The Effect of Heterogeneity of Lung Structure on Particle Deposition in the Rat Lung

Werner Hofmann*,1, Bahman Asgharian{dagger}, Ralph Bergmann*, Satish Anjilvel{ddagger} and Fred J. Miller{dagger}

* Institute of Physics and Biophysics, University of Salzburg, Hellbrunner Str. 34, A-5020, Salzburg, Austria; {dagger} Chemical Industry Institute of Toxicology, Research Triangle Park, North Carolina 27709; and {ddagger} Department of Neuroscience, New York State Psychiatric Institute, West New York, New York 10032

Received July 1, 1999; accepted October 8, 1999


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
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 multiple-path 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.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
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 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, 1995Go; Hofmann et al., 1989Go; Hofmann et al., 1993Go; Hofmann and Bergmann, 1998Go; Koblinger and Hofmann, 1995Go; Martonen et al., 1992aGo,bGo; Schum and Yeh, 1980Go; Yu and Xu, 1986Go).

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 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
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
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, 1978Go), its major advantage is that it incorporates actual lung measurements and thus considers the asymmetric features of the lung.

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., 1976Go), while the acinar structure is based on data for the Sprague-Dawley rat (Koblinger et al., 1995Go; Mercer and Crapo, 1987Go). 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., 1976Go; Schum and Yeh, 1980Go), 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, 1980Go), all bronchial airway diameters and lengths are isotropically scaled down to functional residual capacity, FRC = 0.4 x 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., 1979Go) 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., 1995Go), resulting in highly variable acinar airway volumes. Since the lungs were maintained at FRC during the fixation procedure (Mercer and Crapo, 1987Go), 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 mm3 in the MPL model (Yeh et al., 1979Go), if scaled down to FRC, as compared to an average volume of 1.88 mm3 in the SL model (Mercer and Crapo, 1987Go). 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., 1991Go), i.e., intersubject variability may safely be neglected. Consequently, the MPL model properly describes the bronchial airway morphology. b) Morphometric measurements (Mercer and Crapo, 1987Go) 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 cross-sectional 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., 1987Go). 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
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
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 µm, for two defined breathing conditions. Based on measurements of TV and breathing frequencies (f) in Long-Evans rats (Mauderly et al., 1979Go; Wiester et al., 1988Go), the following respiratory parameters were assumed for quiet and heavy breathing conditions (Anjilvel and Asgharian, 1995Go): 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 in both models, assuming a nasal volume of 0.42 ml (Anjilvel and Asgharian, 1995Go).

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 1Go 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 µm. For particles between 0.2 and 2 µm, the SL model predicts higher deposition fractions. For particles larger than 2 µm, 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.



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FIG. 1. Total deposition as a function of particle size (10 nm–10 µm) for both the MPL and the SL model under quiet and heavy breathing conditions.

 
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. 2Go). For ultrafine particles smaller than 0.07 µm, 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 µm, the MPL model predicts a slightly larger deposition fraction. As practically the same equations for deposition 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.



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FIG. 2. Bronchial deposition as a function of particle size (10 nm–10 µm) for both the MPL and the SL model under quiet and heavy breathing conditions.

 
In the case of acinar deposition, apparent differences in airway structure do indeed lead to differences in particle deposition, as illustrated in Figure 3Go, although average acinar volumes are similar in both models. For both breathing maneuvers, a consistent pattern emerges: below about 0.2 µm, 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 µm 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 1Go).



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FIG. 3. Acinar deposition as a function of particle size (10 nm–10 µm) for both the MPL and the SL model under quiet and heavy breathing conditions.

 

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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
 
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 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
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 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 1Go 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 rate0.2 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 reverse-transformed 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 1Go. 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 1Go (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 4Go (for quiet breathing) and Figure 5Go (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 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.



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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 µm) for quiet breathing conditions in the MPL, SL, and hybrid lung models.

 


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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 µm) for heavy breathing conditions in the MPL, SL and hybrid lung models.

 
Comparison of Figures 4 and 5GoGo with Figure 3Go 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.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
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 (Table 1Go) 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 mm3 to a maximum of 3.45 mm3, an almost 30-fold difference, while the extreme among TB path lengths varied by less than 5% (45.3 mm to 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 µm, dropping to a value of 45% at 10 µm (Menache et al., 1995Go) (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-µm particles is nearly 100% (Hofmann and Bergmann, 1998Go). 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., 1976Go), the acinar airway geometries attached to them were either an idealized airway structure for no specific rat strain (Yeh et al., 1979Go) or derived from morphometric measurements on the Sprague-Dawley rat (Mercer and Crapo, 1987Go). 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.


    NOTES
 
1 To whom correspondence should be addressed. Fax: ++43-662-8044-150. E-mail: werner.hofmann{at}sbg.ac.at. Back


    REFERENCES
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
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