 1991) and the mucous clearance rate throughout the T-B tree was also taken from NRC (1991). The DCF was obtained by multiplying the number of a particles emitted by 218Po and 214Po for the exposure of 1 WLM with the
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Fig. 1. A simpli"ed #ow-chart of the programs used for calculations.
corresponding conversion coe$cients. After obtaining the DCFs in di!erent generations of T-B tree, an average one was calculated by weighting them with the surface area in the corresponding generation. A #ow chart of the used programs is given in Fig. 1.
3. Input data In order to compare the results obtained using di!erent morphometry models, two separate programs were created. The "rst one simulated an asymmetrical lung model related to the Yeh}Schum lung model. The second code simulated symmetrical lung model as adopted in ICRP66. Two sets of data for the symmetrical model were used, i.e., the Weibel A model and James model presented in ICRP66. All other variables in the models were kept the same during the calculations. The Yeh}Schum and Weibel models and the associated human body weights were taken from the original references. The dimension of airway tubes of the 3 models were listed in Tables 1 and 2. Since the lengths and diameters of airway tubes in 15th and 16th generations were not given for all lobes in the original Yeh}Schum model, these were determined as follows.
10.0 3.09 1.22 0.800 1.27 1.25 0.827 0.988 0.798 0.557 0.401 0.350 0.250 0.194 0.143 0.113! 0.088
2.01 1.75 1.02 0.760 0.650 0.579 0.454 0.355 0.278 0.216 0.158 0.118 0.088 0.070 0.058 0.046! 0.036
10.0 3.09 3.02 2.27 1.34 1.63 1.04 1.04 0.691 0.527 0.394 0.266 0.225 0.172 0.118 0.092! 0.074
Length
Length
Diameter
Right middle
Right upper
2.01 1.75 1.33 0.720 0.620 0.528 0.376 0.317 0.268 0.199 0.147 0.106 0.083 0.064 0.051 0.040! 0.032
Diameter 10.0 3.09 3.02 0.880 1.09 1.33 1.22 0.796 0.803 0.880 0.900 0.591 0.449 0.337 0.257 0.222 0.158
Length
Right lower
!These values were determined according to the method explained in the text.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Generation
Table 1 Dimensions (cm) for the Yeh}Schum asymmetrical model
2.01 1.75 1.33 1.01 0.800 0.650 0.583 0.471 0.367 0.347 0.317 0.249 0.181 0.134 0.101 0.077 0.066
Diameter 10.0 5.63 1.45 1.08 1.02 1.09 1.02 0.751 0.832 0.555 0.482 0.388 0.343 0.267 0.215 0.169! 0.134
Length
Left upper
2.01 1.38 1.03 0.835 0.640 0.533 0.426 0.341 0.307 0.234 0.178 0.135 0.100 0.078 0.061 0.048! 0.038
Diameter
10.0 5.63 1.42 1.33 1.13 0.891 1.02 0.836 0.778 0.771 0.611 0.544 0.431 0.302 0.224 0.188 0.148!
Length
Left lower
2.01 1.38 1.15 0.905 0.680 0.559 0.454 0.365 0.316 0.298 0.286 0.211 0.146 0.102 0.076 0.061 0.048!
Diameter
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Table 2 Dimensions (cm) for the Weibel and ICRP66 symmetrical models Generation
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Weibel model
ICRP66 model
Diameter
Length
Diameter
Length
1.8 1.22 0.83 0.56 0.45 0.35 0.28 0.23 0.186 0.154 0.13 0.109 0.095 0.082 0.074 0.066 0.06
12.0 4.76 1.9 0.76 1.27 1.07 0.90 0.76 0.64 0.54 0.46 0.39 0.33 0.27 0.23 0.20 0.165
1.65 1.2 0.85 0.61 0.44 0.36 0.29 0.24 0.2 0.1651 0.1348 0.1092 0.0882 0.072 0.0603 0.0533
9.1 3.8 1.5 0.83 0.9 0.81 0.66 0.60 0.53 0.4367 0.362 0.3009 0.25 0.2069 0.17 0.138
Table 3 Surface area (cm2) in T-B generations Generation
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
ICRP66
47.17 28.65 16.02 12.72 19.91 29.31 38.48 57.91 85.25 115.97 156.98 211.41 283.74 383.38 525.28 757.19
Weibel
67.86 36.49 19.82 10.70 28.73 37.65 50.67 70.29 95.74 133.76 192.38 273.51 403.41 569.79 876.05 1358.86
Yeh}Schum Unscaled
Scaled
63.15 41.40 26.35 24.98 38.93 67.04 91.69 127.10 193.63 275.48 398.51 476.34 544.31 600.25 700.28 905.0
52.016 34.13 21.72 20.59 32.10 55.27 75.60 104.79 159.64 227.12 328.56 392.73 448.76 494.88 577.36 746.14
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Fig. 2. The variation of surface area with the generation number for Weibel, ICRP66 and Yeh}Schum (scaled and unscaled) models. The total surface areas were also given.
The unknown diameter in generation i was determined by the formulae d "d 2~1@3 (ICRP, 1994) if the diameter was known in generation i!1, and the i i~1 airway length was found based on the constant length-to-diameter ratio. The estimated dimensions were shown with the superscript ! in Table 1. The surface areas in di!erent generations for these 3 models were given in Table 3. The DCFs were calculated in the basal as well as the secretory cells. The results for the basal cells were related only to the "rst 8 generations of the T-B tree, while those for secretory cells were related to the "rst 15 generations. The results were then weighted according to the surface area of the corresponding generation. James (1983) proposed a way to scale down a model according to the lung volume. The volume of 227 cm3 of the Yeh}Schum model was reduced to 169 cm3 using a scaling factor 0.908, since the Yeh}Schum model had a much larger volume than other models. The variation of surface area with the generation number for ICRP66, Weibel, and Yeh}Schum (scaled and unscaled) models were shown in Fig. 2. The total surface areas were also given in the Fig. 2. It can be seen that there are large di!erences among di!erent models starting from the 7th generation.
4. Results The DCFs (in mGy WLM~1) for basal cells obtained using the Yeh}Schum model (scaled and unscaled), were given in Fig. 3 as a function of the particle diameter.
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Fig. 3. The dose conversion factors for basal cells obtained using the Yeh}Schum models (scaled and unscaled) as a function of the particle diameter. The results were for 0.45, 0.54, 1.5 and 3 m3 h~1 of inhaled air corresponding to various levels of physical activities, viz., sleep, rest, light and heavy exercise, respectively.
The results were shown for various breathing rates, corresponding to various levels of physical activities, viz., sleep, rest, light and heavy exercise (0.45, 0.54, 1.5 and 3 m3h~1, respectively). In all cases, the DCFs obtained using the scaled Yeh}Schum model were larger than those using the unscaled model. The DCFs were the largest for particles with diameters of a few nanometeres, which corresponded to unattached Rn progeny. The DCFs decreased with the particle diameter until about 200 nm due to the decreasing di!usional deposition. For larger diameters, they started to increase due to the enhanced deposition by impaction and sedimentation. Fig. 4 gave the DCFs for secretory cells calculated for the same condition as those in Fig. 3. Since secretory cells are closer to the mucous layer which is the source of a particles, the resulting DCFs were higher than those to the basal cells by a factor of 2}3. The pattern of doses for secretory cells resembles that for basal cells. The largest DCFs were obtained for unattached Rn progeny with diameters of a few nm. They decreased until the particles reached a diameter up to 300 nm and then started to increase. The DCFs increased with the level of physical exercise for both basal and secretory cells. This was particularly important for small particles; for larger particles with diameters above 100 nm, this e!ect still existed but was less profound. Fig. 5 gave the DCF ratios for basal cells of the Weibel symmetrical model and the ICRP66 symmetrical model to the Yeh}Schum model. The results were calculated for breathing rates of 0.45, 1.5 and 3 m3 h~1. All ratios were above 1.3. In all cases, the ICRP66 model gave larger DCFs than Weibel model. The results also showed that
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Fig. 4. The dose conversion factors for secretory cells obtained using the Yeh}Schum models (scaled and unscaled) as a function of the particle diameter. The results were for 0.45, 0.54, 1.5 and 3 m3 h~1 of inhaled air corresponding to various levels of physical activities, viz., sleep, rest, light and heavy exercise, respectively.
Fig. 5. Ratio between the dose conversion factors for basal cells given by the ICRP66 and Yeh}Schum models (solid lines) and ratio between the dose conversion factors given by the Weibel and Yeh}Schum models (dashed lines) for 0.45, 1.5 and 3 m3 h~1 of inhaled air. The curve for unscaled Yeh}Schum model for 3 m3h~1 is not shown to avoid too many curves.
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Fig. 6. Ratio between the dose conversion factors for secretory cells given by the ICRP66 and Yeh}Schum models and ratio between the dose conversion factors given by the Weibel and Yeh}Schum models for 0.45 m 3 h~1 of inhaled air.
the Weibel and ICRP66 lung models led to signi"cantly larger DCFs than the Yeh}Schum model. The di!erences between models depended on the particle size and the breathing rate. For aerosols with a diameter of 170 nm, the ICRP66 model gave DCFs larger by a factor of 1.7}1.9. For larger particles with a diameter of 500 nm, the factor ranged in 1.9}2.3. In Fig. 6 the ratios of DCFs for secretory cells were given for breathing rates of 0.45 and 1.5 m3 h~1, which had di!erent patterns from those for basal cells. The di!erent patterns originated from the fact that the basal cells were present in the "rst 8 generations of the T-B tree, while secretory cells were present in 15 generations. E!ectively, all ratios for the unscaled Yeh}Schum model were above those for the scaled model. The di!erences between the various models were less profound than those in the case of basal cells. Fig. 7 gave the variation of DCF with the generation number for basal cells for the particle diameter d "150 nm and a breathing rate of 0.45 m3 h~1 for di!erent p morphometry models. The Weibel model gave a sharp and large maximum at generation 3, while the ICRP model gave a broad and a smaller maximum between the 2nd and the 4th generations. The curve obtained using the Yeh}Schum model had a maximum at the 2nd generation of the T-B tree. Both the scaled and unscaled Yeh}Schum models gave DCFs well below those from the Weibel or ICRP66 models. Fig. 8 gave the variation of DCF with the generation number for secretory cells for the particle diameter d "150 nm and a breathing rate of 1.5 m3 h~1 for di!erent p morphometry models. The Weibel model gave a maximum at the 3rd generation,
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Fig. 7. Variation of the dose conversion factor with the generation number for basal cells for the particle diameter d "150 nm and a breathing rate of 0.45 m3 h~1 for di!erent models. p
Fig. 8. Variation of the dose conversion factor with the generation number for secretory cells for the particle diameter d "150 nm and a breathing rate of 1.5 m3 h~1 for di!erent models. p
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while the ICRP66 and Yeh}Schum models gave maximums at the 2nd generation. The DCF decreased rapidly beyond the maximum with the generation number in all models. After the 4th generation, the Weibel and ICRP66 models were very close to each other. The DCFs calculated with the Yeh}Schum model were lower throughout the whole T-B tree except after the 13th generation.
5. Discussion In the present work, di!erent morphometry models of the human lung were used for determination of the dose conversion factors (DCFs). The use of the Weibel and ICRP66 lung morphometry models led to larger DCFs than the Yeh}Schum model. The distributions of DCFs over the generation were di!erent in various models. The main reason for the di!erences was the di!erent surface areas of the T-B tree as described below. Basal cells were present in the "rst eight generations of the T-B tree. The surface area in the "rst eight generations was 288 cm2 in the ICRP66 model, 350 cm2 in the Weibel model and 503 cm2 in the scaled Yeh}Schum (without trachea). A larger surface area implied a smaller dose, and this explained why the Weibel model gave smaller doses in basal cells than the ICRP66 model. In the unscaled Yeh}Schum model, the surface area was 611 cm2 in the "rst eight generations, which resulted in signi"cantly smaller doses, and thus the large DCF ratio to other models. Another interesting "nding was a di!erent behavior of the ratio curves for the breathing rate of 0.45 m3 h~1 compared to the curves for 1.5 and 3 m3 h~1 shown in Fig. 5. The curves for 0.45 m3 h~1 had weak maximums and then decreased for larger particles, while the curves for larger breathing rates increased monotonously with the particle diameter. The di!erent behavior was caused by di!erent deposition patterns for di!erent #ow velocities. For larger particles, the impactional deposition was more signi"cant for larger #ow velocities, since the Stoke's number is proportional to the mean #ow velocity. Secretory cells were present throughout the entire T-B tree and its total surface area should explain the patterns of the curves in Fig. 6. The new feature when compared to the curves for basal cells was that some ratios were below 1. For example, this happened in the curve of ratio between the DCFs calculated by the Weibel model and the scaled Yeh}Schum model. This was due to the larger surface area after the 13th generation for the Weibel model than for the Yeh}Schum model. In these generations, the surface areas were far larger than those in previous generations. Consequently, they had much larger in#uence when the weighting was done according to the surface area. The surface area in the ICRP66 model was smaller than that in the scaled Yeh}Schum model so that the ratios of DCFs were slightly higher than 1. For the unscaled Yeh}Schum model, the larger surface area in generations 6}13 was dominant, so the curves were above 1. In small size region, i.e., d (25 nm, all curves for p the scaled Yeh}Schum model were well below 1 and reaching 0.6. This was caused by di!erent deposition patterns of the unattached Rn progeny in the "rst few generations for di!erent lung models.
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Another point of interest was the larger di!erence between the curves for the ratio of the ICRP66 model and Weibel model to the Yeh}Schum model. This was due to the much larger surface area of the Weibel model than that of the ICRP66 model after the 12th generation as shown in Fig. 2, which led to a much larger DCF for the ICRP66 model than that for the Weibel model. In the case of basal cells, only the "rst eight generations were relevant, and the surface areas of the eight generations for the Weibel and ICRP66 models were much closer than that of higher generations, so they have similar DCFs. 6. Conclusions In the present work, comparisons among di!erent morphometry models of the lung were presented in terms of the ratios between the dose conversion factors (DCFs) between the Weibel and ICRP66 symmetrical models to the Yeh}Schum asymmetrical models. The ratios for basal cells were always above 1, while those for secretory cells were 1$0.1 (for the scaled Yeh}Schum model). The di!erences caused by using di!erent models were attributed to the di!erent surface areas of the T-B tree in di!erent models. Acknowledgements The present research was supported in part by the research grants 7000640 and 7000658 from the City University of Hong Kong. References Chang, I. Y., Gri"th, W. C., Shyr, L. J., Yeh, H. C., Cuddihy, R. G., & Seiler, F. A. (1991). Software for the draft NCRP respiratory tract dosimetry model. Radiation Protection Dosimetry, 38(1/3), 193}199. Cheng, Y. S., Su, Y. F., Yeh, H. C., & Swift, D. L. (1993). Deposition of thoron progeny in human head airways. Aerosol Science and Technology, 18, 359}375. ICRP, International Commission on Radiological Protection (1994). Human Respiratory tract model for radiological protection. A Report of Committee 2 of the ICRP66. ICRP Publication 66. Ann. ICRP 24/(1/4), Oxford: Pergamon Press. ICRU, International Commission on Radiological Units and Measurements (1993). Stopping powers and ranges for protons and alpha particles. ICRU Report 49. Ingham, D. B. (1975). Di!usion of aerosols from a stream #owing through a cylindrical tube. Journal of Aerosols Science, 6, 125}132. James, A. C. (1983) Dosimetry aspects of exposure to radon and thoron daughter product. Report by a Group of Experts of the OECD Nuclear Energy Agency. James, A. C., Stahlhofen, W., Rudolf, G., Egan, M. J., Nixon, W., Gehr, P., & Brian, J. K. (1991). The respiratory tract deposition model proposed by the ICRP Task group. Radiation Protection Dosimetry, 38(1/3), 159}165. NRC, National Research Council (1991). Comparative dosimetry of radon in mines and homes. Washington DC: National Academic Press. Weibel, E. R. (1963). Morphometry of the human lung. Berlin: Springer. Yeh, H. C., & Schum, G. M. (1980). Model of human lung airways and their application to inhaled particle deposition. Bulletin of Mathematical Biology, 42, 461}480.
E!ects of di!erent lung morphometry models on the calculated dose conversion factor from Rn progeny D. NikezicH !,", K.N. Yu!,*, T.T.K. Cheung!, A.K.M.M. Haque!, D. Vuc\ icH # !Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Kowloon, Hong Kong "Faculty of Sciences, University of Kragujevac, 34000 Kragujevac, Yugoslavia #Faculty of Technology, University of Nis\ , Lescovac, Yugoslavia Received 9 November 1998; accepted 1 April 1999
Abstract To investigate the e!ect of di!erent morphometry models on the calculation of the dose conversion factor, three morphometry models were used, namely Yeh}Schum asymmetrical lung model, as well as Weibel and ICRP66 symmetrical models. The original Yeh}Schum model was scaled according to the volume of the standard man, and the results for both the scaled and unscaled models were presented. Dose conversion factors (in mGy WLM~1) were obtained as a function of particle diameter, breathing rate and generation number. Comparison among di!erent lung morphometry models showed that the Weibel and ICRP66 models gave larger dose conversion factors than the Yeh}Schum model, which was explained by the di!erence in their total surface areas of the tracheo-bronchial tree. The distribution of dose conversion factor in the "rst few generations was also found to be di!erent among the examined models. ( 1999 Elsevier Science Ltd. All rights reserved. Keywords: Lung model; Dosimetric model; Rn; Rn progeny
1. Introduction Inhaled Rn progeny are the most important source of irradiation of the human respiratory tract. Calculation of the dose delivered by short-lived Rn progeny to the * Corresponding author. Tel.: #852-2788-7812; fax: #852-2788-7830. E-mail address: [email protected] (K.N. Yu) 0265-931X/99/$ - see front matter ( 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 5 - 9 3 1 X ( 9 9 ) 0 0 0 4 4 - 2
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tracheo-bronchial (T-B) tree requires many models such as the deposition model, clearance model, dose calculation model and morphometry model of the T-B tree. However, all these models varied in di!erent investigations, and the results (e.g., the dose conversion factors, denoted by DCFs in the following) were di!erent from each other. It is di$cult to clarify the di!erence of models and estimate the e!ects of a model on the "nal results (e.g., from a particular morphometry model to another morphometry model). In the present work, we aimed to "nd out the e!ects of the di!erence of morphometry models on the DCFs for Rn progeny by "xing other parameters. These models were the Yeh}Schum asymmetrical model (Yeh & Schum, 1980), the Weibel symmetrical model (Weibel, 1963) and the ICRP66 symmetrical model (ICRP, 1994).
2. The calculation model Short-lived Rn progeny were usually taken to be homogeneously distributed in the mucous layer. The a particles emitted in the mucous layer lost their energy in the tissue of the bronchi epithelium. The amount of the energy deposited in the target cells depended on the stopping power of the a particles in the tissue. The stopping power of heavily charged particles in a medium was given by the Bethe}Bloch expression, and the formula for the non-relativistic case is dE z2e4 2m v2 ! " 1 NZ ln e , (1) dx 4pe2m v2 I 0 e where z is the atomic number of the projectile, e the electron charge, v the velocity of 1 the projectile, Z the e!ective atomic number of the stopping medium, N the number of atoms per unit volume, m the rest mass of electron and I"11.5 Z is the mean e ionizing potential of the medium The Bethe}Bloch (BB) theoretical treatment was based on the Born approximation applied to collisions between heavy particles and the atomic electrons. The use of the Born approximation required the criterion z e2/mvA1. This condition was well 1 satis"ed for high velocity and small charge of the incident particle. In the case of a particles stopping in tissue, this condition is not ful"lled in the low-energy region below 2 MeV. In addition, other physical processes took place such as capture and release of electrons by the projectile particle, so the BB formula was not applicable in this energy region. The reasonably adequate experimental information about slowing down of the a particles in tissue was given in ICRU49 (ICRU, 1993). The data given by ICRU49 were "tted by the seventh-order polynomial dE ! "c #c E#c E2#c E3#c E4#c E5#c E6#c E7, 1 2 3 4 5 6 7 8 dx
(2)
where c "332.201, c "11465.805, c "!34405.805, c "65160.750, c "!74817.644, 1 2 3 4 5 c "48668.099, c "!16413.770 and c "!2225.653. This polynomial was ap6 7 8 plied in the low-energy region below 2 MeV.
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In the higher energy region (above 2 MeV), the di!erences between the BB expression and the ICRU49 experimental data exceed 5%, so the BB formula was not again used in this region. In this region, another 6th-order polynomial "t was used with the parameters as c "3467.934, c "!1577.94579, c "459.644431, c "!81.19981, 1 2 3 4 c "8.44979, c "!0.47563 and c "0.01115. The di!erences between these data 5 6 7 and the experimental data were below 2% in energy region of 2}8 MeV. Therefore, Eq. (2) with two sets of the parameters were employed to determine the absorbed doses per unit exposure to Rn progeny in sensitive cells of the bronchial epithelium. This involved two phases. First, the absorbed dose per unit surface activity on the inner bronchi wall was determined. Here, the bronchi wall represented by the model of the Nuclear Research Council (NRC, 1991), and later adopted in ICRP66 was used. Monte Carlo simulations of propagation the a particle in tissue and air inside the bronchi were performed, which consisted of the following (usual) steps: (1) Sampling of starting points of a particles in the mucous layer (assuming a homogeneous distribution of a emitters in the mucous layer) and starting directions for propagation of a particles; (2) Calculation of the coordinates of entrance points where the a particles enter the layers of secretory and basal cells. The distance between starting and entrance points was calculated based on the obtained coordinates. The energy loss was then determined by the following equation.
P
P
X E0 E dE dx"X" , (3) dEdx 0 Ex where E (MeV) is the energy of an a particle, which has an initial energy E , after x 0 passing a distance X (lm) in the tissue. When the a particle crossed the lumen of the tube, the density di!erence of air and tissue was considered and X was given in cm in this case. The unknown quantity of E was determined by the iteration x procedure since the integral was not solvable analytically. (3) Determination of the energy deposited in the layers of secretory and basal cells as a di!erence between input and output energies. Steps (1)}(3), which created histories of a particles, were repeated a large number of times. The absorbed dose in the interested layers (basal and secretory cells) per one emitted a particle was then obtained as the average value for all particle histories. This quantity, called the conversion coe$cient (CC), was given in units of MeV per a particle. These simulation procedures, described above from steps (1) to (3), formed the basis of our "rst computer program called CCOEF (conversion coe$cient). The results obtained in the "rst phase of calculation were used in the second phase of calculation. There was a major di!erence in the second phase between the present model and the ICRP66 model which was a compartment model. In our model each airway tube in generations 1}15 was treated separately. The main objective in the second phase was to obtain the equilibrium activity and the number of emitted a particles N of Rn progeny in every airway tube for the exposure of 1 WLM. a
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The equilibrium activity is the activity of some Rn progeny in an airway in generation j, which is established as the balance between the processes which increase its activity (deposition # decay of the parent nuclide in the radioactive chain # activity cleaned and transported by mucus from generations 'j) and those processes which decrease its activity (decay, transfer to blood, cleaned and transported by mucus into generations (j). N was found in the present paper as the number of a particles per a WLM. The product of N ) CC gave the DCF (in mGy WLM1) for the sensitive cells. a The second program consisted of a few modules as follows. (1) Determination of air#ow distribution throughout the T-B tree; (2) Determination of deposited fraction in every airway tube; (3) Determination of activity deposited in some tube per one breath (by taking into account the "ltration in the previous airway system); (4) Determination of the number of atoms M of the ith Rn progeny in the jth ij generation using dM B i,j" ij#A #2j M !(j #j #j )M , (4) i~1,j c,j`1 i,j`1 i b c,j i,j dt j i where B is the activity of ith Rn progeny deposited in the jth generation per unit time ij (in Bq s~1m~2), A was equilibrium activity (in Bq m~2), j the decay constant of the ij i ith Rn progeny (in s~1), j the mucous clearance rate in the jth generation and j is cj b the transfer rate to blood (all j's in s~1). 2.1. Nasal xltration Nasal "ltration is important for small particles as well as for large particles. In the present work, the formulas for nasal deposition by James et al. (1991) were used g "1!e~kD0.5V~1@8 (5) 5) for thermodynamical deposition, with D as the di!usion coe$cient, k a constant and < the volumetric #ow rate, and 1 (6) g "1! ae 3]10~4d2 <#1 ae for aerodynamic deposition where d is the aerodynamic particle diameter calculated ae by iteration as described in ICRP66. Di!erent values of the constant k for Eq. (5) could be found in the literatures; ICRP66 recommended k"18, NRC took k"7.7 and Cheng, Su, Yeh and Swift (1993) obtained k"12.65. The value of 18 resulted in the largest "ltration of ultra"ne particles (unattached fraction), which considerably diminished the dose delivered by them. In the present work k"7.7 was adopted, so as to consider the most conservative case. Eqs. (5) and (6) gave the deposition in the entire extrathoracic (ET) region and additional formulas for deposition in the larynx and other extrathoracic organs
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were not used. In the case of mouth-breathing, the "ltration was smaller by a factor of 2, so that k"3.9 was used in the present paper. 2.2. Deposition in T-B tree Deposition in airway tubes in the T-B tree was determined as the competitive sum of three di!erent processes, namely, di!usional, impactional and sedimental deposition. Di!usional deposition in a tube was calculated using the equation from Ingham (1975): g "1!0.819e~14.63D!0.0976e~89.22D!10.0325e~228D!0.0509e~125.9D2@3, h (7) where D"(plD/4<), l is the length of the airway tube, D the di!usion coe$cient of particles and < is the #ow rate. The di!usion coe$cient was calculated di!erently during inspiration and expiration, i.e., D(x)"D#1.08ud for inspiration and D(x)"D#0.37ud for expiration, where D is the di!usion coe$cient calculated by Ck¹ D" , (8) 3pkd p where k is the Boltzman constant, ¹ the temperature in K, k the viscosity of air, d the p diameter of the particles, u the convective #ow velocity, d the diameter of an individual airway for the #ow being considered and C is the Cunningham slip factor. The Ingaham's equation should be corrected for turbulent #ow in the "rst 6 generations as given by ICRP66: 2 p )) . cor"1#100e~(-0'(100`[email protected]
(9)
Impactional deposition was calculated by g
"aSb, (10) imp where a and b are constants depending on the generation number, and S is the Stoke's number (see NRC 1991 for details). Sedimental deposition g was calculated by the sed formula given in Chang, Gri"th, Shyr, Yeh, Cuddihy, and Seiler (1991) as
A
B
4gCod2¸ cos U p g "1!exp ! , sed 9pR<
(11)
where ¸ and R are the length and the radius of the tube, respectively, o is density of the particles, g"9.81 m s ~2 and U is the inclination angle relative to gravity (U"0 for a horizontal tube). Furthermore, the transfer into the blood was characterized by the half time of ¹"600 min (NRC, 1991) and the mucous clearance rate throughout the T-B tree was also taken from NRC (1991). The DCF was obtained by multiplying the number of a particles emitted by 218Po and 214Po for the exposure of 1 WLM with the
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Fig. 1. A simpli"ed #ow-chart of the programs used for calculations.
corresponding conversion coe$cients. After obtaining the DCFs in di!erent generations of T-B tree, an average one was calculated by weighting them with the surface area in the corresponding generation. A #ow chart of the used programs is given in Fig. 1.
3. Input data In order to compare the results obtained using di!erent morphometry models, two separate programs were created. The "rst one simulated an asymmetrical lung model related to the Yeh}Schum lung model. The second code simulated symmetrical lung model as adopted in ICRP66. Two sets of data for the symmetrical model were used, i.e., the Weibel A model and James model presented in ICRP66. All other variables in the models were kept the same during the calculations. The Yeh}Schum and Weibel models and the associated human body weights were taken from the original references. The dimension of airway tubes of the 3 models were listed in Tables 1 and 2. Since the lengths and diameters of airway tubes in 15th and 16th generations were not given for all lobes in the original Yeh}Schum model, these were determined as follows.
10.0 3.09 1.22 0.800 1.27 1.25 0.827 0.988 0.798 0.557 0.401 0.350 0.250 0.194 0.143 0.113! 0.088
2.01 1.75 1.02 0.760 0.650 0.579 0.454 0.355 0.278 0.216 0.158 0.118 0.088 0.070 0.058 0.046! 0.036
10.0 3.09 3.02 2.27 1.34 1.63 1.04 1.04 0.691 0.527 0.394 0.266 0.225 0.172 0.118 0.092! 0.074
Length
Length
Diameter
Right middle
Right upper
2.01 1.75 1.33 0.720 0.620 0.528 0.376 0.317 0.268 0.199 0.147 0.106 0.083 0.064 0.051 0.040! 0.032
Diameter 10.0 3.09 3.02 0.880 1.09 1.33 1.22 0.796 0.803 0.880 0.900 0.591 0.449 0.337 0.257 0.222 0.158
Length
Right lower
!These values were determined according to the method explained in the text.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Generation
Table 1 Dimensions (cm) for the Yeh}Schum asymmetrical model
2.01 1.75 1.33 1.01 0.800 0.650 0.583 0.471 0.367 0.347 0.317 0.249 0.181 0.134 0.101 0.077 0.066
Diameter 10.0 5.63 1.45 1.08 1.02 1.09 1.02 0.751 0.832 0.555 0.482 0.388 0.343 0.267 0.215 0.169! 0.134
Length
Left upper
2.01 1.38 1.03 0.835 0.640 0.533 0.426 0.341 0.307 0.234 0.178 0.135 0.100 0.078 0.061 0.048! 0.038
Diameter
10.0 5.63 1.42 1.33 1.13 0.891 1.02 0.836 0.778 0.771 0.611 0.544 0.431 0.302 0.224 0.188 0.148!
Length
Left lower
2.01 1.38 1.15 0.905 0.680 0.559 0.454 0.365 0.316 0.298 0.286 0.211 0.146 0.102 0.076 0.061 0.048!
Diameter
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Table 2 Dimensions (cm) for the Weibel and ICRP66 symmetrical models Generation
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Weibel model
ICRP66 model
Diameter
Length
Diameter
Length
1.8 1.22 0.83 0.56 0.45 0.35 0.28 0.23 0.186 0.154 0.13 0.109 0.095 0.082 0.074 0.066 0.06
12.0 4.76 1.9 0.76 1.27 1.07 0.90 0.76 0.64 0.54 0.46 0.39 0.33 0.27 0.23 0.20 0.165
1.65 1.2 0.85 0.61 0.44 0.36 0.29 0.24 0.2 0.1651 0.1348 0.1092 0.0882 0.072 0.0603 0.0533
9.1 3.8 1.5 0.83 0.9 0.81 0.66 0.60 0.53 0.4367 0.362 0.3009 0.25 0.2069 0.17 0.138
Table 3 Surface area (cm2) in T-B generations Generation
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
ICRP66
47.17 28.65 16.02 12.72 19.91 29.31 38.48 57.91 85.25 115.97 156.98 211.41 283.74 383.38 525.28 757.19
Weibel
67.86 36.49 19.82 10.70 28.73 37.65 50.67 70.29 95.74 133.76 192.38 273.51 403.41 569.79 876.05 1358.86
Yeh}Schum Unscaled
Scaled
63.15 41.40 26.35 24.98 38.93 67.04 91.69 127.10 193.63 275.48 398.51 476.34 544.31 600.25 700.28 905.0
52.016 34.13 21.72 20.59 32.10 55.27 75.60 104.79 159.64 227.12 328.56 392.73 448.76 494.88 577.36 746.14
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Fig. 2. The variation of surface area with the generation number for Weibel, ICRP66 and Yeh}Schum (scaled and unscaled) models. The total surface areas were also given.
The unknown diameter in generation i was determined by the formulae d "d 2~1@3 (ICRP, 1994) if the diameter was known in generation i!1, and the i i~1 airway length was found based on the constant length-to-diameter ratio. The estimated dimensions were shown with the superscript ! in Table 1. The surface areas in di!erent generations for these 3 models were given in Table 3. The DCFs were calculated in the basal as well as the secretory cells. The results for the basal cells were related only to the "rst 8 generations of the T-B tree, while those for secretory cells were related to the "rst 15 generations. The results were then weighted according to the surface area of the corresponding generation. James (1983) proposed a way to scale down a model according to the lung volume. The volume of 227 cm3 of the Yeh}Schum model was reduced to 169 cm3 using a scaling factor 0.908, since the Yeh}Schum model had a much larger volume than other models. The variation of surface area with the generation number for ICRP66, Weibel, and Yeh}Schum (scaled and unscaled) models were shown in Fig. 2. The total surface areas were also given in the Fig. 2. It can be seen that there are large di!erences among di!erent models starting from the 7th generation.
4. Results The DCFs (in mGy WLM~1) for basal cells obtained using the Yeh}Schum model (scaled and unscaled), were given in Fig. 3 as a function of the particle diameter.
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Fig. 3. The dose conversion factors for basal cells obtained using the Yeh}Schum models (scaled and unscaled) as a function of the particle diameter. The results were for 0.45, 0.54, 1.5 and 3 m3 h~1 of inhaled air corresponding to various levels of physical activities, viz., sleep, rest, light and heavy exercise, respectively.
The results were shown for various breathing rates, corresponding to various levels of physical activities, viz., sleep, rest, light and heavy exercise (0.45, 0.54, 1.5 and 3 m3h~1, respectively). In all cases, the DCFs obtained using the scaled Yeh}Schum model were larger than those using the unscaled model. The DCFs were the largest for particles with diameters of a few nanometeres, which corresponded to unattached Rn progeny. The DCFs decreased with the particle diameter until about 200 nm due to the decreasing di!usional deposition. For larger diameters, they started to increase due to the enhanced deposition by impaction and sedimentation. Fig. 4 gave the DCFs for secretory cells calculated for the same condition as those in Fig. 3. Since secretory cells are closer to the mucous layer which is the source of a particles, the resulting DCFs were higher than those to the basal cells by a factor of 2}3. The pattern of doses for secretory cells resembles that for basal cells. The largest DCFs were obtained for unattached Rn progeny with diameters of a few nm. They decreased until the particles reached a diameter up to 300 nm and then started to increase. The DCFs increased with the level of physical exercise for both basal and secretory cells. This was particularly important for small particles; for larger particles with diameters above 100 nm, this e!ect still existed but was less profound. Fig. 5 gave the DCF ratios for basal cells of the Weibel symmetrical model and the ICRP66 symmetrical model to the Yeh}Schum model. The results were calculated for breathing rates of 0.45, 1.5 and 3 m3 h~1. All ratios were above 1.3. In all cases, the ICRP66 model gave larger DCFs than Weibel model. The results also showed that
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Fig. 4. The dose conversion factors for secretory cells obtained using the Yeh}Schum models (scaled and unscaled) as a function of the particle diameter. The results were for 0.45, 0.54, 1.5 and 3 m3 h~1 of inhaled air corresponding to various levels of physical activities, viz., sleep, rest, light and heavy exercise, respectively.
Fig. 5. Ratio between the dose conversion factors for basal cells given by the ICRP66 and Yeh}Schum models (solid lines) and ratio between the dose conversion factors given by the Weibel and Yeh}Schum models (dashed lines) for 0.45, 1.5 and 3 m3 h~1 of inhaled air. The curve for unscaled Yeh}Schum model for 3 m3h~1 is not shown to avoid too many curves.
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Fig. 6. Ratio between the dose conversion factors for secretory cells given by the ICRP66 and Yeh}Schum models and ratio between the dose conversion factors given by the Weibel and Yeh}Schum models for 0.45 m 3 h~1 of inhaled air.
the Weibel and ICRP66 lung models led to signi"cantly larger DCFs than the Yeh}Schum model. The di!erences between models depended on the particle size and the breathing rate. For aerosols with a diameter of 170 nm, the ICRP66 model gave DCFs larger by a factor of 1.7}1.9. For larger particles with a diameter of 500 nm, the factor ranged in 1.9}2.3. In Fig. 6 the ratios of DCFs for secretory cells were given for breathing rates of 0.45 and 1.5 m3 h~1, which had di!erent patterns from those for basal cells. The di!erent patterns originated from the fact that the basal cells were present in the "rst 8 generations of the T-B tree, while secretory cells were present in 15 generations. E!ectively, all ratios for the unscaled Yeh}Schum model were above those for the scaled model. The di!erences between the various models were less profound than those in the case of basal cells. Fig. 7 gave the variation of DCF with the generation number for basal cells for the particle diameter d "150 nm and a breathing rate of 0.45 m3 h~1 for di!erent p morphometry models. The Weibel model gave a sharp and large maximum at generation 3, while the ICRP model gave a broad and a smaller maximum between the 2nd and the 4th generations. The curve obtained using the Yeh}Schum model had a maximum at the 2nd generation of the T-B tree. Both the scaled and unscaled Yeh}Schum models gave DCFs well below those from the Weibel or ICRP66 models. Fig. 8 gave the variation of DCF with the generation number for secretory cells for the particle diameter d "150 nm and a breathing rate of 1.5 m3 h~1 for di!erent p morphometry models. The Weibel model gave a maximum at the 3rd generation,
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275
Fig. 7. Variation of the dose conversion factor with the generation number for basal cells for the particle diameter d "150 nm and a breathing rate of 0.45 m3 h~1 for di!erent models. p
Fig. 8. Variation of the dose conversion factor with the generation number for secretory cells for the particle diameter d "150 nm and a breathing rate of 1.5 m3 h~1 for di!erent models. p
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while the ICRP66 and Yeh}Schum models gave maximums at the 2nd generation. The DCF decreased rapidly beyond the maximum with the generation number in all models. After the 4th generation, the Weibel and ICRP66 models were very close to each other. The DCFs calculated with the Yeh}Schum model were lower throughout the whole T-B tree except after the 13th generation.
5. Discussion In the present work, di!erent morphometry models of the human lung were used for determination of the dose conversion factors (DCFs). The use of the Weibel and ICRP66 lung morphometry models led to larger DCFs than the Yeh}Schum model. The distributions of DCFs over the generation were di!erent in various models. The main reason for the di!erences was the di!erent surface areas of the T-B tree as described below. Basal cells were present in the "rst eight generations of the T-B tree. The surface area in the "rst eight generations was 288 cm2 in the ICRP66 model, 350 cm2 in the Weibel model and 503 cm2 in the scaled Yeh}Schum (without trachea). A larger surface area implied a smaller dose, and this explained why the Weibel model gave smaller doses in basal cells than the ICRP66 model. In the unscaled Yeh}Schum model, the surface area was 611 cm2 in the "rst eight generations, which resulted in signi"cantly smaller doses, and thus the large DCF ratio to other models. Another interesting "nding was a di!erent behavior of the ratio curves for the breathing rate of 0.45 m3 h~1 compared to the curves for 1.5 and 3 m3 h~1 shown in Fig. 5. The curves for 0.45 m3 h~1 had weak maximums and then decreased for larger particles, while the curves for larger breathing rates increased monotonously with the particle diameter. The di!erent behavior was caused by di!erent deposition patterns for di!erent #ow velocities. For larger particles, the impactional deposition was more signi"cant for larger #ow velocities, since the Stoke's number is proportional to the mean #ow velocity. Secretory cells were present throughout the entire T-B tree and its total surface area should explain the patterns of the curves in Fig. 6. The new feature when compared to the curves for basal cells was that some ratios were below 1. For example, this happened in the curve of ratio between the DCFs calculated by the Weibel model and the scaled Yeh}Schum model. This was due to the larger surface area after the 13th generation for the Weibel model than for the Yeh}Schum model. In these generations, the surface areas were far larger than those in previous generations. Consequently, they had much larger in#uence when the weighting was done according to the surface area. The surface area in the ICRP66 model was smaller than that in the scaled Yeh}Schum model so that the ratios of DCFs were slightly higher than 1. For the unscaled Yeh}Schum model, the larger surface area in generations 6}13 was dominant, so the curves were above 1. In small size region, i.e., d (25 nm, all curves for p the scaled Yeh}Schum model were well below 1 and reaching 0.6. This was caused by di!erent deposition patterns of the unattached Rn progeny in the "rst few generations for di!erent lung models.
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Another point of interest was the larger di!erence between the curves for the ratio of the ICRP66 model and Weibel model to the Yeh}Schum model. This was due to the much larger surface area of the Weibel model than that of the ICRP66 model after the 12th generation as shown in Fig. 2, which led to a much larger DCF for the ICRP66 model than that for the Weibel model. In the case of basal cells, only the "rst eight generations were relevant, and the surface areas of the eight generations for the Weibel and ICRP66 models were much closer than that of higher generations, so they have similar DCFs. 6. Conclusions In the present work, comparisons among di!erent morphometry models of the lung were presented in terms of the ratios between the dose conversion factors (DCFs) between the Weibel and ICRP66 symmetrical models to the Yeh}Schum asymmetrical models. The ratios for basal cells were always above 1, while those for secretory cells were 1$0.1 (for the scaled Yeh}Schum model). The di!erences caused by using di!erent models were attributed to the di!erent surface areas of the T-B tree in di!erent models. Acknowledgements The present research was supported in part by the research grants 7000640 and 7000658 from the City University of Hong Kong. References Chang, I. Y., Gri"th, W. C., Shyr, L. J., Yeh, H. C., Cuddihy, R. G., & Seiler, F. A. (1991). Software for the draft NCRP respiratory tract dosimetry model. Radiation Protection Dosimetry, 38(1/3), 193}199. Cheng, Y. S., Su, Y. F., Yeh, H. C., & Swift, D. L. (1993). Deposition of thoron progeny in human head airways. Aerosol Science and Technology, 18, 359}375. ICRP, International Commission on Radiological Protection (1994). Human Respiratory tract model for radiological protection. A Report of Committee 2 of the ICRP66. ICRP Publication 66. Ann. ICRP 24/(1/4), Oxford: Pergamon Press. ICRU, International Commission on Radiological Units and Measurements (1993). Stopping powers and ranges for protons and alpha particles. ICRU Report 49. Ingham, D. B. (1975). Di!usion of aerosols from a stream #owing through a cylindrical tube. Journal of Aerosols Science, 6, 125}132. James, A. C. (1983) Dosimetry aspects of exposure to radon and thoron daughter product. Report by a Group of Experts of the OECD Nuclear Energy Agency. James, A. C., Stahlhofen, W., Rudolf, G., Egan, M. J., Nixon, W., Gehr, P., & Brian, J. K. (1991). The respiratory tract deposition model proposed by the ICRP Task group. Radiation Protection Dosimetry, 38(1/3), 159}165. NRC, National Research Council (1991). Comparative dosimetry of radon in mines and homes. Washington DC: National Academic Press. Weibel, E. R. (1963). Morphometry of the human lung. Berlin: Springer. Yeh, H. C., & Schum, G. M. (1980). Model of human lung airways and their application to inhaled particle deposition. Bulletin of Mathematical Biology, 42, 461}480.