Particle Deposition in a Cast of Human Tracheobronchial Airways

Abstract

Regional particle deposition efficiency and deposition patterns were studied experimentally in a human airway replica made from an adult cadaver. The replica includes the oral cavity, pharynx, larynx, trachea, and four generations of bronchi. This study reports deposition results in the tracheobronchial (TB) region. Nine different sizes of monodispersed, polystyrene latex fluorescent particles in the size range of 0.93–30 μm were delivered into the lung cast with the flow rates of 15, 30, and 60 l min^{− 1}. Deposition in the TB region appeared to increase with the increasing flow rate and particle size. Comparison of deposition data obtained from physical casts showed agreement with results obtained from realistic airway replicas that included the larynx. Deposition data obtained from idealized airway models or replicas showed lower deposition efficiency. We also compared experimental data with theoretical models based on a simplified bend and bifurcation model. A deposition equation derived from these models was used in a lung dosimetry model for inhaled particles, and we demonstrated that there was general agreement with theoretical models. However, the agreement was not consistent over the large range of Stokes number. The deposition efficiency was found as a function of the Stokes number, bifurcation angle, and the diameters of parent and daughter tubes. An empirical model was developed for the particle deposition efficiency in the TB region based on the experimental data. This model, combined with the oral deposition model developed previously, can be used to predict the particle deposition for inertial effects with improved accuracy.

INTRODUCTION

The tracheobronchial (TB) airways consist of repeated bifurcating tubes (Weibel 1963). Aerosol deposition in the TB region is a concern in the development of lung diseases, including asthma and bronchogenic cancer. Accurate dosimetric determination is important in assessing realistic risks of inhalation hazards from ambient and occupational exposure. Four major deposition mechanisms include diffusion, gravitational settling, inertial impaction, and interception. Diffusion and gravitational settling are important in small airways, whereas inertial impaction is dominant in the upper TB region. Interception is essential in preventing deposition of fibrous aerosol.

Both experimental and theoretical studies have been used to study regional airway deposition. Made from glass or metal, physical casts of a TB tree from one to several symmetrical bifurcations and having the dimensions of Weibel's idealized airway geometry (Weibel 1963) were used in experimental observations of flow patterns (Schroter and Sudow 1969), as well as aerosol deposition patterns (Ferron 1977; Myojo 1987, 1990; Kim and Iglesias 1989; Kim and Garcia 1991; Kim and Fisher 1999). These idealized airway models were useful in understanding the flow pattern and deposition mechanisms. Realistic airway replicas made from cadavers have also been used in deposition studies (Schlesinger and Lippmann 1972; Schlesinger et al. 1977; Gurman et al. 1984; Chan et al. 1978; Cohen et al. 1990; Cheng et al. 1999; Sussman et al. 1991; Smith et al. 2001). Deposition data obtained from realistic airway replicas had large variations and were more difficult to interpret, especially in terms of comparison with theoretical models. However, it is important to understand the differences in deposition patterns between a realistic airway model and those of an idealized airway model.

Several theoretical models have also been developed to predict initial deposition in the tracheobronchial airways. Deposition models for bends have been developed that showed that the Stokes number, bend angle, and curvature ratio are the main parameters in the analytical expression of the deposition (Cheng and Wang 1975; Yeh et al. 1976; Diu and Yu 1980; Cheng et al. 1999). Balásházy et al. (1990) have improved the bend model by considering different flow profiles in the bend and by showing ways to adopt a simple bend to the bifurcation geometry. Based on a stopping distance concept, Cai and Yu (1988) showed that inertial deposition in an idealized symmetrical bifurcation is a function of Stokes number, bifurcation angle, and ratio of parent and daughter tube diameters. Deposition equations derived from these models have been used in lung deposition models to predict the deposition pattern in the human respiratory tract.

A number of authors have reported using computer simulation to study particle deposition in the human lung. Hofmann and Koblinger (1990a, 1990b, 1992) used a Monte Carlo method to model aerosol deposition in the human lung. Ferron et al. (1991) simulated air flow with heat and water vapor transported into two-dimensional bifurcations. Balásházy et al. (1991) and Eisner (1993) also studied particle deposition in airway bifurcation models. Balásházy (1994) analyzed the particle trajectories in a three-dimensional bronchial airway bifurcation. These investigators used a Navier-Stokes solver but neglected the effects of turbulence. Martonen et al. (1993) studied the fluid dynamics of the human larynx and upper TB airways using a numerical technique. They found that the formation of the laryngeal jet strongly affects airflow patterns in the trachea, the bifurcation zone, and the main bronchi. While their computation included a standard k-ϵ turbulence model, they did not report any results concerning the intensity of the turbulence. Asgharian and Anjilvel (1994) numerically simulated the inertial and gravitational deposition of particles in a square cross section of a bifurcating passage. Li and Ahmadi (1995) performed detailed computer simulations of particle transport and deposition in the first lung bifurcation. They showed that airway turbulence strongly affects the particle deposition rate. In addition, the importance of accurate anisotropic modeling of the directional intensities of turbulence was emphasized for the correct evaluation of the deposition rate. Based on the laminar-to-turbulent airflow analysis of Zhang and Kleinstreuer (2003a, 2003b), they and Zhang et al. (2004) simulated and analyzed airflow structures and particle depositions in a representative human upper airway model, i.e., from mouth to the third generation of the TB tree. Their numerical report was in good agreement with data obtained from idealized airway models.

In this article we describe aerosol deposition in a realistic human airway replica as a function of flow rate and particle size. The deposition pattern was compared to several theoretical models and experimental data obtained from idealized airway models and glass bifurcation models. Comparison with theoretical models was important because some of these deposition models have been used to calculate lung deposition patterns of inhaled particles.

MATERIAL AND METHODS

Airway Replica

Figure 1 shows the human airway cast used in the present study, including the oral cavity, pharynx, larynx, trachea, and four generations of bronchi. The oral portion of the cast was molded from a dental impression of an oral cavity of a human volunteer, while the other airway portions of the cast were made from a cadaver (Cheng et al. 1997). The process of making the replica, and the dimension of the oral cavity and the particle deposition in this area were also investigated by Cheng et al. (1999). The production mold for our cast was made using Dow-E silicone rubber (Dow Corning, Midland, MI, USA). Wax was poured into the production mold; after the wax solidified, the cast was carefully taken out. To minimize the effect of electrostatic deposition, an electrically conductive silicone rubber compound ((KE-4576, one-component RTV) GemTech, Grapevine, TX, USA) was applied to the wax mold used to make the cast. In the deposition experiment, the inside wall of the cast was coated with silicon oil (Dow Corning 550) to minimize particle bounce. This study focused on the results of particle deposition in the TB region of the cast. As shown in Figure 1, the TB cast was cut into several segments after the experiment to investigate the local particle deposition. In order to compare our results with other studies, the cast was separated into trachea (generation 0) and four generations. The sum of segments 8D, 9D, and 10D was considered as trachea, which has no bifurcation in this region. From the first to the fourth generation, the upper bifurcation was considered in the corresponding generation. For this TB cast, the first generation only has one daughter tube (13F). Another one is right-connected with the second bifurcation (14G), which is considered in the second generation. Only two bifurcations in the fourth generation (32K and 33K) are included in the TB cast. The rest of the terminal bifurcations (20I, 22I, and 23I) belong to the third generation. Table 1 lists the dimensions of each part of the TB cast, including the angles of each bifurcation. Airflow distribution in each terminal tube of the cast was measured using a hot-wire anemometer probe (Model 8470, TSI Inc., St. Paul, MN, USA). Velocity measurements at terminal segments were made at flow rates of 15, 30, and 60 l min^{− 1}. The overall flow distribution in our model was approximately 62% to the right lung and 38% to the left lung, similar to what has been reported by Cohen et al. (1990).

Figure 1 Schematic of the upper respiratory airway replica.

Table 1 Airway dimensions

	Parent (cm)		Daughter (cm)
	L0	D0	L1	D1	L2	D2	Whole bifurcation angle (^ˆ)	Plane angle (^ˆ)
Trachea
(8D + 9D+ 10D)	7.44	1.58
1st bifurcation
11E + 13F	0.35	1.9	0.32 (to F1)	1.23 (to F1)	1.76 (to F2)	0.71 (to F2)	35	0
2nd bifurcation
14G + 16H + 17H	0.38	1.23	1.11 (to 16H)	0.64 (to 16H)	1.24 (to 17H)	0.94 (to 17H)	84	15
15G + 18H + 19H	1.26	0.65	0.8 (to 18H)	0.3 (to 18H)	0.63 (to 19H)	0.67 (to 19H)	35	10
3rd Generation
20I + 1/2 (24J) + 1/2 (25J)	0.37	0.63	0.5 (to 24J)	0.52 (to 24J)	0.5 (to 25J)	0.54 (to 25J)	80	25
21I + 26J + 27J	0.66	0.9	0.26 (to 26J)	0.82 (to 26J)	0.26 (to 27J)	0.6 (to 27J)	35	30
22I + 1/2 (28J) + 1/2 (29J)	0.24	0.77	0.5 (to 28J)	0.6 (to 28J)	0.5 (to 29J)	0.6 (to 29J)	50	20
23I + 1/2 (30J) + 1/2 (31J)	0.15	0.67	0.5 (to 30J)	0.6 (to 30J)	0.5 (to 31J)	0.55 (to 31J)	78	40
4th Generation
32K + 1/2 (34L) + 1/2 (35L)	0.3	0.82	0.5 (to 34L)	0.59 (to 34L)	0.5 (to 35L)	0.64 (to 35L)	75	12
33K + 1/2 (36L) + 1/2 (37L)	0.84	0.6	0.5 (to 36L)	0.52 (to 36L)	0.5 (to 37L)	0.49 (to 37L)	92	60

Aerosol Generation and Experimental Set-Up

Nine different sizes of polystyrene latex fluorescent particles in the size range of 0.93–30 μ m were used in this study (0.93, 1.79, and 2.79 μ m from Polysciences, Warrington, PA, USA; 4.0 μ m from Interfacial Dynamics, Portland, OR, USA; and 6.07, 9.80, 16.0, 23.8, and 30 μ m from Duke Scientific, Palo Alto, CA, USA). Particle sizes were determined using an optical or electron microscope and image analyzer. Particles > 5 μ m were generated as a dry powder from a small-scale powder disperser (Model 3433, TSI Inc.) (Chen et al. 1995), and particles < 5 μ m were generated from a Respirgard II® nebulizer (Marquest Medical Products Inc., Englewood, CO, USA). The aerosols passed through a Kr-85 tube to bring the particle charge to Boltzmann's equilibrium, and then entered the TB cast through the oral cavity. Each terminal tube of the cast was connected to a filter (Versapor® 3000, Gelman Sciences, Bedford, CT, USA) and rotameter. The flow rate through each branch was determined prior to the particle deposition study with a velocity transducer (Model 8170, TSI Inc.) at a total flow rate of 15, 30, and 60 l min^{− 1}. The cast was cut into segments, as mentioned previously, after the deposition experiment. Fluorescent material in the particles that deposited in the cast and in the filter was extracted using ethyl acetate. The resultant solution was then filtered using a nylon membrane (0.2 μ m, Dow Corning, Midland, MI, USA) and the fluorescent content of the filtered solution was measured using a fluorescence spectrometer (Hitachi, Danbury, CT, USA). The deposition fraction in each airway segment was calculated from this measurement.

Theoretical Models

Three theoretical models were used to compare our experimental data in this study. These deposition models focused on inertial deposition, which should be the dominant deposition mechanism for the particle sizes used in this study. They were also used in lung deposition models to estimate regional deposition and dose for inhaled particles. Simple bend models have been used to estimate deposition in bifurcation of the TB region as well as in the oral cavity (Cheng and Wang 1975; Yeh et al. 1976; Cheng et al. 1999). A bifurcation can also be considered combining two bends together. Based on a rotational flow profile, the following equation that predicts the particle deposition efficiency (η) of a bend can be used to estimate deposition in an airway bifurcation:

where the Stokes number, Stk, can be defined as d _a ² U/36μ R ₀, d _a, the particle aerodynamic diameter; U is mean velocity through the parent tube; and μ is air viscosity.

A method was developed by Cai and Yu (1988) to predict the particle deposition in an idealized, symmetrical airway bifurcation. This method only considered the impaction and interception mechanisms based on the concept of the stop and interception distances of a particle in the cross section of the daughter tube. For uniform flow, the deposition efficiency can be obtained as follows:

where F is the function of bifurcation angle (α) and the ratio of radius for daughter (R) and parent (R ₀) tubes, given by:

The last theoretical model used in this study was developed by Balásházy et al. (1990). They presented the simultaneous action of inertial impaction and gravitational forces on a particle moving in three-dimensional circular bends. The particle deposition efficiency can be obtained with the following expressions:

where

h is the radius of curvature, and r ₀ is the distance between critical trajectory at the bend inlet and center of the curvature that can be calculated with Equation (3) in Balásházy et al. (1990).

RESULTS

Deposition in the Tracheal Region

Particle deposition in the trachea depends on the flow in this region, which has been shown to be turbulent because of laryngeal jet. Our experimental data from the tracheal region were obtained in a realistic physical model containing the oral cavity and larynx. Figure 2 shows the deposition efficiency in the trachea for the different flow rates as a function of Stokes number. Our data were compared with results obtained using realistic airway casts with a mechanical larynx (Chan and Lippmann 1980) and without a larynx (Schlesinger et al. 1977). Good agreement was evident for the two experimental data sets using a realistic cast with a larynx. The data from Schlesinger et al. showed lower deposition efficiency than that shown in the current study and the study by Chan and Lippmann (1980).

Figure 2 Comparison of tracheal deposition in the replica with reported lung cast deposition data. The fitted curve was based on current data and the data of Chan and Lippmann (1980) and Schlesinger et al. (1977).

Deposition in the Upper Bronchial Region

Figure 3 shows the comparison of our deposition efficiency in the first generation with the data of Chan and Lippmann (1980) and several theoretical models (Balásházy et al. 1990; Cai and Yu 1988; Cheng et al. 1999). Chan and Lippmann's results basically showed agreement with our results. Since this region of our lung cast is an uneven bifurcation that only has one daughter tube (13 F; Figure 1), the comparison with the theoretical model, which normally considered an even bifurcation, is not appropriate. However, because the particles mostly deposit in the carina of a bifurcation, one daughter tube could only slightly affect the deposition efficiency. The particle deposition efficiency of theoretical models from Cai and Yu (1988) and Balásházy et al. (1990) are lower than our experimental data in the first generation. The deposition model, based on a bend, developed by Cheng et al. (1999) has better agreement with our results in this region. Furthermore, the slopes of all three models were basically the same and were smaller than the experimental data.

Figure 3 Comparison of the deposition efficiency in the first generation of the replica with reported lung cast deposition data and theoretical models.

There are two bifurcations in the second generation. The dimensions of these two bifurcations are different, as shown in Table 1. Figure 4 gives the particle deposition efficiency in the second generation of the lung cast. Because there is more than one bifurcation after the first generation, and each bifurcation has its own dimension, the multiple lines may apply for the models of Cai and Yu (1988) and Balásházy et al. (1990). It also shows the experimental data from Chan and Lippmann (1980) and the theoretical predictions in this generation for the comparison. The deposition efficiency of Chan and Lippmann's model in this region was in good agreement with our data. Cai and Yu's model (1988) predicted very well the particle deposition efficiency in the Stokes number range of 0.005–0.3. However, it predicted high deposition for the Stokes number below 0.01. The model of Balásházy et al. (1990) predicted lower deposition efficiency than our experimental data, whereas the model of Cheng et al. (1999) gave a slightly higher prediction. The slopes of these three numerical models varied with the slope of the experimental data in the Stokes number below 0.01.

Figure 4 Comparison of the deposition efficiency in the second generation of the replica with reported lung cast deposition data and theoretical models.

Kim and colleagues also did some experimental studies for the particle deposition in the idealized bifurcations (Kim and Iglesias 1989; Kim and Fisher 1999). Their studies were based on asymmetrical glass bifurcations with the dimensions approximating the third- to fifth-generation human bronchial airways of Weibel's (1963) model. Our experimental results in the third and fourth generation were also compared with the data from Kim and Fisher (1999) and Kim and Iglesias (1989). The lung replica used in this study is a four-generation lung cast, while the fourth generation is incomplete. Although there were only two bifurcations in the fourth generation, the particle deposition data in these two bifurcations was assumed to represent each bifurcation in this generation. Figures 5 and 6 show the particle deposition results of our study in the third and fourth generations, respectively, compared with other experimental data and numerical models. Our data showed very good agreement with the results of Chan and Lippmann (1980) in both the third and fourth generations. However, both the third and fourth generations' data from Kim and Fisher (1999) and Kim and Iglesias (1989) were lower than the experimental data obtained by Chan and Lippmann (1980) and this study.

Figure 5 Comparison of the deposition efficiency in the third generation of the replica with reported lung cast experimental data, bifurcation deposition data, and theoretical models.

Figure 6 Comparison of the deposition efficiency in the fourth generation of the replica with reported lung cast experimental data, bifurcation deposition data, and theoretical models.

NEW EMPIRICAL MODEL

Tracheal Region

Because there is no theoretical model to predict the particle deposition in the tracheal region, the following equation can be used to fit our experimental data and the data obtained by Chan and Lippmann (1980):

This model assumed a well-mixed flow profile caused by the turbulence (Cheng et al. 1999). Two constant parameters were obtained by nonlinear regression software (SigmaPlot, SPSS, Chicago, IL, USA), a = 6.40 ± 1.69 and b = 1.19 ± 0.11. The fitted curve is shown in Figure 2.

Bronchial Airways

Particle deposition in each generation (excluding trachea) of the lung cast showed good agreement with literature values, especially the results of Chan and Lippmann (1980), in which a realistic lung cast was used. However, the comparison with three deposition models was less satisfactory. Cai and Yu's model (1988) was close to our data but still could not predict the deposition efficiency with the Stokes number below 0.005. Another disadvantage of their model is that the deposition efficiency could be over 100% for a large Stokes number. Thus, Equation (6) was also considered as the basic expression to predict the particle deposition efficiency in each bifurcation of the cast.

The experimental data for each bifurcation was regressed with Equation (6), and the result for the constant values a and b is listed in Table 2. Since the value b was relatively constant between 1.2 and 1.42 for every bifurcation of the cast, we considered b as a constant value, which is not changed with the dimension of the bifurcation. The average b value, 1.34 ± 0.08, can be used in Equation (6). The value a, however, was changed with the bifurcation size from 2.7 to 11.6. It is very difficult to find the relationship of value a with the cast size. The only relationship we obtained is the F value from of Cai and Yu's model (1988), which is the function of the bifurcation angle and diameter of the parent and daughter tubes. Table 2 also lists the F value for each bifurcation, and Figure 7 shows value a as a function of value F. All data were related with a linear curve except two data points: the first generation, and bifurcation 14G of the second generation. A linear equation of a = 5.39F can be obtained if those two points were ignored. Thus, Equation (6) can be simply expressed:

Figure 7 The constant value a in Equation (6) as a function of F value obtained in Equation (3). The solid circles were not regressed.

Table 2 Constant values obtained by data regression from Equation (6) for each bifurcation of the lung cast

	Location	F(α, R/R0)*	a	b
First bifurcation	11E + 13F	0.750	11.600	1.342
Second bifurcation	14G + 16H + 17H	1.326	4.765	1.411
	15G + 18H + 19H	0.695	3.924	1.427
Third bifurcation	20I + 1/2 (24J) + 1/2 (25J)	0.973	5.254	1.358
	21I + 26J + 27J	0.485	2.793	1.395
	22I + 1/2 (28J) + 1/2 (29J)	0.691	5.490	1.222
	23I + 1/2 (30J) + 1/2 (31J)	0.926	4.568	1.294
Fourth bifurcation	32K + 1/2 (34L) + 1/2 (35L)	1.025	4.764	1.393
	33K + 1/2 (36L) + 1/2 (37L)	1.078	5.546	1.214

To check the validity of the empirical model listed in Equation (7), the model was compared with all experimental data for the deposition efficiency in each bifurcation. Figure 8 shows all four generations but only one bifurcation for each generation. Since the empirical model is based on the dimensions of a bifurcation, the bifurcations in the same generation could have different expressions. The lung cast used in this study has a total nine bifurcations within four generations. Thus, nine expressions were obtained in this study. The current model was also applied to the construction of the lung cast used by Chan and Lippmann (1980). Figure 9 compares all lung cast data, including Chan and Lippmann's data, with the empirical model developed in this study. All expression lines obtained by generations of our and Chan and Lippmann's lung cast were between the solid lines in Figure 9 and have good agreement with the experimental data.

Figure 8 Comparison of experimental data with developed empirical model in four generations. Only one bifurcation is shown for generations two to four.

Figure 9 Comparison of all deposition data from the current study and the data from Chan and Lippmann (1980) with the developed empirical model.

DISCUSSION

Our results show similar deposition efficiency to the reported data in the experimental studies. Those studies were based on the idealized bifurcation models or lung cast models. Our results showed good agreement with the data reported by Chan and Lippmann (1980), who also used a lung cast in their study (Figures 2, 3, 4, 5 and 6). In the tracheal region, the deposition efficiency with the larynx effect is generally larger than without it. This indicates that the larynx affects the flow pattern of the tracheal region, causing more particles to be deposited here. Because the cast used by Chan and Lippmann (1980) has a different configuration compared to the cast we used, there is still a slight difference for the particle deposition in the third generation. However, in the other generations very good agreement was obtained when comparing our data with theirs. In addition to comparing our lung cast data with that of Chan and Lippmann, we also compared our results with the data reported by Kim and Fisher's (1999) idealized glass bifurcation models. Because the glass bifurcations only represented the third to fifth generation of Weibel's (1963) lung model, comparison was made only to the third and fourth generations (Figures 5 and 6). Results showed that Kim and Fisher's data were slightly lower than the deposition data obtained in this study. This may be due to several reasons, including the fact that the glass models were symmetric and had smooth surfaces, which means they were likely to have lower deposition than the realistic airway replicas with asymmetrical bifurcation and rough surfaces. Also, the idealized glass models do not include a larynx. We already showed that inclusion of the larynx is important in enhancing deposition in the trachea by simulating the turbulent flow conditions. It is likely that the turbulence induced by the laryngeal jet could persist in the first few generations of the tracheobronchial airways, resulting in higher deposition efficiencies. As shown in Figures 3, 4, 5 and 6, we also compared our results to several theoretical deposition models based on the bend model or idealized bifurcation models. Comparing our data with that of the theoretical models indicated that our data were in general agreement with the experimental data, especially that reported by Cai and Yu (1988). This comparison indicated that these deposition equations for inertial mechanism were reasonable for the deposition calculation.

However, the agreement was not consistent over the entire range of the Stokes number. This was because the relationship between the deposition efficiency in the airways and the Stokes number for the experimental data and theoretical models was different. In all three theoretical models the deposition efficiency is approximately linearly related to the Stokes number (η ≅ Stk). In experimental measurements obtained in idealized models, as well as in realistic airway replicas, the deposition efficiency is related to the Stokes number as η ≅ Stk^a. The value of “a” ranged from 1.2 to 1.4 for this study and data reported by Chan and Lippmann (1980). For the idealized glass bifurcation model the value of “a” was reported as 1.5 (Kim and Fisher 1999). This was to be expected because the theoretical model was based on idealized bend or bifurcation models. Also, the flow profiles used in the theoretical model were either uniform flow or fully developed flow. The secondary flow, which was evident in some studies (Schroter and Sudow 1969), was not considered when developing these idealized models.

The empirical model that we developed based on the experimental data would probably improve the deposition calculation in the lung dosimetric models. The developed particle deposition model of the TB region can be combined with the oral cast model developed by Cheng et al. (1999) as a whole airway model and applied to the different areas. The pharmaceutical application is a good example. Many medical inhalers are designed to use the oral inhalation mode to deliver drugs to the TB and/or lower region to treat some respiratory diseases. The present study will be a good model for evaluating the drug delivery efficiency of medical inhalers. The current model can also be used to investigate particle inhalation dosimetry and deposition patterns of air pollutants and occupational hazards.

Acknowledgments

The authors are grateful to G. A. Feather and B. Chen for technical assistance, and V. Fisher and B. Cleveland for reviewing this manuscript. This research was supported by the U.S. National Institute of Occupational Safety and Health, Grant R01 OH03900.

Notes

*Calculated from Equation (16) of Cai and Yu (1988).