53, 430 – 437 (2000)
Copyright © 2000 by the Society of Toxicology
TOXICOLOGICAL SCIENCES
The Effect of Heterogeneity of Lung Structure on Particle
Deposition in the Rat Lung
Werner Hofmann,* ,1 Bahman Asgharian,† Ralph Bergmann,* Satish Anjilvel,‡ and Fred J. Miller†
*Institute of Physics and Biophysics, University of Salzburg, Hellbrunner Str. 34, A-5020, Salzburg, Austria; †Chemical Industry Institute of Toxicology,
Research Triangle Park, North Carolina 27709; and ‡Department of Neuroscience, New York State Psychiatric Institute, West New York, New York 10032
Received July 1, 1999; accepted October 8, 1999
Differences in particle deposition patterns between human and
rat lungs may be attributed primarily to their differences in
breathing patterns and airway morphology. Heterogeneity of lung
structure is expected to impact acinar particle deposition in the
rat. Two different morphometric models of the rat lung were used
to compute particle deposition in the acinar airways: the multiplepath lung (MPL) model (Anjilvel and Asgharian, 1995, Fundam.
Appl. Toxicol. 28, 41–50) with a fixed airway geometry, and the
stochastic lung (SL) model (Koblinger and Hofmann, 1988, Anat.
Rec. 221, 533–539) with a randomly selected branching structure.
In the MPL model, identical acini with a symmetric subtree (Yeh
et al., 1979, Anat. Rec. 195, 483– 492) were attached to each
terminal bronchiole, while the respiratory airways in the SL model
are represented by an asymmetric stochastic subtree derived from
morphometric data on the Sprague-Dawley rat (Koblinger et al.,
1995, J. Aerosol. Med. 8, 7–19). In addition to the original MPL
and SL models, a hybrid lung model was also used, based on the
MPL bronchial tree and the SL acinar structure. Total and regional deposition was calculated for a wide range of particle sizes
under quiet and heavy breathing conditions. While mean total
bronchial and acinar deposition fractions were similar for the
three models, the SL and hybrid models predicted a substantial
variation in particle deposition among different acini. The variances of acinar deposition in the MPL model were consistently
much smaller than those for the SL and the hybrid lung model.
The similarity of acinar deposition variations in the two latter
models and their independence on the breathing pattern suggests
that the heterogeneity of the acinar airway structure is primarily
responsible for the heterogeneity of acinar particle deposition.
Key Words: inhalation; particle deposition; rat; lung morphology; mathematical modeling.
In order to estimate the risk from inhalation exposure to a
specific particulate substance, one must determine the distribution of doses throughout the lung. In vivo exposures of
human test subjects to toxic substances are legally prohibited at
the high levels necessary to produce observable reactions.
Because of this, the rat has frequently been used as a human
To whom correspondence should be addressed. Fax: ⫹⫹43-662-8044150. E-mail: [email protected].
1
surrogate in inhalation toxicology. Indeed, various modeling
efforts have been published in recent years on the calculation
of particle deposition in the various regions of the rat lung
(Anjilvel and Asgharian, 1995; Hofmann et al., 1989; Hofmann et al., 1993; Hofmann and Bergmann, 1998; Koblinger
and Hofmann, 1995; Martonen et al., 1992a,b; Schum and
Yeh, 1980; Yu and Xu, 1986).
Differences in particle deposition patterns between human
and rat lungs may be attributed primarily to their differences in
breathing patterns and airway morphology. Most published
models of particle deposition in the rat lung are based on the
extensive morphometric measurements of Raabe et al. (1976),
which provide a complete set of data for bronchial airways in
the Long-Evans rat. In their symmetric single-path models of
the whole lung and of the five lobes, Yeh et al. (1979) simplified the measured rat bronchial geometry by determining
average values for diameters and lengths of airways in each
airway generation. The application of single-path models
greatly facilitates the computational procedures involved in
particle deposition calculations. Through detailed statistical
analyses of the originally measured data, Koblinger and Hofmann (1988) developed an asymmetric stochastic lung (SL)
model in which airway parameters are characterized by probability density functions and statistical correlations among
them. Due to the statistical nature of this morphometric lung
model, Monte Carlo methods are applied to the random selection of individual paths for the computation of inhaled particle
deposition. Finally, Anjilvel and Asgharian (1995) defined a
multiple-path model of the rat lung (MPL), which is closely
based on the actually measured anatomic data. Deposition of
inhaled particles in this model is computed for each airway
along the different paths from the trachea to the terminal
bronchioles. Thus, the asymmetry of the bronchial morphologies of both the SL model and the MPL model allow for the
experimentally observed intrasubject variability in airway dimensions within a given airway generation.
Due to the scarcity of morphometric data available at that
time, Yeh et al., (1979) supplemented their bronchial tree
model with a regular dichotomous pulmonary branching structure, based on theoretical considerations regarding the number
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PARTICLE DEPOSITION IN THE RAT LUNG
and dimensions of acinar airways rather than on experimental
data. As a consequence of this, acinar airway dimensions do
not refer to a specific strain. In a later study, Mercer and Crapo
(1987) provided a quantitative description of the ventilatory
units of the Sprague-Dawley rat, based on the three-dimensional reconstruction of alveolar duct systems. Their measurements indicated that the branching of the alveolar ducts did not
fit a regular dichotomous pattern, displaying considerable variations in the branching pattern and in the number of bronchiole-alveolar duct junctions. Based on the measurements of four
ventilatory units, Mercer and Crapo (1987) derived a typical
path model of the acinar tree by computing average diameters
and lengths, and number of airway segments in each generation. The same morphometric data were later statistically analyzed by Koblinger et al. (1995), applying the same statistical
techniques previously used for the analysis of the bronchial
tree data. Their stochastic asymmetric model provides information on the frequency distributions of the number of acinar
airways, their diameters and lengths, and the correlations
among them.
In the present study, two different morphometric models of
the rat lung were used for the computation of particle deposition in bronchial and acinar airways: the MPL model of Anjilvel and Asgharian (1995), consisting of a fixed asymmetric
bronchial tree and a symmetric acinar subtree (note: a subtree
is defined as a dichotomously branching system that originates
from a given airway distal to the trachea), and the SL model of
Koblinger et al. (1995) with a stochastic asymmetric bronchial
and acinar airway structure. In addition to the original MPL
and SL models, a hybrid lung model was also used, based on
the MPL bronchial tree and the SL acinar structure. Because
similar deposition equations were used for each model, it is
anticipated that any differences in particle deposition can be
attributed to corresponding differences in lung morphology.
MATERIALS AND METHODS
Description of the Deposition Models
The philosophy of constructing the MPL model and the SL model has been
described in detail in the original papers of Anjilvel and Asgharian (1995) for
the MPL model, and in Koblinger and Hofmann (1988) and Koblinger et al.
(1995) for the SL model. Thus only the salient features of both models will
briefly be discussed here.
The tracheobronchial (TB) tree of the MPL model is directly taken from the
morphometric measurements by Raabe et al. (1976) for the Long-Evans rat.
This database comprises the branching structure of the TB tree and the length,
diameter, branching angle, and gravity angle of each of the 4807 conducting
airways with 2404 terminal bronchioles. Each terminal bronchiole is followed
by an eight-generation symmetric acinus similar to that by Yeh et al. (1979),
thereby assuming that each acinus has the same structure and volume. This
airway tree is stored within a computer in a data structure of connected nodes
known as the binary tree. For the reconstruction of the airway system and the
calculation of various parameters including deposition, standard tree traversal
algorithms are used. Although the mathematical approach of the MPL model
for particle deposition calculations is similar to that of a single-path model (Yu,
1978), its major advantage is that it incorporates actual lung measurements and
thus considers the asymmetric features of the lung.
431
The stochastic model of the rat lung morphology describes the inherent
asymmetry and variability of the airway system in terms of frequency distributions (or probability density functions) of airway diameters, lengths, and
branching angles, and their correlations. The stochastic model of the rat lung
used in the present computations is derived from measurements of the TB tree
of the Long-Evans rat (Raabe et al., 1976), while the acinar structure is based
on data for the Sprague-Dawley rat (Koblinger et al., 1995; Mercer and Crapo,
1987). For the calculation of particle deposition, the random paths of inspired
particles through the SL structure are simulated by selecting randomly the
sequence of airways for each individual particle, applying Monte Carlo techniques. Within a given bifurcation, only the average deposition behavior of an
ensemble of particles is considered, i.e., deposition is computed by the commonly used equations. Particle deposition in the whole lung can then be
computed by repeating the simulations of random paths many times, typically
on the order of a few thousand.
Although the bronchial morphologies of both the SL model and the MPL
model are based on the same morphometric data (Raabe et al., 1976; Schum
and Yeh, 1980), the MPL model has a fixed asymmetric bronchial tree, in
contrast to a stochastic, though correlated, asymmetric bronchial tree in the SL
model. Due to the monopodial structure of the rat lung, the number of
bronchial airway generations along each particle’s path can vary substantially,
ranging from 7 to 33 in the MPL model, and from 4 to 33 in the SL model. In
terms of average numbers of airway generations, the bronchial tree of the SL
model with 15.1 generations is slightly shorter than that of the MPL model
with 17.2 generations (for comparison, the whole lung model of Yeh et al.
(1979) has 16 bronchial generations). This suggests that the random sampling
from frequency distributions and their correlations leads to slightly fewer
bronchial airway generations than in the original morphometric database they
were derived from. As the linear airway dimensions measured by Raabe et al.
(1976) refer to total lung capacity (TLC) (Schum and Yeh, 1980), all bronchial
airway diameters and lengths are isotropically scaled down to functional
residual capacity, FRC ⫽ 0.4 ⫻ TLC, in both lung models by a constant linear
scaling factor. Upon inspiration, each airway is assumed to expand at the same
rate, i.e., linear airway dimensions at a given tidal volume (TV) are normalized
to a total lung volume of FRC ⫹ TV/2.
In contrast to the relatively similar bronchial trees, acinar airway geometries
are fundamentally different in both models. In the MPL model, identical acini
with a symmetric subtree consisting of eight generations (Yeh et al., 1979) are
attached to each terminal bronchiole. Due to the same number of acinar airway
generations with fixed dimensions along each path, all acini have the same
volume. For comparison, the respiratory airways in the SL model are represented by an asymmetric subtree with variable tube dimensions and number of
airway generations (Koblinger et al., 1995), resulting in highly variable acinar
airway volumes. Since the lungs were maintained at FRC during the fixation
procedure (Mercer and Crapo, 1987), the originally measured dimensions are
used in the SL model; in the MPL model, the same linear scaling procedure,
as defined above for the bronchial region, has been applied here. Despite the
apparent structural differences in acinar morphology, acinar volumes are quite
similar: 2.016 mm 3 in the MPL model (Yeh et al., 1979), if scaled down to
FRC, as compared to an average volume of 1.88 mm 3 in the SL model (Mercer
and Crapo, 1987). Likewise, the average number of acinar airway generations
in the SL model is 6.9, though varying from 2 to 13, only slightly smaller than
the eight generations in the MPL model (note: Rodriguez et al. [1987] reported
an average value of 6.2).
Although both the MPL and the SL model include an asymmetric bronchial
tree model, it is the MPL model that represents the pure effect of intrasubject
variability in airway dimensions. Due to the stochastic airway selection procedure, the SL model includes also, at least to some extent, the effect of
intersubject variability, thus producing a slightly greater variability in airway
geometry. As a consequence of this, a hybrid lung model was constructed for
the following reasons: a) the branching structure of the bronchial region does
not vary appreciably between healthy rats of the same strain, weight, and
gender (Ménache et al., 1991), i.e., intersubject variability may safely be
neglected. Consequently, the MPL model properly describes the bronchial
432
HOFMANN ET AL.
airway morphology. b) Morphometric measurements (Mercer and Crapo,
1987) have shown that the acinar structure is highly variable within a given rat,
i.e., intrasubject variability must be considered. This necessitates the use of the
stochastic acinar model. As a consequence of this, the hybrid lung model
combines the MPL bronchial tree with the SL acinar structure. The comparison
between the SL model and the hybrid lung model also allows us to investigate
the effect of bronchial airway geometry (MPL vs. SL) on the variability of
acinar deposition.
In case of an asymmetric bronchial airway structure, the partitioning of the
airflow at each bifurcation must be considered. In the MPL model, flow
splitting in a given airway is proportional to its distal volume, which is
consistent with the notion that each acinus is supplied with the same amount
of air (or, in other words, that each lobe expands and contracts at the same
rate). Because all airway dimensions are stored in the computer, distal volumes
can be determined for each airway by traversing up the bronchial tree. Due to
the random selection of the inhaled particle’s path during inspiration, this
information is not available in the SL model. Instead, flow splitting in main and
lobar bronchi is proportional to lobar volumes, while flow splitting within
lobes is determined by the relationship between flow asymmetry and crosssectional area asymmetry (the latter is computed at each bifurcation from the
selected daughter diameters) derived by Phillips and Kaye (1997), which is
also based on proportionality to distal volumes.
In the MPL model, the alveolar volume is equally distributed among all
alveolar ducts, i.e., an effective diameter is used for all eight alveolar duct
generations. For comparison, the probability of entering an alveolus is explicitly incorporated into the SL model as a function of acinar airway diameter and
generation number (Rodriguez et al., 1987). Consequently, deposition is computed separately for the cylindrical parts of the alveolar ducts and for the
alveoli.
Particle deposition in individual airways due to the various physical deposition mechanisms is computed in both models by different analytical equations. The deposition efficiency equations used in the MPL model are those
proposed by Ingham (1975) for diffusion, by Cai and Yu (1988) for impaction,
and by Wang (1975) for sedimentation. Corresponding equations for the SL
model are by Cohen and Asgharian (1990) and Ingham (1975) for diffusion in
upper and peripheral airways, respectively, and by Yeh and Schum (1980) for
both impaction and sedimentation. While the diffusion and sedimentation
deposition equations in both models produce very similar results, predictions
of impaction deposition based on Cai and Yu (1988) are slightly higher than
those using the formula by Yeh and Schum (1980). This suggests that potential
differences in particle deposition patterns will be caused primarily by differences in lung morphology and not by the use of different deposition equations.
RESULTS
Total and regional, i.e., bronchial and acinar, deposition was
calculated for a wide range of spherical unit density particles,
ranging in diameter from 10 nm to 10 ␮m, for two defined
breathing conditions. Based on measurements of TV and
breathing frequencies (f) in Long-Evans rats (Mauderly et al.,
1979; Wiester et al., 1988), the following respiratory parameters were assumed for quiet and heavy breathing conditions
(Anjilvel and Asgharian, 1995): TV ⫽ 2.1 ml, f ⫽ 102 min –1
(quiet breathing), and TV ⫽ 2.7 ml, f ⫽ 131 min –1 (heavy
breathing).
As this paper focuses on the effects of different airway
morphologies on particle deposition in bronchial and acinar
airways, deposition in nasal passages has not explicitly been
accounted for in this study. However, the transit time of particles passing through the nasal passages has been considered
FIG. 1. Total deposition as a function of particle size (10 nm–10 ␮m) for
both the MPL and the SL model under quiet and heavy breathing conditions.
in both models, assuming a nasal volume of 0.42 ml (Anjilvel
and Asgharian, 1995).
Total and Regional Deposition
First, the effects of the two airway geometries on the prediction of total and regional deposition will be investigated.
Total deposition as a function of particle size under quiet and
heavy breathing conditions is plotted in Figure 1 for both the
MPL and the SL model. Total deposition fraction predicted by
the MPL model is higher than that of the SL model for particles
smaller than 0.2 ␮m. For particles between 0.2 and 2 ␮m, the
SL model predicts higher deposition fractions. For particles
larger than 2 ␮m, both models predict similar deposition fractions. Because total deposition is a relatively insensitive indicator of the factors governing particle deposition in the lungs,
the partitioning of deposition fractions among bronchial and
acinar airways will be investigated next.
As noted before, the bronchial morphologies of both the SL
model and the MPL model are based on the same morphometric data, the only difference being that the MPL model has a
fixed asymmetric bronchial tree, in contrast to a stochastic
asymmetric bronchial tree in the SL model. It is therefore
anticipated that bronchial deposition should also be similar in
both models, which is indeed borne out by the model predictions (Fig. 2). For ultrafine particles smaller than 0.07 ␮m,
deposition in the SL model is slightly higher than that in the
MPL model for both breathing modes. For submicron particles
greater than 0.07 ␮m, the MPL model predicts a slightly larger
deposition fraction. As practically the same equations for dep-
PARTICLE DEPOSITION IN THE RAT LUNG
433
is caused primarily by the higher filtration efficiency of upstream bronchial airways.
Corresponding calculations of acinar deposition were also
performed with the above defined hybrid lung model by using
the flow rate and particle concentration distributions in the
terminal bronchioles of the bronchial MPL model as input to
the stochastic acinar model. The random selection of flow rates
and particle concentrations from the MPL model is consistent
with the observation that the volume of a given acinus is not
correlated with the bronchial path length leading to that acinus.
In other words, bronchial and acinar airways are statistically
independent from each other. Because the filtering efficiencies
of the bronchial airways are so similar in both models, acinar
deposition and, consequently, total deposition in the hybrid
model is practically the same as in the stochastic model.
Variability of Acinar Deposition
FIG. 2. Bronchial deposition as a function of particle size (10 nm–10 ␮m)
for both the MPL and the SL model under quiet and heavy breathing conditions.
osition by Brownian motion are used in both models, the small
differences may be attributed to minor differences in bronchial
morphology and/or flow distribution. That such differences do
exist is borne out by the observation that bronchial deposition
of large particles is nearly the same in both models despite
slight differences in predicted deposition efficiencies in single
airways due to the use of different analytical formulations. The
higher deposition of larger particles and the smaller deposition
of submicron particles for heavy breathing relative to the quiet
breathing are consistent with the dependence of relevant physical deposition mechanisms on flow rate.
In the case of acinar deposition, apparent differences in
airway structure do indeed lead to differences in particle deposition, as illustrated in Figure 3, although average acinar
volumes are similar in both models. For both breathing maneuvers, a consistent pattern emerges: below about 0.2 ␮m,
acinar deposition is higher in the MPL model than in the SL
model, whereas the opposite can observed for particles in the
0.2 to 2 ␮m region. In addition to differences in acinar airway
structure, this difference in acinar deposition may also be
caused by model-specific differences in terminal bronchiolar
flow rates (see Table 1).
Except for the largest and the smallest particle sizes, deposition is relatively independent of the assumed breathing pattern. For quiet breathing, the increased residence time in acinar
airways increases deposition by sedimentation, while the
smaller deposition of ultrafine particles during quiet breathing
Due to the identical airway geometry in each acinus, the
variability of acinar deposition in the MPL model is caused
exclusively by differences in bronchial pathways leading to an
acinus. For comparison, the SL model considers also the additional effect of variability in acinar pathways. In this method,
variations in acinar deposition are caused by two factors: a) the
variability in the distribution of flow rates and particle concentrations leaving the terminal bronchioles and entering the acinar region; and b) the variability in acinar pathways and related
acinar volumes.
First, differences in the acinar input data, i.e., flow rates and
FIG. 3. Acinar deposition as a function of particle size (10 nm–10 ␮m) for
both the MPL and the SL model under quiet and heavy breathing conditions.
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HOFMANN ET AL.
TABLE 1
Flow Rates and Relative Particle Concentrations at the Exit of the Terminal Bronchioles in the Multiple-Path Lung
and the Stochastic Lung Model
MPL a
SL a
MPL b
SL b
Flow rate (cm 3 s –1)
Diameter (␮m)
0.01
0.1
1
10
2.26 ⫻ 10 –3
(⫾ 6.06 ⫻ 10 –5)
0.506
0.951
0.952
0.049
(⫾
(⫾
(⫾
(⫾
0.074)
0.010)
0.017)
0.107)
4.90 ⫻ 10 ⫺3
(1.10 ⫻ 10 –3, 1.53 ⫻ 10 ⫺3)
0.592
0.958
0.955
0.115
(⫾
(⫾
(⫾
(⫾
0.178)
0.079)
0.142)
0.132)
3.74 ⫻ 10 –3
(⫾ 1.01 ⫻ 10 ⫺4)
0.610
0.961
0.935
0.008
(⫾
(⫾
(⫾
(⫾
0.065)
0.008)
0.028)
0.621)
8.14 ⫻ 10 –3
(1.83 ⫻ 10 –3, 2.56 ⫻ 10 –3)
0.654
0.973
0.969
0.099
(⫾
(⫾
(⫾
(⫾
0.165)
0.019)
0.022)
0.127)
Note. Values in table body represent relative particle concentrations at entrance to acinar region.
a
Quiet breathing.
b
Heavy breathing.
particle concentrations exiting the bronchial tree, between the
two bronchial models will be identified. The mean flow rates in
the terminal bronchioles in both models are listed in Table 1 for
quiet and heavy breathing conditions. The distribution of the
flow rates in the SL model for heavy and quiet breathing on the
original scale were severely skewed. A Box-Cox transformation was applied to normalize the data. Flow rate 0.2 was found
to be an acceptable transformation (p-value for normality by
the Kolmogorov-Smirnov test for heavy breathing ⫽ 0.08; for
quiet breathing ⫽ 0.2). The mean and standard deviation for
the transformed data were calculated. The mean and endpoints
for 1 standard deviation confidence interval were then reversetransformed to the original scale by raising these values to the
5th power. The mean and endpoints for 1 standard deviation
confidence interval are shown in Table 1. Comparison of the
mean flow rates reveals that the flow rates in the SL model are
about 2.2 times higher than those in the MPL model for both
breathing patterns, i.e., particles in the SL model enter the
acinar region at a higher speed. However, if flow rates are
normalized to the same number of bronchial airways (note: the
MPL model has, on average, two more bronchial airway generations than the SL model), flow rates are comparable in both
bronchial morphologies. This is borne out by the similarity in
their bronchial deposition patterns.
There is another distinct difference between the two models
that will also affect acinar deposition: whereas flow rates in the
MPL model are nearly identical in each terminal bronchiole,
flow rates in the SL model exhibit a strongly asymmetric
distribution, with maximum velocities being about ten times
the average. Thus, different bronchial airway selection and
flow splitting schemes lead to different flow patterns in terminal bronchioles, despite using the same morphometric data
base and the same assumption for flow partitioning (i.e., proportional to distal volume) in both models.
In addition to the above differences in flow rates, there are
also differences in the concentrations of particles at the exit of
terminal bronchioles in both models. Relative particle concentrations, i.e., normalized to a concentration of 1 at the entrance
of the trachea, for four selected particle sizes are compiled in
Table 1 (note: in the SL model, statistical weights are computed, which are equivalent to relative concentrations). Except
for the smallest and the largest particle sizes, for which particle
concentrations in the SL model are higher than those in the
MPL model, exit concentrations are very similar in both models. It should be noted, however, that flow rates and particle
concentrations are correlated in both models and that both
factors determine the fate of inhaled particles in the acinar
region.
Second, the variability in acinar deposition resulting from
the above discussed differences in bronchial pathways and, in
case of the SL and the hybrid lung model, from the variability
in the acinar airway geometry will be determined. Variations of
deposition in individual acini will be expressed by the coefficient of variation (CV), which is the standard deviation of the
distribution of deposition fractions normalized to the mean
acinar deposition.
The dependence of the coefficient of variation of acinar
deposition on particle diameter is presented in Figure 4 (for
quiet breathing) and Figure 5 (for heavy breathing) for the
three lung models employed in the present study. Because only
bronchial pathways vary in the MPL model (same flow rates,
but different numbers of particles in terminal bronchioles),
whereas acinar pathways are identical, the coefficients of variation are much smaller than for the two other models. For
comparison, bronchial (different flow rates and different numbers of particles in terminal bronchioles) and acinar pathways
vary in the SL model, thus leading to much wider distributions,
as illustrated by their larger CVs. Finally, the hybrid model,
which also reflects bronchial (MPL) and acinar (SL) pathway
variability, produces distributions that are very similar to those
predicted by the SL model. This suggests that the effect of
bronchial morphology (MPL vs. SL) on acinar deposition is
PARTICLE DEPOSITION IN THE RAT LUNG
FIG. 4. Coefficient of variation (standard deviation divided by the mean)
of the acinar deposition distribution as a function of particle size (10 nm–10
␮m) for quiet breathing conditions in the MPL, SL, and hybrid lung models.
negligible (despite their differences in flow rates and particle
concentrations). Consequently, the variability of acinar deposition is determined primarily by the variability of the acinar
airway system.
Comparison of Figures 4 and 5 with Figure 3 also indicates
that the maximum of the coefficient of variation in both the SL
and the hybrid model coincides with the minimum of average
acinar deposition, and vice versa. This dependence of the CV
of acinar deposition on particle size is caused by purely statistical reasons, as more deposition events in acinar airways
reduce the statistical uncertainty of the average value. Furthermore, the magnitude of the coefficients of variation and their
dependence on particle size are very similar for both breathing
patterns, suggesting that acinar deposition variations are
caused primarily by airway variability and not by variations in
breathing parameters.
435
(Table 1) of the bronchial MPL model were used as input data
to the stochastic acinar deposition model. Flow splitting in a
given airway of the MPL model is considered as being proportional to the alveolar volume distal to that airway. Examining acinar deposition in this manner essentially invokes the
assumption that there is no fixed relationship between the
length of the TB path to an acinus and the volume of that
acinus. In order to establish the statistical independence between TB path length and ventilatory unit volume in the lungs
of rats, two levels of analysis were explored, one on a lobar
scale and the other on a region-specific scale.
For the lobar or macro analysis, the anatomical model of
Yeh et al. (1979) for a Long-Evans black and white hooded rat
was used, which provides the TB path length and volume of
each lobe as well as the acinar volume of the lobe. For
example, the right apical lobe has the shortest overall TB path
length and the smallest acinar volume, while the right diaphragmatic lobe has the longest TB path length but a acinar
volume somewhat smaller than that of the left lung. As a result,
there is no significant correlation (p ⫽ 0.31) between TB path
length and acinar volume, implying that the size of an acinus
bears no relationship to its distance from the trachea.
For the region-specific or micro analysis, we used the TB
and ventilatory unit data obtained by Mercer et al. (1991) from
a serial reconstruction of 43 ventilatory units in the lower left
lung of a Sprague-Dawley rat. Note that ventilatory unit volume ranged from a minimum of 0.12 mm 3 to a maximum of
3.45 mm 3, an almost 30-fold difference, while the extreme
among TB path lengths varied by less than 5% (45.3 mm to
DISCUSSION
In the present study three different morphologic models of
the rat lung were used to predict particle deposition in acinar
airways: a) the MPL model of Anjilvel and Asgharian (1995),
consisting of a fixed asymmetric bronchial tree and a symmetric acinar subtree; b) the SL model of Koblinger et al. (1995),
with stochastic asymmetric bronchial and acinar airway structures; and c) a hybrid lung model, based on the MPL bronchial
tree and the SL acinar structure.
In the case of the hybrid lung model, random selections of
flow rates and particle concentrations in terminal bronchioles
FIG. 5. Coefficient of variation (standard deviation divided by the mean)
of the acinar deposition distribution as a function of particle size (10 nm–10
␮m) for heavy breathing conditions in the MPL, SL and hybrid lung models.
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HOFMANN ET AL.
47.3 mm). The Pearson correlation coefficient, which can be
used to establish the degree of linear association between a pair
of variables, between TB path length and ventilatory unit
volume was – 0.13 (p ⫽ 0.42) and thus not significantly different from zero. In other words, bronchial path length and
acinar volume are statistically independent from each other.
Moreover, the correlation coefficient between acinar volume
and radius of the terminal bronchiole leading to that acinus was
0.09 (p ⫽ 0.55), again indicating that both parameters are not
statistically correlated. It should be noted that the random
selection of acinar airways in the SL model is based on that
assumption.
In the case of acinar deposition, model-specific differences
in airway structure between the MPL and the SL model lead to
differences in particle deposition, despite the similarity of
average acinar volumes in both models. There may be various
reasons for this difference in acinar deposition, such as a much
higher average flow rate in terminal bronchioles in the SL
model. In addition, while average acinar volumes are similar,
the acinar volume in the SL model is composed of acinar
airways with smaller diameters, compensated, however, by a
larger total number of acinar airways. In addition, the same
average lung morphology does not necessarily lead to the same
average deposition, as the corresponding distributions of airway parameters are quite different.
It should also be noted here that flow splitting in the bronchial airway bifurcations of the SL model is based on distal
volumes and not on cross-sectional ratios as in our earlier
studies (e.g., Koblinger and Hofmann, 1995). The reason for
replacing the cross-sectional area ratio by the flow asymmetry
relationship of Phillips and Kaye (1997), based on distal volumes, is that the flow asymmetry is consistently higher than the
area asymmetry for a given bifurcation. As a consequence of
the preference of main stem transport, bronchial deposition of
submicron particles is now slightly higher than in the older
model, whereas acinar deposition is consistently reduced for all
particle sizes.
To evaluate the effects of different airway morphologies on
particle deposition in the lungs, deposition was normalized to
the number of particles entering the trachea. However, under
realistic inhalation conditions, lung deposition is reduced by
particle inhalability and nasal deposition. For example, inhalability in rats starts to deviate by more than 5% from 100%
already at 0.5 ␮m, dropping to a value of 45% at 10 ␮m
(Menache et al., 1995) (note: inhalability also depends on the
direction and velocity of airflow surrounding the head). Furthermore, large and small particles at both ends of the size
spectrum simulated here are effectively removed by nasal
passages, e.g., the nasal deposition efficiency of 10-␮m particles is nearly 100% (Hofmann and Bergmann, 1998). Thus, to
relate the computed deposition fractions for a given particle
size to measured particle concentrations in exposure chambers,
they must be multiplied by their inhalability and nasal penetration probabilities. It should be emphasized, however, that
these considerations do not alter the relative distribution of
particles among acinar airways.
While all three models are based on the same morphometric
data for the bronchial tree of the Long-Evans rat (Raabe et al.,
1976), the acinar airway geometries attached to them were
either an idealized airway structure for no specific rat strain
(Yeh et al., 1979) or derived from morphometric measurements on the Sprague-Dawley rat (Mercer and Crapo, 1987).
However, corresponding morphometric data for the acinar airways in the Long-Evans rat are presently not available. For the
time being, we assumed that airway dimensions and structural
relationships are similar in the Long-Evans and Sprague-Dawley rats.
Anjilvel and Asgharian (1995) have previously shown that,
even in the case of identical acini, a small fraction of pulmonary acini can receive nearly twice the average acinar deposition because of the asymmetry of the conducting airways. If the
stochastic acinar model is attached to the same bronchial tree
geometry, variability in acinar deposition further increases by
factors between 3 and 10, depending on particle size. As a
result, local doses in acinar airways may vary by an order of
magnitude. This variability has important implications for toxicologic effects and predictions of potential human risk.
In conclusion, all three lung models employed in the
present study predict substantial variability in particle deposition among different acini. The variances of acinar deposition in the MPL model are consistently much smaller
than those for the SL and the hybrid lung model. The
similarity of acinar deposition variations in the two latter
models suggests that the heterogeneity of the acinar airway
structure is primarily responsible for the heterogeneity of
acinar particle deposition. Our results also suggest that
characterizing and using the distribution of dose rather than
point estimates of dose is likely to lead to improved risk
assessments of inhaled particles.
ACKNOWLEDGMENTS
This research was supported in part by the Commission of the European
Communities, Contract No. FI4P-CT95-0025. The authors also thank Dr.
Barbara Kuyper for her editorial assistance in manuscript preparation.
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