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Prediction of particle deposition in the human lung using realistic models of lung ventilation
Aerosol Science 37 (2006) 1209 – 1221 www.elsevier.com/locate/jaerosci
Prediction of particle deposition in the human lung using realistic models of lung ventilation B. Asghariana,∗ , O.T. Pricea , W. Hofmannb a CIIT Centers for Health Research, Durham, NC 27709, USA b Department of Physics and Biophysics, University of Salzburg, Austria
Received 9 September 2005; received in revised form 4 January 2006; accepted 16 January 2006
Abstract Realistic predictions of inhaled particle deposition in various locations of the human lung depend mainly on accurate descriptions of the lung geometry and ventilation. Models of airflow distribution in the human lung by uniform and nonuniform lung expansions were used to calculate particle deposition in various lobes and regions of stochastically generated human lungs. To study the influence of lung geometry, 30 asymmetric stochastic lungs were generated and used in the calculations. Lobar airflow in each lung varied in accordance with lobar properties. The calculated airflow distributions indicated that the airflow rate entering each lobe of a given lung was similar for uniform and nonuniform lung expansions. Particle deposition was also found to be similar for uniform and nonuniform lung expansion models at rest breathing. The predicted deposition was in agreement with experimental measurements of regional and total depositions when considering lung size variation in a population. The coupled lung ventilation and deposition models can aid in detailed predictions of inhaled particle deposition in the human lungs. 䉷 2006 Elsevier Ltd. All rights reserved. Keywords: Particle deposition; Lung ventilation; Airway expansion; Regional deposition; Site-specific deposition; Microdosimetry
1. Introduction Inhaled airborne particles are distributed among lung airways in accordance with airflow ventilation. Traveling particles may deposit preferentially in lung airways as a result of external forces exerted on them (Brain & Valberg, 1979; Hatch & Gross, 1964; Lippmann & Altshuler, 1976; Medinsky, Asgharian, & Schlosser, 1997). Particle deposition in the lung may be undesirable for particles originating in the environment that can cause injury or deleterious effects if not removed effectively by lung clearance mechanisms (Bates, 1992; Dockery & Pope, 1994; Lipfert, 1994; Ostro, 1993; Pope, Bates, & Raizenne, 1995a; Pope, Dockery, & Schwartz, 1995b). Targeting particles to deposit in a specific site within the respiratory tract may be desirable for pharmaceutical aerosols whereby effective treatment is only possible if therapeutic aerosols can reach the desired site (Niven, 1995; Smith & Bernstein, 1996). Thus, determining the fate of inhaled particles in the lung is important in human health assessment.
∗ Corresponding author. Tel.: +1 919 558 1342; fax: +1 919 558 1300.
E-mail address: [email protected] (B. Asgharian). 0021-8502/$ - see front matter 䉷 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jaerosci.2006.01.002
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There are various experimental investigations on particle deposition in human lungs (ICRP, 1994). In addition to measurements, there are various mathematical models to determine the fate of inhaled particles in the lung. These models supplement measurements to describe underlying physical mechanisms and thus aid in optimal design of inhalation studies. Deposition modeling is particularly useful when experiments are not feasible. Mathematical models predict regional deposition fraction of inhaled particles during a breathing cycle from which tissue dosimetry can be assessed and linked to biological outcome to establish exposure–dose-response relationships. Various types of mathematical models of particle deposition exist. In the most basic form, models can be semi-empirical and based on deposition measurements (Rudolf, Gebhart, Heyder, Schiller, & Stahlhofen, 1986; Rudolf, Kobrich, & Stahlofen, 1990). These models are generally useful in the range of measurements used to construct the model. Mechanistic models which may be deterministic or stochastic describe physical processes that affect particles while traveling in lung airways. Lung geometry, breathing parameters, particle characteristics, and breathing scenarios can be submitted as model parameters for deposition calculations (Anjilvel & Asgharian, 1995; Broday & Georgopoulos, 2001; Koblinger & Hofmann, 1990; Mitsakou, Helmis, & Housiadas, 2005). A number of mechanistic models exist to predict particle deposition in the lungs of humans. The predicted deposition in the tracheobronchial (TB) and alveolar regions of the lung by these models compares favorably with available deposition measurements (Asgharian, Hofmann, & Bergmann, 2001; Koblinger & Hofmann, 1990; Subramaniam, Asgharian, Freijer, Miller, & Anjilvel, 2003;Yeh & Schum, 1980;Yu, 1978). Application of these models to realistically predict deposition at the airway level (site-specific or microdosimetry) must be validated because the models are either typical-path with a symmetrical lung geometry (Broday & Georgopoulos, 2001; Martonen & Schroeter, 2003a, 2003b; Martonen, Schroeter, Hwang, Fleming, & Conway, 2000; Mitsakou et al., 2005; Sarangapani & Wexler, 2000; Subramaniam et al., 2003) or multiple-path but with a limited account of lung ventilation (Asgharian et al., 2001; Koblinger & Hofmann, 1990). Lung ventilation is a major determinant in particle deposition calculations (Asgharian, Ménache, & Miller, 2004)—a priori for any realistic site-specific calculations. Whether single- or multiple-path, the flow field in these models is often assumed to be fully developed laminar (parabolic) flow and particle deposition is calculated based on a particle mass balance in each region of the lung. Typical-path models have been shown to accurately predict regional deposition in the lung because the lung geometry is made up of airways of average size in each generation (Asgharian et al., 2001). Validation of multiple-path models is not straightforward because site-specific measurements are difficult to obtain. Recent efforts to relate biological response to local and site-specific deposition in place of averaged regional deposition emphasizes the need for a morphometrically based, asymmetric lung geometry in the deposition model to allow the calculation of lobar and local deposition of particles. More realistic geometries such as one proposed by Koblinger and Hofmann (1990) are instrumental to calculating site-specific deposition. Accurate models for airflow partitioning among lung airways are needed in particle deposition calculations as particle deposition at a site in the lung has been shown to be related to the volume of inhaled air passing through that location (Asgharian et al., 2004). Thus, a realistic lung ventilation model must be used in particle deposition modeling for accurate site-specific predictions of particles. In this article, we examine two models of lung ventilation (Chang & Yu, 1999; Yu, 1978). These models are used in a multiple-path deposition model to compute regional and lobar deposition of particles in the lung. The predicted results of particle deposition are compared to highlight the impact of airflow on particle deposition. Using the most suitable lung ventilation model, the deposition model is validated by comparing the regional and total deposition predictions with available experimental data.
2. Particle deposition modeling Development of a mathematical model to describe deposition of particles in the respiratory tract involves three components. The first component is a geometrical model of the lung including all relevant airway dimensions from the trachea down to alveolar sacs. Next, airflow profile and lung ventilation in all airways of the lung must be specified. Finally, a mathematical model of particle transport in the lung must be developed that accounts for the particle mass balance (amount entering, exiting, depositing, or remaining suspended) in the lung during breathing. Deposition calculations are performed during a breathing cycle that includes inhalation, pause, and exhalation. Most often, similar breathing scenarios are assumed to exist among all breaths. Thus, deposition calculations for one breath are multiplied by exposure duration to find total deposition in the lung. Multiple breaths have to be considered when, due to particle
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dispersion, a fraction of particles remain in the lung at the end of exhalation. For the sake of completeness, each component of deposition modeling is briefly described below for the model used in this study. 3. Lung geometry The lung geometry is represented by an asymmetric tree structure for the TB region and a symmetric seven-generation alveolar region attached to each terminal bronchiole. The TB geometry was developed based on the analyses of Koblinger and Hofmann (1990) who constructed a TB tree with asymmetric airway branching system. First, based on available morphometric measurements (Raabe, Yeh, Schum, & Phalen, 1976), distribution functions for length, diameter, branching angle, cross-sectional area of the daughter tubes, gravity angle and correlations between these parameters were obtained as a function of airway generation (Koblinger & Hofmann, 1985). Second, the number of pathways (or terminal bronchioles) was selected. Finally, starting from the trachea and traveling down each pathway systematically, both daughter airway dimensions were selected at each bifurcation from the distribution functions for airway parameters and the TB tree was completed. Creation of multiple lung geometries is possible by this approach (Asgharian et al., 2001; Hofmann, Asgharian, & Winkler-Heil, 2002). We generated 30 asymmetric bronchial trees in this study to evaluate air transport and particle deposition in the lungs of human adults. The number of the bronchial trees was large enough to reflect variation among the population, and thus to some extent account for intersubject variability. The terminal airways of the human bronchial tree provided the root tree for each alveolar acinus. Each bronchial tree in the current model was supplemented by attaching identical acinar regions of Yeh, Schum, and Duggan (1979) to the end of each terminal bronchiole. The structure of the acinar region for each lung was similar to the last seven generations of the typical-path model of Yeh et al. (1979) for humans. However, since the number of terminal bronchioles differed among the bronchial trees, the acinar airway dimensions and alveolar volumes attached to each alveolar duct and sac were uniformly rescaled in each lung to ensure identical pulmonary volumes among all lung geometries. Hence, this study investigates air transport and particle deposition in lungs with similar lung volumes but different bronchial structures. 4. Models of lung ventilation Apportioning of inhaled air among various lobes and airways of the lung directly impacts distribution and deposition of airborne particles. The distribution of air in lung airways is found by the governing equations of airflow transport. Various models of flow distribution exist that vary in their degree of complexity. Examples of lung ventilation models are empirical models that are based on measurements in replica casts of airway bifurcations and thus are geometry independent and models that assume lung airways to be rigid and flow splitting to be proportional to daughter airway dimensions (Kitaoka & Suki, 1997). These models are physiologically unrealistic and unsuitable for implementation in lung deposition models. Airflow into the lung is the result of difference in pressure between extrathoracic airways and pleural cavity. At the end of expiration, pressure is atmospheric throughout lung airways and there is no movement of air. Simultaneous action of diaphragm contraction and rib cage expansion creates a decrease in the pleural pressure, negative alveolar pressure, and flow of air into the lung. During the inhalation, the pressure in the lung drops to a minimum value at the time point when flow acceleration ceases and then rises back to zero by the end of inhalation. Exhalation is the reverse although the pattern of breathing may vary. The pressure difference that causes the flow of air into and out of the lung has several components (Otis, McKerrow, Barylett, Mead, & McIllroy, 1956): P = KE + P + PC + Pt + Pi ,
(1)
where the first term on the right-hand side of Eq. (1) denotes the change of kinetic energy in the air as convective flow diminishes in distal airways. Subsequent terms in the equation denote pressure drops due to viscous effects, lung compliance, tissue resistance, and flow irreversibility which is caused by repeated acceleration and deceleration of inhaled air. At normal breathing tissue resistance and flow irreversibility are small and can be neglected. Therefore, the pressure drop that causes air movement in the lung is primarily due to lung elastic (recoil) properties and viscous
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effects. In addition, pressure variation in the pleural cavity will lead to the nonlinearity of lung expansion as the pressure at the apex of the lung is more negative than that at the base and consequently, the airways in the upper lobes are more expanded at rest and remain less distensible during breathing (Bryan et al., 1966; Michels & West, 1978). Pedley, Sudlow, and Milic-Emili (1972) proposed a 2-lobe model of lung ventilation that was modified by Bake, Wood, Murphy, Macklem, and Milic-Emili (1974) for higher breathing flow rates. Following the steps proposed by Chang and Yu (1999) to extend the 2-lobe model to the entire lung airway branching system, the following equation is obtained for the flow rate through daughter branches of an airway bifurcation: ⎧ K (1 − v )TLC (DV − v TLC ) d(DV ) 3/2 ⎫2/3 d2 0 d2 d1 0 d1 d2 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ K (1 − v )TLC (DV − v TLC ) dt d 0 d d 0 d ⎪ ⎪ 1 1 2 2 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ DVd1 − v0 TLCd1 ⎪ ⎪ ⎪ ⎪ + ⎨ ⎬ d(DVd1 ) kK d1 (1 − v0 TLCd1 ) Qd1 = = , (2a) ⎪ ⎪ ⎡ ⎤ dt ⎪ ⎪ DVd1 ⎪ ⎪ ⎪ ⎪ ln 1 − ⎪ ⎪ ⎪ ⎪ mTLCd1 ⎢ ⎥ ⎪ ⎪ ⎪ ⎪ ⎢ ⎥ ⎪ ⎪ × ⎪ ⎪ ⎪ ⎪ ⎣ ⎦ ⎪ ⎪ DVd2 1 − bZ d2 ⎩ ⎭ − ln 1 − + ln mTLCd2 1 − bZ d1 d(DVd2 ) d(DVP ) d(DVd1 ) (2b) = − = Qp − Qd1 , dt dt dt where DVdi and Qdi are the distal volume of and the flow rate through daughter branch i, m = 1.04 is an empirical constant, v0 = 0.05 is the fractional regional lung volume constant, TLCi is the lung capacity distal to airway i, Ki is the resistive pressure constant in airway i, k is the elastic constant, b is the rate of change of the regional fractional lung volume with distance from trachea, and Zi is the vertical distance from the center of volume of airway i, 3/2 ⎧ FRC TLC ⎪ ⎪ Ki = 1000R , ⎪ ⎪ TLC 1000TLCi ⎪ ⎪ ⎪ ⎪ ⎪ 0.101 ⎪ 2 ⎪ ⎪ ⎨ k = g (cm s /gm), (3) g ⎪ ⎪ ⎪ b = 0.017 + 0.006 (1/cm), ⎪ ⎪ 981 ⎪ ⎪ ⎪ ⎪ ⎪ 1 ⎪ ⎪Z = V z , ⎩ TLC =1 Qd2 =
in which g(gm/cm s2 ) is the gravitational constant, R = 0.295 (gm/cm4 s) is the overall resistance of the lung at total lung capacity (TLC), FRC is the lung functional capacity, V is the volume of airway , and is the total number of airways of the lung. The initial condition for Eqs. (2) is found by substituting for Qd1 = 0 in Eqs. (2) and solving for initial volume DVd1 1 − bZ d2 − 1 + DVp mTLCd2 1 − bZ d1 DVd1 = . (4) TLCd2 (1 − bZ d2 ) 1+ TLCd1 (1 − bZ d1 ) Eqs. (2)–(4) are solved per airway bifurcation to find distal volume and airflow rate in each daughter branch. In practice, the flow rate in only the first few generations are needed to be calculated from Eqs. (2) to (4) since the Reynolds number sharply drops to below one after a few generations and the airflow becomes quasi-steady. The flow rate in the airways under quasi-steady conditions may be found by differentiating Eq. (4) to find: Qd1 =
Qp . TLCd2 (1 − bZ d2 ) 1+ TLCd1 (1 − bZ d1 )
(5)
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In this study, Eqs. (2)–(4) are used to find airflow rates in central airways of the lung, and Eqs. (5) and (2) to find the flow rates for airways in the five lobes of the human lung. Lung expansion is nonlinear (nonuniform) as evident from the functional form of Eq. (2). However, models of lung ventilation for use in deposition calculations, often assume linear (uniform) expansion and contraction of airways (e.g., Koblinger & Hofmann, 1990; Yu, 1978) which implies identical elastic properties among various regions of the lung regardless of the distention state of the region. Consequently, all five lobes of the lung expand and contract at the same rate that is equal to that for the entire lung. Yu (1978) showed that for a uniformly expanding and contracting lung, the flow rate, Q, through an airway is related to time change of the cross-sectional area, A, by jQ jA =− , jx jt
(6)
where t is the elapsed time and x is lung depth from the apex of the trachea. The solution to Eq. (6) at time t, typically the time at the midpoint between the lung at rest (t = 0) and the end of inhalation, is given by (Yu, 1978) V (x) DV(x) = Q0 , (7) Q(x) = Q0 1 − TLV TLV where Q0 is the inhalation airflow rate at the proximal end of the trachea, V (x) is the lung volume at a depth x, DV(x) is the volume distal to the given airway at depth x, and TLV is the total lung volume (FRC + VT /2, in which FRC is the functional residual capacity or lung volume at rest and VT is the tidal volume or the volume of inhaled air). Thus, during uniform expansion and contraction, airflow rate at any location in an airway is proportional to the lung volume distal to that airway (Anjilvel& Asgharian, 1995; Koblinger & Hofmann, 1990). Invoking Eq. (7) for each airway bifurcation, airflow rates at the distal and proximal ends of the parent and daughter airways are found to be (Anjilvel & Asgharian, 1995) Qd1 =
DVd1 Qp , DVp − Vp
(8a)
Qd2 =
DVd2 Qp , DVp − Vp
(8b)
where Vp is the volume of the parent airway. For the case of a symmetric tree structure (typical- or single-path as found in the lobar regions of the 5-lobe symmetric geometry), DVd = (DVp − Vp )/2 and, thus Eq. (8) simplifies to Qd1 = Qd2 = 21 Qp ,
(9)
which is the same as that for symmetric, rigid airways. Starting from the trachea and traversing down the lung tree branching structure, the set of Eqs. (8) can be solved to find airflow distribution in subsequent lung airways for uniform expansion and contraction of the lung.
5. Mathematical model for particle deposition calculations The multiple-path deposition model used to calculate particle losses in the lung is described by Anjilvel and Asgharian (1995) and Asgharian et al. (2001). Briefly, deposition of uncharged particles in the airways occurs by the three primary mechanisms of impaction, sedimentation, and diffusion (Cai &Yu, 1988; Ingham, 1975; Pich, 1972). Each loss mechanism within an airway is represented by a deposition efficiency that is defined as the fraction of entering particles that deposited in the airway. Different deposition efficiencies are assumed linearly independent and simply added to obtain the combined deposition efficiency. Particles are assumed to be monodisperse and uniformly distributed in the tidal air. Axial diffusion and convective mixing (dispersion) of particles are neglected. The multiple-path deposition model calculates deposition fractions of particles at various locations in an asymmetric lung structure during a single breathing cycle in several steps. First, the airflow rates and velocities in all airways of the lung are calculated. Second, the aerosol transport and distribution in the tidal air across lung airways are found. The combined deposition efficiency of particles in each airway by various loss mechanisms is used to calculate aerosol concentrations at the proximal and
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distal ends of each airway. Finally, a mass balance on the traveling particles in each airway is performed, and deposition fraction per airway, generation, region, and lobe of the lung is calculated.
6. Results and discussions The flow distribution models based on uniform and nonuniform lung expansion rates were studied in relation to their impact on particle deposition in the lung. The lung geometry and lung ventilation models were used by the deposition model to calculate deposition fractions for particles in the size range of 0.01 to 10 m in various lobes and regions of the lung and in the entire lung. The results are described below. 6.1. Lobar flow rate The airflow rates delivered to each lobe of the asymmetric human lung were calculated for the two flow models given by Eqs. (2), (5), and (8). A tracheal inhalation flow rate of Q0 = 250 ml/s which corresponded to a breathing tidal volume of 625 ml at 2.5 s inhalation time and a TLC value of near 5300 ml was used in the calculations. The fraction of tracheal flow rate delivered to each lobe of the human lung is given in Fig. 1. While the corresponding left and right lobes receive similar airflows, the largest portion flows into the basal lobes because these lobes are larger than the others and are more compliant. The right middle lobe receives the least flow due to its small volume. Predicted flow fractions going to different lobes are similar for uniform and nonuniform lung expansion models indicating that lung expansion can be assumed to be nearly uniform at normal breathing conditions. Fractional lobar capacities at different volumes of inhaled air for uniform and nonuniform lung expansion rates are shown in Fig. 2. For simplicity, the 5-lobe symmetric but structurally different model of Yeh and Schum (1980) was used to compute lobar flow rates. Fractional lobar capacity, defined as the ratio of lobar volume (DVi ) to lobar capacity (TLCi ) for lobe i, was plotted against fractional lung capacity, which is defined the same way (TLV/TLC). The line of identity representing the same lobar and lung capacity is also shown in Fig. 2. When air flows into the lung, fractional lung capacity is expected to increase from 0.4 to 1 at maximum lung capacity. For the uniform expansion model, the fraction of lobar capacity, which is also an indication of lobar state of distension, is the same for each lobe and equal
Fig. 1. Fraction of tracheal flow rate going to each lobe of the lung predicted by uniform and nonuniform lung ventilation models.
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Fig. 2. Lobar capacity as a function of lung capacity for distensible airway models of uniform and nonuniform expansion in a 5-lobe symmetric lung geometry.
to the overall lung expansion for any inhaled volume of air (FRC/TLC)i = FRC/TLC. The line overlaps with the line of identity. The predicted lines of fractional lobar capacity for nonuniform airway expansion by compliance and resistance are different for each lobe. At rest, upper lobes are more expanded than the lower lobes due to the gravity induced pressure gradient in the pleural region. Thus, the upper lobes will be less compliant than the lower lobe during subsequent breathing as the slope of the lines representing fractional lobar capacity will be smaller for the upper lobes than the lower lobes. The lines will merge when the lung is inflated to its total capacity. Overall, all lines have similar values, particularly as the volume of inhaled air is increased. Nonuniformity is small and decreases with increasing lung volume. Thus, the uniform lung expansion model appears to be adequate for most scenarios to describe airflow transport in the lung. 6.2. Regional deposition The airflow distribution models were used in the multiple-path deposition model to calculate deposition fractions of particles in the TB, alveolar, and lobar regions of 30 human lung geometries. A lung volume (FRC) of 3300 ml and a minute ventilation of 7.5 lpm were used in the computations. Fig. 3 shows the deposition results in the TB and alveolar region by endotracheal breathing (i.e., bypassing extrathoracic region). The shaded areas represent the range of deposition predictions for 30 lung geometries obtained by the method of Koblinger and Hofmann (1990). Deposition results based on uniform and nonuniform lung expansions are practically identical and indistinguishable. In addition, particle deposition appears to be weakly dependent on airway arrangement in the TB region for particles between 0.05 to 1 m, and alveolar region for particles between 0.2 to 4 m because of narrow distribution of particle deposition. The greatest influence of TB airway structure on particle deposition is observed for coarse particles in the TB region and ultrafine particles in the alveolar region most likely due to geometry-dependence of impaction losses in the TB region and TB filtering effects carried into the alveolar region, respectively. Lung depositions (sum of deposition in TB and alveolar regions in Fig. 3) using either lung ventilation model are presented in Fig. 4. For 30 stochastically generated asymmetric lung geometries, predictions are generally less dependent on the structural variation of TB airways. Since deposition prediction of the uniform expansion model is nearly identical to that of the nonuniform expansion model and is computationally less intensive, it is recommended for deposition predictions. The results of Figs. 3 and 4 give practical guidelines in the design of inhalation studies.
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Fig. 3. Predicted regional deposition fraction by uniform and nonuniform expansions for a lung FRC = 3300 ml and minute ventilation of 7.5 lpm via endotracheal breathing.
Fig. 4. Total lung deposition in the lung for a lung FRC = 3300 ml and minute ventilation of 7.5 lpm via endotracheal breathing.
For the region of interest (i.e., TB, PUL, and the entire lung), particle sizes should be selected for exposure studies that yield smallest variation in deposition due to intersubject variation. However, since deposition for these particle sizes are generally small, a higher exposure concentration or longer exposure duration are required to allow detectable measurements.
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Fig. 5. Regional deposition fraction of particles in the left lower lobe of the lung based on uniform and nonuniform lung expansion a lung FRC=3300 ml and minute ventilation of 7.5 lpm via endotracheal breathing.
6.3. Lobar deposition Lung regional deposition fractions by uniform and nonuniform expansions of the lung are practically the same and indistinguishable (Figs. 3 and 4). This is because uniform expansion represents the average expansion (and thus average volume) of all lobes (Fig. 5) and regional particle deposition has been shown to be directly related to the volume of inspired air in that region of the lung (Asgharian et al., 2004). The agreement can be extended to lobar deposition results for the same reason. Fig. 5 compares deposition fractions in the TB and alveolar regions of the left lower lobe in a typical stochastically generated asymmetric lung geometry. Lobar deposition was calculated as the sum of particle deposition fractions in all airways within the lobe. It excluded deposition in central airways since these airways were common to all lobes. The two flow models give almost identical predictions except for coarse particles in the TB region and ultrafine particles in the alveolar region where slight differences are observed. Similar observation is made for other lobes. Thus, at normal breathing conditions, lung expansion is nearly uniform. To examine lobar differences, lobar deposition fraction in the same asymmetric lung geometry is shown in Fig. 6. Deposition in the TB region (Fig. 6A) is largest in the lower lobes followed by deposition in the upper lobes. The smallest deposition occurs in the right middle lobe. The trend of TB deposition among the various lobes is in proportion to lobar volume. Lower lobes with the largest volume have largest particle deposition, and the right middle lobe, with the smallest lobar volume, has lowest deposition predictions. There is also a significant deposition of coarse particles in the central (common) airways of the lung. Consequently, a reduction of TB deposition with increasing particle size is observed for coarse particles near 10 m. Fig. 6B is the lobar deposition fraction in the alveolar region. The pattern of deposition as a function of lobe for the alveolar region is the same as that in the TB region since lobar deposition is directly proportional to lobar volume. The deposition curve for all lobes shows two peaks for ultrafine and coarse particle size due to the TB filtering effects. 6.4. Comparison with experimental measurements Deposition predictions by the uniform airway expansion model were tested by comparing with existing measurements. Heyder, Gebhart, Rudolf, and Stahlhofen (1986) has compiled measurements of deposition fractions from earlier studies for particles ranging in size from ultrafine to coarse when inhaled under various breathing maneuvers. Our predictions gave very similar comparisons for all datasets in the study, but, in the interest of space, we only selected two sets
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Fig. 6. Regional deposition fraction of particles in five lobes of the lung for a uniform lung expansion, FRC = 3300 ml and minute ventilation of 7500 ml via endotracheal breathing. (A) TB region, (B) alveolar region.
Fig. 7. Comparison of predicted deposition fraction by uniform expansion of the lung with reported measurements of Heyder et al. (1986) shown by . The shaded area represents the variation in deposition predictions from 30 lung geometries. The predictions are for oral breathing with a tidal volume of 500 ml, breathing period of 4 s, and FRC = 3000 ml. (A) TB deposition, (B) alveolar deposition, (C) total deposition.
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Fig. 8. Comparison of predicted deposition fraction by uniform expansion of the lung with reported measurements of Heyder et al. (1986) shown by . The shaded area represents the variation in deposition predictions from 30 lung geometries. The predictions are for nasal breathing with a tidal volume of 500 ml, breathing period of 4 s, and FRC = 3000 ml. (A) TB deposition, (B) alveolar deposition, (C) total deposition.
of measurements for comparison. Measurements were conducted in subjects with a breathing tidal volume of 500 ml, breathing frequency of 15 bpm, and an FRC of 3000 ml. These values were averages for all subjects who participated in the study. The results are presented in Figs. 7 and 8 for oral and nasal breathing, respectively. Model predictions were carried out in 30 stochastic lung geometries. The range of predicted deposition fractions is indicated in each figure. Deposition predictions in the TB region for both oral and nasal breathing were higher than measurements (Figs. 7A and 8A) and subsequently the alveolar predictions were lower (Figs. 7B and 8B) due to the filtering effects of the central airways and the TB region of each lobe. One reason for the discrepancy could be the way regional depositions were calculated from retention measurements. Deposition in the TB and alveolar regions are distinguished by their clearance half times during post exposure time. Slow bronchial clearance (Scheuch, Kreyling, Haas, & Stahlhofen, 1993; Stahlhofen, 1989; Stahlhofen, Koebrich, Rudolf, & Scheuch, 1990; Stahlhofen, Scheuch, & Bailey, 1994) had not been yet discovered at the time of the study by Heyder et al. (1986). The authors assigned the slowly cleared bronchial deposition to the alveolar region, thereby reducing the bronchial deposition and increasing alveolar deposition. Overall, predictions of total deposition fractions (Figs. 7C and 8C) were in good agreement with reported measurements. Measurements fell within the range of predicted deposition for the fine and coarse particles and were slightly lower than that for ultrafine particles. 6.5. Concluding remarks Various models of lung ventilation have been used by investigators to study airflow and particle deposition in the lung. Models assuming a flow of air through rigid airways of the lung are physiologically unrealistic and produce
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unrealistic velocity values as airflow in the most distal airways of the lung (alveolar sacs) does not diminish. Thus, prediction of particle deposition by this type of airflow in the lung cannot be reliable. In this study, the lung ventilation model based on uniform expansion and contraction of lung airways was shown to be most practical for computational analysis as airflow and particle deposition predictions were similar to that of a more detailed model considering lung compliance and airway resistance (nonuniform airway expansion). Use of this model is recommended for regional and site-specific predictions due to its simplicity, ease of implementation, and fast computation time at normal breathing conditions. Scenarios exist when uniform expansion and contraction may not be representative of lung physiologic behavior. For example, lung ventilation may be altered under hypergravity or high breathing rates. In addition, typical deposition predictions are made at the sitting upright position while this orientation is changed during sleep or physical activities. In addition, many lung diseases are known to modify airway geometry that will directly affect lobar airflow and subsequent particle deposition. Under these circumstances, more detailed models that account for airway resistance and tissue compliance will likely be required to compute particle deposition in the lung. Acknowledgments This research was supported in part by member companies of the American Chemistry Council through its LongRange Research Initiative, and NIH Grant number 1 RO1 HL073598-01A1. References Anjilvel, S., & Asgharian, B. (1995). A multiple-path model of particle deposition in the rat lung. Fundamental and Applied Toxicology, 28, 41. Asgharian, B., Hofmann, W., & Bergmann, R. (2001). Particle deposition in a multiple-path model of the human lung. Aerosol Science and Technology, 34, 332. Asgharian, B., Ménache, M. G., & Miller, F. J. (2004). Modeling age-related particle deposition in humans. Journal of Aerosol Medicine, 17, 213. Bake, B., Wood, L., Murphy, B., Macklem, P. T., & Milic-Emili, J. (1974). Effect of inspiratory flow rate on regional distribution of inspired gas. Journal of Applied Physiology, 37, 8. Bates, D. V. (1992). Health indices of adverse effects of air pollution: The question of coherence. Environmental Research, 59, 336. Brain, J. D., & Valberg, P. A. (1979). Deposition of aerosol in the respiratory tract. American Review of Respiratory Disease, 120, 1325. Broday, D. M., & Georgopoulos, P. G. (2001). Growth and deposition of hygroscopic particulate matter in the human lung. Aerosol Science and Technology, 34, 144. Bryan, A. C., Milic-Emili, J., & Pengelly, D. (1966). Effect of gravity on the distribution of pulmonary ventilation. Journal of Applied Physiology, 21, 778. Cai, F. S., & Yu, C. P. (1988). Inertial and interceptional deposition of spherical particles and fibers in a bifurcating airway. Journal of Aerosol Science, 19, 679. Chang, Y. H., & Yu, C. P. (1999). A model of ventilation distribution in the human lung. Aerosol Science and Technology, 30, 309. Dockery, D. W., & Pope, C. A., III. (1994). Acute effects of particulate air pollution. Annual Review of Public Health, 15, 107. Hatch, T. F., & Gross, P. (1964). Pulmonary deposition and retention of inhaled aerosols. New York: Academic Press. Heyder, J., Gebhart, G., Rudolf, C. F., & Stahlhofen, W. (1986). Deposition of particles in the human respiratory tract in the size range 0.005–15m. Journal of Aerosol Science, 17, 811. Hofmann, W., Asgharian, B., & Winkler-Heil, R. (2002). Modeling intersubject variability of particle deposition in human lungs. Journal of Aerosol Science, 33, 219. Ingham, D. B. (1975). Diffusion of aerosols from a stream flowing through a cylindrical tube. Journal of Aerosol Science, 6, 125. International Commission on Radiological Protection (ICRP). (1994). Human respiratory tract model for radiological protection, Publication 66. Oxford, UK: Pergamon Press; Annals of ICRP, 24, 272. Kitaoka, H., & Suki, B. (1997). Branching design of the bronchial tree based on a diameter-flow relationship. Journal of Applied Physiology, 82, 968. Koblinger, L., & Hofmann, W. (1985). Analysis of human lung morphometric data for stochastic aerosol deposition calculations. Physics in Medicine and Biology, 30, 541. Koblinger, L., & Hofmann, W. (1990). Monte Carlo modeling of aerosol deposition in human lungs. Part I: Simulation of particle transport in a stochastic lung structure. Journal of Aerosol Science, 21, 661. Lipfert, F. W. (1994). Air pollution and community health: A critical review and data sourcebook. New York, NY: Van Nostrand Reinhold. Lippmann, M., & Altshuler, B. (1976). In: A. Ben-David, & M.A. Klingberg (Eds.), Air pollution and the lung, Aharaonson (pp. 25–48). Wiley, New York: Halstead Press. Martonen, T. B., & Schroeter, J. D. (2003a). Risk assessment dosimetry model for inhaled particulate matter: I. Human subjects. Toxicology Letters, 138, 119. Martonen, T. B., & Schroeter, J. D. (2003b). Risk assessment dosimetry model for inhaled particulate matter: II. Laboratory surrogates (rat). Toxicology Letters, 138, 133.
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Martonen, T. B., Schroeter, J. D., Hwang, D., Fleming, J. S., & Conway, J. H. (2000). Human lung morphology models for particle deposition studies. Inhalation Toxicology, 4, 109. Medinsky, M. A., Asgharian, B., & Schlosser, P. M. (1997). Toxicokinetics: Inhalation exposure and absorbtion of toxicants. In I. G. Snipes, C. A. McQueen, & A. J. Gandolfi (Eds.), Comprehensive toxicology (Vol. 1, pp. 63–97). New York, NY: Elsevier Sciences Ltd. Michels, D. B., & West, J. B. (1978). Distribution of pulmonary ventilation and perfusion during short periods of weightlessness. Journal of Applied Physiology, 45, 987. Mitsakou, C., Helmis, C., & Housiadas, C. (2005). Eulerian modeling of lung deposition with sectional representation of aerosol dynamics. Journal of Aerosol Science, 36, 75. Niven, R. W. (1995). Delivery of biotherapeutics by inhalation aerosol. Critical Reviews in Therapeutic Drug Carrier Systems, 12, 151. Ostro, B. (1993). The association of air pollution and mortality: Examining the case for inference. Achieves of Environmental Health, 48, 336. Otis, A. B., McKerrow, C. B., Barylett, R. A., Mead, J., & McIllroy, M. B. (1956). Mechanical factors in distribution of pulmonary ventilation. Journal of Applied Physiology, 8, 427. Pedley, T. J., Sudlow, M. F., & Milic-Emili, J. (1972). A non-linear theory of the distribution of pulmonary ventilation. Respiratory Physiology, 15, 1. Pich, J. (1972). Theory of gravitational deposition of particles from laminar flows in channels. Journal of Aerosol Science, 3, 351. Pope, C. A., III., Bates, D. V., & Raizenne, M. E. (1995a). Health effects of particulate air pollution: Time for reassessment. Environmental Health Perspectives, 103, 472. Pope, C. A., Dockery, D. W., & Schwartz, J. (1995b). Review of epidemiological evidence of health effects of particulate air pollution. Inhalation Toxicology, 7, 1. Raabe, O. G., Yeh, H.-C., Schum, G. M., & Phalen, R. F. (1976). Tracheobronchial geometry: Human, dog, rat, hamster. LF-53. Albuquerque, New Mexico: Lovelace Foundation. Rudolf, G., Gebhart, J., Heyder, J., Schiller, Ch. F., & Stahlhofen, W. (1986). An empirical formula describing aerosol deposition in man for any particle size. Journal of Aerosol Science, 17, 350. Rudolf, G., Kobrich, R., & Stahlofen, W. (1990). Modeling and algebraic formulation of regional aerosol deposition in man. Journal of Aerosol Science, 21(Suppl. 1), S403. Sarangapani, R., & Wexler, A. S. (2000). The role of dispersion in particle deposition in human airways. Toxicological Sciences, 54, 229. Scheuch, G., Kreyling, W., Haas, F., & Stahlhofen, W. (1993). The clearance of polystyrene particles from human intrathoracic airways. Journal of Aerosol Medicine, 6(Suppl.), 47. Smith, S. J., & Bernstein, J. A. (1996). Therapeutic uses of lung aerosols. Lung Biology and Health Disease, 94, 233. Stahlhofen, W. (1989). Human lung clearance following bolus inhalation of radioaerosols. Extrapolation of dosimetric relationships for inhaled particles and gases (pp. 153–166). Washington, DC: Academic Press. Stahlhofen, W., Koebrich, R., Rudolf, G., & Scheuch, G. (1990). Short-term and long-term clearance of particles from the upper human respiratory tract as function of particle size. Journal of Aerosol Science, 21(Suppl. 1), S407. Stahlhofen, W., Scheuch, G., & Bailey, M. R. (1994). Measurement of the tracheobronchial clearance of particles after aerosol bolus inhalation. In J. Dodgson, & R. I. McCallum (Eds.), Inhaled particles VII, Proceedings of an international symposium on inhaled particles organized by the British Occupational Hygiene Society (pp. 16–22). Annals of Occupational Hygiene, 189. Subramaniam, R. P., Asgharian, B., Freijer, J. I., Miller, F. J., & Anjilvel, S. (2003). Analysis of lobar differences in particle deposition in the human lung. Inhalation Toxicology, 15, 1. Yeh, H. C., & Schum, G. T. M. (1980). Models of human lung airways and their application to inhaled particle deposition. Bulletin of Math Biology, 42, 461. Yeh, H. C., Schum, GT. M., & Duggan, M. T. (1979). Anatomical models of the tracheobronchial and pulmonary regions of the rat. Anatomical Record, 195, 483. Yu, C. P. (1978). Exact analysis of aerosol deposition during steady state breathing. Powder Technology, 21, 55.
Prediction of particle deposition in the human lung using realistic models of lung ventilation B. Asghariana,∗ , O.T. Pricea , W. Hofmannb a CIIT Centers for Health Research, Durham, NC 27709, USA b Department of Physics and Biophysics, University of Salzburg, Austria
Received 9 September 2005; received in revised form 4 January 2006; accepted 16 January 2006
Abstract Realistic predictions of inhaled particle deposition in various locations of the human lung depend mainly on accurate descriptions of the lung geometry and ventilation. Models of airflow distribution in the human lung by uniform and nonuniform lung expansions were used to calculate particle deposition in various lobes and regions of stochastically generated human lungs. To study the influence of lung geometry, 30 asymmetric stochastic lungs were generated and used in the calculations. Lobar airflow in each lung varied in accordance with lobar properties. The calculated airflow distributions indicated that the airflow rate entering each lobe of a given lung was similar for uniform and nonuniform lung expansions. Particle deposition was also found to be similar for uniform and nonuniform lung expansion models at rest breathing. The predicted deposition was in agreement with experimental measurements of regional and total depositions when considering lung size variation in a population. The coupled lung ventilation and deposition models can aid in detailed predictions of inhaled particle deposition in the human lungs. 䉷 2006 Elsevier Ltd. All rights reserved. Keywords: Particle deposition; Lung ventilation; Airway expansion; Regional deposition; Site-specific deposition; Microdosimetry
1. Introduction Inhaled airborne particles are distributed among lung airways in accordance with airflow ventilation. Traveling particles may deposit preferentially in lung airways as a result of external forces exerted on them (Brain & Valberg, 1979; Hatch & Gross, 1964; Lippmann & Altshuler, 1976; Medinsky, Asgharian, & Schlosser, 1997). Particle deposition in the lung may be undesirable for particles originating in the environment that can cause injury or deleterious effects if not removed effectively by lung clearance mechanisms (Bates, 1992; Dockery & Pope, 1994; Lipfert, 1994; Ostro, 1993; Pope, Bates, & Raizenne, 1995a; Pope, Dockery, & Schwartz, 1995b). Targeting particles to deposit in a specific site within the respiratory tract may be desirable for pharmaceutical aerosols whereby effective treatment is only possible if therapeutic aerosols can reach the desired site (Niven, 1995; Smith & Bernstein, 1996). Thus, determining the fate of inhaled particles in the lung is important in human health assessment.
∗ Corresponding author. Tel.: +1 919 558 1342; fax: +1 919 558 1300.
E-mail address: [email protected] (B. Asgharian). 0021-8502/$ - see front matter 䉷 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jaerosci.2006.01.002
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There are various experimental investigations on particle deposition in human lungs (ICRP, 1994). In addition to measurements, there are various mathematical models to determine the fate of inhaled particles in the lung. These models supplement measurements to describe underlying physical mechanisms and thus aid in optimal design of inhalation studies. Deposition modeling is particularly useful when experiments are not feasible. Mathematical models predict regional deposition fraction of inhaled particles during a breathing cycle from which tissue dosimetry can be assessed and linked to biological outcome to establish exposure–dose-response relationships. Various types of mathematical models of particle deposition exist. In the most basic form, models can be semi-empirical and based on deposition measurements (Rudolf, Gebhart, Heyder, Schiller, & Stahlhofen, 1986; Rudolf, Kobrich, & Stahlofen, 1990). These models are generally useful in the range of measurements used to construct the model. Mechanistic models which may be deterministic or stochastic describe physical processes that affect particles while traveling in lung airways. Lung geometry, breathing parameters, particle characteristics, and breathing scenarios can be submitted as model parameters for deposition calculations (Anjilvel & Asgharian, 1995; Broday & Georgopoulos, 2001; Koblinger & Hofmann, 1990; Mitsakou, Helmis, & Housiadas, 2005). A number of mechanistic models exist to predict particle deposition in the lungs of humans. The predicted deposition in the tracheobronchial (TB) and alveolar regions of the lung by these models compares favorably with available deposition measurements (Asgharian, Hofmann, & Bergmann, 2001; Koblinger & Hofmann, 1990; Subramaniam, Asgharian, Freijer, Miller, & Anjilvel, 2003;Yeh & Schum, 1980;Yu, 1978). Application of these models to realistically predict deposition at the airway level (site-specific or microdosimetry) must be validated because the models are either typical-path with a symmetrical lung geometry (Broday & Georgopoulos, 2001; Martonen & Schroeter, 2003a, 2003b; Martonen, Schroeter, Hwang, Fleming, & Conway, 2000; Mitsakou et al., 2005; Sarangapani & Wexler, 2000; Subramaniam et al., 2003) or multiple-path but with a limited account of lung ventilation (Asgharian et al., 2001; Koblinger & Hofmann, 1990). Lung ventilation is a major determinant in particle deposition calculations (Asgharian, Ménache, & Miller, 2004)—a priori for any realistic site-specific calculations. Whether single- or multiple-path, the flow field in these models is often assumed to be fully developed laminar (parabolic) flow and particle deposition is calculated based on a particle mass balance in each region of the lung. Typical-path models have been shown to accurately predict regional deposition in the lung because the lung geometry is made up of airways of average size in each generation (Asgharian et al., 2001). Validation of multiple-path models is not straightforward because site-specific measurements are difficult to obtain. Recent efforts to relate biological response to local and site-specific deposition in place of averaged regional deposition emphasizes the need for a morphometrically based, asymmetric lung geometry in the deposition model to allow the calculation of lobar and local deposition of particles. More realistic geometries such as one proposed by Koblinger and Hofmann (1990) are instrumental to calculating site-specific deposition. Accurate models for airflow partitioning among lung airways are needed in particle deposition calculations as particle deposition at a site in the lung has been shown to be related to the volume of inhaled air passing through that location (Asgharian et al., 2004). Thus, a realistic lung ventilation model must be used in particle deposition modeling for accurate site-specific predictions of particles. In this article, we examine two models of lung ventilation (Chang & Yu, 1999; Yu, 1978). These models are used in a multiple-path deposition model to compute regional and lobar deposition of particles in the lung. The predicted results of particle deposition are compared to highlight the impact of airflow on particle deposition. Using the most suitable lung ventilation model, the deposition model is validated by comparing the regional and total deposition predictions with available experimental data.
2. Particle deposition modeling Development of a mathematical model to describe deposition of particles in the respiratory tract involves three components. The first component is a geometrical model of the lung including all relevant airway dimensions from the trachea down to alveolar sacs. Next, airflow profile and lung ventilation in all airways of the lung must be specified. Finally, a mathematical model of particle transport in the lung must be developed that accounts for the particle mass balance (amount entering, exiting, depositing, or remaining suspended) in the lung during breathing. Deposition calculations are performed during a breathing cycle that includes inhalation, pause, and exhalation. Most often, similar breathing scenarios are assumed to exist among all breaths. Thus, deposition calculations for one breath are multiplied by exposure duration to find total deposition in the lung. Multiple breaths have to be considered when, due to particle
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dispersion, a fraction of particles remain in the lung at the end of exhalation. For the sake of completeness, each component of deposition modeling is briefly described below for the model used in this study. 3. Lung geometry The lung geometry is represented by an asymmetric tree structure for the TB region and a symmetric seven-generation alveolar region attached to each terminal bronchiole. The TB geometry was developed based on the analyses of Koblinger and Hofmann (1990) who constructed a TB tree with asymmetric airway branching system. First, based on available morphometric measurements (Raabe, Yeh, Schum, & Phalen, 1976), distribution functions for length, diameter, branching angle, cross-sectional area of the daughter tubes, gravity angle and correlations between these parameters were obtained as a function of airway generation (Koblinger & Hofmann, 1985). Second, the number of pathways (or terminal bronchioles) was selected. Finally, starting from the trachea and traveling down each pathway systematically, both daughter airway dimensions were selected at each bifurcation from the distribution functions for airway parameters and the TB tree was completed. Creation of multiple lung geometries is possible by this approach (Asgharian et al., 2001; Hofmann, Asgharian, & Winkler-Heil, 2002). We generated 30 asymmetric bronchial trees in this study to evaluate air transport and particle deposition in the lungs of human adults. The number of the bronchial trees was large enough to reflect variation among the population, and thus to some extent account for intersubject variability. The terminal airways of the human bronchial tree provided the root tree for each alveolar acinus. Each bronchial tree in the current model was supplemented by attaching identical acinar regions of Yeh, Schum, and Duggan (1979) to the end of each terminal bronchiole. The structure of the acinar region for each lung was similar to the last seven generations of the typical-path model of Yeh et al. (1979) for humans. However, since the number of terminal bronchioles differed among the bronchial trees, the acinar airway dimensions and alveolar volumes attached to each alveolar duct and sac were uniformly rescaled in each lung to ensure identical pulmonary volumes among all lung geometries. Hence, this study investigates air transport and particle deposition in lungs with similar lung volumes but different bronchial structures. 4. Models of lung ventilation Apportioning of inhaled air among various lobes and airways of the lung directly impacts distribution and deposition of airborne particles. The distribution of air in lung airways is found by the governing equations of airflow transport. Various models of flow distribution exist that vary in their degree of complexity. Examples of lung ventilation models are empirical models that are based on measurements in replica casts of airway bifurcations and thus are geometry independent and models that assume lung airways to be rigid and flow splitting to be proportional to daughter airway dimensions (Kitaoka & Suki, 1997). These models are physiologically unrealistic and unsuitable for implementation in lung deposition models. Airflow into the lung is the result of difference in pressure between extrathoracic airways and pleural cavity. At the end of expiration, pressure is atmospheric throughout lung airways and there is no movement of air. Simultaneous action of diaphragm contraction and rib cage expansion creates a decrease in the pleural pressure, negative alveolar pressure, and flow of air into the lung. During the inhalation, the pressure in the lung drops to a minimum value at the time point when flow acceleration ceases and then rises back to zero by the end of inhalation. Exhalation is the reverse although the pattern of breathing may vary. The pressure difference that causes the flow of air into and out of the lung has several components (Otis, McKerrow, Barylett, Mead, & McIllroy, 1956): P = KE + P + PC + Pt + Pi ,
(1)
where the first term on the right-hand side of Eq. (1) denotes the change of kinetic energy in the air as convective flow diminishes in distal airways. Subsequent terms in the equation denote pressure drops due to viscous effects, lung compliance, tissue resistance, and flow irreversibility which is caused by repeated acceleration and deceleration of inhaled air. At normal breathing tissue resistance and flow irreversibility are small and can be neglected. Therefore, the pressure drop that causes air movement in the lung is primarily due to lung elastic (recoil) properties and viscous
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effects. In addition, pressure variation in the pleural cavity will lead to the nonlinearity of lung expansion as the pressure at the apex of the lung is more negative than that at the base and consequently, the airways in the upper lobes are more expanded at rest and remain less distensible during breathing (Bryan et al., 1966; Michels & West, 1978). Pedley, Sudlow, and Milic-Emili (1972) proposed a 2-lobe model of lung ventilation that was modified by Bake, Wood, Murphy, Macklem, and Milic-Emili (1974) for higher breathing flow rates. Following the steps proposed by Chang and Yu (1999) to extend the 2-lobe model to the entire lung airway branching system, the following equation is obtained for the flow rate through daughter branches of an airway bifurcation: ⎧ K (1 − v )TLC (DV − v TLC ) d(DV ) 3/2 ⎫2/3 d2 0 d2 d1 0 d1 d2 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ K (1 − v )TLC (DV − v TLC ) dt d 0 d d 0 d ⎪ ⎪ 1 1 2 2 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ DVd1 − v0 TLCd1 ⎪ ⎪ ⎪ ⎪ + ⎨ ⎬ d(DVd1 ) kK d1 (1 − v0 TLCd1 ) Qd1 = = , (2a) ⎪ ⎪ ⎡ ⎤ dt ⎪ ⎪ DVd1 ⎪ ⎪ ⎪ ⎪ ln 1 − ⎪ ⎪ ⎪ ⎪ mTLCd1 ⎢ ⎥ ⎪ ⎪ ⎪ ⎪ ⎢ ⎥ ⎪ ⎪ × ⎪ ⎪ ⎪ ⎪ ⎣ ⎦ ⎪ ⎪ DVd2 1 − bZ d2 ⎩ ⎭ − ln 1 − + ln mTLCd2 1 − bZ d1 d(DVd2 ) d(DVP ) d(DVd1 ) (2b) = − = Qp − Qd1 , dt dt dt where DVdi and Qdi are the distal volume of and the flow rate through daughter branch i, m = 1.04 is an empirical constant, v0 = 0.05 is the fractional regional lung volume constant, TLCi is the lung capacity distal to airway i, Ki is the resistive pressure constant in airway i, k is the elastic constant, b is the rate of change of the regional fractional lung volume with distance from trachea, and Zi is the vertical distance from the center of volume of airway i, 3/2 ⎧ FRC TLC ⎪ ⎪ Ki = 1000R , ⎪ ⎪ TLC 1000TLCi ⎪ ⎪ ⎪ ⎪ ⎪ 0.101 ⎪ 2 ⎪ ⎪ ⎨ k = g (cm s /gm), (3) g ⎪ ⎪ ⎪ b = 0.017 + 0.006 (1/cm), ⎪ ⎪ 981 ⎪ ⎪ ⎪ ⎪ ⎪ 1 ⎪ ⎪Z = V z , ⎩ TLC =1 Qd2 =
in which g(gm/cm s2 ) is the gravitational constant, R = 0.295 (gm/cm4 s) is the overall resistance of the lung at total lung capacity (TLC), FRC is the lung functional capacity, V is the volume of airway , and is the total number of airways of the lung. The initial condition for Eqs. (2) is found by substituting for Qd1 = 0 in Eqs. (2) and solving for initial volume DVd1 1 − bZ d2 − 1 + DVp mTLCd2 1 − bZ d1 DVd1 = . (4) TLCd2 (1 − bZ d2 ) 1+ TLCd1 (1 − bZ d1 ) Eqs. (2)–(4) are solved per airway bifurcation to find distal volume and airflow rate in each daughter branch. In practice, the flow rate in only the first few generations are needed to be calculated from Eqs. (2) to (4) since the Reynolds number sharply drops to below one after a few generations and the airflow becomes quasi-steady. The flow rate in the airways under quasi-steady conditions may be found by differentiating Eq. (4) to find: Qd1 =
Qp . TLCd2 (1 − bZ d2 ) 1+ TLCd1 (1 − bZ d1 )
(5)
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In this study, Eqs. (2)–(4) are used to find airflow rates in central airways of the lung, and Eqs. (5) and (2) to find the flow rates for airways in the five lobes of the human lung. Lung expansion is nonlinear (nonuniform) as evident from the functional form of Eq. (2). However, models of lung ventilation for use in deposition calculations, often assume linear (uniform) expansion and contraction of airways (e.g., Koblinger & Hofmann, 1990; Yu, 1978) which implies identical elastic properties among various regions of the lung regardless of the distention state of the region. Consequently, all five lobes of the lung expand and contract at the same rate that is equal to that for the entire lung. Yu (1978) showed that for a uniformly expanding and contracting lung, the flow rate, Q, through an airway is related to time change of the cross-sectional area, A, by jQ jA =− , jx jt
(6)
where t is the elapsed time and x is lung depth from the apex of the trachea. The solution to Eq. (6) at time t, typically the time at the midpoint between the lung at rest (t = 0) and the end of inhalation, is given by (Yu, 1978) V (x) DV(x) = Q0 , (7) Q(x) = Q0 1 − TLV TLV where Q0 is the inhalation airflow rate at the proximal end of the trachea, V (x) is the lung volume at a depth x, DV(x) is the volume distal to the given airway at depth x, and TLV is the total lung volume (FRC + VT /2, in which FRC is the functional residual capacity or lung volume at rest and VT is the tidal volume or the volume of inhaled air). Thus, during uniform expansion and contraction, airflow rate at any location in an airway is proportional to the lung volume distal to that airway (Anjilvel& Asgharian, 1995; Koblinger & Hofmann, 1990). Invoking Eq. (7) for each airway bifurcation, airflow rates at the distal and proximal ends of the parent and daughter airways are found to be (Anjilvel & Asgharian, 1995) Qd1 =
DVd1 Qp , DVp − Vp
(8a)
Qd2 =
DVd2 Qp , DVp − Vp
(8b)
where Vp is the volume of the parent airway. For the case of a symmetric tree structure (typical- or single-path as found in the lobar regions of the 5-lobe symmetric geometry), DVd = (DVp − Vp )/2 and, thus Eq. (8) simplifies to Qd1 = Qd2 = 21 Qp ,
(9)
which is the same as that for symmetric, rigid airways. Starting from the trachea and traversing down the lung tree branching structure, the set of Eqs. (8) can be solved to find airflow distribution in subsequent lung airways for uniform expansion and contraction of the lung.
5. Mathematical model for particle deposition calculations The multiple-path deposition model used to calculate particle losses in the lung is described by Anjilvel and Asgharian (1995) and Asgharian et al. (2001). Briefly, deposition of uncharged particles in the airways occurs by the three primary mechanisms of impaction, sedimentation, and diffusion (Cai &Yu, 1988; Ingham, 1975; Pich, 1972). Each loss mechanism within an airway is represented by a deposition efficiency that is defined as the fraction of entering particles that deposited in the airway. Different deposition efficiencies are assumed linearly independent and simply added to obtain the combined deposition efficiency. Particles are assumed to be monodisperse and uniformly distributed in the tidal air. Axial diffusion and convective mixing (dispersion) of particles are neglected. The multiple-path deposition model calculates deposition fractions of particles at various locations in an asymmetric lung structure during a single breathing cycle in several steps. First, the airflow rates and velocities in all airways of the lung are calculated. Second, the aerosol transport and distribution in the tidal air across lung airways are found. The combined deposition efficiency of particles in each airway by various loss mechanisms is used to calculate aerosol concentrations at the proximal and
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distal ends of each airway. Finally, a mass balance on the traveling particles in each airway is performed, and deposition fraction per airway, generation, region, and lobe of the lung is calculated.
6. Results and discussions The flow distribution models based on uniform and nonuniform lung expansion rates were studied in relation to their impact on particle deposition in the lung. The lung geometry and lung ventilation models were used by the deposition model to calculate deposition fractions for particles in the size range of 0.01 to 10 m in various lobes and regions of the lung and in the entire lung. The results are described below. 6.1. Lobar flow rate The airflow rates delivered to each lobe of the asymmetric human lung were calculated for the two flow models given by Eqs. (2), (5), and (8). A tracheal inhalation flow rate of Q0 = 250 ml/s which corresponded to a breathing tidal volume of 625 ml at 2.5 s inhalation time and a TLC value of near 5300 ml was used in the calculations. The fraction of tracheal flow rate delivered to each lobe of the human lung is given in Fig. 1. While the corresponding left and right lobes receive similar airflows, the largest portion flows into the basal lobes because these lobes are larger than the others and are more compliant. The right middle lobe receives the least flow due to its small volume. Predicted flow fractions going to different lobes are similar for uniform and nonuniform lung expansion models indicating that lung expansion can be assumed to be nearly uniform at normal breathing conditions. Fractional lobar capacities at different volumes of inhaled air for uniform and nonuniform lung expansion rates are shown in Fig. 2. For simplicity, the 5-lobe symmetric but structurally different model of Yeh and Schum (1980) was used to compute lobar flow rates. Fractional lobar capacity, defined as the ratio of lobar volume (DVi ) to lobar capacity (TLCi ) for lobe i, was plotted against fractional lung capacity, which is defined the same way (TLV/TLC). The line of identity representing the same lobar and lung capacity is also shown in Fig. 2. When air flows into the lung, fractional lung capacity is expected to increase from 0.4 to 1 at maximum lung capacity. For the uniform expansion model, the fraction of lobar capacity, which is also an indication of lobar state of distension, is the same for each lobe and equal
Fig. 1. Fraction of tracheal flow rate going to each lobe of the lung predicted by uniform and nonuniform lung ventilation models.
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Fig. 2. Lobar capacity as a function of lung capacity for distensible airway models of uniform and nonuniform expansion in a 5-lobe symmetric lung geometry.
to the overall lung expansion for any inhaled volume of air (FRC/TLC)i = FRC/TLC. The line overlaps with the line of identity. The predicted lines of fractional lobar capacity for nonuniform airway expansion by compliance and resistance are different for each lobe. At rest, upper lobes are more expanded than the lower lobes due to the gravity induced pressure gradient in the pleural region. Thus, the upper lobes will be less compliant than the lower lobe during subsequent breathing as the slope of the lines representing fractional lobar capacity will be smaller for the upper lobes than the lower lobes. The lines will merge when the lung is inflated to its total capacity. Overall, all lines have similar values, particularly as the volume of inhaled air is increased. Nonuniformity is small and decreases with increasing lung volume. Thus, the uniform lung expansion model appears to be adequate for most scenarios to describe airflow transport in the lung. 6.2. Regional deposition The airflow distribution models were used in the multiple-path deposition model to calculate deposition fractions of particles in the TB, alveolar, and lobar regions of 30 human lung geometries. A lung volume (FRC) of 3300 ml and a minute ventilation of 7.5 lpm were used in the computations. Fig. 3 shows the deposition results in the TB and alveolar region by endotracheal breathing (i.e., bypassing extrathoracic region). The shaded areas represent the range of deposition predictions for 30 lung geometries obtained by the method of Koblinger and Hofmann (1990). Deposition results based on uniform and nonuniform lung expansions are practically identical and indistinguishable. In addition, particle deposition appears to be weakly dependent on airway arrangement in the TB region for particles between 0.05 to 1 m, and alveolar region for particles between 0.2 to 4 m because of narrow distribution of particle deposition. The greatest influence of TB airway structure on particle deposition is observed for coarse particles in the TB region and ultrafine particles in the alveolar region most likely due to geometry-dependence of impaction losses in the TB region and TB filtering effects carried into the alveolar region, respectively. Lung depositions (sum of deposition in TB and alveolar regions in Fig. 3) using either lung ventilation model are presented in Fig. 4. For 30 stochastically generated asymmetric lung geometries, predictions are generally less dependent on the structural variation of TB airways. Since deposition prediction of the uniform expansion model is nearly identical to that of the nonuniform expansion model and is computationally less intensive, it is recommended for deposition predictions. The results of Figs. 3 and 4 give practical guidelines in the design of inhalation studies.
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Fig. 3. Predicted regional deposition fraction by uniform and nonuniform expansions for a lung FRC = 3300 ml and minute ventilation of 7.5 lpm via endotracheal breathing.
Fig. 4. Total lung deposition in the lung for a lung FRC = 3300 ml and minute ventilation of 7.5 lpm via endotracheal breathing.
For the region of interest (i.e., TB, PUL, and the entire lung), particle sizes should be selected for exposure studies that yield smallest variation in deposition due to intersubject variation. However, since deposition for these particle sizes are generally small, a higher exposure concentration or longer exposure duration are required to allow detectable measurements.
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Fig. 5. Regional deposition fraction of particles in the left lower lobe of the lung based on uniform and nonuniform lung expansion a lung FRC=3300 ml and minute ventilation of 7.5 lpm via endotracheal breathing.
6.3. Lobar deposition Lung regional deposition fractions by uniform and nonuniform expansions of the lung are practically the same and indistinguishable (Figs. 3 and 4). This is because uniform expansion represents the average expansion (and thus average volume) of all lobes (Fig. 5) and regional particle deposition has been shown to be directly related to the volume of inspired air in that region of the lung (Asgharian et al., 2004). The agreement can be extended to lobar deposition results for the same reason. Fig. 5 compares deposition fractions in the TB and alveolar regions of the left lower lobe in a typical stochastically generated asymmetric lung geometry. Lobar deposition was calculated as the sum of particle deposition fractions in all airways within the lobe. It excluded deposition in central airways since these airways were common to all lobes. The two flow models give almost identical predictions except for coarse particles in the TB region and ultrafine particles in the alveolar region where slight differences are observed. Similar observation is made for other lobes. Thus, at normal breathing conditions, lung expansion is nearly uniform. To examine lobar differences, lobar deposition fraction in the same asymmetric lung geometry is shown in Fig. 6. Deposition in the TB region (Fig. 6A) is largest in the lower lobes followed by deposition in the upper lobes. The smallest deposition occurs in the right middle lobe. The trend of TB deposition among the various lobes is in proportion to lobar volume. Lower lobes with the largest volume have largest particle deposition, and the right middle lobe, with the smallest lobar volume, has lowest deposition predictions. There is also a significant deposition of coarse particles in the central (common) airways of the lung. Consequently, a reduction of TB deposition with increasing particle size is observed for coarse particles near 10 m. Fig. 6B is the lobar deposition fraction in the alveolar region. The pattern of deposition as a function of lobe for the alveolar region is the same as that in the TB region since lobar deposition is directly proportional to lobar volume. The deposition curve for all lobes shows two peaks for ultrafine and coarse particle size due to the TB filtering effects. 6.4. Comparison with experimental measurements Deposition predictions by the uniform airway expansion model were tested by comparing with existing measurements. Heyder, Gebhart, Rudolf, and Stahlhofen (1986) has compiled measurements of deposition fractions from earlier studies for particles ranging in size from ultrafine to coarse when inhaled under various breathing maneuvers. Our predictions gave very similar comparisons for all datasets in the study, but, in the interest of space, we only selected two sets
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Fig. 6. Regional deposition fraction of particles in five lobes of the lung for a uniform lung expansion, FRC = 3300 ml and minute ventilation of 7500 ml via endotracheal breathing. (A) TB region, (B) alveolar region.
Fig. 7. Comparison of predicted deposition fraction by uniform expansion of the lung with reported measurements of Heyder et al. (1986) shown by . The shaded area represents the variation in deposition predictions from 30 lung geometries. The predictions are for oral breathing with a tidal volume of 500 ml, breathing period of 4 s, and FRC = 3000 ml. (A) TB deposition, (B) alveolar deposition, (C) total deposition.
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Fig. 8. Comparison of predicted deposition fraction by uniform expansion of the lung with reported measurements of Heyder et al. (1986) shown by . The shaded area represents the variation in deposition predictions from 30 lung geometries. The predictions are for nasal breathing with a tidal volume of 500 ml, breathing period of 4 s, and FRC = 3000 ml. (A) TB deposition, (B) alveolar deposition, (C) total deposition.
of measurements for comparison. Measurements were conducted in subjects with a breathing tidal volume of 500 ml, breathing frequency of 15 bpm, and an FRC of 3000 ml. These values were averages for all subjects who participated in the study. The results are presented in Figs. 7 and 8 for oral and nasal breathing, respectively. Model predictions were carried out in 30 stochastic lung geometries. The range of predicted deposition fractions is indicated in each figure. Deposition predictions in the TB region for both oral and nasal breathing were higher than measurements (Figs. 7A and 8A) and subsequently the alveolar predictions were lower (Figs. 7B and 8B) due to the filtering effects of the central airways and the TB region of each lobe. One reason for the discrepancy could be the way regional depositions were calculated from retention measurements. Deposition in the TB and alveolar regions are distinguished by their clearance half times during post exposure time. Slow bronchial clearance (Scheuch, Kreyling, Haas, & Stahlhofen, 1993; Stahlhofen, 1989; Stahlhofen, Koebrich, Rudolf, & Scheuch, 1990; Stahlhofen, Scheuch, & Bailey, 1994) had not been yet discovered at the time of the study by Heyder et al. (1986). The authors assigned the slowly cleared bronchial deposition to the alveolar region, thereby reducing the bronchial deposition and increasing alveolar deposition. Overall, predictions of total deposition fractions (Figs. 7C and 8C) were in good agreement with reported measurements. Measurements fell within the range of predicted deposition for the fine and coarse particles and were slightly lower than that for ultrafine particles. 6.5. Concluding remarks Various models of lung ventilation have been used by investigators to study airflow and particle deposition in the lung. Models assuming a flow of air through rigid airways of the lung are physiologically unrealistic and produce
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unrealistic velocity values as airflow in the most distal airways of the lung (alveolar sacs) does not diminish. Thus, prediction of particle deposition by this type of airflow in the lung cannot be reliable. In this study, the lung ventilation model based on uniform expansion and contraction of lung airways was shown to be most practical for computational analysis as airflow and particle deposition predictions were similar to that of a more detailed model considering lung compliance and airway resistance (nonuniform airway expansion). Use of this model is recommended for regional and site-specific predictions due to its simplicity, ease of implementation, and fast computation time at normal breathing conditions. Scenarios exist when uniform expansion and contraction may not be representative of lung physiologic behavior. For example, lung ventilation may be altered under hypergravity or high breathing rates. In addition, typical deposition predictions are made at the sitting upright position while this orientation is changed during sleep or physical activities. In addition, many lung diseases are known to modify airway geometry that will directly affect lobar airflow and subsequent particle deposition. Under these circumstances, more detailed models that account for airway resistance and tissue compliance will likely be required to compute particle deposition in the lung. Acknowledgments This research was supported in part by member companies of the American Chemistry Council through its LongRange Research Initiative, and NIH Grant number 1 RO1 HL073598-01A1. References Anjilvel, S., & Asgharian, B. (1995). A multiple-path model of particle deposition in the rat lung. Fundamental and Applied Toxicology, 28, 41. Asgharian, B., Hofmann, W., & Bergmann, R. (2001). Particle deposition in a multiple-path model of the human lung. Aerosol Science and Technology, 34, 332. 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