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OCR for page 367
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
OCR for page 368
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.
OCR for page 369
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.
OCR for page 370
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
OCR for page 371
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. )
OCR for page 372
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
OCR for page 373
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.
OCR for page 374
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.
OCR for page 375
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).
OCR for page 376
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
OCR for page 377
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
OCR for page 378
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
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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).
OCR for page 379
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
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1 1 1 1 1 1 1
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o 10-7
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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
OCR for page 380
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
OCR for page 381
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
OCR for page 382
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.
. . .
OCR for page 383
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.
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OCR for page 386
Representative terms from entire chapter:
liquid lining
