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Transport and Uptake of Inhaled Gases JAMES S. ULTMAN Pennsylvania State University Implications of Lung Anatomy / 324 Upper Airways / 325 Conducting Airways / 327 Respiratory Zone / 328 Nonuniformities in Ventilation and Perfusion / 329 Fundamentals of Mass Transport / 331 Thermodynamic Equilibria / 331 Diffusion and Reaction Rates / 332 Individual Mass Transfer Coefficients / 336 Overall Mass Transfer Coefficients / 337 Longitudinal Gas Transport / 340 Mathematical Models / 341 Compartment Models / 342 Distributed-Parameter Upper Air-way Models / 346 Distributed-Parameter Lower Airway Models / 349 Experiments / 352 In Vitro Methods / 352 In Vivo Animal Experiments / 354 In Vivo Human Subject Studies / 358 Summary / 361 Summary of Research Recommendations / 361 Air Pollution, the Automobile, and Public Health. (3 1988 by the Health Effects Institute. National Academy Press, Washington, D.C. 323

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324 Transport and Uptake of Inhaled Gases When a pollutant gas is breathed, its trans- port through the highly branched tracheo- bronchial tree results in a unique internal distribution of concentration and uptake rates. A major factor complicating the study of these processes is the fact that gases with different molecular properties can exhibit different internal dose distribu- tions. Highly water-soluble gases, such as sulfur dioxide (SO2), are essentially re- moved by the upper airways, the primary site of respiratory defense. A highly reac- tive gas of only moderate solubility, such as ozone (03), can reach the tracheobronchial tree, where it reacts with the protective mucous layer and eventually damages un- derlying tissue in the small bronchioles. A gas that has limited aqueous activity but is highly reactive with hemoglobin, such as carbon monoxide (CO), is able to penetrate further to the respiratory zone and diffuse to the pulmonary circulation in quantity. The guiding philosophy presented in this chapter is that direct measurements on hu- man volunteers can be minimized by using mathematical models to anticipate uptake rates and identify target tissues of poten- tially hazardous species. An ideal model enables one to calculate dose distribution from basic anatomic and physicochemical parameters and to estimate the effects of pathological airway derangements and changes in ventilatory demand. But in . . . . . - many situations it Is more practical to use models that simply extrapolate measure- ments from laboratory animals to humans. In either case, it is necessary to validate proposed models with experiments, and for that reason both theoretical and labora- tory methodologies are discussed in this paper. The role of physicochemical factors in the absorption of gas species from a flow- ing airstream is of central concern to chem- ical engineers who design industrial gas separation equipment. Many of the same concepts used to develop gas absorption or chromatographic separation processes can be applied with some modification to the lung. Two widely read sources on this subject are Bird et al. (1960), a fundamental treatise on fluid flow and diffusion phe- nomena, and Treybal (1980), a textbook that describes conventional design meth- ods. Complementing this engineering knowledge is a wealth of physiology liter- ature concerning the influence of lung anat- omy and mechanics on the distribution of foreign gases (for example, Engel and Paiva 1985~. In this chapter, we will integrate these separate fields as Hills (1974) has done for normal respiratory gases. Although the material here is intended to encompass all pollutant gases those already recognized as well as those still unrecognized an en- cyclopedic review has not been attempted. Rather, basic concepts and methods are stressed to provide a general overview, and concrete examples with respect to three species- S02, 03, and CO have been used to illustrate the spectrum of solubility and reactivity effects. This article begins with two sections devoted to issues at the heart of mathemat- ical model development: first, lung anat- omy and its influence on aerodynamics; and- second, fundamentals of diffusion and chemical reaction and their characterization in terms of mass transfer coefficients. The next two sections address the structure of alternative mathematical models and their validation by experimental measurements. O O ~ Implications of Lung Anatomy This section, in presenting an overview of lung anatomy and its influence on aerody- namics and hemodynamics, focuses on the human respiratory system. Although most of the concepts are also valid for animals (see Schlesinger, this volume), the numer- ical values used to illustrate specific ana- tomic and functional features are typical of normal adult humans. As a supplement to these data, table 1 has been included to indicate the difference in scale between the lungs of humans and animals. The pulmonary airways consist of three distinct functional units. The upper air- ways, extending from the nares and lips to the larynx, are the primary sites at which the temperature and humidity of inspired air are equilibrated to body conditions. The conducting airways, a branched-tube net

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James S. Ultman 325 Table 1. Comparisons Among Anatomical Measurements Related to Breathing in Humans and Laboratory Animals Anatomical Large Small Small MeasurementHumanDog Dog Monkey Rabbit Rat Mouse . . . Body weight (kg) 74 22.8 11.2 3.71 3.6 0.14 0.023 Total lung volume 4,341 1,501 736 184 79 6.3 0.74 (ml) Total alveolar surface 143 90 41 13 5.9 0.39 0.068 (m2) Total capillary surface 126 72 33 12 4.7 0.41 0.059 (m2) Total capillary volume 213 119 50 15 7.2 0.48 0.084 (ml) Mean air-blood barrier 2.22 1.42 1.64 1.52 1.51 1.42 1.25 thickness (,um) SOURCE: Adapted with permission from Gil (1982, tables 1 and 2). Copyright CRC Press, Boca Raton, Fla. work originating at the trachea and extend- ing to include terminal bronchioles, pro- vide an orderly yet compact expansion of flow cross-section. The respiratory zone, composed of all the alveolated airways and airspaces, is responsible for oxygenation of and carbon dioxide removal from the pul- monary capillaries. Taken together, the conducting airways and respiratory zone are referred to as the lower respiratory tract, and since they contain no gas ex- change surface, the upper and conducting airways combined are often called the ana- tomic dead space. The respiratory zone, with a volume of about 3 liters compared to the 160 ml of anatomic dead space, contains most of the functional residual gas volume, and yet the total path length of 6 mm along alveolated airways is only a fraction of the 40 cm between the nose and the terminal conduct- ing airways. In other words, the total cross-sectional area in the respiratory zone is much greater than in the dead space. However, this total is the sum of the cross- sections of a large number of small passages in which the axial diffusion distance is very short. Therefore, longitudinal mixing of fresh inspired air with residual gas is fa- vored in the respiratory zone, whereas bulk flow with little mixing of fresh and residual air occurs in the dead space (Go mez 1965~. The walls of the upper and conducting airways are composed of an inner mucosal layer, a submucosal layer, and an outer adventitia. The mucosal layer, sometimes called the mucous membrane, contains cil- iated epithelium and mucus-producing goblet cells, with additional mucus-pro- ducing glands located in the submucosal layer. In the lumen of these airways, cilia are surrounded by a low-viscosity pericil- iary fluid, above which high-viscosity mu- cus floats. The cilia beat in an organized unidirectional fashion, propelling this mu- cous blanket from the lower respiratory tract to the oropharynx with a daily clear- ance of about 100 ml. Blood is supplied to the lower respira- tory tract through the bronchial arteries, which arise from the aorta and deliver oxygen to conducting airways, and through the pulmonary circulation that perfuses the respiratory zone via the pul- monary artery. During rest, the bronchial circulation constitutes only 1 percent of the total 5 liter/min of systemic arterial blood flow, and it feeds sparsely distributed cap- illaries in the submucosal layer of bronchial tissue. In contrast, the entire output of the right heart enters the pulmonary circulation to supply the dense meshwork of capillaries in the walls of the alveoli. Upper Airways During quiet breathing, a typical tidal vol- ume is 500 ml at a frequency of 12 breaths/ min. corresponding to a minute volume of 6 liters/mint Under these conditions, air normally enters the nose and flows by way of the nasopharynx, pharynx, and larynx to

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326 the trachea. In the nose, the convoluted well-perfused surface of the nasal turbinates with its large specific surface area of 8 cm2/ml provides an efficient site for ab- sorption of soluble gases. Alternatively, air may follow a path from the mouth directly to the pharynx, thereby depriving the in- spirate of purification by the nose. Most individuals breathe exclusively through their nose when minute volume is below 34 liters, but during vigorous exercise when ventilatory demand is larger, 45 to 60 per- cent of respired air is inspired orally (Nii- nimaa et al. 1980, 1981~. The presence of a nasal obstruction or even a disease of the lower respiratory tract such as asthma can also exaggerate oral breathing, making the lung more likely to be exposed to pollutant gases. The geometry of upper airways is irreg- ular and variable, depending on the point of air access, on the breathing pattern, and on the state of mucous membrane engorge- ment by nasal blood flow. Perhaps this explains why no mathematical model of its anatomy has been established. Roughly speaking, upper airway volume is 50 ml, with a path length of 17 cm from lips to glottis and 22 cm from nares to glottis. As respired gas flows through the upper air- ways, it encounters a series of sudden con- tractions and expansions in cross-section leading to corresponding accelerations and decelerations in gas velocity (figure 1~. This is quite different from the steady flow of gases in straight tubes of constant cross- section. The nature of flow in a tube is character- ized by the Reynolds number (Re), the dimensionless ratio of inertial force to fric . . tlona resistance: Re = Vd/A u (1) where d is tube diameter, V is volumetric flow rate, A is cross-sectional area available for flow, and v is kinematic viscosity. In sufficiently long straight tubes, flow is fully developed and the Reynolds number uniquely determines whether the velocity field is laminar (Re ~ 2100), turbulent (Re > 4000), or in transition between these two regimes (4000 > Re > 2100~. In laminar flow, material moves along fixed axial 30t 254 cue O 20 LO In oh 15 o 10 5 _V Transport and Uptake of Inhaled Gases 12 11 10 Bronchial / x generations\ | - ~ ,6 x ~9t 1 ~i, V 5 10 15 20 25 30 35 40 45 DISTANCE FROM NASAL TIP (cm) to Figure 1. Cross-sectional area available for gas flow. Axial velocity (m/see for flow of 200 ml/see) during quiet respiration is also shown at selected "V" (velocity) points. (Adapted with permission from Swift and Proctor 1977, p. 68, by courtesy of Marcel Dekker, Inc.) streamlines so that radial transport can only occur by molecular diffusion. In turbulent flow, the mixing action of turbulent eddies facilitates radial transport of gas species to the tube wall, a favorable condition for gas absorption. Because of disturbances created by geo- metric irregularities, flow in the upper air- ways is never fully developed. For exam- ple, the inspired airstream that is propelled through the glottic constriction into the trachea forms a confined jet immediately downstream of the larynx. Large velocity gradients within the jet generate turbulent eddies at Reynolds numbers well below the fully developed transition value of 2100 (Simone and Ultman 1982), and these ed- dies can increase radial mixing as gas flows downstream, even during quiet inspiration. Also, the rapid deceleration of air passing from the ostium internum to the turbinated structures can induce turbulence in the nose (Swift and Proctor 1977~. In addition to the promotion of turbu- lence, three other phenomena unique to the upper airways may enhance gas absorption.

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James S. Ultman 327 First, fresh mucus swept into the tubinates from the paranasal sinuses supplements the capacity of the nasal passages for airborne pollutants. Second, the nasal mucosa and submucosa are well perfused with blood flowing countercurrent to the mucus flow, and this is a favorable configuration for gas absorption (Brain 1970~. Third, because increased blood flow can elicit an erectile response in surrounding tissue, vasodila- tion by cholinergic pollutants may increase gas absorption both by increasing capillary surface and by reducing the lateral diffusion distance in the nasal passages. Conducting Airways The conducting airways, also referred to as the tracheobronchial tree, are a series of more or less dichotomously branched tubes originating at the larynx and extending just proximal to the point where alveolated airways arise. Those branches containing cartilage are defined as bronchi and gener- ally occupy the first 10 or so generations. The more distal cartilage-free branches are defined as bronchioli. Although volume changes in the trachea and major bronchi are minimized by stiff cartilage rings em- bedded in the airway walls, the smaller bronchi and the bronchioli undergo isotropic volume changes in proportion to changes in lung volume (Hughes et al. 1972~. Raabe (1982) reviewed several numerical models of the tracheobronchial tree, which may be divided into two categories: the so-called symmetric models, in which a regular dichotomy of branching exists at every generation and all branches in a given generation have the same diameters and the same lengths, and the asymmetric models, which account for the unequal distribution of lung lobes three on the right and two on the left or for irregularities within the lobes themselves. Whereas a symmetric model is an idealization wherein the geom- etry of all transport paths from larynx to terminal bronchioles is identical, in the more realistic asymmetric model, airway diameters and lengths and even the number of branch divisions may differ along alter- native paths. For example, in Horsfield and Cumming's asymmetric model (1968), there are between 8 and 25 branchings with a corresponding distribution in path lengths from 7 to 23 cm between the trachea and the respiratory lobules. On the other hand, in Weibel's symmetric model A (1963, p. 136) there are 16 branchings with an equal length of 13 cm along all conducting airway paths. A symmetric model is a convenient start- ing point for the analysis of diffusion and flow because all transport paths are equiv- alent. Weibel's widely used model A por- trays the conducting airways as an expand- ing network of dichotomously branching tubes, wherein generation number, z, in- creases from zero at the trachea to 16 at the terminal bronchioli and 23 at the terminal alveolar sacs. Each generation contains 2Z branches. Figure 2 summarizes the important geometric features of this model (top) and their impact on gas flow (bottom). Although the diameters of individual branches gener- ally decrease with increasing z, beyond the eighth generation the total surface available for gas absorption, S. is a strongly increasing function of longitudinal distance, y. Increases in the summed cross-section available for flow, A, parallel those for S so that axial velocity as well as branch Reynolds number fall dramatically as gas is transported distally. During quiet respiration, the velocity is suf- ficiently low that Re does not exceed the upper limit of 2100 for fully developed lami- nar flow in any branch, but during moderate exercise, Re values in excess of 2100 indicate the possibility of turbulent flow in the trachea and first four generations. The entry length fraction, L/Le, is the ratio of actual airway length, L, to length, Le' required for flow to become fully de- veloped (Olson et al. 1970~. Entry length fractions are less than unity proximal to the seventh generation, implying that velocity fields within the trachea and major bronchi do not reach fully developed behavior, even during quiet breathing. This explains how it is possible for random velocity fluctuations to be observed in bronchial airway casts at inspiratory flows well within the laminar Reynolds number range (Dekker 1961; Olson et al. 1973~. Such turbulence was undoubtedly due to the propagation of incompletely dissipated ed- dies from the upper airway segment of the

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328 cast. Ordered flow disturbances consisting of a paired vortex pattern during inspira- tion and a quadruple vortex pattern during expiration have also been reported in iso- lated bronchi at Reynolds numbers within the laminar range (Schroter and Sudlow 1969~. The radial mixing brought about by these lateral flow circulations aids in trans- port of gas species toward the airway walls. Accompanying the decrease in branch diameters between trachea and terminal bronchioles, there is a progressive decrease in airway wall thickness and tissue perfu- sion rate. There are also fewer mucus- secreting elements and less ciliated epithe- lium, which reduces mucus velocity and thickness. Estimates of some relevant mu- cus, tissue, and blood flow parameters are presented in table 2. Transport and Uptake of Inhaled Gases AIRWAY GENERATION, z 0 1 2 4 6 8 1216 'T I ~'i I I I I I I I Trln E to 4 - UJ 3 1 - <~ 2.0 E N - 1.6 at; z - 1.2 up _ u' 0.8 O _ 00.4 _ En 0 v 800C - cr m 600C at in 400C o at ~ 200C Lid r in LlLe (exercise) / I LlLe (rest) ~ | '\\ 11 Re (rest) \\ / / ~? / _-~-- ~---~-- ~ --~-~ 0.12 0.14 0.16 0.18 0.20 0.22 0.24 ~ Re (exercise) 8 2 3) ~ 2.0 z z I O - r ID LONGITUDINAL DISTANCE, y(m) Figure 2. Geometric and aerodynamic characteristics of a symmetric tracheobron- chial model. All values were derived for Weibel's model A (Weibel 1963) scaled to a functional residual capacity of 3 liters. Entry length fraction was computed with the equation of Olson et al. (1973). Flows of 0.4 and 1.6 liters/sec have been used for rest and exercise conditions, respectively. Respiratory Zone The respiratory zone is defined by the presence of regions containing membra- nous outpouchings the alveoli normally responsible for gas exchange. An individual alveolus has a characteristic diameter of about 0.2 mm, and its shape may be mod- eled in various ways: a truncated sphere, a truncated cone, or a cylindrical wedge (Weibel 1963, p. 60~. The fine structure of the alveolar wall consists of little more than a shell-like mesh of pulmonary capillaries enclosed in a layer of airway epithelium covered by a thin surfactant film, and therefore the blood-gas barrier imposed by the alveolar membrane is only about 2 ,um thick. Because the pulmonary capillaries are short, typically 10 ,um long, there is

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James S. Ultman 329 Table 2. Conducting Airway Parametersa Airway Diameter/Lengthb Mucus ThicknessC Tissue Thickness Blood Flowe Mucus Velocity' (lo~2 m) (10-6 m) (10-4 m) (10-7 m3/sec) (10-4 m/see) Trachea 1.6/12 7 8 1.7 2.5 Main bronchi 1.0/6.0 7 5 0.6 1.7 Lobar bronchi 0.4/3.0 7 2 0.2 0.50 Segmental 0.2/1.5 7 1 0.09 0.067 bronchi Subsegmental 0.15/0.5 7 0.75 0.2 0.010 bronchi Terminal 0. 06/0.3 4.2 0.30 1.7 0.00033 bronchioles a Parameter values are based on a single airway branch. b Landahl (1950). c National Research Council (1977, table 7-3). Computed as 5% of airway diameter (DuBois and Rogers 1968). e DuBois and Rogers (1968, table 2). extensive branching in the capillary mesh, and the associated pulmonary blood flow resembles a moving sheath of fluid inter- rupted by regularly spaced posts of tissue (Rosenquist et al. 1973~. When packed together to form the lung parenchyma, the alveoli give a honeycomb appearance, with a specific surface area greater than 200 cm2/ml airspace volume. The edges of contact between adjacent al- veoli, called alveolar sepia, protrude into the airspace, thereby partitioning gas and impeding axial diffusion near the airway wall. Because their walls are so thin and have such a large specific surface, alveoli are well suited to normal gas exchange and probably to the absorption of air pollutants as well. To illustrate this, consider that an erythrocyte, which normally resides in the pulmonary capillaries for only 1 see, has sufficient time to come to equilibrium with alveolar oxygen (O2) and carbon dioxide (CO2) partial pressures. The fraction of airway wall occupied by alveoli increases with distal distance from the first alveolated airway to the blind- ended alveolar sacs that terminate every path of the tracheobronchial tree. As was the case for the conducting airways, both symmetric and asymmetric models have been proposed for the respiratory zone. In Weibel's model A, there are seven symmet- ric generations of respiratory airways, and along the 6-mm path leading from the first respiratory bronchioli to the alveolar sacs, the air-tissue surface available for gas ex- change increases from 0.16 to 39 m2 per generation. Simultaneously, the flow cross- section increases from 0.03 to 1.2 m2 with a concomitant drop in branch Reynolds number from 0.5 to 0.01 during quiet breathing. More recent work by Hansen and Ampaya (1975) indicates that Weibel's model significantly underestimates both tissue surface and flow cross-section, but in either case it is reasonable to conclude that the influence of gas flow is negligible and transport in the respiratory zone occurs principally by diffusion. The distal airway model of Parker et al. (1971 ) is an example of an asymmetric model of the respiratory zone. It is a di- chotomously branching network in which the total number of branchings varies from three to eight along different airway paths. In addition, this model incorporates distri- butions of alveoli, from 7 to 25 alveoli per duct (mean 15.9) and from 8 to 15 alveoli per sac (mean 9.6), rather than the fixed values of 20 alveoli in each duct and 17 in each sac of Weibel's symmetric model. Nonuniformities in Ventilation and Perfusion If the lungs were perfectly symmetric and mechanical tissue properties and forces were uniform among generations, then air

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330 Transport and Uptake of Inhaled Gases 20 ~ 15 z 10 c' cr: MEL 5 O ~.1- ~ ~ ~ ~ L 200 400 600 800 1000 1200 TRANSIT TIME TO ALVEOLAR DUCTS (arbitrary units) Figure 3. Frequency distribution of transit time from the carina to the alveolar ducts. (Adapted with permission from Horsfield and Cumming 1968, p. 379, and from the American Physiological Society.) flow and blood flow to all sibling branches would also be uniform. In this idealized situation, the local concentration and up- take rate of inhaled pollutants could vary only with respect to longitudinal position along the equivalent airway transport paths. In the real lung, however, both small-scale (intraregional) and large-scale (interregional) inhomogeneities exist, and they may impose a difference in dose be- tween equivalent structural units. For ex- ample, two terminal bronchioles located in different lobes of the lung might experience different pollutant exposure levels. 0.15 0.10 O c ~ J ~ Cal CC or 0.05 Two specific types of nonuniformities normally present in the lung have been well documented. First, because of anatomic asymmetries, there is a natural distribution of path lengths between the larynx and the respiratory zone, with shorter path lengths containing less gas volume than longer path lengths. If the rate of alveolar expansion distal to these paths is uniform, the transit times for fresh inspired gas to reach the alveoli by different paths will differ (figure 3), and there will be differences in time of exposure among equivalent structural units. Second, under the influence of grav- ity, when the body is upright, there is more ventilation and more blood flow near the bottom of the lungs than near the top (figure 41. In addition to the effects caused individually by the distribution of ventila- tion, VA, and perfusion, Q. the VA/Q ratio has special importance regarding gas up- take in the respiratory zone. That is, if a pollutant is to continuously absorb into the respiratory zone, it must first reach an alveolus and ultimately be removed by the pulmonary circulation. Therefore, alveoli that receive little local ventilation (that is, V^/Q is small) are as incapable of continu- ously absorbing soluble gases as are ade- quately ventilated alveoli that receive an Q - Base ~ A/Q - f Apex 5 4 3 2 RIB NUMBER ~3 ~2 ] it: Figure 4. Ventilation/perfusion ratio, VA/Q, from base to apex of the normal upright human lung. (Adapted with permission from West 1977, p. 202, and from Academic Press, Orlando, Fla.)

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lames S. Ultman 331 . . abnormally small blood flow (that is, VA/Q is large). This implies that gas uptake is maximized at some intermediate value of the ventilation/perfusion ratio. Fundamentals of Mass Transport A complete description of mass transport consists of three basic elements: the mass conservation equation, rate equations for diffusion and chemical reaction, and ther- modynamic equilibrium expressions. The mass conservation equation balances the rate at which a species may appear with the rate of its accumulation in a spatial region of interest often called the control volume. Given that the permissible modes of ap- pearance are convection, diffusion, and chemical reaction, the mass conservation equation has the form Rate of Accumulation Net Input Net Input Net Rate of Rate by + Rate by + Production Bulk Flow Diffusion by Reaction (2) The mathematical expression of mass con- servation is a differential field equation ap- plicable to any three-dimensional time- varying problem (Bird et al. 1960, p. 559), but in practice the general equation must be simplified by selecting a set of physically realistic assumptions. This will be consid- ered in detail in the next section, which is devoted to mathematical modeling. In this section, attention is focused on the fundamentals of thermodynamic equilibria and rate expressions for diffusion and chemical reaction. The formulation of mass transfer coefficients to describe transverse transport and the use of retention parame- ters and mixing coefficients to characterize longitudinal transport are also described. Thermodynamic Equilibria Phase equilibrium refers to the distribution of a species between adjacent immiscible phases. Suppose, for example, that a liquid phase containing a physically dissolved spe cies X is placed in contact with gas contain- ing an arbitrary partial pressure Px of the same solute species. Thereafter, molecules of X will continually redistribute between the liquid and gas phases, altering Ax until it reaches a stationary value p* referred to as the equilibrium partial pressure or the gas tension. In this equilibrium state, the ratio of the molar concentration Cx of species X in the liquid phase to the corresponding value of p* in the gas phase is a parameter, cYX, called the Bunsen solubility coefficient: Ax = CXIPX (3) Generally, cut is a function of temperature only, its value being equivalent to the mo- lar volume of the liquid divided by Henry's Law constant. Therefore, when tempera- ture is fixed, the dissolved species concen- tration is a linear function of gas tension. The solubility coefficients of most foreign gases in mucus, tissue, and blood are not precisely known and must be approxi- mated by values measured in readily avail- able solvents such as water (table 3) and hydrocarbon oils. Chemical reaction equilibrium can im- pose additional constraints on solute con- centrations. During chemical reactions, molecular combinations and decomposi- tions can both occur such that a dissolved pollutant species is reversibly bound to another endogenous species. Typical of such reactions are the aqueous ionization of SO2 to form bisulfite; the ionization of CO2 to form bicarbonate; and the binding of 02, C02' or CO to hemoglobin. To exemplify the underlying reaction equilib- rium, consider the ionization of SO2 in water given by the stoichiometric equation SO2 + H2O = H+ + HSO3 (4) Although HSO3 also undergoes a weak dissociation to SO32-, equation 4 is a suffi- ciently accurate model of the overall proc- ess (Schroeter 1966, p. 17~. As the concentration of SO2 is depleted by the formation of HSO3, the law of mass action dictates that the forward reaction rate must slow down. Simultaneously, the concentration of bisulfite builds up, and this leads to an increase in reverse reaction rate. This progressively decreasing forward

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332 Transport and Uptake of Inhaled Gases Table 3. Estimates of Physical Properties for Various Gases Diffusivity in Aira Aqueous DifFusivityb Aqueous Solubility' First-Order Reactivity Gas Dx (10-s m2/sec) Dx (10-9 m2/sec) ax (kg-mol/m3/Pa) kr (103/sec) SO2 1.15 2.14 9.13 x 10-6 0 O3 2.11 3.06 5.62 x 10-8 1.2(m):50(t):5(b) CO 2.17 3.06 8.09 x 10-9 0 a Chapman-Enskog equation (Bird et al. 1960, p. 510). b Wilke-Chang equation (Bird et al. 1960, p. 515). c Computed from Henry's Law coefficients (National Research Council 1977, table 7-1). ~ Miller et al. (1985, table 3) for mucus (m), tissue (t), and blood (b). . . . rate anc increasing reverse rate continues until the two rates are equal and the con- centrations of all species become stationary. In this equilibrium state, the concentrations of reactants and products possess a specific algebraic relationship. For the SO2 ioniza- tion reaction, (Ke) SO2 = CHSO3 CH/ CSO~ (5) where (Ke)So2, the reaction equilibrium constant specific to the ionization of SO2, is a function of temperature (Pearson et al. 1951). In pure water, where hydroxyl ion con- centration is low, electroneutrality dictates that bisulfite and hydrogen ion concentra- tions are approximately equal, and the summed concentration of SO2 in the unre- acted form CsO2 and in the reacted form CHSO3 can then be expressed as CSO2 + CHSO3 ~SO2PSO2 + t(Ke~sO2ctso2pso2]~/2 (6) This equation illustrates the ability of a reversible chemical reaction to increase the capacity of a solution for gaseous solute. To emphasize the importance of this, figure 5a compares the physical solubility of SO2 to the corresponding level of bisulfite ions. Clearly, the concentration of reacted spe- cies is far greater than the concentration of physically dissolved species, and the rela- tionship of bisulfite concentration to gas tension is nonlinear. In mucus and tissue, increases in hydrogen ion concentration occurring with SO2 ionization are probably suppressed by the buffering action of other solutes, and as equation 5 indicates, the bisulfite concentration would be even larger than in pure water. To provide a unified treatment of the dissolved and reversibly bound forms of a soluble gas, a reactive capacitance coeff~- cient, ,13x, analogous to the solubility coef- ficient, can be defined as the derivative of the reacted solute concentration, Cal. with respect to gas tension: - xr7 Ax = dCxr/dPx (7) Unlike ox, which is independent of Px*, the reactive capacitance coefficient for a revers- ibly bound solute species is generally a decreasing function of gas tension (figure 5b). Diffusion and Reaction Rates Transport of any species occurs by a com- bination of diffusion and convection. Whereas convection is the translation of molecules at the mean flow velocity, diffu- sion is the transport that occurs in response to a concentration gradient whether or not any net flow occurs. Fick's First Law is the general rate equation that accounts for con- vection and diffusion (Bird et al. 1960, p. 502), and for the special case of one-dimen- sional diffusion of species X in the absence of flow, it reduces to MX =-DxSd(Cx/dz) (8) where MX is the mass transport rate of species X; dCx/dz is the concentration gra- dient in the diffusion direction, z; S is the surface area perpendicular to z; Dx is the molecular diffusion coefficient; and the negative sign indicates that diffusion is along the path of decreasing concentration. Strictly speaking, equation 8 is valid only for solutions composed of two species, but Fick's Law may also be applied to multi

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James S. Ultman 333 A 3 co E o ~ 2 A - z z UJ at o 0 1 o UJ B HSO3 / 4 _ E to 3 _ o UJ z > LL. 1 tar 2 SON \ 1, \ ~ ~HSO3 \ ' - - 0 0.5 1 .0 0 0.1 0.5 1 .0 GAS TENSION PSO2 (Pa) Figure 5. Solubility of sulfur dioxide at 37C in pure water. A: The Physical solubility of SO2 and its equilibrium concentration as reacted SOL (that is, HSO3 ) are compared. B: In the graphical construction of average reactive capacitance at SO2 tensions between 0.1 and 0.5 Pa, a horizontal line is drawn so that the areas I and I' are equal. Note that 1 Pa is equivalent to 21.5 ppm of SO2 when total pressure is 1 atm. component solutions when the solute spe- cies of interest is present at sufficiently low concentration or partial pressure relative to the solvent species (Bird et al. 1960, p. 571). Chang et al. (1975) analyzed situa- tions in the airway lumen where multicom- ponent diffusion effects may be important, but the existence of similar phenomena in mucus and tissue have not been investigated. The lung consists of gas, tissue, and blood regions, and the customary assertion that phase equilibrium applies at the inter- faces between regions leads to correspond . . . . . . . . sing c .~scont~nu~t~es In species concentration. This mathematical inconvenience can be circumvented by substituting, in Fick's Law, the gas tension gradient for the con . . centratlon grac lent. MX =-aXDxS(dp */dZ) (9) The product, axDx, sometimes called Krogh's constant of diffusion (Dejours 1981), indicates that the diffusion rate of gases with a small diffusion coefficient can be significant when compensated by a suf- ficiently large solubility. A useful form of equation 9 results for the case of steady-state diffusion through a planar barrier of thickness 1. Then the transport rate MX is constant and equation 9 can be integrated with the result that MX = (~xDxIl)S~x~-Pxo) (10) where Phi and phi are the gas tensions at the two sides of the barrier. Thus, the tension of an inert gas is linearly distributed in the diffusion direction, and the proper driving force for diffusion is the gas tension differ- ence (figure 6a). If a gas species undergoes reversible

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356 Transport and Uptake of Inhaled Gases ~0 - G 6.0 C,' 5.0 G 6 .L 6 I G . . LU z z 40 10 5 3 2 1.5 FLOW RATE (liters/min) 4.0 3.0 2.0 1 000 100 dig, 0.31 + 0.003 ppm - ~ O3 / ,~ 0.80 ~ 0.001 ppm i/ / '' 10 1 f ~ I ~ 0 0.3 TRANSIT TIME (m i n /l iter) _ calm_ .v 0.2 ~_ 0.4 0.6 0.8 1.0 13.0 14.0 TRANSIT TIME (min/liter) Figure 21. Effect of airflow on the absorption of various foreign gases along the nasotracheal path of the upper airways. (Adapted with permission from Aharonson et al. 1974, p. 656, and from the American Physiological Society.) cient is much less sensitive to flow than is the nasotracheal coefficient. For O3, how- ever, there is an astonishing similarity of flow sensitivity for the nasotracheal and the orotracheal paths, and at both inlet concen- trations reported. With the exception of the orotracheal value for SO2, the values of m are all the same order of magnitude but somewhat less than the 0.854 value re- ported for km in physical models (table 5, entry la). The smaller flow dependence of the in viva data is probably due to diffusion resistances in tissue and mucous layers that are not directly affected by gas flow. Animal data also suggest that both O3 and SO2 uptake are sensitive to atmospheric concentration. This effect is portrayed by the Px/Pxj tracheal penetration values in fig- ure 22. The SO2 data (Strandberg 1964) were obtained from free-breathing rabbits who inspired a pollutant mixture of known composition from a head chamber. Tra- cheal samples were obtained at peak inspi- ratory flow (I) and peak expiratory flow (E), the former sample being representative of upper airway absorption and the latter indicative of lower airway uptake. The O3 data were obtained on dogs by applying subatmospheric pressure to a tracheos- tomy, thereby withdrawing pollutant mix Table 7. Comparison of Absorption Characteristics of the Nose and Mouth Nasotracheal Steady Flow Inspired Concentration (liters/min) Px,,/Px; 0.001 0.032 0.283 0.631 0.408 0.733 R TKmS (10 4m3/sec) Orotracheal m pX`~/p.~' R TKmS (10 4m3/sec) m l ppm SO2a 3.5 35 26-34 ppm O3 3.5-6.5 35-45 3.5-6.5 35-45 78-80 ppm O3 4.03 20.1 1.05 3.07 0.747 2.07 0.70 0.0044 0.660 0.52 0.665 0.884 0.49 0.732 0.902 3.17 2.42 0.340 0.822 0.260 0.687 a Frank et al. (1969). b Yokoyama and Frank (1972).

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James S. Ultman Lit 1.0 cr 6 ~ To I O 0.50 cr _ ~ 6 Al I S02(1) \ ~' 03(1) \ // ~ SO2(E) . o 10-2 10-1 1 10 1o2 INLET CONCENTRATION (ppm) 1n2 Figure 22. The concentration dependence of SO2 penetration (Strandberg 1964) in rabbits and O3 penetration (Vaughan et al. 1969) in dogs. Both inspiratory (I) and expiratory (E) samples were obtained in the trachea. lures from a reservoir into the nose and through the upper airways (Vaughan et al. 1969~. Tracheal concentration was deter- mined by sampling from a tracheostomy tube while the dog breathed spontaneously through the caudal portion of the tracheos- tomy. These data reveal that penetration of SO2 through the upper airways is inversely re- lated to its inlet concentration, but penetra- tion of O3 is directly related to concentra- tion. It is possible to attribute the behavior of O3 to a saturation limitation in chemical reaction rate as concentration increases. Such reaction kinetics are common for a variety of biochemical reactions and are often described by the Michaelis-Menten equation (Mahler and Cordes 1968, p. 153~. It is difficult to conceive of a purely phys- ical explanation for the concentration de- pendence of SO2 penetration. Rather, it has been postulated that short exposures to high levels of SO2 stimulate mucus secre- tion, thereby reducing penetration as com- pared to exposures at low concentrations (Brain 1970~. Far less information is available for ab- sorption in the lower airways than for uptake in the upper airways. In experi- ments where the lower airways of dogs were surgically isolated from the upper airways, penetration of O3 to the respira- tory airspaces estimated as the ratio of expired-to-inspired partial pressures was 357 ~n3 from 0.15 to 0.20, depending on the me- chanical ventilation rate and the inlet con- centration (Yokoyama and Frank 1972~. And in free-breathing rabbits (figure 22), the analogous ratio for SO2 was from 0.2 to 0.4. Because of the naturally reversing res- piratory flow in the latter experiments, some Resorption of pollutant may have occurred during expiration, as pollutant- depleted air from distal airways passed over the pollutant-rich tissue and mucus in more proximal airways. Therefore, the expira . . . . . . . t1on-to-1nsp1rat1on partial pressure ratios may be somewhat larger than the actual lower airway penetrations. An important factor to consider in the design of uptake experiments is exposure time of the animal to the pollutant. Whereas an acute exposure results in data relevant to transport in a healthy animal lung, chronic exposure can result in ana- tomic and functional derangements that further affect the absorption process. All the investigations cited above utilized short exposures, usually less than an hour. How- ever, Moorman et al. (1973) measured O3 absorption into the upper airways of dogs that were chronically exposed for 8 to 24 hr. and compared the results with data from acutely exposed dogs. Their results show that in dogs, penetration through the nasotracheal path is generally greater dur- ing chronic exposure than during acute exposure. These investigators hypothesized

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358 Transport and Uptake of Inhaled Gases that decreased mucus flow due to chronic exposure was responsible for the increased penetration. Recommendation 4. Using a consistent experimental protocol, total uptake of se- lected pollutants should be measured in different animal species and then used to develop basic rules of extrapolation. In Vivo Human Subject Studies Extensive research into the transport of foreign gases in the human lung has been directed toward the development of non- invasive tests of pulmonary function. To a large extent, progress in this area has been stimulated by the development of reliable fast-responding gas analyzers. Literature on the use of inert insoluble gases for the characterization of gas mixing and distribu- tion is extensive (Engel and Paiva 1985~. One of the most widely used lung func- tion tests employing inert insoluble gas is the multibreath wash-out (Fowler et al. 1952~. In this measurement, the end-ex- pired nitrogen fraction is recorded for a series of regular breaths following a change . . . . ,~ . in 1nsplrec . gas mixture trom room air to pure oxygen. If the lungs behaved in ac- cordance with the static Bohr model, then a semilogarithmic plot of expired nitrogen fraction versus breath number would be a straight line having a slope and intercept from which dead space and alveolar vol- ume could be determined. However, for patients with diseased lungs, this plot is far from linear, and even in normal subjects, expired nitrogen fraction exhibits multiex- ponential rather than single-exponential decay. Such nonideal behavior has been successfully simulated using multicompart- ment models with ventilation inhomoge- neities between parallel regions (Robertson et al. 1950~. Most research on reactive foreign gases has been devoted to the uptake of CO. Because the absorption of this species is limited by diffusion through the alveolar membranes, decreased CO uptake can serve as an indicator of parenchymal tissue abnormalities. In the single-breath method, CO diffusing capacity is computed from the ratio of final-to-initial alveolar con- centration measured during a series of breath-holding periods of known duration (Apthorp and Marshall 1961~. The diffu- sion-limited form of equation 27 (that is, Bo = 0) is appropriate for this calculation, and it predicts that a semilogarithmic plot of alveolar concentration ratio versus breath- holding time has a slope proportional to KmS. Roughton and Forster (1957) recog- nized that pulmonary diffusing capacity is composed of a true membrane-diffusing capacity and a hemoglobin reaction capac- ity that is proportional to capillary blood volume (eq. 25~. Moreover, they devel- oped a method of estimating the capillary blood volume by measuring the change in reaction capacity at different levels of in- spired O2. Although the method is fraught with difficulties, primarily because a unique value of alveolar concentration must be in- ferred from expired gas analysis, the single- breath CO uptake procedure as standardized by Ogilvie et al. (1957) is still in use. There has also been considerable interest in soluble nonreactive gases such as acety- lene. Since the absorption of acetylene is perfusion-limited, it can be used as an indicator of pulmonary blood flow, Q. Acetylene uptake has been measured by the same breath-holding procedure developed for CO, and the data were then analyzed with equation 27. For a moderately soluble gas, the Bo parameter is large enough that a semilogarithmic plot of expired alveolar concentration versus breath-holding time should have a slope proportional to Q. To study in detail the influence of solubility on uptake, Cander and Forster (1959) per- formed single-breath experiments using five different nonreactive gases including acetylene. Their results depart from the theory in two important ways, particularly for the most soluble gases, ethyl ether and acetone (figure 23~. First, the "percent of initial alveolar con- centration" does not extrapolate to the ex- pected value of 100 percent at zero breath- holding time. This was attributed to an initially rapid absorption of the foreign gas into parenchymal tissue, thereby causing an instantaneous drop in alveolar partial pres- sure. By extending the mathematical model

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James S. Ultman 359 ~ ' 30 u, oh ~5 :~ ._ ~ 0 F ID A: ~ ~ c ~ g A: ~ ~ ~ 3 100 ~ h. 50 _ 10 5 b _~ W~ _ 04, _ 1 _ ~v -~ N2`J - - o . _ 1 0 1 0 20 30 40 50 BREATH-HOLDING TIME (see) Figure 23. Breath-holding uptake data for five inert gases of increasing solubility obtained in a series of single breaths. (Adapted with permission from Cander and Forster 1959, p. 544, and from the Amer ican Physiological Society.) to account for this, Cander and Forster were able to estimate reasonable values of the tissue volume. Second, the semiloga- rithmic plots are not linear. Instead, as breath-holding time increases, the alveolar concentration data become progressively larger than expected from a linear extrapo- lation of the initial data. Cander and Forster attributed this result to the contamination of expired alveolar gas with foreign gas that was initially absorbed into conducting air- way tissues. Although no formal model was proposed, this behavior could un- doubtedly be predicted by a multicompart- ment simulation that accommodates de- sorption processes during expiration. By combining individual measurements into one multiple-gas test, it is possible to simultaneously estimate several transport parameters for the same subject. Moreover, since the parameters are measured under a single set of conditions, their values and the relations among their values may be more reliable than if each was measured under conditions that must necessarily differ, even if only slightly. An example of such an approach is the work of Sackner et al. (1975) who performed a series of breath- holding experiments on subjects inspiring a gas mixture containing helium (to assess alveolar volume), CO (to evaluate mem brane-diffusing capacity and capillary blood volume), and acetylene (to determine blood flow). Whereas Sackner's study used a single-compartment static model to ana- lyze the uptake data, Saidel et al. (1973) used a more sophisticated multicompart- ment model to elucidate both ventilation distribution and uptake dynamics. These investigators carried out parame . . . . ter estimation experiments in two stages. They first performed multibreath wash-out measurements in which uptake of the ni- trogen test gas is negligible. By matching simulations (eq. 28) to these data, flow fraction parameters, Ok, governing distri- bution of volume and ventilation among the four distensible lower-airway compart- ments (figure 12a) could be evaluated for each subject. Then, the subjects were ad- ministered a steady-state uptake test in which a dilute CO-air mixture was in- spired and the end-tidal concentration and uptake of CO was measured during con- secutive breaths. By using the fkj ventila- tion parameters already established from the nitrogen wash-out data, simulations of CO uptake data could be performed to estimate the parenchymal diffusion param- eters, KmS. In humans as in animals, it is also possi- ble to study uptake in the upper airways independent of the lower airways. For ex- ample, Speizer and Frank (1966) described an experiment in which cooperating sub- jects inhaled a 15-ppm mixture of SO2-air into the nose, while inspiratory and expi- ratory samples were automatically with- drawn through a nasal sampling tube just inside the nares and a pharyngeal sampling tube was inserted through the mouth. By comparing concentrations between the nose and pharynx, it was clear that SO2 penetration beyond the upper airways was only 1 percent during inspiration. And be- cause the pharyngeal concentration was on the order of 0.4 ppm during both inspiration and expiration, it appears that the lower airways neither absorbed nor desorbed a de- tectable quantity of SO2. However, the ex- pired nasal concentration was 2 ppm, five times larger than the pharyngeal value, indi- cating that Resorption from the nasal pas- sages was promoted during expiration

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360 Transport and Uptake of Inhaled Gases by the flow calf air that had horn strinn~H of SO2 during inspiration. This temporal countercurrent exchange process enhances the protective capability of the upper air- ways. That is, in addition to preventing pollutants from reaching lower airways, countercurrent exchange reduces pollutant loading in the upper airway mucosa. Up to this point, the discussion has fo- cused on physicochemical problems, namely, absorption rates and internal con- centration distributions of foreign gases. From a medical point of view, however, these physicochemical descriptions are use- ful only if they correspond to functional abnormalities. The connection between characterization of local dose on the one hand, and graded response of lung function on the other, has clearly been established for SO2. In particular, it is well known that acute exposure to SO2 leads to a reversible increase in airway flow resistance because of bronchoconstriction mediated by neural chemical sensors (Frank 1970~. Because these sensors are particularly abundant near the larynx and carina, it should be possible to correlate local dose at these sites with airway resistance. Amdur (1966) used pub- lished SO2 penetration values obtained by Strandberg (1964) on free-breathing rabbits in conjunction with her own airway flow- resistance values measured in guinea pigs and graphed the logarithm of airway resis- tance increase versus the logarithm of tra- cheal concentration. This local dose/re- sponse plot was linear with a slope of 0.6, corresponding to an approximate square root dependence of airway resistance in- crease on tracheal SO2 concentration. Going one step further, Kleinman (1984) hypothesized that if changes in airway re- sistance are directly related to the dose of SO2 reaching the postpharyngeal airways, then apparent differences in response that have been observed during rest, exercise, free breathing, and breathing through a mouthpiece (figure 24a) can be explained by the dependence of upper airway pene- tration on flow rate and on the point of air access. Kleinman presented a quantitative analysis in which equation 32 was used to convert the inhaled dose rate, Vpx, of the nine data points in figure 24a into their Is a) o Q x a) A 200 o c a) C`7 LU oh CO UJ An: - CO As llJ of I 200 400 600 800 POSTPHARYNGEAL DOSE RATE, VpxO(~g/min) Figure 24. Dose/response data for increased airway resistance following exposure to SO2. A: Correlation with respect to inhaled dose. B: Improved correlation with respect to postpharyngeal dose. (Adapted with permission from Kleinman 1084, pp. 33, 35, and from the Air Pollution Control Association.) 400 300 100 400 300 200 100 A Mouth breathing (exercise) / Mouth breathing (rest) I_ g ~ ~ Natural breathing (exercise) I I I ~ I 1 1 1 1 1 1 1 200 400 600 800 1000 1200 INHALFn nORF RATE An. (,,~lmin] ~ ~Xj~-~ ~ B / / o corresponding postpharyngeal dose rate, Vpx. The flow fraction entering the nose, In, Divas evaluated as a function of airflow by assembling available human subject data; and the nasotracheal penetration, (PxO/Px)n' and orotracheal penetration, (PxO/Px'jm' were both modeled by a formula similar to equation 34, with separate values of KmS for the nose and for the mouth estimated on the basis of mixed data from dogs and man. When the change in airway resistance is replotted against the predicted values of postpharyngeal dose (figure 24b), the dose/ response correlation is considerably im- proved relative to the use of inhaled dose (figure 24a). Oulrey et al. (1983) performed a similar analysis of SO2 dose/response, but used a larger data set composed of 23 grouped measurements of airway resistance. They concluded that the increase in specific air

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lames S. Ultman 361 way resistance is best correlated with the square of postpharyngeal penetration. Recommendation 5. Noninvasive pul- monary function tests such as the CO uptake method should be extended to the evaluation of pollutant transport in hu- mans. Summary Mathematical models can serve several pur- poses in the analysis of pollutant gas up- take. In order of increasing importance, a model can be used to correlate experimen- tal measurements made under differing en- vironmental or respiratory conditions; to extrapolate data obtained on laboratory an- imals to those values expected in humans; and to estimate sites and rates of uptake under conditions for which no data are available. There is no single model that best serves all these tasks. Rather, there may be a different model appropriate to each. For example, in data correlation and in extrap- olation, a compartment model can incor- porate important physiologic phenomena (for example, geometric asymmetry, air- flow nonuniformities, ventilation/perfu- sion inequalities) within a mathematical framework that requires little detailed in- formation for its development and only modest computational power for its imple- mentation. On the other hand, a distribut- ed-parameter model, which requires more elaborate input and more complex numer- ical algorithms to solve, is capable of pre- dicting outcomes from first principles. Whatever the nature of the model se- lected, it is assembled from four basic building blocks. First, an idealized geome- try accounting for the structure of the airways, tissue, and blood spaces must be decided upon. Then material balance equa- tions describing the time-dependent and possibly spatially distributed transport of pollutant are formulated. At the foundation of these material balances are the basic thermodynamic equilibrium, diffusional flux, and chemical reaction rate equations. Finally, using a specified set of pulmonary function parameters as forcing functions (for example, respiratory and pulmonary blood flows), the material balance equa- tions are solved to provide a numerical simulation of pollutant uptake. Experimental measurements are neces- sary to provide the geometric and physico- chemical data required as inputs to a model and also to validate predictions by the model. Ideally, this is accomplished by a combination of separate experiments. For example, basic thermodynamic and reac- tion rate data can be obtained from in vitro systems such as isolated perfused lungs or excised tissue samples, whereas predicted uptake rates might be verified with nonin- vasive measurements in human subjects or invasive measurements in intact anlma s. Clearly, an adequate quantification of pollutant gas transport and uptake is an interdisciplinary problem. Its solution re- quires the modeling skills of engineers and physicists, as well as the biological exper- tise of biochemists, toxicologists, and physiologists. And if some scientists should choose to straddle two or more disciplines, then so much the better! Summary of Research Recommendations Recommendation 1 Objective. There is a critical need to quantify the chemical Basic Property Data interaction of specific pollutants with mucus, tissue, and blood. Besides determining solubility and Dyson coed~c~ents, it Is essential to determine the coefficients in reaction rate equations. The difficulty of this task is complicated by the fact that the associated thermodynamics are undoubtedly nonideal, and nonlin ear concentration effects are likely.

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362 Transport and Uptake of Inhaled Gases Motivation. The descriptions of pollutant chemistry that are con- tained in this chapter were intended to be illustrative of quantitative methods, but were not completely accurate. In particular, physical properties in biological media were represented by aqueous values, and in the absence of chemical rate data, it was necessary to assume either instantaneous reaction or first-order kinetics. To develop reliable mathematical models and provide sound interpretation of absorption data, basic property data remain to be established, even for the most common pollutants. For example, the explanation of concentration effects in O3 and SO2 uptake data is still somewhat speculative, largely because of our ignorance of the underlying chemistry. Approaches. The use of isolated tissue preparations, such as tissue cultures or excised organ segments, could provide more direct measurements of biochemical properties than are possible in the entire organ. For example, by incorporating such a preparation into a flow-through or batch reactor, it is possible to determine a reaction rate expression using the well-established engineering principles of reactor design. Recommendation 2 Objective. A serious effort is needed to analyze mass transport Individual Mass through individual diffusion barriers, particularly the mucous Transfer Coefficients layer, the bronchial wall, and the alveolar capillary network. Undoubtedly, the sparsely perfused bronchial wall will require different mass transfer theory than the richly perfused plate-and post structure of the alveolar walls. And the analysis of diffusion through the mucous blanket, because it may have a discontinuous dynamically changing conformation, poses unique challenges. Motivation. At the core of any mathematical model of pollutant uptake are the individual mass transfer coefficients for the diffusion barriers. The values of mass transfer coefficients presented in this chapter were merely estimates. Considerable refinement is neces sary. Approaches. Although some physical modeling may be appro priate, it is also possible to perform computations based on existing geometric and hydrodynamic data. DuBois and Rogers (1968) have illustrated the application of diffusion theory to the bronchial wall; mechanical engineers have reported methods for analyzing trans port in interrupted flows similar to those in the pulmonary circulation (Wieting 1975~; and chemical engineers have developed a surface renewal theory to deal with dynamically changing inter faces such as the gas/mucus boundary (Astarita 1967~. Recommendation 3 Objective. To analyze total uptake of pollutants and to predict Ventilation and dose distribution, mathematical models that account for ventilation Perfusion Effects and perfusion limitations, including their regional distribution, should be developed and validated. Motivation. It is clear that there is a nonuniform distribution of ventilation and perfusion, even in a normal lung. And the possi bility of diffusion and perfusion limitations exists for all pollutant gases. These interrelated phenomena have not been systematically investigated for pollutant gases, and yet it seems likely that they will have an impact on uptake distribution.

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.Iames S. Ultman 363 Approaches. A combination of measurement and mathematical modeling is necessary. The use of isolated perfused lung prepara- tions could allow the measurement of total uptake under conditions where the overall ventilation/perfusion ratio is controlled. More- over, intravascular tracer methods previously developed for deter- mining ventilation/perfusion ratios in humans (Wagner 1981) might also be applied to an isolated lung. In analyzing data, distributed-param eter models may be unnecessarily complicated. Multicompartment lumped-parameter models are probably more appropriate. Recommendation 4 Objective. Using a consistent experimental protocol, total up Extrapolation take of select pollutants should be measured in different animal Modeling species and then used to develop basic rules of extrapolation. More specifically, these uptake data could be correlated using known interspecies differences in lung volume, surface area, breathing rate, and rate-limiting mass transfer coefficients within the framework of an appropriate mathematical model. Motivation. There is virtually no information in the literature that allows prediction of uptake by the human lung from data obtained in smaller laboratory animals. This represents a critical problem in setting air quality standards in cases where measure ments on humans do not exist or cannot be taken. Approaches. Yokoyama (1984) described an enclosure, similar to a closed-circuit metabolic chamber, in which the total O3 uptake by a free-breathing rat could be monitored, without the need to anesthetize the animal. Using such a device, or possibly several chambers of different sizes, it would be possible to amass total uptake data on a series of different animal species. This data base could be analyzed with a simple compartment model that treats the animal and the chamber as two separate subsystems. Recommendation 5 Objective. Noninvasive pulmonary function tests such as the CO Noninvasive uptake method should be extended to the evaluation of pollutant gas Methods transport in humans. The data from such experiments, particularly when several indicator gases are used simultaneously, can be analyzed with an appropriate mathematical model to extract considerable information about regional inhomogeneities in uptake rate and dose. Motivation. To date, most pollutant uptake data have been obtained in animals using protocols that required heavy sedation, and in some cases, extreme surgical procedures. Moreover, these measurements were made in the absence of complementary tests that characterize other important functional features such as the distribution of ventilation. Approaches. It would be useful to extend the methodology of Saidel et al. (1973) to soluble and reactive pollutants. Naturally, the multicompartment model used by these investigators to simulate CO uptake must be generalized to include absorption into the upper airway and conducting airway compartments. Also, because of limitations in gas analyzer response and the potential health hazard during continual exposure, it may not be practical to use the steady-state uptake technique; the single-breath, breath-holding method may be a better choice.

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364 Acknowledgment This work was supported in part by Na- tional Institutes of Health Grant HL-20347. References Aharonson, E. F., Menkes, H., Gurtner, G., Swift, D. L., and Proctor, D. F. 1974. Effect of respiratory airflow rate on removal of soluble vapors by the nose, J. Appl. Physiol. 37:654-657. Amdur, M. O. 1966. Respiratory absorption data and SO2 dose-response curves, Arch. Environ. Health 12:729-732. Apthorp, G. H., and Marshall, R. 1961. Pulmonary diffusing capacity: a comparison of breath-holding and steady-state methods using carbon monoxide, J. Olin. Invest. 40:1775-1784. Astarita, G. 1967. Mass Transfer with Chemical Reac- tion, Elsevier, New York. Bird, R. B., Stewart, W. E., and Lightfoot, E. N. 1960. Transport Phenomena, Wiley, New York. Bohr, C. 1891. Uber die lungenatmung, Skand. Arch. Physiol. 2:236-268. Brain, J. D. 1970. The uptake of inhaled gases by the nose, Ann. Otol. Rhinol. Laryugol. 79:529-539. Cander, L., and Forster, R. E. 1959. Determination of pulmonary parenchymal tissue volume and pulmo- nary capillary blood flow in man, J. Appl. Physiol. 14:541-551. Chang, H. K., Tai, R. C., and Farhi, L. E. 1975. Some implications of ternary diffusion in the lung, Respir. Physiol. 23:109-120. Cumming, G., Horsfield, K., and Preston, S. B. 1971. Diffusion equilibrium in the lungs examined by nodal analysis, Respir. Physiol. 12:329-345. Dayan, J., and Levenspiel, O. 1969. Dispersion in smooth pipes with adsorbing walls, Ind. Eng. Chem. Fundam. 8:84(}842. Dejours, P. 1981. Principles of Comparative Respiratory Physiology, Elsevier, New York, ch. 5. Dekker, E. 1961. Transition between laminar and turbulent flow in human trachea, J. Appl. Physiol. 16:106~1064. DuBois, A. B., and Rogers, R. M. 1968. Respiratory factors determining the tissue concentrations of inhaled toxic substances, Respir. Physiol. 5:34-52. Dungworth, D. L., Castleman, W. L., Chow, C. K., Mellick, P. W., Mustafa, M. G., Tarkington, B., and Tyler, W. 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Health 18:315-322. Gil, J. 1982. Comparative morphology and ultrastruc- ture of the airways, In: Mechanisms in Respiratory Toxicology (H. W. Witschi and P. Nettesheim, eds.), ch. 1, CRC Press, Boca Raton, Fla. Gomez, D. M. 1965. A physico-mathematical study of lung function in normal subjects and in patients with obstructive diseases, Med. Thorac. 22:275-294. Graham, B. L., Dosman, J. A., and Cotton, D. J. 1980. A theoretical analysis of the single breath diffusing capacity for carbon dioxide, IEEE Trans. Biomed. Eng. BME-27 4:221-227. Haggard, H. W. 1924. The absorption, distribution, and elimination of ethyl ether; I. Amount of ether absorbed in relation to concentration inhaled and its fate in the body, J. Biol. Chem. 59:737-751. Hanna, L. M., and Scherer, P. W. 1986. Measurement of local mass transfer coeff~cients in a cast model of the upper respiratory tract, Trans. Am. Soc. Mech. Eng. 108:12-18. Hansen, J. E., and Ampaya, E. P. 1975. Human air spaces, sizes, areas and volumes, J. Appl. Physiol. 38:99~995. Henderson, Y., Chillingworth, F. P., and Whitney, J. L. 1915. The respiratory dead space, Am.J. Physiol. 38:1-19. Hills, B. A. 1974. Gas Transfer in the Lung, Cambridge University Press, Cambridge, Mass. Himmelblau, D. M., and Bishoff, K. B. 1968. Process Analysis and Simulation: Deterministic Systems, Wiley, New York. Hobler, T. 1966. Mass Transfer in Absorbers, ch. 5, Pergamon, New York. Hori, Y., and Suzuki, S. 1984. Estimation of the rate of absorption of atmospheric pollutants in respira- tory conducting airways by mass transfer theory, J. Jpn. Soc. Air Pollut. 4:263-270. Horsfield, K., and Cumming, G. 1968. Morphology of the bronchial tree in man, J. Appl. Physiol. 24: 373-383. Hughes, J. M., Hoppin, F. G., and Mead, J. 1972. Effect of lung inflation on bronchial length and diameter in excised lungs, J. Appl. Physiol. 32: 2~35. Ichioka, M. 1972. 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