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The effect of polydispersity of radioactive aerosols on the activity distribution in the human lung
J. Aerosol Sci., Vol. 20, No. 8, pp. 1313-1316, 1989. Printed in Great Britain.
0021-8502/89 $3.00 + 0.00 Pergamon Press plc
THE EFFECT OF POLYDISPERSITY OF RADIOACTIVE AEROSOLS ON THE ACTIVITY DISTRIBUTION IN THE HUMAN LUNG 1 Werner Hofmann
2 and Laszlo Koblinger
1 Division of Biophysics, University of Salzburg, A-5020 Salzburg, Austria 2 Health Physics Department, Central Research I n s t i t u t e for Physics, P.O. Box 49, H-1525 Budapest, Hungary
INTRODUCTION Aerosol deposition studies in human subjects are typically conducted with monodisperse aerosols, thus providing information about the deposition pattern of inhaled particles in the lungs as a function of particle size. Environmental or medicinal aerosols, however, are usually characterized by a wide range of particle diameters (polydisperse aerosols). For radioactively labelled aerosols, the distribution of the activity deposited within the human respiratory tract is further affected by the labelling technique. In this simulation effort we distinguish three different scenarios: i. Each aerosol particle carries the same amount of activity irrespective of its size, i.e., the activity distribution in the lung is determined solely by the geometrical properties of the carrier aerosol. 2. The activity of an aerosol particle is proportional to its surface area, e.g., if radioactive particles are attached to already generated aerosols. Here, the attachement probability of radioactive nuclides to aerosol particles depends on the surface area, such as for ambient radon progeny aerosols. 3. The activity of an aerosol particle is proportional to its volume, e.g. if the aerosol is produced after labelling, such as the generation of radioaerosols from a homogeneous radioactive solution. Consequently, for the inhalation of polydlsperse, radioactive aerosols, the distribution of the activity deposited within the human lung may differ from the distribution of the number of deposited particles. In the present text, therefore, we want to study the effect of different labelling techniques on the total amount of the activity deposited, and its regional distribution.
DEPOSITION MODEL The computer code IDEAL-2 (Kobllnger and Hofmann, 1988; 1989) has been used to compute total and regional, i.e. tracheobronchlal (TB) and pulmonary (P), deposition fractions within a stochastic morphometrlc model of the human lung structure (Kobllnger and Hofmann, 1985; 1989). In this deposition model, the branching airway system of the lung is represented by a sequence of bifurcation units (Koblinger and Hofmann, 1989). The geometry of the pathways is selected in a random fashion for each individual particle, while deposition probabilities for diffusion, Impaction and sedimentation are calculated analytically. For most purposes, the lognormal distribution provides a reasonably good fit to commonly encountered particle slze data (Phalen, 1984), characterized by a median diameter and a geometric standard deviation (ag). In the present simulations, we have selected three different median diameters, namely 0.03, 0.3 and 3 ~m. This choice is based on the shape of the total deposition curve (Fig. I) as a function of particle diameter: While the 0.3 ~m diameter particle is located in the minimum of the curve, the 0.03 and 3 pm diameter particles lle somewhere in the middle of the symmetrically rising portions of the deposition curve. For all three lognormal slze distributions, a geometric standard deviation of og= 2.5 was selected. The size distributions, however, were truncated at 2 ag on both sides, i.e. all particles have diameters which are larger than one fifth of the median and smaller than five times the median value.
1313
1314
W. HOFMANN and L. KOBLINGER
- -
total deposition
. ~
....
frccL,on deposded inthe lrocheo- bronchial region -- -- -- fraction deposO.ed in the pulmonary region
08 o7
' / =" g 05 -
/
\\
/
/ /
\
/
/ //
~\
\
/
03-
\
/
,: '\ ' ,\
\\ \ \\\
/
\ 01
0
,
\
"\x\
/' \\
, 2
\
, 5
///
, 1(~1
~
~ 5
l 1
r--2
--n 5
i~0
port,tie diometer ()am)
Fig.
I. Total and regional d e p o s i t i o n fractions as functions of particle diameter (tidal volume = 1000 cm 3 , b r e a t h i n g cycle time = 4 s).
RESULTS Table 1 presents theoretical p r e d i c t i o n s of the total and regional (TB, P) activity deposition fractions for 0.03 ~ m median d i a m e t e r size distributions. The first row refers to a m o n o d l s p e r s e aerosol of the same size, and the subsequent rows illustrate the effect of p o l y d l s p e r s e aerosols labelled by an activity which is p r o p o r t i o n a l to number, surface area and volume of its carrier aerosol. The relative standard deviations, characterizing the statistical u n c e r t a i n t y of the Monte Carlo calculations, are less than 6% for all data p r e s e n t e d in Tables 1 to 3. The p o l y d l s p e r s l t y of the 0.08 ~ m median diameter particles, relative to monodlsperse aerosols of the same diameter, does not influence appreciably total deposition, since particles either smaller or larger than the median act in opposite d i r e c t i o n s upon p a r t i c l e deposition (Fig. I). If the radioactive labelling is p r o p o r t i o n a l to surface area and volume, larger particles carry more activity; thus the total a c t i v i t y deposition decreases (see Fig. I). The relative d i s t r i b u t i o n among the two lung regions is also affected by the labelling technique, indicating a decrease of the relative TB deposition and, consequently, an increase in the relative P deposition. Corresponding results for 0.3 ~ m median diameter aerosol are given in Table 2. Here, particles both larger and smaller than the median have higher deposition p r o b a b i l i t i e s than the median d i a m e t e r particles (Fig. I). Thus, total a c t i v i t y d e p o s i t i o n fractions for p o l y d i s p e r s e aersols are higher than like-slzed m o n o d i s p e r s e aerosols. In addition, labelling proportional to surface area and volume slightly reduces TB deposition, and, conversely, increases P deposition. Activity d e p o s i t i o n results for 3 p m median d i a m e t e r aerosols are listed in Table 3. In this case, p o l y d l s p e r s i t y has again no major effect on total deposition relative to m o n o d i s p e r s e particles (see Fig. I). The regional dispersion, however, is s i g n i f i c a n t l y modified, since larger particles have relatively high d e p o s i t i o n p r o b a b i l i t i e s in the bronchial tree due to the impaction d e p o s i t i o n mechanism. If the largest particles carry the m a j o r i t y of the radioactive nuclides, as a result of the surface area or volume proportionality, bronchial a c t i v i t y d e p o s i t i o n further increases. The distribution of the a c t i v i t y d e p o s i t i o n fractions throughout the tracheobronchlal region is plotted in Fig. 2 for 3 ~m median diameter aerosols. If particles are labelled p r o p o r t i o n a l l y to their surface areas or volumes, fractional activity depositions in bronchial airway generations
Activity distribution in the human lung
1315
Table I. Deposited activity fractions of radioactively labelled aerosols (median diameter = 0.03 pm).
Aerosol properties
Total
Monodisperse
0.667
Activity deposition fractions Tracheobronchial Pulmonary (% of total) (% of total) 0.128
0.539
(19%)
(81%)
0.683
0.156 (23%)
0.527 (77%)
proportional to surface area
0.443
0.083 (14%)
0.380 (86%)
proportional volume
0.407
0.048 (12~)
0.359 (88%)
Polydisperse ( o g = proportional to number
2.5)
to
Table 2. Deposited activity fractions of radioactively labelled aerosols (median diameter = 0.3 ~m).
Aerosol properties
Total
Activity deposition fractions Tracheobronchial Pulmonary (% of total) (% of total)
Monodisperse
0.137
0.018 (13%)
0.119 (87%)
Polydisperse ( o g = 2.5) proportional to number
0.211
0.026 (12%)
0.185 (88%)
proportional to surface area
0.259
0.024 (9%)
0.235 (91%)
proportional to volume
0.309
0.026 (8%)
0.283 (92%)
Table 3. Deposited activity fractions of radioactively labelled aerosols (median diameter = 3 ~m).
Aerosol properties
Total
Monodisperse
0.542
Activity deposition fractions Tracheobronchial Pulmonary (% of total) (% of total) 0.109
0.433
(20%)
(80%)
0.575
0.189 (SS%)
0.386 (67%)
proportional to surface area
0.767
0.500 (65%)
0.267 (35%)
proportional volume
0.825
0.599 (73%)
0.226 (27%)
Polydisperse (og = 2.5) proportional £o number
to
1316
W. HOFMANN and L. KOBLINGER
increase in general. In addition, d e p o s i t i o n fractions are shifted to upper bronchial bifurcations. For example, 28% of the inhaled monodisperse particles are deposited in the first six bifurcations. This fraction increases to S1% for p o l y d i s p e r s e aerosols, and to 40 and 43% if particles are labelled relative to their surface areas and volumes, respectively.
10+ m o n o d ~ s p e r s e aerosols [ o g - n o r m a ~ d { s t r i b u t l o n 69 = 25 portlcJes ere Lc~betLed p r o p o r t ~ o n c ' ;, to t h e i r v number ~, s u r f a c e o vokume
5
~ 05 ~
-
0.1
1
I
,
,
,
,
5
,
,
,
,
I0
.
.
.
.
.
.
.
15
i
20
bifurcc, t i o n u n i t n u m b e r
FiE.
2. A c t i v i t y d e p o s i t i o n fractions in t r a c h e o b r o n c h i a l airways for m o n o d i s p e r s e and p o l y d i s p e r s e aerosols labelled with different techniques (median diameter = S ~m). The relative standard deviations are less than 15~ for all data points.
CONCLUSIONS For the inhalation of ambient radioactive aerosols or the interpretation of deposition data of r a d i o a c t i v e l y labelled aerosols, e.g. in nuclear medicine, information on the p a r t i c l e slze d i s t r i b u t i o n and the labelling p r o c e d u r e is required. An example may illustrate their effect on the a c t i v i t y deposition: For 3 ~m m o n o d l s p e r s e aerosols, total d e p o s i t i o n is 54%, and 80% of it occurs in the p u l m o n a r y region. If particle diameters are lognormally distributed, having the same median d i a m e t e r and a geometrical standard deviation of 2.5, then total d e p o s i t i o n may be as high as 8S% (volume proportionality), and most of the activity, i.e., 73%, is deposited in the t r a c h e o b r o n c h l a l region.
ACKNOWLEDGEMENTS This research was sponsored by the Austrian and the H u n g a r i a n Academy of Sciences, and funded in part by the J u b i l M u m s f o n d s of the Osterrelchlsche Natlonalbank, Project No. 2911.
REFERENCES Kobllnger, L. and Hofmann, W. (1985) A n a l y s i s of human lung m o r p h o m e t r i c data for s % o c h a s t l c aerosol d e p o s i t i o n calculations. Phys. Med. Biol. 30, 541. Kobllnger, L. and Hofmann, W. (1988) Monte Carlo model for aerosol d e p o s i t i o n in human lungs. Ann. occup. HyE. 32, Suppl. 1, 65. Koblinger, L. and Hofmann, W. (1989) Monte Carlo modeling of aerosol d e p o s i t i o n in human lunEs. Part I: Simulation of random walks of inhaled particles in a s t o c h a s t i c lung structure. Submitted to J. Aerosol Scl. Fhalen, R.F. (1984) Inhalation Studies: F o u n d a t i o n s and Techniques. CRC Press, Boca Raton, FL.
0021-8502/89 $3.00 + 0.00 Pergamon Press plc
THE EFFECT OF POLYDISPERSITY OF RADIOACTIVE AEROSOLS ON THE ACTIVITY DISTRIBUTION IN THE HUMAN LUNG 1 Werner Hofmann
2 and Laszlo Koblinger
1 Division of Biophysics, University of Salzburg, A-5020 Salzburg, Austria 2 Health Physics Department, Central Research I n s t i t u t e for Physics, P.O. Box 49, H-1525 Budapest, Hungary
INTRODUCTION Aerosol deposition studies in human subjects are typically conducted with monodisperse aerosols, thus providing information about the deposition pattern of inhaled particles in the lungs as a function of particle size. Environmental or medicinal aerosols, however, are usually characterized by a wide range of particle diameters (polydisperse aerosols). For radioactively labelled aerosols, the distribution of the activity deposited within the human respiratory tract is further affected by the labelling technique. In this simulation effort we distinguish three different scenarios: i. Each aerosol particle carries the same amount of activity irrespective of its size, i.e., the activity distribution in the lung is determined solely by the geometrical properties of the carrier aerosol. 2. The activity of an aerosol particle is proportional to its surface area, e.g., if radioactive particles are attached to already generated aerosols. Here, the attachement probability of radioactive nuclides to aerosol particles depends on the surface area, such as for ambient radon progeny aerosols. 3. The activity of an aerosol particle is proportional to its volume, e.g. if the aerosol is produced after labelling, such as the generation of radioaerosols from a homogeneous radioactive solution. Consequently, for the inhalation of polydlsperse, radioactive aerosols, the distribution of the activity deposited within the human lung may differ from the distribution of the number of deposited particles. In the present text, therefore, we want to study the effect of different labelling techniques on the total amount of the activity deposited, and its regional distribution.
DEPOSITION MODEL The computer code IDEAL-2 (Kobllnger and Hofmann, 1988; 1989) has been used to compute total and regional, i.e. tracheobronchlal (TB) and pulmonary (P), deposition fractions within a stochastic morphometrlc model of the human lung structure (Kobllnger and Hofmann, 1985; 1989). In this deposition model, the branching airway system of the lung is represented by a sequence of bifurcation units (Koblinger and Hofmann, 1989). The geometry of the pathways is selected in a random fashion for each individual particle, while deposition probabilities for diffusion, Impaction and sedimentation are calculated analytically. For most purposes, the lognormal distribution provides a reasonably good fit to commonly encountered particle slze data (Phalen, 1984), characterized by a median diameter and a geometric standard deviation (ag). In the present simulations, we have selected three different median diameters, namely 0.03, 0.3 and 3 ~m. This choice is based on the shape of the total deposition curve (Fig. I) as a function of particle diameter: While the 0.3 ~m diameter particle is located in the minimum of the curve, the 0.03 and 3 pm diameter particles lle somewhere in the middle of the symmetrically rising portions of the deposition curve. For all three lognormal slze distributions, a geometric standard deviation of og= 2.5 was selected. The size distributions, however, were truncated at 2 ag on both sides, i.e. all particles have diameters which are larger than one fifth of the median and smaller than five times the median value.
1313
1314
W. HOFMANN and L. KOBLINGER
- -
total deposition
. ~
....
frccL,on deposded inthe lrocheo- bronchial region -- -- -- fraction deposO.ed in the pulmonary region
08 o7
' / =" g 05 -
/
\\
/
/ /
\
/
/ //
~\
\
/
03-
\
/
,: '\ ' ,\
\\ \ \\\
/
\ 01
0
,
\
"\x\
/' \\
, 2
\
, 5
///
, 1(~1
~
~ 5
l 1
r--2
--n 5
i~0
port,tie diometer ()am)
Fig.
I. Total and regional d e p o s i t i o n fractions as functions of particle diameter (tidal volume = 1000 cm 3 , b r e a t h i n g cycle time = 4 s).
RESULTS Table 1 presents theoretical p r e d i c t i o n s of the total and regional (TB, P) activity deposition fractions for 0.03 ~ m median d i a m e t e r size distributions. The first row refers to a m o n o d l s p e r s e aerosol of the same size, and the subsequent rows illustrate the effect of p o l y d l s p e r s e aerosols labelled by an activity which is p r o p o r t i o n a l to number, surface area and volume of its carrier aerosol. The relative standard deviations, characterizing the statistical u n c e r t a i n t y of the Monte Carlo calculations, are less than 6% for all data p r e s e n t e d in Tables 1 to 3. The p o l y d l s p e r s l t y of the 0.08 ~ m median diameter particles, relative to monodlsperse aerosols of the same diameter, does not influence appreciably total deposition, since particles either smaller or larger than the median act in opposite d i r e c t i o n s upon p a r t i c l e deposition (Fig. I). If the radioactive labelling is p r o p o r t i o n a l to surface area and volume, larger particles carry more activity; thus the total a c t i v i t y deposition decreases (see Fig. I). The relative d i s t r i b u t i o n among the two lung regions is also affected by the labelling technique, indicating a decrease of the relative TB deposition and, consequently, an increase in the relative P deposition. Corresponding results for 0.3 ~ m median diameter aerosol are given in Table 2. Here, particles both larger and smaller than the median have higher deposition p r o b a b i l i t i e s than the median d i a m e t e r particles (Fig. I). Thus, total a c t i v i t y d e p o s i t i o n fractions for p o l y d i s p e r s e aersols are higher than like-slzed m o n o d i s p e r s e aerosols. In addition, labelling proportional to surface area and volume slightly reduces TB deposition, and, conversely, increases P deposition. Activity d e p o s i t i o n results for 3 p m median d i a m e t e r aerosols are listed in Table 3. In this case, p o l y d l s p e r s i t y has again no major effect on total deposition relative to m o n o d i s p e r s e particles (see Fig. I). The regional dispersion, however, is s i g n i f i c a n t l y modified, since larger particles have relatively high d e p o s i t i o n p r o b a b i l i t i e s in the bronchial tree due to the impaction d e p o s i t i o n mechanism. If the largest particles carry the m a j o r i t y of the radioactive nuclides, as a result of the surface area or volume proportionality, bronchial a c t i v i t y d e p o s i t i o n further increases. The distribution of the a c t i v i t y d e p o s i t i o n fractions throughout the tracheobronchlal region is plotted in Fig. 2 for 3 ~m median diameter aerosols. If particles are labelled p r o p o r t i o n a l l y to their surface areas or volumes, fractional activity depositions in bronchial airway generations
Activity distribution in the human lung
1315
Table I. Deposited activity fractions of radioactively labelled aerosols (median diameter = 0.03 pm).
Aerosol properties
Total
Monodisperse
0.667
Activity deposition fractions Tracheobronchial Pulmonary (% of total) (% of total) 0.128
0.539
(19%)
(81%)
0.683
0.156 (23%)
0.527 (77%)
proportional to surface area
0.443
0.083 (14%)
0.380 (86%)
proportional volume
0.407
0.048 (12~)
0.359 (88%)
Polydisperse ( o g = proportional to number
2.5)
to
Table 2. Deposited activity fractions of radioactively labelled aerosols (median diameter = 0.3 ~m).
Aerosol properties
Total
Activity deposition fractions Tracheobronchial Pulmonary (% of total) (% of total)
Monodisperse
0.137
0.018 (13%)
0.119 (87%)
Polydisperse ( o g = 2.5) proportional to number
0.211
0.026 (12%)
0.185 (88%)
proportional to surface area
0.259
0.024 (9%)
0.235 (91%)
proportional to volume
0.309
0.026 (8%)
0.283 (92%)
Table 3. Deposited activity fractions of radioactively labelled aerosols (median diameter = 3 ~m).
Aerosol properties
Total
Monodisperse
0.542
Activity deposition fractions Tracheobronchial Pulmonary (% of total) (% of total) 0.109
0.433
(20%)
(80%)
0.575
0.189 (SS%)
0.386 (67%)
proportional to surface area
0.767
0.500 (65%)
0.267 (35%)
proportional volume
0.825
0.599 (73%)
0.226 (27%)
Polydisperse (og = 2.5) proportional £o number
to
1316
W. HOFMANN and L. KOBLINGER
increase in general. In addition, d e p o s i t i o n fractions are shifted to upper bronchial bifurcations. For example, 28% of the inhaled monodisperse particles are deposited in the first six bifurcations. This fraction increases to S1% for p o l y d i s p e r s e aerosols, and to 40 and 43% if particles are labelled relative to their surface areas and volumes, respectively.
10+ m o n o d ~ s p e r s e aerosols [ o g - n o r m a ~ d { s t r i b u t l o n 69 = 25 portlcJes ere Lc~betLed p r o p o r t ~ o n c ' ;, to t h e i r v number ~, s u r f a c e o vokume
5
~ 05 ~
-
0.1
1
I
,
,
,
,
5
,
,
,
,
I0
.
.
.
.
.
.
.
15
i
20
bifurcc, t i o n u n i t n u m b e r
FiE.
2. A c t i v i t y d e p o s i t i o n fractions in t r a c h e o b r o n c h i a l airways for m o n o d i s p e r s e and p o l y d i s p e r s e aerosols labelled with different techniques (median diameter = S ~m). The relative standard deviations are less than 15~ for all data points.
CONCLUSIONS For the inhalation of ambient radioactive aerosols or the interpretation of deposition data of r a d i o a c t i v e l y labelled aerosols, e.g. in nuclear medicine, information on the p a r t i c l e slze d i s t r i b u t i o n and the labelling p r o c e d u r e is required. An example may illustrate their effect on the a c t i v i t y deposition: For 3 ~m m o n o d l s p e r s e aerosols, total d e p o s i t i o n is 54%, and 80% of it occurs in the p u l m o n a r y region. If particle diameters are lognormally distributed, having the same median d i a m e t e r and a geometrical standard deviation of 2.5, then total d e p o s i t i o n may be as high as 8S% (volume proportionality), and most of the activity, i.e., 73%, is deposited in the t r a c h e o b r o n c h l a l region.
ACKNOWLEDGEMENTS This research was sponsored by the Austrian and the H u n g a r i a n Academy of Sciences, and funded in part by the J u b i l M u m s f o n d s of the Osterrelchlsche Natlonalbank, Project No. 2911.
REFERENCES Kobllnger, L. and Hofmann, W. (1985) A n a l y s i s of human lung m o r p h o m e t r i c data for s % o c h a s t l c aerosol d e p o s i t i o n calculations. Phys. Med. Biol. 30, 541. Kobllnger, L. and Hofmann, W. (1988) Monte Carlo model for aerosol d e p o s i t i o n in human lungs. Ann. occup. HyE. 32, Suppl. 1, 65. Koblinger, L. and Hofmann, W. (1989) Monte Carlo modeling of aerosol d e p o s i t i o n in human lunEs. Part I: Simulation of random walks of inhaled particles in a s t o c h a s t i c lung structure. Submitted to J. Aerosol Scl. Fhalen, R.F. (1984) Inhalation Studies: F o u n d a t i o n s and Techniques. CRC Press, Boca Raton, FL.