The Role of Dispersion in Particle Deposition in Human Airways

Ramesh Sarangapani*,1 and Anthony S. Wexler{dagger}

* The K. S. Crump Group, ICF Consulting, Research Triangle Park, North Carolina 27709; {dagger} University of Delaware, 126 Spencer Lab, Newark, Delaware 19716

Received March 30, 1999; accepted November 1, 1999


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 APPENDIX
 REFERENCES
 
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.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 APPENDIX
 REFERENCES
 
Recent epidemiologic studies have shown an association between daily mortality and exposure to particulate air pollution (Anderson et al., 1997Go; Dockery et al., 1993Go). 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, 1994Go; Kaw and Waseem, 1992Go), the first step in the chain of events leading to particulate toxicity is its regional dosimetry in the lung (Miller et al., 1995Go). 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, 1995Go) 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, 1993Go; Ingham, 1975Go; Pich, 1972Go). 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, 1995Go; Taulbee and Yu, 1975Go).

Deposition models can be broadly classified as trumpet models (Taulbee and Yu, 1975Go) or compartmental models (Anjilvel and Asgharian, 1995Go). Trumpet models are single-path 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., 1997Go; Heyder et al., 1988Go). Dispersion arises due to a convective mixing process between the inhaled bolus and the residual air in the lung (Heyder et al., 1988Go). 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, 1999Go) but few agree with the available 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, 1982Go). 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, 1994Go; Sarangapani and Wexler, 1999Go). Studies on aerosol bolus transport in hollow airway casts by Briant and Lippmann (1992) support this hypothesis. Using 0.5-µm 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, 1975Go). This effective diffusivity is obtained from nitrogen bolus experiments under fully developed laminar flow conditions in a straight tube (Ultman, 1985Go). 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, 1999Go). 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
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 APPENDIX
 REFERENCES
 
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. 1Go) 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 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 ({eta}) in turn is a function of flow parameters, particle characteristics, and the particle residence time in the compartment.



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FIG. 1. Schematic showing movement of particle-laden inhaled air with a parabolic and plug velocity profile in a variable cross section channel.

 
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 Dc1 = QCiT{eta}c1, where C1 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: Nc2 = QC2(T - LA/2Q), where C2 is the average particle concentration at the entrance to the second compartment. The total number of particles depositing in the second compartment is then Dc2 = Nc2{eta}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, 1995Go). 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, 1999Go). 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, 1963Go). 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 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 intra- and 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, 1985Go).

The human lung can be broadly divided into a conducting region and an intra-acinar or pulmonary region (Weibel, 1963Go). 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 (Haefeli-Bleuer and Weibel, 1988Go). 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, 1999Go).

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 Qi is the flow rate entering the ith compartment, Ci is the uniform particle concentration at the compartment entrance, and ti is the time taken by the tip of the fluid front to reach the entrance to the ith compartment, then the total number of particles crossing this compartment during an inhalation time T is . The number of particles depositing due to the combined action of diffusion and sedimentation is

where {eta}sd is the combined deposition efficiency due to diffusion and sedimentation. If FDi is the fractional displacement in the ith compartment, then the flow rate and particle concentration at the compartment exit is , respectively. The particle loss due to impaction is then


where {eta}imp is the impaction efficiency. The uniform particle concentration entering the next compartment is .

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 and are the flow rates in the two daughter compartments and and the exit particle concentrations, then the flow averaged particle concentration at the entrance to the parent compartment is

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

and the number of particles depositing due to the combined action of diffusion and sedimentation is

where ti and ti+1 are the time taken by the fluid front to reach the entrance and exit of the ith 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.


    RESULTS AND DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 APPENDIX
 REFERENCES
 
In vivo deposition experiments in humans and animals provide total particle dose to the lung. Figure 2Go compares model-derived 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 µm) and substantially higher deposition for coarse particles (>3 µm) and ultrafine particles (<50 nm). Although the experimental data show a large scatter due to intersubject variability (Schlesinger, 1995Go), 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, 1994Go) for the coarse-mode and ultrafine particles, but all models seem to underpredict total lung deposition for the fine mode particles (Fig. 2Go).



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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, 1995Go). 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., 1989Go; ICRP, 1994Go).

 
High ambient PM10 levels correlate with increased hospital admissions, decrements in lung function, and increased reporting of respiratory symptoms. PM10 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., 1996Go). 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, 1997Go). Furthermore, controlled in vivo studies on rats have also shown that the fine mode of PM10 (0.1–1.0 µm) is the subrange of ambient particles likely to be responsible for the epidemiologic effects (Kleinman et al., 1995Go). 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., 1990Go). Analysis of insoluble particles in bronchoalveolar lavage fluid from non-occupationally exposed individuals (Dumortier et al., 1994Go; Falchi et al., 1996Go) 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, 1997Go) 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 2Go 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. 2Go). We had stated previously that dispersion is a result of both axial streaming during inhalation and radial mixing during 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 resting-phase 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. 3Go). 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 particle-laden 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, 1982Go). 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.



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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.

 
Figure 4Go 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 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 throughout 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 µm 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, 1999Go).



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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.

 
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 5Go shows model-derived total deposited fraction for 3, 0.3, and 0.03 µm 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 deposition, 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.



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FIG. 5. Plot showing total deposited fraction for three different particle sizes (0.03, 0.3, and 3.0 µm) using two different airway models.

 
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 6Go 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.



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FIG. 6. Regional deposition fraction in the conducting and pulmonary airways—a comparison of model predictions with and without accounting for dispersion.

 

    APPENDIX
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 APPENDIX
 REFERENCES
 
The sedimentation deposition efficiency as obtained by Pich (1972) is

where

L is the compartment length, R the compartment radius, U the mean fluid velocity in the compartment, ug the particle terminal velocity, {rho} the particle density, d the particle diameter, g the gravitational acceleration, µ the viscosity of air, and C the slip correction factor. The diffusional deposition efficiency as obtained by Ingham (1975) is


where

and D is the particle diffusivity. The combined deposition efficiency is given by (Chen and Yu, 1993Go)

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:

Exhalation:


    ACKNOWLEDGMENTS
 
This work was supported by EPRI. The authors wish to acknowledge the helpful comments by Dr. Bahman Asgharian, CIIT.


    NOTES
 
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. Back


    REFERENCES
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 APPENDIX
 REFERENCES
 
Anderson, H. R., Spix, C., Medina, S., Schouten, J. P., Castellsague, J., Rossi., G., Zmirou, D., Touloumi, G., Wojtyniak, B., Ponka, A., Bacharova, L., Schwartz, J., and Katsouyanni, K. (1997). Air pollution and daily admissions for chronic obstructive pulmonary disease in 6 European cities: results from the APHEA project. Eur. Respir. J. 10, 1064–1071.[Abstract/Free Full Text]

Anjilvel, S., and Asgharian, B. (1995). A multiple-path model of particle deposition in the rat lung. Fundam. Appl. Toxicol. 28, 41–50.[ISI][Medline]

Haefeli-Bleuer, B., and Weibel, E. R. (1988). Morphometry of the human pulmonary acinus. Anat. Rec. 220, 401–414.[ISI][Medline]

Brand, P., Rieger, C., Schulz, H., Beinert, T., and Heyder, J. (1997). Aerosol bolus dispersion in healthy subjects. Eur. Respir. J. 10, 460–467.[Abstract/Free Full Text]

Briant, J. K., and Lippmann, M. (1992). Particle transport through a hollow canine airway cast by high-frequency oscillatory ventilation. Exp. Lung Res. 18, 385–407.[ISI][Medline]

Chen, Y. K., and Yu, C. P. (1993). Particle deposition from duct flows by combined mechanism. Aero. Sci. Tech. 19, 389–395.

Churg, A., and Brauer, M. (1997). Human lung parenchyma retains PM2.5. Am. J. Respir. Crit. Care Med. 155, 2109–2111.[Abstract]

Churg, A., Wright, J. L., and Stevens, B. (1990). Exogenous mineral particles in the human bronchial mucosa and lung parenchyma. I. Nonsmokers in the general population. Exp. Lung. Res. 16, 159–175.[ISI][Medline]

Dockery, D. W., Pope, A. C., 3d., Xu, X., Spengler J. D., Ware J. H., Fay, M. E., Ferris B. G., and Speizer, F. E. (1993). An association between air pollution and mortality in six U.S. cities. N. Engl. J. Med. 329, 1753–1759.[Abstract/Free Full Text]

Dumortier, P., De Vuyst, P., and Yernault, J. C. (1994). Comparative analysis of inhaled particles contained in human bronchoalveolar lavage fluids, lung parenchyma and lymph nodes. Environ. Health Perspect. 102(suppl 5), 257–259.

Edwards (1994). A general theory of the macrotransport of nondepositing particles in the lung by convective dispersion. J. Aerosol Sci. 25, 543–565.[ISI]

Edwards (1995). The macrotransport of aerosol particles in the lung: aerosol deposition phenomena. J. Aerosol Sci. 26, 293–317.[ISI]

Egan, M. J., Nixon, W., Robinson, N. I., James, A. C., and Phalen, R. F. (1989). Inhaled aerosol transport and deposition calculations for the ICRP Task Group. J. Aerosol Sci. 20, 1305–1308.[ISI]

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.

Hext, P. M. (1994). Current perspectives on particulate induced pulmonary tumours. Hum. Exp. Toxicol. 13, 700–715.[ISI][Medline]

Heyder, J., Blanchard, J. D., Feldman, H. A., and Brain, J. D. (1988). Convective mixing in human respiratory tract: estimates with aerosol boli. J. Appl. Physiol. 64, 1273–1278.[Abstract/Free Full Text]

ICRP (1994). Human respiratory tract model for radiological protection: A report of a task group of the international commission on radiological protection. ICRP Publication 66, Ann. ICRP, 24(1–3), 267–272.

Ingham, D. B. (1975). Diffusion of aerosols from a stream flowing through a cylindrical tube. J. Aerosol Sci. 6, 125–132.

Kaw, J. L., and Waseem, M. (1992). Some advances in dust-related pulmonary toxicology during the last decade. J. Sci. Ind. Research 51, 791–801.

Kaye, S. R., and Phillips, C. G. (1997). The influence of the branching pattern of the conducting airways on flow and aerosol deposition parameters in the human, dog, rat, and hamster. J. Aersol. Sci. 28(7), 1291–1300.

Kim, C. S., and Iglesias, A. J. (1989). Deposition of inhaled particles in bifurcating airway models: I. Inspiratory deposition. J. Aerosol Med. 2, 1–14.

Kim, C. S., Iglesias, A. J., and Garcia, L. (1989). Deposition of inhaled particles in bifurcating airway models: II. Expiratory deposition. J. Aerosol Med. 1, 15–27.

Kleinman, M. T., Bhalla, D. K., Mautz, W. J., and Phalen, R. F. (1995). Cellular and immunologic injury with PM-10 inhalation. Inhal. Toxicol. 7, 589–602.[ISI]

Koblinger, L., and Hofmann, W. (1985) Analysis of human lung morphometric data for stochastic aerosol deposition calculations. Phys. Med. Biol. 30, 541–556.[ISI][Medline]

Miller, F. J., Anjilvel, S., Menache, M. G., Asgharian, B., and Gerrity T. R. (1995). Dosimetric issues relating to particulate toxicity. Inhal. Toxicol. 7, 615–632.[ISI]

Muir, D. C. F. (1967). Distribution of aerosol particles in exhaled air. J. Appl. Physiol. 2, 210–214.

Pich, J. (1972). Theories of gravitational deposition of particles from laminar flows in channel. J. Aerosol Sci. 3, 351–361.

Raabe, O. G., Yeh, H. C., Schum, G. M., and Phalen, R. F. (1976). Tracheobronchial Geometry: Human, Dog, Rat, and Hamster. LF-53. Lovelace Foundation, Albuquerque, New Mexico.

Sarangapani, R., and Wexler, A. S. (1999). Modeling aerosol bolus dispersion in human airways: J. Aerosol Sci. 30(10), 1345–1362.

Scherer, P. W., and Haselton, F. R. (1982). Convective exchange in oscillatory flow through bronchial-tree models. J. Appl. Physiol. 53, 1023–1033.[Abstract/Free Full Text]

Schlesinger, R. B. (1995). Deposition and clearance of inhaled particles. In Concepts in Inhalation Toxicology (R. O. McClellan and R. F. Henderson, Eds.), pp. 191–224.

Schwartz, J., Dockery, D. W., and Neas, L. M. (1996). Is daily mortality associated specifically with fine particles? J. Air Waste Manage. Assoc. 46, 927–939.[ISI]

Taulbee, D. B., and Yu, C. P. (1975). A theory of aerosol deposition in the human respiratory tract. J. Appl. Physiol. 3, 77–85.

Taulbee, D. B., Yu, C. P., and Heyder, J. (1978). Aerosol transport in the human lung from analysis of single breaths. J. Appl. Physiol. 44(5), 803–812.

Ultman, J. S. (1985). Gas transport in the conducting airways. In Gas Mixing and Distribution in the Lung (L. A. Engel, and M. Paiva, Eds.), Vol. 25, pp. 63–136. Marcel Dekker, Inc., New York.

Weibel, E. R. (1963). Morphometry of the Human Lung. pp. 110–143. Academic Press, New York.

Wilson, W. E., and Suh, H. H. (1997). Fine particles and coarse particles: concentration relationships relevant to epidemiologic studies. J. Air Waste Manage. Assoc. 47, 1238–1249.[ISI]

Yeh, H. C., and Schum, G. M. (1980). Models of human lung airways and their application to inhaled particle deposition. Bull. Math. Biol. 42, 461–480.[ISI][Medline]





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