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Dosimetry Modeling of Inhalec! Toxic Reactive Gases JOHN H. OVERTON FREDERICK). MILLER U.S. Environmental Protection Agency Applications of Dosimetry Modeling / 368 Anatomical, Physiological, and Chemical Considerations / 368 Anatomical Models / 368 Liquid Lining of the Respiratory Tract / 369 Lung Tissue and Blood / 371 Physical and Chemical Factors Affecting Absorption of Reactive Gases / 372 Solubility / 372 Molecular Diffusion / 372 Convection in Respiratory Tract Fluids / 373 Chemical Reactions / 374 Dosimetry Modeling / 375 Upper Respiratory Tract and Total Respiratory Tract Models / 376 Lower Respiratory Tract Models / 376 Influence of Anatomical and Physiological Factors / 377 Influence of Physicochemical Factors / 380 Importance of Experimental Data / 382 Summary l 382 Summary of Research Recommendations / 383 Air Pollution, the Automobile, and Public Health. (3 1988 by the Health Effects Institute. National Academy Press, Washington, D.C. Copyright is not claimed for this chapter, which is in the public domain. Disclaimer: This document has been reviewed in accordance with U.S. Environ- mental Protection Agency policy and approved for publication. Mention of trade names or commercial products does not constitute endorsement or recommendation for use. 367
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368 Dosimetry Modeling of Inhaled Toxic Reactive Gases Applications of Dosimetry Modeling This chapter reviews modeling of the ab- sorption of inhaled toxic reactive gases in the respiratory tracts of humans and ani- mals. It focuses on our knowledge and understanding of the processes and factors influencing absorption and on mathemati- cal dosimetry models and their use. The processes and factors considered are mainly those associated with the fluids and tissues of the respiratory tract. (A discussion of transport in airway lumens and air spaces is presented by Ultman in this volume. ) Con- sideration of reactive gases such as carbon monoxide, which are transferred out of the respiratory tract and require a consideration of processes and factors outside this region, are beyond the scope of the review. Mathematical dosimetry models mod- els that predict the uptake and distribution of absorbed gases in the respiratory tract- facilitate the integration of our knowledge and understanding of the physical, chemi- cal, and biological processes involved in ab- sorption. For example, the gathering of in- formation to develop models identifies areas where information is missing; performing sensitivity studies with models can be used to determine the more important parameters and processes as well as to indicate those needing further research; and comparing pre- dicted results to experimental data can be used to focus attention on needed theoretical and experimental research. Furthermore, since knowledge of dose is an essential component of quantitative risk assessment, dosimetry modeling has an im- portant role in the extrapolation of animal toxicologic results to humans. Dosimetry models can be used to estimate exposure levels that result in the same dose in dif- ferent animals of the same or different species for use in comparing toxicologic effects, as well as to assist in experimental design. Predicted regional or local doses can be correlated with observed health ef- fects, thereby allowing the prediction of effects in situations for which experiments are not feasible. Ultimately, in order to assess human health effects, models can be used to establish general principles and guidelines for the evaluation and integra- tion of the results of clinical, epidemio- logic, and animal studies. The review begins with a discussion of the physiological and chemical factors that must be quantified for dosimetry model- ing. These factors are considered relative to anatomical models and to the characteris- tics of the liquid lining of the upper and lower respiratory tracts and their associated blood and tissue. Physicochemical proces- ses such as solubility, chemical reactions, molecular diffusion, and convective trans- port are explained, and needs relative to dosimetry modeling are outlined. Several dosimetry models are surveyed and a dis- cussion of their major features and assump- tions is provided. Examples of uses of the models are illustrated, and the importance of and need for experimental data to be used in the dosimetry models are discussed. Anatomical, Physiological, and Chemical Considerations This section discusses some of the biologi- cal aspects of the mammalian respiratory tract that must be understood and quanti- fied in order to develop dosimetry models. Anatomical models are discussed as well as the physical, chemical, and structural char- acteristics of respiratory tract fluids and tissues. For more information about res- piratory tract structure, see the chapters by Schlesinger and by Ultman, this vol- ume. Anatomical Models Knowledge of the dimensions of the lumen of the airways and of the air spaces of an animal's respiratory tract are important for a number of reasons. For example, unequal path lengths to equivalent morphological areas in lungs may result in significantly different doses; incorrect surface areas can result in erroneous predictions of uptake; and an incorrect tracheobronchial volume would result in erroneous estimates of the quantity of gas delivered by convection to the pulmonary region.
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Overton and Miller 369 Respiratory tract dimensions useful to dosimetry modeling are an important facet of anatomical models. One type of model organizes the many branching airways of the lower respiratory tract (airways distal to and including the trachea) into sequential segments (also called generations, and other groupings have been used as well). Associated with each segment are idealized airways, in that all model airways of a given sequential segment are assumed to be the same size. Each model airway has the average length and diameter of all or some of the actual or real airways associated with the segment. The pulmonary region can be characterized by specifying the volume and surface area of the average alveoli as well as the number of alveoli per airway. Probably the best known lower-respira- tory-tract anatomical model (LRT model) is the one developed by Weibel (1963) for humans. The branching structure of the airways is assumed to be dichotomous and there is only one unique model path from the trachea to a given terminal unit (alve- olar sac). However, all of the model paths (A 8.4 million) are equivalent, requiring that only one path be considered for dosim- etry modeling. More recently, anatomical models have been developed that take into account some of the actual variability in different paths. The models of Yeh and Schum (1980) for human lungs and of Yeh et al. (1979) for rat lungs are examples. In addition to a model for the whole lunges) of each species, these investigators also reported lobar models. With more detailed anatomical models such as these, the effects of intralung differences on predicted uptake and on dose at equiv- alent but differently located morphological sites can be investigated. Most LRT models are not cased on morphometric measurements of lung vol- umes during normal breathing (see, for example, Weibel 1963; Yeh et al. 1979; Yeh and Schum 1980~. To use such data for dosimetry modeling, the data should be modified to better represent the lung size for the breathing conditions being consid- ered. Procedures for modifying reported lung dimensions to those experienced dur- ing a breathing cycle are needed. Upper respiratory tract (airways proxi- mal to the trachea) dimensions also have been reported in terms of sequential seg- ments along the path of air flow. Dimen- sions of the upper respiratory tracts of several animals are given by Schreider and Raabe (1981b). Measurements of cross-sec- tional areas and perimeters along the air path allow for estimating local volumes, surface areas, and other parameters, such as the gas-phase mass transfer coefficient, nec- essary for dosimetry modeling. By con- trast, only the length, volume, and surface area of a species upper respiratory tract can be reported (see, for example, Swenberg et al. 1983~. Other models (see, for example, Kliment 1973; . Schreider and Hutchens 1980) have more than one segment but report only the lengths and volumes. With surface areas for each segment, even these simplistic upper-respiratory tract anatomi- cal models (URT models) could prove use- ful in dosimetry modeling. Liquid Lining of the Respiratory Tract Upper Respiratory Tract and Tracheabron- chial Region. The epithelium of the upper respiratory tract of mammals is covered by a continuous two-layer liquid (Morgan et al. 1984) of viscous mucus (the epiphase) overlying a serous, or periciliary, fluid (the hypophase) in which the cilia move in a coordinated fashion (Lucas and Douglas 1934~. For more information on the major functions of the mucous/serous/cilia sys- tem, see Kaliner et al. (1984~. In the tracheobronchial region, the liquid lining is similar in structure to that of the upper respiratory tract (see figure 1~. Pro- ceeding distally, from a thickness of 10 to 15 ,um in the trachea, the mucous layer decreases in thickness to where, in the smallest bronchioles of healthy animals, there is no mucus (Gil and Weibel 1971~. However, where there is mucus, it may not form a continuous layer. The pericil- iary layer is about as thick as the cilia are long, 4 to 6 mm, depending on location. Whether or not this layer is thinner in the regions not occupied by groups of ciliated cells apparently is not discussed in the literature.
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370 Dosimetry Modeling of Inhaled Toxic Reactive Gases BC GC NCC i , ,.,, CC ] L~-} Hypophase t Figure 1. Diagram of the airway epithelium. Lumi- nal or superficial cells include ciliated (CC), goblet or mucous (GC), conciliated serous (NCC), and brush (BrC); a basal cell (BC) is also represented. The epiphase or mucous layer is depicted as discontinuous, being made up of flakes, as it is viewed by some researchers. The hypophase is composed of a low- viscous periciliary fluid in which cilia beat or move in such a way as to propel mucus toward the glottis. (Adapted with permission fromJeffery and Reid 1977, p. 198, by courtesy of Marcel Dekker, Inc.) There are two basic concepts as to the extent to which mucus covers the pericil- iary layer. Some researchers see the mucus forming a continuous blanket (Luchtel 1978; Kaliner et al. 1984~; whereas others view the mucous layer as being made up of discrete flakes and droplets (figure 1; see Jeffery and Reid 1977; van As 1977~. In either case, reported values for mucous thickness suggest large thickness variations in airways of the same generation as well as in a given airway. Thus, there could be selective locations in airways of the same generation that are at different risk from exposure to inhaled gases. From the view- point of dosimetry modeling and predict- ing the quantities of absorbed gas by a given compartment (for example, mucous layer, periciliary layer, epithelial layer), the thickness distribution of mucus, as a func- tion of location, is of considerable impor- tance. Going from the tracheobronchial region to the pulmonary region, the liquid lining probably is continuous with the thinner lining of the pulmonary region; however, . . . . . . . no quantitative c escrlptlon ot the transition was found in the literature. Since this tran . . . . ~ . . SltlOn region IS a p ace ot maximum tissue damage from gases such as nitrogen diox- ide (NO2) and ozone (03), an understand- ing of lining thickness here could be impor . . . . . tent in quantifying centrlaclnar upta ~e. Most of what is known about the chem nqing ~ical constituents of the tracheobronchial region liquid lining comes from ravage data from patients with pulmonary diseases such as asthma, cystic fibrosis, and chronic bronchitis. Only recently have data been 7 Tissue obtained from patients without lung prob lems (see, for example, Woodward et al. 1982~. However, techniques are still needed to collect the periciliary fluid since most of the present approaches recover the mucus of the epiphase (Boat and Cheng 1980~. Lavage fluid is separated into two compo nents, the insoluble constituents (gel por tion) and the soluble materials (sol por tlon) . w nether or not this latter watery substance is chemically similar to the peri ciliary fluid is not known. The gel portion, often considered equivalent to mucus, has four major constituents: glycoprotein (2-3 percent), lipids (0.~0. 5 percent), proteins (0.1-0.5 percent), and water (95 percent) (Lopez-Vidriero and Reid 1980~. However, disease may modify proportions of the constituents. Pulmonary Region. The pulmonary epi thelium is considered to be covered, at least in part, by an acellular lining composed of a serous fluid, possibly serum transudate, from 0.01 to as much as several microns thick, but on the average about 4 percent of the air-to-blood distance (Weibel 1973~. Covering this fluid and separating it from air is a 0.002- to 0.01-mm-thick surface active monomolecular film called surfac tant (Clements and Tierney 1965~. Hills (1982) has suggested the possibility of a discontinuous pulmonary liquid lining, the pulmonary surfaces being largely dry. Obviously, the uncertainty in the physical nature of the pulmonary acellular lining presents problems to dosimetry modeling and to the interpretation of toxic effects that are similar to problems posed by the uncer tainty in the nature of the tracheobronchial . . . region . ~lqulc . . .lnlng. Information on the chemical composi tion of the pulmonary region liquid lining comes mainly from analysis of the insolu ble fraction of pulmonary ravage material. This fraction, corresponding to the mono layer surfactant material, is 8(~90 percent
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Overton and Miller lipid, 1(~20 percent protein, and 1-2 per- cent carbohydrates (Sahu and Lynn 1977~. The unsaturated fatty acid composition of the insoluble part of pulmonary ravage fluid and their estimated effective concentrations are reported by Miller et al. (1985~. The serous fluid, because of its greater thick- ness, probably has more influence on gas absorption than the thinner surfactant layer; however, the fluid is seldom ana- lyzed. Further characterization (chemical and physical) of the thicker serous layer is needed. Lung Tissue and Blood Most of the epithelium of the upper respi- ratory tract is pseudostratified and colum- nar. Luminal cell types are goblet, ciliated, and nonciliated, with their relative abun- dance dependent on location Jeffery and Reid 1977; Mygrind et al. 1982~. Columnar cells (ciliated and unciliated) are covered by 300 to 400 microvilli up to 2 ,um long, helping to increase exchange processes across the epithelium as well as preventing dryness (Mygrind et al. 1982~. In the tracheobronchial region, cells are either ciliated or nonciliated. Nonciliated cells can be further classified as secretory (serous, Clara, goblet) or nonsecretory (brush, intermediate). The relative num- bers and types of cells depend on location in the respiratory tract as well as on species (see, for example, Castleman et al. 1975~. Figure 1 illustrates some of these cells and their relationship to the liquid lining. Respiratory bronchioles, if present, are transitional airways, and their cellular makeup reflects this. The cells change in nature proceeding distally from the termi- nal bronchioles. For example, in monkeys, the cells are initially cuboidal and are re- placed toward the distal end by squamous- type cells similar to alveolar type I cells (see, for example, Castleman et al. 1975~. In addition, the respiratory bronchioles have outpockets of alveoli whose number increases distally from the bronchioles. Tissue of the alveolar septum (figure 2) is, for the most part, a three-layered struc- ture composed of the alveolar epithelium, an intermediate interstitium, and the capil 371 lary endothelium. The thickness of this structure is from 0.4 ,um to less than 0.8 ,um, depending on location and species. The capillary endothelium is made up of simple squamous cells that are thin and cover large areas. Alveolar epithelium is composed mainly of type I and type II cells. Type I cells are similar to endothelial cells, with broad thin cytoplasmic sheets extend- ing from a bulkier nuclear region. This thin (0.1- to 0.2-,um thick) cell facilitates gas exchange (Burr) 1985) since it covers from 90 to 97 percent of the alveolar surface area. Type II cells are cuboidal and are believed to be the source of surfactant (Burr) 1985~. Capillaries are an integral part of the pulmonary alveolar structure (figure 2~. Blood flowing through the capillaries is composed of plasma and blood cells in about equal proportion. Gases not depleted by reactions in the air/blood barrier may Figure 2. Electron micrograph of interalveolar septa, including alveolar capillaries (C) containing erythrocytes (EC), endothelial cells and nuclei (EN and NEN, respectively), type I and II epithelial cells (EP1 and EPP, respectively), the interstitial space (IN), and the alveolar air space (A). (Adapted with permission from Gehr et al. 1978, and Elsevier Science Publishers. )
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372 Dosimetry Modeling of Inhaled Toxic Reactive Gases penetrate to capillary blood and react fur- ther with blood components. The chemical makeup of tissue and blood is not much different than that of the liquid lining mainly water with traces of glyco- proteins, lipids, proteins, as well as smaller molecules. However, the relative amounts or concentrations of the molecular compo- nents of the major constituents can be very different (Miller et al. 1985~. Physical and Chemical Factors Affecting Absorption of Reactive Gases In general, the absorption of gases is af- fected by diffusion, convection, and, if relevant, chemical reactions in the gas phase (lumen and air spaces) as well as by solubility, diffusion, convection, and chem- ical reactions in the liquids and tissues of the respiratory tract. In this section, the concepts and nature of solubility, diffusion, convection, and chemical reactions are dis- cussed as they apply to dosimetry model- ing. (For a discussion of gaseous transport in the lumen of the airways, see Ultman, this volume.) Solubility Solubility refers to the ability of a medium to absorb a gas. There are many different definitions for solubility, including Bun- sen's, Kuenen's, Ostwald's, and Henry's laws (Clever and Battino 1975~. In equilib- rium conditions, these definitions relate quantities of a gas in the gas phase to quantities of the gas in a liquid. For dosim- etry modeling, one of the most convenient definitions of solubility is Henry's law, expressed as Cg = HE where Cg and Cal are, respectively, the gas- and liquid-phase molar concentrations of the absorbed gas, and H is Henry's law constant for this particular formulation. This law only ap- plies to the free or uncombined form of a trace gas in solution and can be used to quantify the concentration of the molecular form of the trace gas in a liquid, even if the absorbed gas is involved in chemical reac tions. The constant is a function of temper- ature and the molecular properties of the liquid and the gas; however, for constant temperature and the ranges of ambient con- centrations of trace gases, the coefficient H can be considered constant. Henry's law constants have been deter- mined for many gases in water (see, for example, Altman and Dittmer 1971; Na- tional Research Council 1977~. Often these values are used as approximations for in vivo values. Altman and Dittmer (1971) give data on Henry's law constants for a few gases, such as oxygen (02), carbon dioxide (CO2), and NO2, in water and in several biological fluids and tissues. In gen- eral, there is not much variation in the constant for a given gas among the various substances represented. For most cases, the use of the water value would seem justifi- able. Although incomplete, the data sug- gest that the value of Henry's law constant is not influenced much by different biolog- ical tissues and liquids, indicating that a known value for one tissue or liquid may be a good approximation for missing val- ues. Henry's law can be extended to trace gases in equilibrium in two different media with a common interface. In this situation, the ratio of the concentrations in the two media is the ratio of the Henry's law con- stant of the two gases. This ratio is called the distribution coefficient or the partition coefficient. Altman and Dittmer (1971) give a table of partition coefficients for several biologi- cal tissues and fluids. The values are close to one (to within 15 percent), suggesting that animal fluids and tissues are very similar with respect to Henry's law constant. 7 Molecular Diffusion Molecular diffusion is a result of the ran- dom motions of molecules, an action that redistributes molecules so that there is a net flow from regions of high concentration to regions of lower concentration (Danck- werts 1970). The process often is described in terms of the diffusional flux, which is the net rate of transfer (due to random motion) of mass or molecules across a plane perpen
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Overton and Miller 373 dicular to a given direction. Mathemati- ~'' cally, the flux is expressed as F = -D (dc/dx), where dc/dx is the concentration gradient along the given direction; and F is the diffusional flux (Danckwerts 1970~. The formula is often referred to as Fick's law and can be used to describe diffusion in gases, liquids, and tissues. D is the molec ular diffusion coefficient and is defined by the above equation; its units are (length)2/ time and its value depends on the properties of the molecule and the medium. According to Sherwood et al. (1975), the diffusion of small molecules such as O2 and CO2 in solutions of biological proteins is approximately the same as in polymer so- lutions; however, diffusion in polymers does not follow a simple pattern. Never- theless, the diffusion coefficients of small molecules in dilute polymer solutions hav- ing constituents similar to those of biolog- ical fluids and tissues are probably similar to, but smaller than, the value for diffusion in water. These conclusions most likely apply for small molecules other than O2 and CO2, such as O3, NO2, and formalde- hyde (HCHO). Unfortunately, for the larger biological molecules, diffusion coef- ficients may be difficult to estimate from water values, and measurements in biolog- ical substances may be necessary. The molecular diffusion coefficients of a few gases such as O2 and CO2 in biological fluids and tissues have been measured. Val- ues are generally less than in water. For example, the values for O2 in water, ox serum, frog muscle, dog connective tissue, and rat lung tissue are, respectively, 3 x 0-5, 1.7 x 10-5, 1.2 x 10-5, 0.97 x 10-5, and 2.3 x 10-5 cm2/sec at 37°C (Altman and Dittmer 1971~. Convection in Respiratory Tract Fluids There are two lung fluids in which convec- tion may play a role in the absorption of reactive gases the liquid lining of the up- per respiratory tract and the tracheobron- chial region, and capillary blood. Both fluids are in motion, and absorption may be enhanced by the removal of absorbed gases from a location or the replenishing of bio- chemical reactants. in modeling, to account for convection, the flow rates of the fluids are needed. In some cases, mucous flow rates in the upper respiratory tract (see, for example, Morgan et al. 1984) and airways of the tracheobron- chial region have been measured (see, for example, Iravani and van As 1972~. In addition, rates in all airways have been estimated on the basis of clearance data from selected airways, anatomical data, and other assumptions (see, for example, van As 1977; Miller et al. 1978~. For example, Velasquez and Morrow (1984) applied ki- netic equations to data on particle retention in five airway zones (based on airway di- ameter) of guinea pigs to estimate transport rates in each airway generation. The calcu- lated mucociliary (particle) rates ranged from 0.001 mm/min in the distal bron- chioles to approximately 8 mm/min in the trachea. However, mucociliary rates are not necessarily the same as the liquid lining flow rates, and further data or assumptions must be used to estimate convection veloc . . tles. Pulmonary capillary blood flows have been measured by Horimoto et al. (1981), among others, as well as theoretically cal- culated by Zhuang et al. (1983~. However, capillary blood flow measurements for the upper respiratory tract and the tracheo- bronchial region were not found in the literature; no doubt, reasonable estimates could be obtained if needed. On the other hand, because the air/blood barrier in these regions is much thicker than it is in the pulmonary region, reactive gases (within the scope of this chapter) will not reach the capillaries proximal to the pulmonary region. Heck and coworkers (1983) demon- strated that either HCHO or, most proba- bly, its reaction products were transferred to tissues and fluids outside the upper res- piratory tract. Also, NO2 products are known to be transferred out of the lung (Postlethwait and Mustafa 1981~. Presum- ably, capillary blood flow is a major factor in the transfer, suggesting that in develop- ing dosimetry models the effect on gas absorption by the removal of reactants and products from the lung by blood must be considered relative to its effect on absorp- tion.
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374 Dosimetry Modeling of Inhaled Toxic Reactive Gases Chemical Reactions Chemical reactions occur as a result of the collision of molecules whereby the interac- tion of the colliding molecules (reactants) results in one or more different molecules (products). For modeling purposes, the and fluids. rates ot reaction or the rates ot change ot concentrations (for example, moles per liter per second) are important because the rates are the means whereby the loss and gain of chemical species are quantified. In general, rates are a complicated function of the local concentration of each of the reactants and products involved. Theoretically, all of the chemical species involved and the reaction rate constants are needed to characterize a reacting system for modeling purposes. In practice, however, complete information is not always avail- able; even if reaction rates are known, the products or the product formation rates, or both, may not have been measured. This poses no problem in modeling systems of reacting compounds if the unknown prod- ucts do not react significantly with the known species. Even if this is not the case, approximations are often possible that will allow the modeling of absorption of the reacting gases. Much of the results of mathematical modeling of the absorption and chemical reaction of gases in thin films, found in chemical engineering and mass transfer books (see, for example, Astarita 1967; Danckwerts 1970), are applicable to the thin layers of the liquid lining, tissues, and capillaries of the lung. The film theory models are most relevant since turbulence is not expected to be an important transport mechanism. Disturbances due to cilia and blood motion may prove the exception; however, these processes can be taken into account. The main constituent of lung tissue and fluids is water, 85-95 percent; thus, the chemistry of absorbed gases in water is of interest. Many toxic gases react with water, affecting the absorption rate as well as creating products that may, in turn, react with the absorbed gases and the biological constituents. For example, O3, NO2, sul- fur dioxide (SO2), ammonia (NH3), and CO2 react with water as well as interact in water (see Durham et al. 1981, 1984~. These reactions lead to the formation of sulfate, bisulfite, nitrite, and nitrate mole- cules, and have the potential for changing pH. Thus, water reactions could have an indirect or direct adverse effect on tissue With the introduction of biochemical constituents, the reacting system becomes more complex. However, depending on conditions, some of the reactions will be more important than others. If necessary, the important reactions can be determined by chemical kinetic modeling to gain infor- mation that will allow simplification of the system for use in dosimetry modeling by keeping only the important reactions. HCHO, NO2, and O3 are toxic reactive gases derived from mobile sources. Their reactions with lung constituents are briefly discussed as examples of the types of reac- tions that should be considered in formu- lating dosimetry models. Formaldehyde. HCHO is a by-product of normal body metabolism, and in small , . . . . qUantltleS IS not toxic. t IS extreme y reac- tive, even with itself, and the unhydrated form reacts rapidly with water (Gerberich et al. 1980; National Research Council 1981; Madestau 1982). It is highly reactive with amines and reacts with proteins, amino acids, nucleic acid, and histones as well (National Research Council 1981~. HCHO has also been found to damage DNA (Ballenger 1984) implying that DNA is directly attacked by HCHO or reacts with HCHO reaction products. The reactive compounds are thought to bind to specific sites on single-stranded DNA. HCHO does not react with double- stranded DNA (Swenberg et al. 1983~. A two-step mechanism has been suggested tor tne reaction of HCHO with amino groups, such as those that compose pro- teins and nucleic acid. The first step is fast and reversible; the second is irreversible, forming a stable product (Swenberg et al. 1983~. Nitrogen Dioxide. NO2, as well as other oxides of nitrogen such as NO, is toxic.
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Overton and Miller 375 The reactions of NO2 with water lead to nitrous acid (HNO2), which may form nitrosamines that are carcinogenic; also, NO2 reacts with unsaturated fatty acids to form radicals leading to the autooxidation of unsaturated fatty acids and to HNO2 (Pryor 1981~. According to Postlethwait and Mustafa (1981), over 70 percent of the NO2 absorbed by a ventilated perfused rat lung was converted to nitrite (NO2-~. They also concluded that nonwater sub- stances (that is, biological constituents) played the major role in the conversion. Ozone. According to Menzel (1976), O3 is the most toxic of the oxidizing air pol- lutants, its toxic effects being a result of its oxidative properties. Although it reacts with almost all classes of biological sub- stances, biochemical, physiological, and morphological evidence indicates that cellu- lar membranes are the site of toxicity (Men- zel 1984), suggesting lipids as a major target. Olefins are particularly sensitive to 03, the Criegee mechanism being the accepted mechanism of reaction (Menzel 1976; Pryor et al. 1983~. In this process, O3 attacks the carbon double bond in the unsaturated fatty acid. The generation of free radicals also plays a role in toxicity; however, the non- radical reaction is considered dominant for most unsaturated fatty acids (Pryor et al. 1983~. Although vitamin E is known to protect unsaturated fatty acids as well as entire animals against some of the effects of O3 by scavenging radicals, the vitamin does not interfere with the nonradical Crie- gee process (Pryor et al. 1983~. Rate constants for the reaction of O3 with some biological unsaturated fatty ac- ids are known, for example, in carbon tetrachloride (Razumovskii and Zaikov 1972~; however, in viva rate constants in biological substances are for the most part lacking. For example, the extent to which O3 is able to penetrate membranes and react with unsaturated fatty acids in lipids is unknown (Pryor et al. 1983~. According to Pryor and coworkers (1983), O3 also reacts with amino acids and proteins. In water the only amino acids found to react with O3 are, in order of decreasing reactivity: cysteine, tryptophan or methionine, tyrosine, hystidine, cystine, and phenylalanine. Although the mecha- n~sms tor damage to proteins are not well known, there is evidence for a radical path and, possibly, for a nonradical Criegee process. The reactions of O3 with sugars and nucleic acids have not been studied; however, sugar reactions are expected to be slow. Dosimetry Modeling By dosimetry models we mean mathemat- ical or experimental models that predict, simulate, or are used to explain the quanti- tative uptake or absorption of gases in specific regions or locations. The formula- tion of such a model for inhaled gases requires information on the physical, bio- logical, and chemical properties of the res- piratory tract, as discussed previously, as well as an understanding of the nature of gas transport in the lumen and air spaces (as discussed by Ultman, this volume). The processes and features modeled are very complex, and essential information is often missing. By its very nature, a model is a simplified representation of a real process or object; complex processes and geome- tries are reduced to their essences with some aspects omitted and others retained. Using a model to explore the effects of assumptions, combined with comparisons of simulation results or predictions with experimental data leads to more useful models and, more important, to a better understanding of the chemical, physical, and biological processes modeled. A survey of mathematical dosimetry models and their basic features is presented. This is followed by a discussion of results obtained by using models to predict the uptake and distribution of toxic gases in the respiratory tract. Emphasis is placed on examples that illustrate the sensitivity of predicted results to uncertainties in physical, chemical, and biological factors. Finally, the relationship between dosimetry modeling and experi- mental data is considered. Dosimetry models constructed from experimental equipment are considered by Ultman (this volume).
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376 Dosimetry Modeling of Inhaled Toxic Reactive Gases Upper Respiratory Tract and Total Respiratory Tract Models We are not aware of any URT or total respiratory tract dosimetry model that has been developed to predict the absorption of toxic reactive gases. The two URT models discussed below were developed to analyze experimental data and to estimate parame- ters, although they could be used with modifications for predicting dose or up- take. Chang and coworkers (1983) devised a very simple dosimetry model that they used to better understand species differ- ences in nasal toxicity due to HCHO. This model, for all its simplicity, embodies most of the principles of the most complex do- simetry models, including the use of spe- cies-defining characteristics such as ventila- tory and anatomical parameters. The authors defined the "dose" available for deposition on the nasal surface as the HCHO concentration times the minute volume divided by the nasal cavity surface area. Their "dose" is probably a good . . . estimate since t ne upper respiratory tract absorbs most of the HCHO. Chang and coworkers (1983) concluded that the use of their "dose" helped to understand species differences in nasal toxicity. Aharonson and coworkers (1974) devel- oped a model based on the assumptions of mass balance, approximate steady state, and that the flux of gas to the air/liquid lining interface is proportional to the trace gas-phase partial pressure. They applied the model data on the uptake of acetone, ether, 03, and SO2 in the upper respiratory tract of dogs to estimate the dependence of the effective mass transfer coefficient on flow rates. They concluded that the transfer co- efficients of the four gases increased with increasing airflow rate. Recommendation 1. In order to better understand toxic effects in the upper respi- ratory tract, dosimetry models for this re- gion are needed. These models should be designed so that they augment present LRT models in order to relate lower respiratory tract predictions to ambient concentrations. Simple empirical models, similar to that of Aharonson et al. (1974), may be sufficient if toxic effects only in the lower respiratory ~ . tract are ot interest. Lower Respiratory Tract Models In the model of Mc~ilton and coworkers (1972; see also Morgan and Frank 1977; National Research Council 1977), absorp- tion and transport in the lumen and air spaces are based on a one-dimensional dif- ferential equation that accounts for convec- tion, molecular diffusion, and the loss of gas by wall absorption. On the assumption that transfer is controlled by the liquid lining, the flux of gas to the air/liquid lining interface is defined in terms of a liquid- lining mass transfer coefficient. Chemical reactions are not considered in the liquid lining, and the transfer coefficient is based on the physical properties of O3 and the lining (Henry's law constant, molecular dif- fusion coefficient, and lining thickness) and the requirement that the O3 concentration at the liquid lining/tissue interface be zero. This latter requirement is based on the assumption that O3 reacts instantaneously with the tissue constituents and cannot penetrate to any sig- nificant depth in the tissue compartment (National Research Council 1977~. The model is used in conjunction with the airway model of Weibel (1963) to sim- ulate the uptake of O3 and SO2 in humans. Weibel's anatomical model defines the ra- dii, length, surface areas, and volumes of the lumen and air spaces of each of its 24 generations. A sinusoidal breathing pattern is used, but model lung size is assumed to be constant during "breathing". The liquid lining thickness depends on the generation: "10 ,um in the upper generations, 3-5 ,um in the alveolar ducts, and 0.3 ,um in the alveoli" (National Research Council 1977~. The differential equation developed to take into account the above factors is solved using finite difference methods. The local dose (mass per unit area gained by the airway surface) is computed for each generation. One of the major deficiencies in the model developed by McJilton and co- workers (1972) is the lack of chemical re- actions in the liquid lining. Miller (1977) and, later, Miller and coworkers (1978) developed an O3 dosimetry model to ad- dress this limitation. The formulation of
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Overton and Miller 377 this model is similar to McTilton's model with respect to how lumen and air space transport is modeled and in the use of anatomical models, mass transfer coeff~- cients, and distally decreasing liquid lining thickness. However, differences do exist. For example, the model of Miller and co- workers uses an axial dispersion coefficient to account for air velocity inhomogeneities in place of axial molecular diffusion used by Mc~ilton and coworkers. Furthermore, no assumption is made as to whether the radial flux is limited by the liquid lining. Instead, a gas-phase mass transfer coefficient is cal- culated on the basis of an approximate radial O3 concentration profile and com- bined with the liquid-phase transfer coeffi- cient to obtain an overall mass transfer co- eff~cient. Although such enhancements make the model developed by Miller et al. (1978) more physiologically sophisticated than Mc- ~ilton's, the additions have a minor effect on simulation results. Nevertheless, such en- hancements are necessary to determine what processes and factors are important. Chemical reactions in the liquid lining are accounted for by assuming that the reaction rates of O3 with biochemical con- stituents are so fast that the reactions can be characterized by an "instantaneous reaction regime" similar to that discussed by Asta- rita (1967~. In order to model this descrip- tion, the production rates of biochemical reactants in each generation are required. These are estimated by assuming that the production rates decrease distally, by using tracheal mucous flow rate data, by using data on the surface area of each tracheo- bronchial generation, and by specifying the concentration of the reacting biochemical constituents and their stoichiometry of re- action with O3 (Miller 1977; Miller et al. 1978~. Mucous transport rates, such as those estimated by Velasquez and Morrow (1984), would have been helpful in model- ing the production of biochemical reactants throughout the tracheobronchial region. The concentration of O3 was assumed to be zero at the liquid/tissue interface for rea- sons similar to that given by Mc~ilton et al. (1972~. Thus, O3 did not penetrate into a tissue compartment beyond the liquid/ tissue interface- all tissue absorption took place at the interface. A second model of Miller and co- workers (1985) differs from the first, mainly in how chemical reactions are mod- eled and in the inclusion of tissue and pulmonary blood compartments where re- actions take place. The reactions of O3 with the biological constituents of the liquid lining, tissue, and blood compartments are assumed to be second order; however, the concentrations of the biological constitu- ents remain constant during the time of simulation (Miller et al. 1985~. Thus. the model uses pseudo t~rst-order reactions to account for chemical reactions. The major reactions considered in estimating an effec- tive first-order rate constant are those of O3 with the unsaturated fatty acids. The reac- tions of O3 with the amino acids and con- stituents other than unsaturated fatty acids are assumed relatively ineffective (as far as dosimetry is concerned) and are not included in the estimations of the net con- centration or of the effective rate con stant. Conceptually, in this latest model, trans- port in the gas phase is essentially the same as in the original (Miller et al. 1978) model. However, a recent modification of the model by Overton and Graham (1985) takes into account varying lung dimensions during the breathing cycle. This modifica- tion causes negligible changes in simulation results compared to results without the modification. Mockros et al. (1985) developed a math- ematical simulation model to investigate transport, absorption, and chemical reac- tions of toxic gases in the lower respiratory tract. This model and its predictions of lower respiratory tract uptake of O3 in humans and rabbits is similar to the instan- taneous reaction regime model and predic- tions of Miller et al. (1978~. Influence of Anatomical and Physiological Factors Figure 3 is an example of a simulation using the model of McJilton and associates (see Morgan and Frank 1977~; it illustrates the effect on predicted results of a modification to an anatomical model. The purpose of the simulations was to explore the effects on O3 uptake in humans with modified lung
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378 7 al Nit 5 A 4 CJ) ID 0 3 - ° 2 O 20% obstruction ~J Lobar Rbl Alv -Trachea" ~ ~ ~ , , , , , , , , , , , , , , , , , , , , , If, I 1 3 5 7 9 11 13 15 17 19 21 23 25 MODEL SEGMENTS Figure 3. Results of a simulation using the model of McJilton and associates. Plotted for two simulations are the simulated doses of O3 for humans versus model segment. The position of the trachea, lobar bronchi, respiratory bronchioles (rbl), and alveoli (alv) are indicated. The distance along the airpath from the trachea distally to the end of the airway model was divided into 25 segments, not necessarily corresponding to generations. Simulated "normal" O3 uptake is illustrated by the heavy black line. Shaded areas correspond to dose increases using the same anatomical model, except that the number of airways distal to the seventh Weibel generation (model segment 15) is reduced by 20 percent. (Adapted with permission from Morgan and Frank 1977, p. 183, by courtesy of Marcel Dekker, Inc.) geometry, such as might occur with dis- ease. To simulate a pulmonary mechanical defect, the number of airways distal to the seventh Weibel generation (segment 15) was reduced by 20 percent. The shaded areas correspond to the predicted doses that resulted from modifying the anatomical geometry. The effect of the "pulmonary mechanical defect" is to increase the tissue dose in segments distal to the obstruction or defect. The major increases in dose occur in the pulmonary segments, where for one respiratory bronchiole segment the increase is as much as 17 percent. Both simulation curves have the same general shape. Dose is relatively high in the trachea, decreasing distally to the bronchioles where, at the respiratory bronchioles, there is a sharp increase in dose followed by an even sharper decline in dose. Overton and Miller (1985) applied the Dosimetry Modeling of Inhaled Toxic Reactive Gases first-order chemical reaction model of Miller and coworkers (1985) to different anatomical models of laboratory animals. The results shown in figure 4a were ob- tained using the anatomical model of Kli- ment (1973) for a 160-g rat in which several sequential generations are grouped into nine zones. Figure 4b is a plot of Losers) versus generation using the airway model of Yeh et al. (1979) for a 330-g rat. The corresponding curves in both figures have the same basic shapes, the sharp peak in the first alveolated generation in figure 4b be- ing the major exception. However, accord- ing to Overton and Miller (1985), the ma- jor differences between results are due to the effect of ventilatory parameters on per- cent uptake and on the difference in pre- dicted percent uptake. For a constant minute volume the total uptake of the 160-g rat decreased from 93 percent at 80 breaths/min to only 87 percent at 140 breaths/mint On the other hand, at 80 breaths/min the uptake for the 330-g rat model was 74 percent (19 percentage points co of to 6, Net cn ~ ~ ~10-7 f\` - ~ ~ .E 10-8- ~ Z N r ~ 10~- ~ j Tissue |. TB 6-Pi | o 2 4 6 8 7ONF Net --__76\ _ If Tissue l · TB~. P-l [lllllllllllllllll _ o 4 8 12 16 20 GENERATION Figure 4. Use of the first-order chemical reaction regime dosimetry model of Miller and coworkers to explore the effects of anatomical models on predicted O3 dose in rat lungs is illustrated for generations of the tracheobronchial (TB) and pulmonary (P) regions; dose is normalized to tracheal concentration. (A) Using the anatomical model of Kliment (1973), for a 160-g rat, dose is plotted according to zone (that is, sequential generations of airways), for a tidal (intake) volume of 0.7 ml at 144 breaths/mint (B) Using the anatomical model of Yeh et al. (1979), for a 330-g rat, dose is plotted according to airway generation for a tidal volume of 1.84 ml at 105 breaths/mint Based on Overton and Miller (1985).
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Overton and Miller 379 less than for the 160-g rat), decreasing to 50 ~o-6 percent (37 percentage points less) at 140 breaths/mint Using allometric equations to scale the 330-g rat to 160 g did not reduce the Yeh et al. (1979) rat to a Kliment rat as far as percentage uptake and sensitivity to ventilatory parameters were concerned, a further indication of the importance of an atomic models in predicting uptake. · Recommendation 2. Anatomical mod- els should be developed for different sub- populations diseased, healthy, young, old, and so on of humans and laboratory animals. These models should accurately reflect dimensions associated with physio- logical conditions. The effects of various ventilatory param- eters on tissue dose are illustrated in figure 5. The simulations were performed using the first-order chemical reaction model of Miller et al. (1985) in conjunction with Weibel's (1963) anatomical model for the purpose of estimating the effects of exercise on tissue dose in humans. The four curves presented have the same general shape: Tissue dose increases distally to some gen- eration in the pulmonary region and then rapidly decreases. The location of the peak tissue dose depends on the ventilatory pa- rameters; the higher the tidal volume the more distal the peak. In addition, as the ventilatory parameters increase, so does the quantity of O3 absorbed in the pulmonary region. For the largest minute volume, the pulmonary absorption is 13.6 times as much as for the lowest minute volume (resting state) for the same length of time. On the other hand, for the same increase in ventilatory parameters, the tracheobronchial absorption increases only by a factor of 1.4. In another sensitivity study using a rat ana- tomical model, Overton and Miller (1985) showed that percent uptake was sensitive to tidal volume for a given minute volume. · Recommendation 3. Much of the ven- tilatory data on laboratory animals comes from anesthetized or restrained, quiet ani- mals. Data based on restrained or anesthe- tized animals should be shown to be suff~- cient for modeling purposes, or data that ~ ~ ~ ~ 1 1 1 1 1 1 1 1 1 1 ~ . 1 1 1 1 1 1 1 4;,' ,__-, ^ 03 1 ~\ '\1 Hi: By Al U) o oh Oh F 10-9 > 7 ,~ . o 10-7 - ._ E 10-8 ~3 '.~ '' . ~ 1 1 ~ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 l 0 4 8 12 16 20 AIRWAY GENERATION, z T rig L D ~1 Figure 5. Use of the f~rst-order chemical reaction regime dosimetry model of Miller and coworkers to explore the effects of changes in tidal volume ( VT) and breathing frequency ( f ) on predicted tissue dose of O3 in tracheobronchial (TB) and pulmonary (P) segments of human lungs is illustrated. Curve 1: VT = 500 ml; f = 15 breaths/mint Curve 2: VT = 1,000 ml; f = 15 breaths/mint Curve 3: VT = 1,750 ml; f = 20.3 breaths/mint Curve 4: VT = 2, 250 ml; f = 30 breaths/ min. Tissue dose has been normalized to the tracheal concentration; to obtain dose (mg/cm2-min-~), mul- tiply figure values by the tracheal concentration (mg/m3). (Adapted with permission from Miller et al. 1985, and Academic Press, Inc.) correspond to more realistic conditions should be obtained. There are several important gaps in our understanding of the liquid lining. There is not yet agreement as to whether the epi- phase (mucous layer) of the liquid lining in the tracheobronchial region is continuous. More important, the local values of epi- phase and hypophase thickness throughout the airways are needed. Likewise, the ex- tent and thickness of the pulmonary liquid . . . . . . . . . .~n~ng Is In c dispute. A region ot Importance
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380 Dosimetry Modeling of Inhaled Toxic Reactive Gases for NO2 and O3 iS the centriacinar region where the liquid lining makes a transition from the tracheobronchial region to the pul- monary region; little is known about how the thickness of the liquid lining changes in going from one region to another. Miller and coworkers (1985) illustrated the importance of liquid lining thickness on predicted tissue dose. Their study indicated that a wide variation of tissue doses can be predicted using the range of liquid lining thickness reported in the literature. For example, halving or doubling the liquid lining thickness in the trachea increased or decreased, respectively, the tracheal tissue dose by a factor of more than 10 relative to the control simulation results. Another ex- ample by Miller et al. (1985) illustrates the effect of liquid lining thickness in the first generation of respiratory bronchioles of humans; a decrease in thickness by a factor of 10 resulted in a threefold increase in respiratory bronchiole tissue dose. Recommendation 4. The thickness of the liquid lining of human and experimen- tal animal respiratory tracts should be ac- curately characterized. This includes deter- mining the thickness distribution of the mucous layer (epiphase) and of the under- lying hypophase as a function of airway and morphological location, and determin- ing how the liquid lining varies in thickness in going from the terminal bronchioles into and through the first alveolated duct. Influence of Physicochemical Factors The dosimetry models of Miller et al. (1978, 1985) were developed to simulate the uptake of O3. However, the models will simulate the uptake of any gas whose properties conform to the theoretical as- sumptions of the models. On the assump- tion that the properties of NO2 meet the criterion, Miller and coworkers (1982) used the original model (with the instantaneous reaction regime) in conjunction with Wei- bel's (1963) anatomical model to investigate the effects of Henry's law constant and of the mucous production rate on NO2 uptake in humans. At the time of the simulations, the value of Henry's law constant was uncer ~ - 10-5 3 1 I cd 10-6 E 10-7 o 1 o-8 Cal o z _ 1 0-s ~ I O ~ cn <~, 10 O ·Q ~ Cal to' E cn con 10-7 10-8 10 9 ~ A ~\ TRACHEAL NO2 CONC. 800 ,ug/m3 H = 9628 atmos./mole fraction O O Ko .5 Ko o 1 Ko A , . . . . . . . . . . . . . . . . . . . . to 2 4 6 8 10 12 14 16 18 20 22 AIRWAY GENERATION - _~: O___~_ it_ TRACHEAL NO2 CONC. 800 ,ug/m3 H = 9628 atmos./mole fraction O O Ko .5 Ko o 1 Kit B c I I, I, I, I I I I I, I I to 2 4 6 8 10 12 14 16 18 20 22 AIRWAY GENERATION Figure 6. The instantaneous reaction regime dosim- etry model of Miller and coworkers is used in con- junction with Weibel's (1963) anatomical model to simulate the effect of three mucous production rates (Ko) on the predicted absorption of 800 ,ug/m3 NO2 in human lungs. H (Henry's law constant) = 9,628 atm/mole fraction; O Ko (O), 0.5 Ko (/\), and 1 Ko (A) indicate simulations with no mucous production, one- half of standard, and standard mucous production rates, respectively. The tidal volume and respiration frequency are 500 ml and 15 breaths/min, respec- tively. (A) Predicted NO2 "lost by the lumen" or the net quantity NO2 absorbed per unit area per breath for each generation according to generation number. (B) Predicted tissue dose of NO2 (quantity of NO2 ab- sorbed per unit area of tissue per breath) by generation number. (Adapted with permission from Miller et al. 1982, and Elsevier Science Publishers.) fain, and the necessary quantitative data on the reactions of NO2 with biological constit- uents were missing (and still are). The results are shown in figures 6 and 7. Figures 6a and 6b are dose profiles for the net quantity of NO2 absorbed in each gen- eration and the tissue dose, respectively, for three different mucous production rates (Ko). Mucous production rates in each gen- eration are indicated by 0 (none), 0.5 (half of standard), and 1 (standard). As the mu- cous production rate increases, the amount
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Overton and Miller 381 '°-T o Z. o UJ ~ o D C] ~ t11.9 10-'- . ~ ~3 coin 10-5- ~ lo-6 - 8 - . n-s ___ /N TRACHEAL NO2 CONC. 800 /l9/m3 K=.5 Ko H (atmos./mole fraction) 0 4814 ~ 9628 ol 9256 mu ~I I I 1 1 1 ~I 1 1 1 1 ~I 1 1 1 1 ~I I ' 0 2 4 6 8 10 12 14 16 18 20 22 AIRWAY GENERATION Figure 7. The instantaneous reaction regime dosim- etry model of Miller and coworkers is used to simulate the effect of three values of Henry's law constant on the predicted absorption (tissue dose) of 800 ,ug/m3 NO2 in human lungs. Tissue dose is plotted according to airway generation, using a one-half standard (0.5 Ko) mucous production rate and Henry's law con- stants (atm/mole fraction) of 4,814 (O); 9,628 (/\); and 19,256 (A). The tidal volume and respiration fre- quency were 500 ml and 15 breaths/min, respectively. (Adapted with permission from Miller et al. 1982, and Elsevier Science Publishers.) of NO2 absorbed in each generation in- creases in the tracheobronchial region, but remains the same in the pulmonary region (figure 6a). However, the NO2 tissue dose (figure 6b) decreases in the tracheobron- chial region as the mucous production rate increases, but no change occurs in the pul- monary region where the net and tissue doses are essentially the same. The discontinuity of the tissue dose pro- files for the two largest mucous production rates is a result of the instantaneous reaction regime- either NO2 penetrates to the tis- sue or it does not. In the more recent model, in which first-order chemical reac- tions are assumed, a similiar sensitivity analysis was performed for O3 (Miller et al. 1985~. No discontinuities occurred; how- ever, depending on the mucous chemical rate constant, tissue dose in the trachea could be significantly less than the net dose. Otherwise, increasing the rate constant had the same qualitative effect on the net and tissue dose curves as increasing the mucous production rate did in the older model. Figures 6 and 7 illustrate the predicted results of a dosimetry model in which the . . . instantaneous reaction regime was usec to approximate chemical reactions. The first- order chemical reaction model of Miller et al. (1985) resulted in the predicted tissue doses illustrated in figures 4 and 5. Al- though there are similarities in the tissue dose profiles, there are also differences. For example, for O3, when using Weibel geom- etry and similar ventilatory parameters, the instantaneous reaction regime results in 60 percent uptake (Miller et al. 1978; Mockros et al. 1985~; whereas, the first-order reaction model predicts 89 percent uptake (Miller et al. 1985~. These differences in predicted up- take illustrate the importance of knowing the kinetic mechanisms, rate constants, reactant concentrations, and possibly biochemical re- actant production rates. Unfortunately, quantitative chemical in- formation is, for the most part, lacking; most information available is from studies of chemicals such as amino acids and ole- fins, which can be major biochemical con- stituents. If the reaction chemistry of a mol- ecule is known, then it is necessary to know if it reacts in the same way when it is part of a larger molecule. Such information will make data obtained in nonbiological situa- tions more useful to dosimetry modeling. Recommendation 5. The in vivo kinetic mechanisms of the important reactions of toxic gases with biological substances of the respiratory tract should be determined as well as kinetic reactions under nonbio- logical conditions that are applicable in viva. This would make the present data bases more useful. Recommendation 6. The local concen- trations of bioreactants in the respiratory tract should be identified for different hu- man and animal subpopulations (that is, according to age, gender, health condi- tions, exposure to toxic gases, and so on). The discussion on the values of Henry's law constant and diffusion coefficients in biological tissues and fluids indicates that known values for water or for biological substances may be good estimates for miss- ing data. Unfortunately, values for water or other fluids are not always available or they are highly uncertain. The following . . . . . sensitivity stuc y, using t he instantaneous reaction regime model of Miller and co- workers (1982), shows that a factor of two in the uncertainty of Henry's law constant
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382 Dosimetry Modeling of Inhaled Toxic Reactive Gases mav result in more than a factor of two , difference in predicted tissue dose. In figure 7, tissue doses of NO2 are plotted according to airway generations for three values of Henry's law constant. On the figure, 9,628 atm/mole fraction corre- sponds to a value used in the literature. The other two values are one-half and twice this value. Increasing the constant has a similar effect on tracheobronchial tissue dose as does increasing the mucous production rate (figure 6~; the higher Henry's law constant, the lower the tissue dose. A different effect occurs in the pulmonary region (genera- tions 17-23~. The three curves are not only separated, but cross over at the 19th or 20th generation where the lowest value of Hen- ry's law constant results in the lowest tissue dose. However, the general shape ot the tissue dose profiles from the 15th genera- tion distally is independent of the values of the Henry's law constants used; that is, the curves increase from the 15th generation to peak at the 17th, and then decrease. ~ Recommendation 7. Dosimetry mod- els should be used to determine the impor- tance of the values of the Henry's law constant and liquid- and tissue-phase mo- lecular diffusion coefficients to predictions. Then, if necessary, the value of the param- eters should be measured in vivo. Importance of Experimental Data The importance of experimental uptake data to dosimetry modeling cannot be overem- phasized. With the appropriate type of data, dosimetry modelers can obtain an idea of the reliability of their models and infer which processes have been modeled correctly and which ones need improvements. As previ- ously discussed, the in viva values of physi- cal, biological, and chemical parameters of- ten are not well known. By obtaining data from appropriately designed experiments, the values of some of these parameters could be estimated or refined, resulting in more reliable predictions. Furthermore, if a param- eter's value is considered the same for more than one animal species, then values deter- mined for one species can be applied to other species, extending the usefulness of the data. Methods of model validation and param- eter estimation are needed to provide a link between experimental data and dosimetry models, as well as to provide guidelines for experimental designs. The techniques used to compare experimental and predicted data will determine, to a large extent, the type of data needed. Unfortunately, most dosimetry experiments have not been de- signed for the purpose of validation and estimation. Thus, the extent to which the present data base can be used profitabyv with dosimetry models is limited. ~ Recommendation 8. Methods of model validation and parameter estimation ap- plicable to dosimetry models of toxic reac- tive gases should be identified or devel- aped. Experimental dosimetry data should be obtained for model validation and pa- rameter estimation. Evaluation methods and experimental designs should be devel- oped hand in hand, leading to optimal experimental and evaluation methods. In- tegral to and very much a part of this process is the necessary continuation of the development and refinement of dosimetry models. Summary This chapter focuses on the physical, chem- ical, and biological processes and factors involved in the absorption of reactive gases. Emphasis is placed on the impor- tance of these factors in developing dosim- etry models, with special consideration be- ing given to the role of lung fluids and tissues. Several dosimetry models are dis- cussed and illustrations of predicted results presented to demonstrate the application of the models to the uptake of NO2 and 03, and to demonstrate the use of models in determining the effects of physical, chemi- cal, and biological parameters on dosimetry predictions. Gaps in our knowledge and understanding of the processes of dosime- try are pointed out and research recom- mendations made to increase our under- standing of the processes and to enhance the development of dosimetry models. . . .
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Overton and Miller 383 Summary of Research Recommendations H I G H P R I O R I T Y Recommendation 8 Identify or develop methods of model validation and parameter estimation and obtain experimental dosimetry data for model validation and estimation. MEDIUM PRIORITY Recommendation 1 Dosimetry models should be developed that encompass the . . entire respiratory tract. Recommendation 2 Anatomical models should be developed for different subpop ulations (for example, diseased, healthy, young, old) humans and laboratory animals. Recommendation4 The thickness of the liquid lining of human and laboratory animal respiratory tracts should be accurately characterized. Recommendation 5 The in viva kinetic mechanisms of the important reactions of toxic gases with biological substances of the respiratory tract should be determined. Recommendation 6 The local concentrations of bioreactants in the respiratory tract should be identified for different human and animal subpopula tions, that is, according to age, gender, health conditions, exposure to toxic gases, and so on. LOW PRIORITY Recommendlation3 Ventilatory data from laboratory animals that correspond to realistic conditions should be obtained. Recommendation 7 Values of Henry's law constants and of liquid- and tissue-phase molecular diffusion coefficients that are applicable to respiratory tract tissues and fluids should be obtained. 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,_. Appl. Physiol. 27:654-657. Altman, P. L., and Dittmer, D. S. 1971. Respiration Correspondence should be addressed to John H. Overton or Frederick J. Miller, Toxicology Branch, Inhalation Toxicology Division, Health Effects Re- search Laboratory, U. S. Environmental Protection Agency, Research Triangle Park, NC 27711. and Circulation, Federation of American Societies for Experimental Biology, Bethesda, Md. Astarita, G. 1967. Mass Transfer with Chemical Reac- tion, p. 187, Elsevier, New York. Ballenger, J. J. 1984. Some effects of formaldehyde on the upper respiratory tract, Laryugoscope 94:1411- 1413. Boat, T. F., and Cheng, P. W. 1980. Biochemistry of airway mucus secretions, Fed. Proc. 39:3067-3074. Burri, P. H. 1985. Morphology on respiratory func- tion of the alveolar unit, Int. Arch. Allergy Appl. Immunol. (Suppl. 1) 76:2-12. Castleman, W. L., Dungworth, D. L., and Tyler, W. S. 1975. Intrapulmonary airway morphology in
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Representative terms from entire chapter: