Air Pollution, the Automobile, and Public Health (1988) / Chapter Skim
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Transport and Uptake of Inhaled Gases
Transport and Uptake of Inhaled Gases
Pages 323-366
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From page 323... ...
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.
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This article begins with two sections devoted to issues at the heart of mathematical model development: first, lung anatomy and its influence on aerodynamics; andsecond, 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.
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Taken together, the conducting airways and respiratory zone are referred to as the lower respiratory tract, and since they contain no gas exchange surface, the upper and conducting airways combined are often called the anatomic 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 conducting airways.
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From page 326... ...
The geometry of upper airways is irregular and variable, depending on the point of air access, on the breathing pattern, and on the state of mucous membrane engorgement by nasal blood flow. Perhaps this explains why no mathematical model of its anatomy has been established.
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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 generally occupy the first 10 or so generations.
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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)
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From page 329... ...
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 symmetric 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 exchange increases from 0.16 to 39 m2 per generation.
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In this idealized situation, the local concentration and uptake 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)
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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*
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, the reactive capacitance coefficient for a reversibly bound solute species is generally a decreasing function of gas tension (figure 5b)
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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 difference (figure 6a)
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. When chemical reaction occurs at a finite rate or is not reversible, reactive capacitance can no longer relate the concentration of reacted species to the gas tension.
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. This equation is similar to the inert gas uptake rate with the addition of the Hatta number to provide a proportional correction for the effect of chemical reaction.
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Besides determining solubility and diffusion coefficients, it is essential to determine the coefficients in reaction rate equations. Individual Mass Transfer Coefficients The uptake formulations reveal that transport rate normal to a diffusion barrier is generally proportional to the product of the solubility, surface area, and gas tension difference across the diffusion barrier: Mx = ~xkms~[x,-P x2)
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From page 337... ...
Second, quantitative anatomic models of vascular structure in the bronchial tissue and the upper airways do not exist. Last, blood is a two-phase material composed primarily of plasma and red blood cells, a fact that must be considered when analyzing diffusion within the small blood vessels.
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In the sense that finite values of blood gas tension reduce the driving force for uptake, Pxb is often referred to as a diffusion backpressure. When the flux of species X is equal in all diffusion layers, the overall mass transfer coefficient has the well-known form (Treybal 1980, p.
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282) that SO2 is almost completely absorbed within the upper airways; O3 is transported beyond the upper airways, its uptake being most significant in the distal conducting airways and proximal respiratory branches; and CO absorption occurs deeper within the respiratory zone.
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that divides inspired air containing a foreign gas species from residual air initially devoid of foreign gas (figure 10~. When the foreign gas is chemically inert and insoluble in tissue, it is confined to the airway lumen, and the concentration front is displaced at a volumetric rate identical to the bulk flow rate of the entire gas mixture.
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From page 341... ...
In contrast to bulk transport, which has been visualized in terms of the axial displacement of a concentration front, longitudinal mixing is characterized by the axial spreading or dispersion of transported species about the front. Three basic mechanisms may be responsible for longitudinal mixing: axial diffusion is due to the Brownian motion of individual molecules and is always present, whether or not there is flow; mixing by asymmetry is due to the nonuniform distribution of transport path lengths and to the unequal flow along these paths; and convective diffusion is due to the presence of a velocity profile which causes a progressive separation between the fastermoving molecules near the airway centerline and the slower-moving molecules near the airway wall.
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From page 342... ...
alveolar partial pressure, Pxb is the blood gas tension, and Cx and Car are the molar concentrations in blood of species X in physically dissolved and chemically combined forms, respectively. To solve this equation, it is necessary to provide relationships between Cx, Cxr, and PXb.
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From page 343... ...
Carbon monoxide has a low aqueous solubility, but its reactive capacitance with hemoglobin is so large that the value of Bo is only 0.02, implying diffusion-limited uptake. Moreover, because of its strong affinity for hemoglobin, CO gas tension in pulmonary capillary blood is much below its alveolar partial pressure.
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- MXj (28) k Net Input Rate by Uptake Gas Flow Rate where V is the time-dependent tracheal flow; Vj is compartment volume; PXj is species partial pressure; Ok is the fraction of tracheal flow from compartment j to an adjacent compartment k; and Mx is uptake rate through the walls of compartmentj.
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From page 345... ...
In addition, the analysis was restricted to acute exposure where recirculation of pollutant to afferent capillary blood is negligible. Under these conditions, a steady-state material balance around capillary compartment j results in the following relationship between uptake rate and airway partial pressure: Mxj = KmjSjp~j (29)
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From page 346... ...
indicate that accumulated uptake is negligible when axb < 10-9 kgmol/m3/Pa, but when ax, > 10-s, absorption into the conducting airways is essentially 100 percent. Distributed-Parameter Upper Airway Models The upper and lower respiratory tracts have often been modeled separately as distributed-parameter models, but rarely to
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There are at least two reasons why this separation is natural. First, the upper airways are adapted to perform some functions not shared with the lower respiratory tract: filtering out particulate material and warming and moistening inspired air before it reaches the lower airways.
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to correlate SO2 absorption data obtained in the upper airways. They alternatively applied equation 34 to the nose and to the mouth by using separate values of KmS.
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Each airway zone was bounded by a tissue layer coated with an inner liquid film of either mucus in conducting zones or surfactant in respiratory zones. The principal assumptions in specifying absorption between the gas, liquid, and tissue layers were that the diffusion resistance of the gas boundary layer within the airway lumen is negligible; transport through the liquid film occurs by steadystate diffusion; and chemical reaction occurs exclusively at the liquid/tissue interface, where pollutant is instantaneously consumed.
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In particular, the mucous layer was modeled as a stagnant barrier into which O3 diffuses from the airway lumen and reactive biological substrates simultaneously diffuse from underlying tissue. At the reaction plane where the O3 and substrates meet, they are instantaneously consumed by chemical reaction.
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91.) trom conducting airways to respiratory airspaces, the total mass of O3 absorbed into the respiratory zone was found to be five times that absorbed into conducting airways.
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To analyze total uptake of pollutants and to predict dose distribution, mathematical models that account for ventilation and perfusion limitations, including their regional distribution, should be developed and validated. Experiments In this section, experimental methods that can be used to validate proposed transport models and estimate relevant thermodynamic, diffusion, and reaction parameters are discussed.
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determined local mass transfer coefficients in an adult upper airway cast supplied with a fixed inspiratory airflow of 12 liters/mint The distribution in km values from the external nares to the larynx was highly nonuniform, with the largest value occurring at the entrance of the nasopharynx where there is an abrupt convergence of airflow from the turbinates. Neither Nuckols nor Hannah and Scherer attempted to simulate absorption processes within the airway wall.
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By analyzing such data in conjunction with a suitable mathematical model such as equation 24, global values of mass transfer coefficients could be estimated and the relative importance of perfusion and ventilation limitations could be determined. It might also be desirable to quantify reaction dynamics between pollutants and biological substrates by using isolated tissue samples.
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of a dog. O3 entered the upper airways at a steady airflow of 3.5 liters/min and at the concentration labeled on the curves.
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Figure 21. Effect of airflow on the absorption of various foreign gases along the nasotracheal path of the upper airways.
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In experiments where the lower airways of dogs were surgically isolated from the upper airways, penetration of O3 to the respiratory airspaces estimated as the ratio of expired-to-inspired partial pressures was 357 ~n3 from 0.15 to 0.20, depending on the mechanical ventilation rate and the inlet concentration (Yokoyama and Frank 1972~. And in free-breathing rabbits (figure 22)
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Using a consistent experimental protocol, total uptake of selected 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 noninvasive tests of pulmonary function.
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From page 359... ...
By using the fkj ventilation parameters already established from the nitrogen wash-out data, simulations of CO uptake data could be performed to estimate the parenchymal diffusion parameters, KmS. In humans as in animals, it is also possible to study uptake in the upper airways independent of the lower airways.
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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 focused on physicochemical problems, namely, absorption rates and internal concentration distributions of foreign gases.
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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)
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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.
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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.
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1984. Estimation of the rate of absorption of atmospheric pollutants in respiratory conducting airways by mass transfer theory, J
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1984. Sulfur dioxide and exercise: relationship between response and absorption in upper airways, Air Poll.
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1957. Relative importance of diffusion and chemical reaction rates in determining rate of exchange of gases in the human lung, with special reference to true diffusing capacity of pulmonary membrane and volume of blood in the lung capillaries, J
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