54, 229 –236 (2000)
Copyright © 2000 by the Society of Toxicology
TOXICOLOGICAL SCIENCES
The Role of Dispersion in Particle Deposition in Human Airways
Ramesh Sarangapani* ,1 and Anthony S. Wexler†
*The K. S. Crump Group, ICF Consulting, Research Triangle Park, North Carolina 27709; †University of Delaware,
126 Spencer Lab, Newark, Delaware 19716
Received March 30, 1999; accepted November 1, 1999
Aerosol dispersion and deposition are processes that occur concurrently in human airways. However, dispersion has not been
properly accounted for in most deposition models. In this paper we
have incorporated the latest understanding of dispersion into a
dosimetry model and study the influence of dispersion on particle
deposition in the lung. We show that dispersion influences the
total deposition of inhaled particles and in particular increases the
pulmonary deposition of fine mode particles. We also discuss how
dispersion can help elucidate a number of clinical and epidemiologic results associated with particle deposition in the lung.
Key Words: particulate air pollution; dosimetry model; dispersion; deposition; control volume (CV); human airways.
Recent epidemiologic studies have shown an association
between daily mortality and exposure to particulate air pollution (Anderson et al., 1997; Dockery et al., 1993). Airborne
particulate matter (PM) is a mixture of aerosols of varying
physical and chemical characteristics. Although the exact
mechanism underlying PM induced cytotoxicity is not yet fully
understood (Hext, 1994; Kaw and Waseem, 1992), the first
step in the chain of events leading to particulate toxicity is its
regional dosimetry in the lung (Miller et al., 1995). Deposition
of inhaled particles in the respiratory tract is governed by
factors such as particle size, anatomical features of the airway,
and breathing patterns of individuals. In vivo experiments in
humans give the total particle dose (Schlesinger, 1995) to the
whole lung but cannot elucidate regional values. However,
estimates of regional particulate dosimetry can be obtained
using mathematical models. Extensive effort has been made to
theoretically formulate the individual processes responsible for
particle deposition in the lung, such as impaction, diffusion,
and sedimentation (Chen and Yu, 1993; Ingham, 1975; Pich,
1972). Numerous lung models are available that compute the
deposition efficiency in the respiratory tract by the combined
action of the above processes (Anjilvel and Asgharian, 1995;
Taulbee and Yu, 1975).
Deposition models can be broadly classified as trumpet
1
To whom correspondence should be addressed at ICF Consulting, The
K. S. Crump Group, 3200 Chapel Hill–Nelson Hwy, Suite 101, Research
Triangle Park, NC 27709. Fax: (919) 547-1710.
models (Taulbee and Yu, 1975) or compartmental models
(Anjilvel and Asgharian, 1995). Trumpet models are singlepath models where the lung is approximated by a one-dimensional variable cross-section channel (which resembles a trumpet) with the cross-sectional area being a function of the
generation. Trumpet models track particles confined within a
small control volume (CV) and simulate the breathing process
as the movement of this CV into and out of the channel. These
models use a convection-diffusion type differential equation,
with appropriate boundary conditions, to compute the transport
and deposition of aerosol particles from the CV onto the
respiratory tract.
Compartment models are models where each airway unit is
represented by a discrete and well-mixed compartment. The
lung as a whole is represented by a series of such compartments in a treelike dichotomous structure. Analytical expressions are derived to account for particle loss due to the combined action of impaction, diffusion, and sedimentation in
these compartments. The overall particle deposition in the
respiratory tract is obtained as the cumulative sum of deposition in each airway unit as the inhaled volume moves sequentially through these compartments. Using a compartmental
approach, it is easy to represent an anatomically accurate
airway network, with random airway dimensions and inhomogenous ventilation. Such a detailed representation cannot be
handled using trumpet models, as individual airway units
within a given generation are not differentiated in these models.
Few deposition models take dispersion into account. Edwards (1995) provides a review of the literature. In that work,
dispersion in airways was likened to that in packed beds. In
dispersion, an aerosol bolus introduced into the lung during
inhalation shows a broadening in the concentration profile
during exhalation (Brand et al., 1997; Heyder et al., 1988).
Dispersion arises due to a convective mixing process between
the inhaled bolus and the residual air in the lung (Heyder et al.,
1988). Aerosol deposition and dispersion are processes that
occur concurrently in the airways. As will be shown, dispersion
has a strong influence on the regional deposition pattern of the
aerosols in the lung.
Many dispersion mechanisms have been proposed (Sarangapani and Wexler, 1999) but few agree with the available
229
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SARANGAPANI AND WEXLER
experimental data without tuning adjustable parameters. Sarangapani and Wexler (1999) recently proposed a mechanism for
dispersion based only on simple fluid mechanical principles.
Briefly, dispersion in the human airways is caused by an
irreversibility in the particle velocity profile between inhalation
and exhalation. This primarily is an outcome of the nature of
the secondary fluid flow in a bifurcating geometry. Weak
secondary motion during inhalation results in axial streaming
of the inhaled particles into the daughter branches, causing
inhaled particles to be transported to deeper regions of the lung
than would be expected by the mean fluid front (Scherer and
Haselton, 1982). The relative contribution to dispersion of
mixing processes and streaming processes during inhalation
crucially determines how far a bolus penetrates into the airways and consequently where in the pulmonary airways the
particles deposit (Edwards, 1994; Sarangapani and Wexler,
1999). Studies on aerosol bolus transport in hollow airway
casts by Briant and Lippmann (1992) support this hypothesis.
Using 0.5-␮m aerosol particles as nondiffusible tracers of
convective flow, they have shown that inhaled aerosols penetrate along the axial core as a jet, much deeper than the
volumetric depth of inhalation alone would predict.
Compartment models assume that the inhaled particles are
confined within the mean fluid front and move with a velocity
equal to the mean flow velocity. Such an approximation neglects axial streaming during inhalation and thus does not
account for one of the factors leading to dispersion. Similarly,
trumpet models also assume that the CV moves with the mean
fluid velocity, once again neglecting the effect of axial streaming. However, trumpet models introduce an apparent diffusivity term to account for aerosol dispersion (Taulbee and Yu,
1975). This effective diffusivity is obtained from nitrogen
bolus experiments under fully developed laminar flow conditions in a straight tube (Ultman, 1985). For a gas bolus,
augmented diffusion arises due to the coupling between axial
convection and radial diffusion. Diffusion will not cause aerosol dispersion because the diffusivity of particles is orders of
magnitude lower than that of gases (Sarangapani and Wexler,
1999). Hence, an effective diffusivity derived from gas bolus
experiments cannot be applied directly to model particle dispersion in the human airways. In this paper we develop a
deposition model that incorporates dispersion and then study
its influence on regional particle dosimetry in the lung.
MATERIALS AND METHODS
Influence of Dispersion on Deposition
For a conceptual understanding of the effect of dispersion on deposition, we
evaluate the particle deposition pattern in a contracting channel (Fig. 1) for two
different flow profiles (plug flow and parabolic flow). In a compartmental
approach, this contracting channel is represented by two compartments: a first
compartment of length L and cross sectional area A and a second compartment
of length 2L and area A/2. We are interested in comparing the total number of
particles depositing in the two compartments when the inlet flow has a plug
velocity profile as opposed to a parabolic velocity profile. The number of
FIG. 1. Schematic showing movement of particle-laden inhaled air with a
parabolic and plug velocity profile in a variable cross section channel.
particles depositing in any given compartment is a product of the total number
of particles entering that compartment and the deposition efficiency for the
particles in the compartment. The deposition efficiency (␩) in turn is a function
of flow parameters, particle characteristics, and the particle residence time in
the compartment.
For a fluid flow rate Q with a plug velocity profile, the time taken by the fluid
front to traverse the first compartment is L/(Q/A). Assuming the flow at the
entrance is maintained for a time T, such that T ⫽ LA/Q, the total number of
particles depositing in the first compartment is D c1 ⫽ QC i T ␩ c1 , where C 1 is
the average particle concentration at the entrance to the first compartment. The
number of particles depositing in the second compartment is zero, as the
particle laden fluid front does not penetrate into the second compartment
within the time T. However, if we assume the flow to have a parabolic velocity
profile with an identical flow rate as before, the fluid front will penetrate into
the second compartment. The ratio of the centerline velocity to the mean fluid
velocity gives a quantitative measure of the volume penetrated by the tip of the
inhaled fluid front for a given inhaled volume. Some of the particles that do not
deposit in the first compartment will enter the next compartment. The number
of particles entering the second compartment is the product of the particle
concentration at the exit of the first compartment and the flow time remaining
after the tip of the fluid front enters the second compartment: N c2 ⫽ QC 2 (T ⫺
LA/ 2Q), where C 2 is the average particle concentration at the entrance to the
second compartment. The total number of particles depositing in the second
compartment is then D c2 ⫽ N c2 ␩ c2 . This simple example shows that assigning
appropriate particle velocity profiles becomes critical in accurately evaluating
the regional particle deposition pattern. Current deposition models assign the
bulk fluid velocity to the particles, disregarding the nature of the velocity
profile in the fluid. From the above analysis we can see that such an approximation will not account for the excess axial penetration by the particles due to
the parabolic nature of the velocity profile.
A Lung Model
The human lung has large variability in airway dimensions, inhomogenous
ventilation, asymmetric branching, and numerous other complications. Particle
deposition in the lung may depend on all these morphometric and flow
parameters. In this paper we develop a compartment model of the lung to keep
track of the particle deposition rate in the individual airway units as the inhaled
air traverses the airway network. In a compartmental description, each airway
unit is viewed as a discrete compartment connected to others in a treelike
structure (Anjilvel and Asgharian, 1995). Using this approach we provide a
statistical description of the airway network that captures the variability in
dimensions and flow rates as in a real lung. A detailed description of the lung
model is provided elsewhere (Sarangapani and Wexler, 1999). Only a brief
model description is provided here.
The most widely used morphometric measure for the human airways has
been Weibel’s symmetric lung model (Weibel, 1963). The Weibel model
represents the lung by a symmetric tree structure with regular dichotomous
branching, with all branches of one generation having the same morphometric
properties. This is a highly idealized representation based on a relatively small
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PARTICLE DEPOSITION IN HUMAN AIRWAYS
amount of morphometric data. Kaye and Phillips (1997) have shown that using
Weibel’s data leads to erroneous estimates for the aerosol deposition efficiency
in the lung. Geometric parameters of airways are subject to both large intraand intersubject variations. Yeh and Schum (1980) developed a five-lobed lung
model based on the comprehensive morphometric data on the human bronchial
tree collected by Raabe et al. (1976).
We employ a four-lobe lung model, a slight variation on Yeh and Schum’s
five-lobe model. In our model the four airway branches at the end of the second
generation open into four lobes: the right upper, right lower, left lower, and the left
upper. In order to bring the typical morphometric measures in our four-lobe model
closer to the real lung, irregular features are superimposed on the typical airway by
randomly picking the dimensions for individual airway units from a normal
distribution. This normal distribution for the airway length and diameter has a
mean value as listed in Sarangapani and Wexler (1999) and a standard deviation
set equal to 10% of this mean value (Koblinger and Hofmann, 1985).
The human lung can be broadly divided into a conducting region and an
intra-acinar or pulmonary region (Weibel, 1963). Our lung model comprises 23
generations after the trachea, the first 15 generations forming the conducting
airways and the rest the intra-acinar region. In the intra-acinar region, about
25% of the volume is contained in the lumen and 75% in the alveoli (HaefeliBleuer and Weibel, 1988). As the volume inhaled into the lung is completely
accommodated by the expansion of the alveolar sacs, the percent expansion of
the alveolar sacs can be given as the ratio of the inhaled volume to the total
alveolar sac volume. As the inhaled air traverses the intra-acinar region, a
small fraction of the inhaled volume is displaced from the lumen into the
expanding alveolar sacs and is unavailable for penetration into the latter
generations. This loss to the inhaled volume is modeled as a fraction of the
percent alveolar expansion, called the fractional displacement (FD). Our model
assumes a FD of 20%. Penetration of the inhaled air in the lung depends on
both the flow rate and the flow profile in the airways. Although under
physiologic breathing conditions the flow in the lung is pulsatile, we assume a
steady flow rate in all compartments. For a given flow rate at the trachea, the
mean flow rate in each subsequent airway segment is obtained by weighing it
to the respective lobar volume into which it opens. The actual flow rate is then
derived from a random normal distribution using the above mean values and a
prescribed standard deviation. The model ensures mass conservation both
during inhalation, when the flow is partitioned between two daughter compartments at a bifurcation, and during exhalation, when flow from the two
daughter branches merge at the bifurcation.
Various flow regimes exist in the human airways. Turbulent and transitional
flows are prevalent in the upper airways, whereas in the pulmonary region we
encounter creeping flow. Moreover, entrance effects as the fluid flows from the
parent into the daughter airway will influence the initial flow profile in each
generation. The entrance length is the length required for the flow to develop
from the entrance profile to a parabolic velocity profile. All the above conditions will affect the centerline to mean particle velocity during inhalation and
thereby determine the penetration of the inhaled air. Although the flow may not
be fully developed in the conducting airways, we neglect the entrance effects
and assume a parabolic velocity profile in generation 0 –14, which gives a ratio
of centerline velocity to mean fluid velocity of 2. The presence of alveolar sacs
surrounding the lumen leads to a centerline to mean fluid velocity of 1.36 in the
pulmonary region (Sarangapani and Wexler, 1999).
Modeling Deposition
Using this multipath compartmental lung model, we have developed a
computer algorithm to keep track of particle deposition in each airway unit as
the particle-laden inhaled air traverses the airway network. Particle loss in each
compartment of the tracheobronchial and pulmonary region is primarily due to
impaction, diffusion, and sedimentation. In this section we describe the mathematical formulation to compute particle deposition in each airway compartment during inhalation and exhalation due to the combined action of all the
deposition mechanisms. The model assumes that particles are introduced at the
trachea and does not account for particle loss in the upper respiratory tract (i.e.,
nasal cavity, nasopharynx, pharynx, and larynx). Because impaction loss is
predominant at airway bifurcations, the model assumes that particle loss due to
impaction occurs only at the end of each compartment (i.e., at a bifurcation
point), whereas that due to sedimentation and diffusion occur simultaneously
over the whole length of the compartment.
During inhalation, particle deposition due to sedimentation and diffusion are
computed first, using the flow volume and particle concentration at the compartment entrance. The particle loss due to impaction is computed next, using
these quantities at the compartment exit after accounting for the fractional
displacement and the decrease in particle concentration by the combined action
of the former two mechanisms. Impaction is assumed to be independent of the
other two deposition mechanisms. The model uses empirical relations for
impaction efficiency during inhalation derived as a function of particle Stokes
number. These were obtained using flow experiments in a bifurcating geometry
by Kim and Iglesias (1989). Diffusion and sedimentation are assumed to occur
concurrently and analytical expressions giving the combined deposition efficiency are used in the model (Appendix).
As stated earlier, the number of particles depositing in a given compartment is
a product of the total number of particles entering the compartment and the particle
deposition efficiency in the compartment. If Q i is the flow rate entering the i th
compartment, C i is the uniform particle concentration at the compartment entrance, and t i is the time taken by the tip of the fluid front to reach the entrance to
the i th compartment, then the total number of particles crossing this compartment
during an inhalation time T is N i ⫽ Q iC i(T ⫺ t i). The number of particles
depositing due to the combined action of diffusion and sedimentation is
D sd ⫽ Q i C i 共T ⫺ t i 兲 ␩ sd
where ␩ sd is the combined deposition efficiency due to diffusion and sedimentation. If FD i is the fractional displacement in the i th compartment, then the
flow rate and particle concentration at the compartment exit is Q i (1 ⫺ FD i )
and C i (1 ⫺ ␩ sd ), respectively. The particle loss due to impaction is then
D imp ⫽ Q i 共1 ⫺ FD i 兲关C i 共1 ⫺ ␩ sd 兲兴共T ⫺ t i⫹1 兲 ␩ imp ,
where ␩ imp is the impaction efficiency. The uniform particle concentration
entering the next compartment is C i⫹1 ⫽ C i (1 ⫺ ␩ sd )(1 ⫺ ␩ imp ).
During exhalation, loss due to impaction at the bifurcation is accounted for
prior to the loss due to the combined action of diffusion and sedimentation. If
d
d
d
Q i⫹1
and Q i⫹2
are the flow rates in the two daughter compartments and C i⫹1
d
and C i⫹2
the exit particle concentrations, then the flow averaged particle
concentration at the entrance to the parent compartment is
C ip ⫽
d
d
d
d
C i⫹1
Q i⫹1
⫹ C i⫹2
Q i⫹2
.
d
d
Q i⫹1 ⫹ Q i⫹2
The model uses empirical relations for impaction efficiency derived as a
function of particle Stokes number, obtained using flow experiments in bifurcating geometry during exhalation by Kim et al. (1989) (Appendix). The
particle loss in the parent compartment due to impaction is
D imp ⫽ Q ip C ip 共T ⫺ t i⫹1 兲 ␩ imp .
and the number of particles depositing due to the combined action of diffusion
and sedimentation is
D sd ⫽ Q ip 共1 ⫹ FD i 兲关C ip 共1 ⫺ ␩ imp 兲兴共T ⫺ t i 兲 ␩ sd
where t i and t i⫹1 are the time taken by the fluid front to reach the entrance and
exit of the i th compartment during inhalation. As we have assumed a steady
flow in all compartments, the residence time for the particle-laden fluid in any
given compartment is identical both during inhalation as well as exhalation. In
the next section we use the above set of equations to compute total and regional
particle deposition in the human lung and discuss our results.
232
SARANGAPANI AND WEXLER
FIG. 2. A comparison of model
simulation for the total deposited
fraction in the lung as a function of
particle size to the experimental
data. The experimental observation
shows a large intersubject variability
(Schlesinger, 1995). The model simulations were conducted for a resting
phase flow rate of 250 ml/s at the
trachea, with and without accounting
for dispersion. The model predictions
are also compared to the dosimetry
estimates from the ICRP model
(Egan et al., 1989; ICRP, 1994).
RESULTS AND DISCUSSION
In vivo deposition experiments in humans and animals provide total particle dose to the lung. Figure 2 compares modelderived total lung deposition fraction to experimentally measured total lung dose in humans for a wide range of particle
sizes. These simulations were conducted for a minute ventilation of 7.5 l/min at the trachea. The model predicts the lowest
deposition rates for the fine mode particles (size range 0.1–1.0
␮m) and substantially higher deposition for coarse particles
(⬎3 ␮m) and ultrafine particles (⬍50 nm). Although the experimental data show a large scatter due to intersubject variability (Schlesinger, 1995), the model predictions compare
well with experimental results for the coarse particles and the
ultrafines. However, the model underpredicts total lung deposition for the fine mode particles. The model performance
compares well with other published dosimetry models (ICRP,
1994) for the coarse-mode and ultrafine particles, but all models seem to underpredict total lung deposition for the fine mode
particles (Fig. 2).
High ambient PM 10 levels correlate with increased hospital
admissions, decrements in lung function, and increased reporting of respiratory symptoms. PM 10 consists of various size
fractions (course, fine, and ultrafine) that show different physiologic responses in the lung and have different source characteristics. Analysis of some of the epidemiologic data suggests that ambient fine particle exposure is specifically
responsible for the observed association with daily mortality
(Schwartz et al., 1996). This observation is bolstered by the
fact that fine particles readily infiltrate residential buildings and
the fraction of outdoor particles found suspended indoors is
greater for fine particles because of their longer indoor lifetime
(Wilson and Suh, 1997). Furthermore, controlled in vivo studies on rats have also shown that the fine mode of PM 10
(0.1–1.0 ␮m) is the subrange of ambient particles likely to be
responsible for the epidemiologic effects (Kleinman et al.,
1995). Although the health effects of inhaled PM is a complex
function its biopersistence, it would be interesting to know why
fine-model particles, which have the lowest deposition efficiency, have a high risk.
Autopsy studies on morphologically normal nonsmoking adults
from the general population have shown high concentration of
exogenous fine-mode mineral particles in the apical segmental
bronchus of the lung (Churg et al., 1990). Analysis of insoluble
particles in bronchoalveolar lavage fluid from non-occupationally
exposed individuals (Dumortier et al., 1994; Falchi et al., 1996)
and a more rigorous count of the retained particles in the apical
segments of the lung parenchyma in 10 never-smoking adults
using analytical electron microscopy (Churg and Brauer, 1997)
have also shown a predominance on fine-mode particles in the
lung. It is important to understand how fine-mode particles are
transported and deposited in the apical regions of the pulmonary
airways. The effect of dispersion on deposition may help address
some of these questions.
The model simulations shown in Figure 2 were conducted
with and without accounting for the added penetration of the
fluid front due to axial streaming. Incorporating axial streaming increases the overall particle deposition for the coarse
mode and the ultrafines and provides a better fit to the experimental measurement for these two size ranges, but the improvement is only marginal for the fine-mode particles (Fig. 2).
We had stated previously that dispersion is a result of both
axial streaming during inhalation and radial mixing during
PARTICLE DEPOSITION IN HUMAN AIRWAYS
FIG. 3. Schematic showing axial penetration of the particle laden inhaled
air during inhalation, convective mixing due to dispersion, and the retained
fraction at the end of the breathing cycle.
exhalation. The flow patterns that give rise to this phenomenon
are inherent to a bifurcating geometry. Dispersion causes mixing and transports particles from the inhaled air to the residual
volume in the lung. Under normal breathing conditions the
inhaled volume is equal to the exhaled volume. For restingphase breathing (minute ventilation ⬃7.5 l/min) the inhaled
volume over a period of 2 s is about 500 ml; roughly the same
amount is also exhaled. Dispersion causes this 500 ml of
particle-laden inhaled air to penetrate to a depth of 650 ml at
the end of inhalation. As only 500 ml of this particle-laden air
is exhaled from the lung at the end of the breathing cycle, a
residual volume of 150 ml of particle-laden air is entrained in
the lung (Fig. 3). During the next breathing cycle the effective
inhaled volume of particle laden air is 650 ml. This in turn will
penetrate axially to a depth of 850 ml, resulting in an particleladen entrained volume of 350 ml at the end of the second
breathing cycle. Qualitatively speaking, over a series of breathing cycles these trapped particles will move distally and finally
flood the lung with particles (Scherer and Haselton, 1982). The
total deposited fraction in the lung is then a sum of the particles
that deposit on the airway surface by the combined action of
the three deposition mechanisms during a ventilation cycle and
the particles that are entrained at the end of the cycle and
eventually deposit in the lung.
Figure 4 shows the model-derived deposited fraction and the
retained fraction as a function of particle sizes and compares
the sum of these two fractions to the experimentally measured
lung dose. After accounting for this retained fraction, the
model derived total particle deposited fraction compares well
with the experimental values over the whole range of particle
sizes. This retained fraction is a function of both the ventilation
rate and the particle size. The coarse-mode particles have a
high deposition efficiency in the conducting airways and thus
233
FIG. 4. Plot comparing model derived total deposited fraction to experimental data. The total deposited fraction is a sum of the fraction deposited during the
breathing maneuver and the fraction retained at the end of exhalation.
an insignificant fraction is retained in the reserve volume at the
end of inhalation. Similarly, ultrafine particles have a high
diffusional deposition efficiency and an insignificant fraction is
retained in the reserve volume. Only the fine-mode particles,
which have the lowest overall deposition rate, have a significant fraction that remains suspended in the reserve volume at
the end of the breathing cycle. The trapped fine-mode particles
are transported distally and eventually deposit in the pulmonary region at the end of a few breathing cycles. Hence, even
under conditions of low minute ventilation, dispersion provides
a mechanism for the transport of nondiffusing particles well
beyond the inhaled volume so they can be deposited through-
FIG. 5. Plot showing total deposited fraction for three different particle
sizes (0.03, 0.3, and 3.0 ␮m) using two different airway models.
234
SARANGAPANI AND WEXLER
FIG. 6. Regional deposition fraction in the conducting and pulmonary
airways—a comparison of model predictions with and without accounting for
dispersion.
out the lung. Quantitative estimates of the entrained particle
fraction made by Muir (1967) and Taulbee et al. (1978) using
single-breath inhalation experiments with 0.5 ␮m aerosol particles provide further direct evidence on the effects of dispersion. Their experimental results show an average of 15%
entrained fraction for a resting-phase breathing rate, which
compares well with our model simulation (Sarangapani and
Wexler, 1999).
Another piece of indirect support to the above argument is
obtained by analyzing the effect of changes in airway morphometry on particle dosimetry. As stated earlier, experimental
data show a large scatter in the total deposited fraction. Intersubject variability in airway dimension has been proposed as a
possible reason. To study the effect of variation in airway
dimension on model-derived total lung deposition fraction, we
generated two multipath airway models from random normal
distributions using different standard deviations. Figure 5
shows model-derived total deposited fraction for 3, 0.3, and
0.03 ␮m particles in these two different airway models. The
model predictions show that the variations in airway dimension
affect only the total deposition for the coarse-mode particles
and the ultrafine particles and do not affect the deposition
values for intermediate-sized particles. However experimental
data show a large scatter in the deposited fraction for fine-mode
particles as well. A potential explanation for this is that
whereas the scatter in the fractional deposition for the coarse
mode and ultrafines may be due to intersubject variability in
the airway dimension, the scatter for particles in the intermediate size range is due to differences in exhaled volume.
Although most experiments precisely control the inhaled volume, test subjects could exhale more volume than was inhaled,
depending on the protocol employed. For the coarse-mode
particles and the ultrafines, this will not affect the total depo-
sition, as only a negligible fraction of particles is retained at the
end of the breathing cycle. However, for the intermediate-sized
particles this variability in exhaled volume translates into a
variability in the fraction of particles retained, and thus influence the total lung deposition.
In addition to computing the total lung deposition, we exercised our model to predict regional particle dosimetry. We
broadly divided the lung into a conducting (generations 0 –14)
and a pulmonary region (generations 15–23). Figure 6 shows
the regional deposited fraction as a function of particles size
using models with and without accounting for dispersion.
Although dispersion results in only marginal changes to the
total deposited fraction, it causes a substantial realignment in
the regional deposition pattern. Specifically, accounting for
dispersion results in a small decrease in the conducting airway
deposition fraction and a much larger increase in the pulmonary region. This is because axial streaming causes particles to
spend less time in the conducting region and allows them to
penetrate deeper into the lung. The deeper the particles penetrate into the lung, the smaller are the airway dimensions, and
the particle deposition efficiency due to diffusion and sedimentation increases, enhancing pulmonary deposition. On the other
hand, the shorter residence time in the conducting region
slightly lowers the particle deposition efficiency due to diffusion and sedimentation. However, impaction efficiency, which
is the dominant mode of deposition in the conducting region, is
not altered due to dispersion, and only a marginal change is
observed in the conducting airway deposition fraction. Hence,
our simulations indicate that models that do not properly account for dispersion may overpredict tracheobronchial deposition at the expense of pulmonary deposition. In conclusion,
dispersion and deposition are concurrent processes in the lung.
Properly accounting for dispersion in deposition models may
help explain a number of clinical and epidemiologic results
associated with particle deposition in the lung.
APPENDIX
The sedimentation deposition efficiency as obtained by Pich
(1972) is
␩s ⫽
2
共2␧ 冑1 ⫺ ␧ 2/3 ⫺ ␧ 1/3 冑1 ⫺ ␧ 2/3 ⫹ sin ⫺1 ␧ 1/3 兲
␲
where
␧⫽
3 L ug
,
8R U
ug ⫽
␳ d 2gC
,
18 ␮
L is the compartment length, R the compartment radius, U the
mean fluid velocity in the compartment, u g the particle terminal
velocity, ␳ the particle density, d the particle diameter, g the
gravitational acceleration, ␮ the viscosity of air, and C the slip
PARTICLE DEPOSITION IN HUMAN AIRWAYS
correction factor. The diffusional deposition efficiency as obtained by Ingham (1975) is
␩ d ⫽ 1 ⫺ 0.819 exp共⫺3.66⌬ d 兲 ⫺ 0.0976 exp共⫺22.31⌬ d 兲
⫺ 0.0325 exp共⫺57⌬ d 兲 ⫺ 0.0509 exp共⫺49.96⌬ d2/3 兲
where
⌬d ⫽
DL
UR 2
235
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Edwards (1995). The macrotransport of aerosol particles in the lung: aerosol
deposition phenomena. J. Aerosol Sci. 26, 293–317.
Egan, M. J., Nixon, W., Robinson, N. I., James, A. C., and Phalen, R. F.
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and D is the particle diffusivity. The combined deposition
efficiency is given by (Chen and Yu, 1993)
Falchi, M., Biondo, L., Conti, C., Cipri, A., Demarinis, F., Gigli, B., and
Paoletti, L. (1996). Inorganic particles in bronchoalveolar lavage fluids from
nonoccupationally exposed subjects. Arch. Environ. Health 51(2), 157–161.
␩ sd ⫽ 冑␩ 2s ⫹ ␩ d2 ⫺ 共 ␩ s ␩ d兲 2.
Hext, P. M. (1994). Current perspectives on particulate induced pulmonary
tumours. Hum. Exp. Toxicol. 13, 700 –715.
The empirical relations used in the model for impaction
deposition efficiency in terms of particle stokes number are
obtained from Kim et al. (1989):
Inhalation:
␩
i
imp
⫽ 0.09*ln 共St兲 ⫹ 0.694*ln共St兲 ⫹ 1.342
2
Exhalation:
e
␩ imp
⫽ 0.194*ln 2 共St/ 2兲 ⫹ 1.01*ln共St/ 2兲 ⫹ 1.324
ACKNOWLEDGMENTS
This work was supported by EPRI. The authors wish to acknowledge the
helpful comments by Dr. Bahman Asgharian, CIIT.
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