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OCR for page 323
Transport and Uptake of
Inhaled Gases
JAMES S. ULTMAN
Pennsylvania State University
Implications of Lung Anatomy / 324
Upper Airways / 325 Conducting Airways / 327 Respiratory
Zone / 328 Nonuniformities in Ventilation and Perfusion / 329
Fundamentals of Mass Transport / 331
Thermodynamic Equilibria / 331 Diffusion and Reaction
Rates / 332 Individual Mass Transfer Coefficients / 336 Overall
Mass Transfer Coefficients / 337 Longitudinal Gas
Transport / 340
Mathematical Models / 341
Compartment Models / 342 Distributed-Parameter Upper Air-way
Models / 346 Distributed-Parameter Lower Airway Models / 349
Experiments / 352
In Vitro Methods / 352 In Vivo Animal Experiments / 354 In
Vivo Human Subject Studies / 358
Summary / 361
Summary of Research Recommendations / 361
Air Pollution, the Automobile, and Public Health. (3 1988 by the Health Effects
Institute. National Academy Press, Washington, D.C.
323
OCR for page 324
324
Transport and Uptake of Inhaled Gases
When a pollutant gas is breathed, its trans-
port through the highly branched tracheo-
bronchial tree results in a unique internal
distribution of concentration and uptake
rates. A major factor complicating the
study of these processes is the fact that
gases with different molecular properties
can exhibit different internal dose distribu-
tions. Highly water-soluble gases, such as
sulfur dioxide (SO2), are essentially re-
moved by the upper airways, the primary
site of respiratory defense. A highly reac-
tive gas of only moderate solubility, such as
ozone (03), can reach the tracheobronchial
tree, where it reacts with the protective
mucous layer and eventually damages un-
derlying tissue in the small bronchioles. A
gas that has limited aqueous activity but is
highly reactive with hemoglobin, such as
carbon monoxide (CO), is able to penetrate
further to the respiratory zone and diffuse
to the pulmonary circulation in quantity.
The guiding philosophy presented in this
chapter is that direct measurements on hu-
man volunteers can be minimized by using
mathematical models to anticipate uptake
rates and identify target tissues of poten-
tially hazardous species. An ideal model
enables one to calculate dose distribution
from basic anatomic and physicochemical
parameters and to estimate the effects of
pathological airway derangements and
changes in ventilatory demand. But in
. . . . . -
many situations it Is more practical to use
models that simply extrapolate measure-
ments from laboratory animals to humans.
In either case, it is necessary to validate
proposed models with experiments, and
for that reason both theoretical and labora-
tory methodologies are discussed in this
paper.
The role of physicochemical factors in
the absorption of gas species from a flow-
ing airstream is of central concern to chem-
ical engineers who design industrial gas
separation equipment. Many of the same
concepts used to develop gas absorption or
chromatographic separation processes can
be applied with some modification to the
lung. Two widely read sources on this
subject are Bird et al. (1960), a fundamental
treatise on fluid flow and diffusion phe-
nomena, and Treybal (1980), a textbook
that describes conventional design meth-
ods. Complementing this engineering
knowledge is a wealth of physiology liter-
ature concerning the influence of lung anat-
omy and mechanics on the distribution of
foreign gases (for example, Engel and Paiva
1985~. In this chapter, we will integrate
these separate fields as Hills (1974) has done
for normal respiratory gases. Although the
material here is intended to encompass all
pollutant gases those already recognized
as well as those still unrecognized an en-
cyclopedic review has not been attempted.
Rather, basic concepts and methods are
stressed to provide a general overview, and
concrete examples with respect to three
species- S02, 03, and CO have been
used to illustrate the spectrum of solubility
and reactivity effects.
This article begins with two sections
devoted to issues at the heart of mathemat-
ical model development: first, lung anat-
omy and its influence on aerodynamics; and-
second, fundamentals of diffusion and
chemical reaction and their characterization
in terms of mass transfer coefficients. The
next two sections address the structure of
alternative mathematical models and their
validation by experimental measurements.
O O ~
Implications of Lung Anatomy
This section, in presenting an overview of
lung anatomy and its influence on aerody-
namics and hemodynamics, focuses on the
human respiratory system. Although most
of the concepts are also valid for animals
(see Schlesinger, this volume), the numer-
ical values used to illustrate specific ana-
tomic and functional features are typical of
normal adult humans. As a supplement to
these data, table 1 has been included to
indicate the difference in scale between the
lungs of humans and animals.
The pulmonary airways consist of three
distinct functional units. The upper air-
ways, extending from the nares and lips to
the larynx, are the primary sites at which
the temperature and humidity of inspired
air are equilibrated to body conditions. The
conducting airways, a branched-tube net
OCR for page 325
James S. Ultman
325
Table 1. Comparisons Among Anatomical Measurements Related to Breathing in Humans and
Laboratory Animals
Anatomical Large Small Small
MeasurementHumanDog Dog Monkey Rabbit Rat Mouse
. . .
Body weight (kg) 74 22.8 11.2 3.71 3.6 0.14 0.023
Total lung volume 4,341 1,501 736 184 79 6.3 0.74
(ml)
Total alveolar surface 143 90 41 13 5.9 0.39 0.068
(m2)
Total capillary surface 126 72 33 12 4.7 0.41 0.059
(m2)
Total capillary volume 213 119 50 15 7.2 0.48 0.084
(ml)
Mean air-blood barrier 2.22 1.42 1.64 1.52 1.51 1.42 1.25
thickness (,um)
SOURCE: Adapted with permission from Gil (1982, tables 1 and 2). Copyright CRC Press, Boca Raton, Fla.
work originating at the trachea and extend-
ing to include terminal bronchioles, pro-
vide an orderly yet compact expansion of
flow cross-section. The respiratory zone,
composed of all the alveolated airways and
airspaces, is responsible for oxygenation of
and carbon dioxide removal from the pul-
monary capillaries. Taken together, the
conducting airways and respiratory zone
are referred to as the lower respiratory
tract, and since they contain no gas ex-
change surface, the upper and conducting
airways combined are often called the ana-
tomic dead space.
The respiratory zone, with a volume of
about 3 liters compared to the 160 ml of
anatomic dead space, contains most of the
functional residual gas volume, and yet the
total path length of 6 mm along alveolated
airways is only a fraction of the 40 cm
between the nose and the terminal conduct-
ing airways. In other words, the total
cross-sectional area in the respiratory zone
is much greater than in the dead space.
However, this total is the sum of the cross-
sections of a large number of small passages
in which the axial diffusion distance is very
short. Therefore, longitudinal mixing of
fresh inspired air with residual gas is fa-
vored in the respiratory zone, whereas bulk
flow with little mixing of fresh and residual
air occurs in the dead space (Go mez 1965~.
The walls of the upper and conducting
airways are composed of an inner mucosal
layer, a submucosal layer, and an outer
adventitia. The mucosal layer, sometimes
called the mucous membrane, contains cil-
iated epithelium and mucus-producing
goblet cells, with additional mucus-pro-
ducing glands located in the submucosal
layer. In the lumen of these airways, cilia
are surrounded by a low-viscosity pericil-
iary fluid, above which high-viscosity mu-
cus floats. The cilia beat in an organized
unidirectional fashion, propelling this mu-
cous blanket from the lower respiratory
tract to the oropharynx with a daily clear-
ance of about 100 ml.
Blood is supplied to the lower respira-
tory tract through the bronchial arteries,
which arise from the aorta and deliver
oxygen to conducting airways, and
through the pulmonary circulation that
perfuses the respiratory zone via the pul-
monary artery. During rest, the bronchial
circulation constitutes only 1 percent of the
total 5 liter/min of systemic arterial blood
flow, and it feeds sparsely distributed cap-
illaries in the submucosal layer of bronchial
tissue. In contrast, the entire output of the
right heart enters the pulmonary circulation
to supply the dense meshwork of capillaries
in the walls of the alveoli.
Upper Airways
During quiet breathing, a typical tidal vol-
ume is 500 ml at a frequency of 12 breaths/
min. corresponding to a minute volume of
6 liters/mint Under these conditions, air
normally enters the nose and flows by way
of the nasopharynx, pharynx, and larynx to
OCR for page 326
326
the trachea. In the nose, the convoluted
well-perfused surface of the nasal turbinates
with its large specific surface area of 8
cm2/ml provides an efficient site for ab-
sorption of soluble gases. Alternatively, air
may follow a path from the mouth directly
to the pharynx, thereby depriving the in-
spirate of purification by the nose. Most
individuals breathe exclusively through
their nose when minute volume is below 34
liters, but during vigorous exercise when
ventilatory demand is larger, 45 to 60 per-
cent of respired air is inspired orally (Nii-
nimaa et al. 1980, 1981~. The presence of a
nasal obstruction or even a disease of the
lower respiratory tract such as asthma can
also exaggerate oral breathing, making the
lung more likely to be exposed to pollutant
gases.
The geometry of upper airways is irreg-
ular and variable, depending on the point of
air access, on the breathing pattern, and on
the state of mucous membrane engorge-
ment by nasal blood flow. Perhaps this
explains why no mathematical model of its
anatomy has been established. Roughly
speaking, upper airway volume is 50 ml,
with a path length of 17 cm from lips to
glottis and 22 cm from nares to glottis. As
respired gas flows through the upper air-
ways, it encounters a series of sudden con-
tractions and expansions in cross-section
leading to corresponding accelerations and
decelerations in gas velocity (figure 1~. This
is quite different from the steady flow of
gases in straight tubes of constant cross-
section.
The nature of flow in a tube is character-
ized by the Reynolds number (Re), the
dimensionless ratio of inertial force to fric
. .
tlona resistance:
Re = Vd/A u (1)
where d is tube diameter, V is volumetric
flow rate, A is cross-sectional area available
for flow, and v is kinematic viscosity. In
sufficiently long straight tubes, flow is fully
developed and the Reynolds number
uniquely determines whether the velocity
field is laminar (Re ~ 2100), turbulent (Re
> 4000), or in transition between these two
regimes (4000 > Re > 2100~. In laminar
flow, material moves along fixed axial
30t
254
cue
O 20
LO
In
oh 15
o
10
5
_V
Transport and Uptake of Inhaled Gases
12
11
10
Bronchial /
x generations\ |
- ~ ,6 x ~9t
1 ~i, V
5 10 15 20 25 30 35 40 45
DISTANCE FROM NASAL TIP (cm)
to
Figure 1. Cross-sectional area available for gas
flow. Axial velocity (m/see for flow of 200 ml/see)
during quiet respiration is also shown at selected "V"
(velocity) points. (Adapted with permission from
Swift and Proctor 1977, p. 68, by courtesy of Marcel
Dekker, Inc.)
streamlines so that radial transport can only
occur by molecular diffusion. In turbulent
flow, the mixing action of turbulent eddies
facilitates radial transport of gas species to
the tube wall, a favorable condition for gas
absorption.
Because of disturbances created by geo-
metric irregularities, flow in the upper air-
ways is never fully developed. For exam-
ple, the inspired airstream that is propelled
through the glottic constriction into the
trachea forms a confined jet immediately
downstream of the larynx. Large velocity
gradients within the jet generate turbulent
eddies at Reynolds numbers well below the
fully developed transition value of 2100
(Simone and Ultman 1982), and these ed-
dies can increase radial mixing as gas flows
downstream, even during quiet inspiration.
Also, the rapid deceleration of air passing
from the ostium internum to the turbinated
structures can induce turbulence in the nose
(Swift and Proctor 1977~.
In addition to the promotion of turbu-
lence, three other phenomena unique to the
upper airways may enhance gas absorption.
OCR for page 327
James S. Ultman
327
First, fresh mucus swept into the tubinates
from the paranasal sinuses supplements the
capacity of the nasal passages for airborne
pollutants. Second, the nasal mucosa and
submucosa are well perfused with blood
flowing countercurrent to the mucus flow,
and this is a favorable configuration for gas
absorption (Brain 1970~. Third, because
increased blood flow can elicit an erectile
response in surrounding tissue, vasodila-
tion by cholinergic pollutants may increase
gas absorption both by increasing capillary
surface and by reducing the lateral diffusion
distance in the nasal passages.
Conducting Airways
The conducting airways, also referred to as
the tracheobronchial tree, are a series of
more or less dichotomously branched tubes
originating at the larynx and extending just
proximal to the point where alveolated
airways arise. Those branches containing
cartilage are defined as bronchi and gener-
ally occupy the first 10 or so generations.
The more distal cartilage-free branches are
defined as bronchioli. Although volume
changes in the trachea and major bronchi
are minimized by stiff cartilage rings em-
bedded in the airway walls, the smaller
bronchi and the bronchioli undergo isotropic
volume changes in proportion to changes
in lung volume (Hughes et al. 1972~.
Raabe (1982) reviewed several numerical
models of the tracheobronchial tree, which
may be divided into two categories: the
so-called symmetric models, in which a
regular dichotomy of branching exists at
every generation and all branches in a given
generation have the same diameters and the
same lengths, and the asymmetric models,
which account for the unequal distribution
of lung lobes three on the right and two
on the left or for irregularities within the
lobes themselves. Whereas a symmetric
model is an idealization wherein the geom-
etry of all transport paths from larynx to
terminal bronchioles is identical, in the
more realistic asymmetric model, airway
diameters and lengths and even the number
of branch divisions may differ along alter-
native paths. For example, in Horsfield and
Cumming's asymmetric model (1968),
there are between 8 and 25 branchings with
a corresponding distribution in path lengths
from 7 to 23 cm between the trachea and the
respiratory lobules. On the other hand, in
Weibel's symmetric model A (1963, p. 136)
there are 16 branchings with an equal length
of 13 cm along all conducting airway paths.
A symmetric model is a convenient start-
ing point for the analysis of diffusion and
flow because all transport paths are equiv-
alent. Weibel's widely used model A por-
trays the conducting airways as an expand-
ing network of dichotomously branching
tubes, wherein generation number, z, in-
creases from zero at the trachea to 16 at the
terminal bronchioli and 23 at the terminal
alveolar sacs. Each generation contains 2Z
branches. Figure 2 summarizes the important
geometric features of this model (top) and
their impact on gas flow (bottom). Although
the diameters of individual branches gener-
ally decrease with increasing z, beyond the
eighth generation the total surface available
for gas absorption, S. is a strongly increasing
function of longitudinal distance, y. Increases
in the summed cross-section available for
flow, A, parallel those for S so that axial
velocity as well as branch Reynolds number
fall dramatically as gas is transported distally.
During quiet respiration, the velocity is suf-
ficiently low that Re does not exceed the
upper limit of 2100 for fully developed lami-
nar flow in any branch, but during moderate
exercise, Re values in excess of 2100 indicate
the possibility of turbulent flow in the trachea
and first four generations.
The entry length fraction, L/Le, is the
ratio of actual airway length, L, to length,
Le' required for flow to become fully de-
veloped (Olson et al. 1970~. Entry length
fractions are less than unity proximal to the
seventh generation, implying that velocity
fields within the trachea and major bronchi
do not reach fully developed behavior,
even during quiet breathing. This explains
how it is possible for random velocity
fluctuations to be observed in bronchial
airway casts at inspiratory flows well
within the laminar Reynolds number range
(Dekker 1961; Olson et al. 1973~. Such
turbulence was undoubtedly due to the
propagation of incompletely dissipated ed-
dies from the upper airway segment of the
OCR for page 328
328
cast. Ordered flow disturbances consisting
of a paired vortex pattern during inspira-
tion and a quadruple vortex pattern during
expiration have also been reported in iso-
lated bronchi at Reynolds numbers within
the laminar range (Schroter and Sudlow
1969~. The radial mixing brought about by
these lateral flow circulations aids in trans-
port of gas species toward the airway walls.
Accompanying the decrease in branch
diameters between trachea and terminal
bronchioles, there is a progressive decrease
in airway wall thickness and tissue perfu-
sion rate. There are also fewer mucus-
secreting elements and less ciliated epithe-
lium, which reduces mucus velocity and
thickness. Estimates of some relevant mu-
cus, tissue, and blood flow parameters are
presented in table 2.
Transport and Uptake of Inhaled Gases
AIRWAY GENERATION, z
0 1 2 4 6 8 1216
'T I ~'i I I I I I I I Trln
E
to 4
-
UJ
3
1
- <~ 2.0
E
N
- °1.6
at;
z
- °1.2
up
_ u' 0.8
O
_ 00.4
_ En 0
v
800C
-
cr
m 600C
at
in 400C
o
at
~ 200C
Lid
r
in
LlLe (exercise)
/ I
LlLe (rest) ~ |
'\\ 11
Re (rest) \\ / /
~? /
_-~-- ~---~-- ~ --~-~
0.12 0.14 0.16 0.18 0.20 0.22 0.24
~ Re (exercise)
8
2
3) ~
2.0 z
z
I
O
-
r
ID
LONGITUDINAL DISTANCE, y(m)
Figure 2. Geometric and aerodynamic characteristics of a symmetric tracheobron-
chial model. All values were derived for Weibel's model A (Weibel 1963) scaled to
a functional residual capacity of 3 liters. Entry length fraction was computed with
the equation of Olson et al. (1973). Flows of 0.4 and 1.6 liters/sec have been used for
rest and exercise conditions, respectively.
Respiratory Zone
The respiratory zone is defined by the
presence of regions containing membra-
nous outpouchings the alveoli normally
responsible for gas exchange. An individual
alveolus has a characteristic diameter of
about 0.2 mm, and its shape may be mod-
eled in various ways: a truncated sphere, a
truncated cone, or a cylindrical wedge
(Weibel 1963, p. 60~. The fine structure of
the alveolar wall consists of little more than
a shell-like mesh of pulmonary capillaries
enclosed in a layer of airway epithelium
covered by a thin surfactant film, and
therefore the blood-gas barrier imposed by
the alveolar membrane is only about 2 ,um
thick. Because the pulmonary capillaries
are short, typically 10 ,um long, there is
OCR for page 329
James S. Ultman
329
Table 2. Conducting Airway Parametersa
Airway
Diameter/Lengthb Mucus ThicknessC Tissue Thickness Blood Flowe Mucus Velocity'
(lo~2 m) (10-6 m) (10-4 m) (10-7 m3/sec) (10-4 m/see)
Trachea 1.6/12 7 8 1.7 2.5
Main bronchi 1.0/6.0 7 5 0.6 1.7
Lobar bronchi 0.4/3.0 7 2 0.2 0.50
Segmental 0.2/1.5 7 1 0.09 0.067
bronchi
Subsegmental 0.15/0.5 7 0.75 0.2 0.010
bronchi
Terminal 0. 06/0.3 4.2 0.30 1.7 0.00033
bronchioles
a Parameter values are based on a single airway branch.
b Landahl (1950).
c National Research Council (1977, table 7-3).
Computed as 5% of airway diameter (DuBois and Rogers 1968).
e DuBois and Rogers (1968, table 2).
extensive branching in the capillary mesh,
and the associated pulmonary blood flow
resembles a moving sheath of fluid inter-
rupted by regularly spaced posts of tissue
(Rosenquist et al. 1973~.
When packed together to form the lung
parenchyma, the alveoli give a honeycomb
appearance, with a specific surface area
greater than 200 cm2/ml airspace volume.
The edges of contact between adjacent al-
veoli, called alveolar sepia, protrude into
the airspace, thereby partitioning gas and
impeding axial diffusion near the airway
wall. Because their walls are so thin and
have such a large specific surface, alveoli
are well suited to normal gas exchange and
probably to the absorption of air pollutants
as well. To illustrate this, consider that an
erythrocyte, which normally resides in the
pulmonary capillaries for only 1 see, has
sufficient time to come to equilibrium with
alveolar oxygen (O2) and carbon dioxide
(CO2) partial pressures.
The fraction of airway wall occupied by
alveoli increases with distal distance from
the first alveolated airway to the blind-
ended alveolar sacs that terminate every
path of the tracheobronchial tree. As was
the case for the conducting airways, both
symmetric and asymmetric models have
been proposed for the respiratory zone. In
Weibel's model A, there are seven symmet-
ric generations of respiratory airways, and
along the 6-mm path leading from the first
respiratory bronchioli to the alveolar sacs,
the air-tissue surface available for gas ex-
change increases from 0.16 to 39 m2 per
generation. Simultaneously, the flow cross-
section increases from 0.03 to 1.2 m2 with a
concomitant drop in branch Reynolds
number from 0.5 to 0.01 during quiet
breathing. More recent work by Hansen
and Ampaya (1975) indicates that Weibel's
model significantly underestimates both
tissue surface and flow cross-section, but in
either case it is reasonable to conclude that
the influence of gas flow is negligible and
transport in the respiratory zone occurs
principally by diffusion.
The distal airway model of Parker et al.
(1971 ) is an example of an asymmetric
model of the respiratory zone. It is a di-
chotomously branching network in which
the total number of branchings varies from
three to eight along different airway paths.
In addition, this model incorporates distri-
butions of alveoli, from 7 to 25 alveoli per
duct (mean 15.9) and from 8 to 15 alveoli
per sac (mean 9.6), rather than the fixed
values of 20 alveoli in each duct and 17 in
each sac of Weibel's symmetric model.
Nonuniformities in Ventilation
and Perfusion
If the lungs were perfectly symmetric and
mechanical tissue properties and forces
were uniform among generations, then air
OCR for page 330
330
Transport and Uptake of Inhaled Gases
20
~ 15
z 10
c'
cr:
MEL
5
O ~.1- ~ ~ ~ ~ L
200 400 600 800 1000 1200
TRANSIT TIME TO ALVEOLAR DUCTS
(arbitrary units)
Figure 3. Frequency distribution of transit time
from the carina to the alveolar ducts. (Adapted with
permission from Horsfield and Cumming 1968, p.
379, and from the American Physiological Society.)
flow and blood flow to all sibling branches
would also be uniform. In this idealized
situation, the local concentration and up-
take rate of inhaled pollutants could vary
only with respect to longitudinal position
along the equivalent airway transport
paths. In the real lung, however, both
small-scale (intraregional) and large-scale
(interregional) inhomogeneities exist, and
they may impose a difference in dose be-
tween equivalent structural units. For ex-
ample, two terminal bronchioles located in
different lobes of the lung might experience
different pollutant exposure levels.
0.15
0.10
O c
~ J ~
Cal CC or 0.05
Two specific types of nonuniformities
normally present in the lung have been well
documented. First, because of anatomic
asymmetries, there is a natural distribution
of path lengths between the larynx and the
respiratory zone, with shorter path lengths
containing less gas volume than longer path
lengths. If the rate of alveolar expansion
distal to these paths is uniform, the transit
times for fresh inspired gas to reach the
alveoli by different paths will differ (figure
3), and there will be differences in time of
exposure among equivalent structural
units. Second, under the influence of grav-
ity, when the body is upright, there is more
ventilation and more blood flow near the
bottom of the lungs than near the top
(figure 41. In addition to the effects caused
individually by the distribution of ventila-
tion, VA, and perfusion, Q. the VA/Q ratio
has special importance regarding gas up-
take in the respiratory zone. That is, if a
pollutant is to continuously absorb into the
respiratory zone, it must first reach an
alveolus and ultimately be removed by the
pulmonary circulation. Therefore, alveoli
that receive little local ventilation (that is,
V^/Q is small) are as incapable of continu-
ously absorbing soluble gases as are ade-
quately ventilated alveoli that receive an
Q
-
Base
~ A/Q
-
f
Apex
5 4 3 2
RIB NUMBER
~3
~2
]
it:
Figure 4. Ventilation/perfusion ratio, VA/Q, from base to apex of the normal
upright human lung. (Adapted with permission from West 1977, p. 202, and from
Academic Press, Orlando, Fla.)
OCR for page 331
lames S. Ultman
331
. .
abnormally small blood flow (that is, VA/Q
is large). This implies that gas uptake is
maximized at some intermediate value of
the ventilation/perfusion ratio.
Fundamentals of Mass Transport
A complete description of mass transport
consists of three basic elements: the mass
conservation equation, rate equations for
diffusion and chemical reaction, and ther-
modynamic equilibrium expressions. The
mass conservation equation balances the
rate at which a species may appear with the
rate of its accumulation in a spatial region
of interest often called the control volume.
Given that the permissible modes of ap-
pearance are convection, diffusion, and
chemical reaction, the mass conservation
equation has the form
Rate of
Accumulation
Net Input Net Input Net Rate of
Rate by + Rate by + Production
Bulk Flow Diffusion by Reaction
(2)
The mathematical expression of mass con-
servation is a differential field equation ap-
plicable to any three-dimensional time-
varying problem (Bird et al. 1960, p. 559),
but in practice the general equation must be
simplified by selecting a set of physically
realistic assumptions. This will be consid-
ered in detail in the next section, which is
devoted to mathematical modeling.
In this section, attention is focused on the
fundamentals of thermodynamic equilibria
and rate expressions for diffusion and
chemical reaction. The formulation of mass
transfer coefficients to describe transverse
transport and the use of retention parame-
ters and mixing coefficients to characterize
longitudinal transport are also described.
Thermodynamic Equilibria
Phase equilibrium refers to the distribution
of a species between adjacent immiscible
phases. Suppose, for example, that a liquid
phase containing a physically dissolved spe
cies X is placed in contact with gas contain-
ing an arbitrary partial pressure Px of the
same solute species. Thereafter, molecules
of X will continually redistribute between
the liquid and gas phases, altering Ax until it
reaches a stationary value p* referred to as
the equilibrium partial pressure or the gas
tension. In this equilibrium state, the ratio
of the molar concentration Cx of species X
in the liquid phase to the corresponding
value of p* in the gas phase is a parameter,
cYX, called the Bunsen solubility coefficient:
Ax = CXIPX
(3)
Generally, cut is a function of temperature
only, its value being equivalent to the mo-
lar volume of the liquid divided by Henry's
Law constant. Therefore, when tempera-
ture is fixed, the dissolved species concen-
tration is a linear function of gas tension.
The solubility coefficients of most foreign
gases in mucus, tissue, and blood are not
precisely known and must be approxi-
mated by values measured in readily avail-
able solvents such as water (table 3) and
hydrocarbon oils.
Chemical reaction equilibrium can im-
pose additional constraints on solute con-
centrations. During chemical reactions,
molecular combinations and decomposi-
tions can both occur such that a dissolved
pollutant species is reversibly bound to
another endogenous species. Typical of
such reactions are the aqueous ionization of
SO2 to form bisulfite; the ionization of
CO2 to form bicarbonate; and the binding
of 02, C02' or CO to hemoglobin. To
exemplify the underlying reaction equilib-
rium, consider the ionization of SO2 in
water given by the stoichiometric equation
SO2 + H2O = H+ + HSO3 (4)
Although HSO3 also undergoes a weak
dissociation to SO32-, equation 4 is a suffi-
ciently accurate model of the overall proc-
ess (Schroeter 1966, p. 17~.
As the concentration of SO2 is depleted
by the formation of HSO3, the law of mass
action dictates that the forward reaction
rate must slow down. Simultaneously, the
concentration of bisulfite builds up, and
this leads to an increase in reverse reaction
rate. This progressively decreasing forward
OCR for page 332
332
Transport and Uptake of Inhaled Gases
Table 3. Estimates of Physical Properties for Various Gases
Diffusivity in Aira Aqueous DifFusivityb Aqueous Solubility' First-Order Reactivity
Gas Dx (10-s m2/sec) Dx (10-9 m2/sec) ax (kg-mol/m3/Pa) kr (103/sec)
SO2 1.15 2.14 9.13 x 10-6 0
O3 2.11 3.06 5.62 x 10-8 1.2(m):50(t):5(b)
CO 2.17 3.06 8.09 x 10-9 0
a Chapman-Enskog equation (Bird et al. 1960, p. 510).
b Wilke-Chang equation (Bird et al. 1960, p. 515).
c Computed from Henry's Law coefficients (National Research Council 1977, table 7-1).
~ Miller et al. (1985, table 3) for mucus (m), tissue (t), and blood (b).
. . .
rate anc increasing reverse rate continues
until the two rates are equal and the con-
centrations of all species become stationary.
In this equilibrium state, the concentrations
of reactants and products possess a specific
algebraic relationship. For the SO2 ioniza-
tion reaction,
(Ke) SO2 = CHSO3 CH/ CSO~ (5)
where (Ke)So2, the reaction equilibrium
constant specific to the ionization of SO2,
is a function of temperature (Pearson et al.
1951).
In pure water, where hydroxyl ion con-
centration is low, electroneutrality dictates
that bisulfite and hydrogen ion concentra-
tions are approximately equal, and the
summed concentration of SO2 in the unre-
acted form CsO2 and in the reacted form
CHSO3 can then be expressed as
CSO2 + CHSO3
~SO2PSO2 + t(Ke~sO2ctso2pso2]~/2 (6)
This equation illustrates the ability of a
reversible chemical reaction to increase the
capacity of a solution for gaseous solute.
To emphasize the importance of this, figure
5a compares the physical solubility of SO2
to the corresponding level of bisulfite ions.
Clearly, the concentration of reacted spe-
cies is far greater than the concentration of
physically dissolved species, and the rela-
tionship of bisulfite concentration to gas
tension is nonlinear. In mucus and tissue,
increases in hydrogen ion concentration
occurring with SO2 ionization are probably
suppressed by the buffering action of other
solutes, and as equation 5 indicates, the
bisulfite concentration would be even
larger than in pure water.
To provide a unified treatment of the
dissolved and reversibly bound forms of a
soluble gas, a reactive capacitance coeff~-
cient, ,13x, analogous to the solubility coef-
ficient, can be defined as the derivative of
the reacted solute concentration, Cal. with
respect to gas tension:
- xr7
Ax = dCxr/dPx (7)
Unlike ox, which is independent of Px*, the
reactive capacitance coefficient for a revers-
ibly bound solute species is generally a
decreasing function of gas tension (figure
5b).
Diffusion and Reaction Rates
Transport of any species occurs by a com-
bination of diffusion and convection.
Whereas convection is the translation of
molecules at the mean flow velocity, diffu-
sion is the transport that occurs in response
to a concentration gradient whether or not
any net flow occurs. Fick's First Law is the
general rate equation that accounts for con-
vection and diffusion (Bird et al. 1960, p.
502), and for the special case of one-dimen-
sional diffusion of species X in the absence
of flow, it reduces to
MX =-DxSd(Cx/dz) (8)
where MX is the mass transport rate of
species X; dCx/dz is the concentration gra-
dient in the diffusion direction, z; S is the
surface area perpendicular to z; Dx is the
molecular diffusion coefficient; and the
negative sign indicates that diffusion is
along the path of decreasing concentration.
Strictly speaking, equation 8 is valid only
for solutions composed of two species, but
Fick's Law may also be applied to multi
OCR for page 333
James S. Ultman
333
A
3
co
E
o
~ 2
A
-
z
z
UJ
at
o
0 1
o
UJ
B
HSO3 /
4 _
E
to 3 _
o
UJ
z
>
LL. 1
tar
2
SON
\ 1,
\
~ ~HSO3
\
'
-
-
0 0.5 1 .0 0 0.1 0.5 1 .0
GAS TENSION PSO2 (Pa)
Figure 5. Solubility of sulfur dioxide at 37°C in pure water. A: The Physical solubility of SO2 and its
equilibrium concentration as reacted SOL (that is, HSO3 ) are compared. B: In the graphical construction of
average reactive capacitance at SO2 tensions between 0.1 and 0.5 Pa, a horizontal line is drawn so that the areas
I and I' are equal. Note that 1 Pa is equivalent to 21.5 ppm of SO2 when total pressure is 1 atm.
component solutions when the solute spe-
cies of interest is present at sufficiently low
concentration or partial pressure relative to
the solvent species (Bird et al. 1960, p.
571). Chang et al. (1975) analyzed situa-
tions in the airway lumen where multicom-
ponent diffusion effects may be important,
but the existence of similar phenomena in
mucus and tissue have not been investigated.
The lung consists of gas, tissue, and
blood regions, and the customary assertion
that phase equilibrium applies at the inter-
faces between regions leads to correspond
. . . . . . . .
sing c .~scont~nu~t~es In species concentration.
This mathematical inconvenience can be
circumvented by substituting, in Fick's
Law, the gas tension gradient for the con
. .
centratlon grac lent.
MX =-aXDxS(dp */dZ) (9)
The product, axDx, sometimes called
Krogh's constant of diffusion (Dejours
1981), indicates that the diffusion rate of
gases with a small diffusion coefficient can
be significant when compensated by a suf-
ficiently large solubility.
A useful form of equation 9 results for
the case of steady-state diffusion through a
planar barrier of thickness 1. Then the
transport rate MX is constant and equation 9
can be integrated with the result that
MX = (~xDxIl)S~x~-Pxo) (10)
where Phi and phi are the gas tensions at the
two sides of the barrier. Thus, the tension
of an inert gas is linearly distributed in the
diffusion direction, and the proper driving
force for diffusion is the gas tension differ-
ence (figure 6a).
If a gas species undergoes reversible
OCR for page 356
356
Transport and Uptake of Inhaled Gases
~0
-
G 6.0
C,' 5.0
G
6
.L
6
I
G
. .
LU
z
z
40 10 5 3 2 1.5
FLOW RATE (liters/min)
4.0
3.0
2.0
1 000
100
dig, 0.31 + 0.003 ppm
- ~ O3
/ ,~ 0.80 ~ 0.001 ppm
i/
/ ''
10
1
f
~ I ~
0 0.3
TRANSIT
TIME
(m i n /l iter)
_ calm_
· .v
0.2
~_
0.4 0.6 0.8 1.0 13.0 14.0
TRANSIT TIME
(min/liter)
Figure 21. Effect of airflow on the absorption of various foreign gases along the
nasotracheal path of the upper airways. (Adapted with permission from Aharonson et
al. 1974, p. 656, and from the American Physiological Society.)
cient is much less sensitive to flow than is
the nasotracheal coefficient. For O3, how-
ever, there is an astonishing similarity of
flow sensitivity for the nasotracheal and the
orotracheal paths, and at both inlet concen-
trations reported. With the exception of the
orotracheal value for SO2, the values of m
are all the same order of magnitude but
somewhat less than the 0.854 value re-
ported for km in physical models (table 5,
entry la). The smaller flow dependence of
the in viva data is probably due to diffusion
resistances in tissue and mucous layers that
are not directly affected by gas flow.
Animal data also suggest that both O3 and
SO2 uptake are sensitive to atmospheric
concentration. This effect is portrayed by the
Px/Pxj tracheal penetration values in fig-
ure 22. The SO2 data (Strandberg 1964)
were obtained from free-breathing rabbits
who inspired a pollutant mixture of known
composition from a head chamber. Tra-
cheal samples were obtained at peak inspi-
ratory flow (I) and peak expiratory flow
(E), the former sample being representative
of upper airway absorption and the latter
indicative of lower airway uptake. The O3
data were obtained on dogs by applying
subatmospheric pressure to a tracheos-
tomy, thereby withdrawing pollutant mix
Table 7. Comparison of Absorption Characteristics of the Nose and Mouth
Nasotracheal
Steady Flow
Inspired Concentration (liters/min)
Px,,/Px;
0.001
0.032
0.283
0.631
0.408
0.733
R TKmS
(10 4m3/sec)
Orotracheal
m pX`~/p.~'
R TKmS
(10 4m3/sec)
m
l ppm SO2a
3.5
35
26-34 ppm O3 3.5-6.5
35-45
3.5-6.5
35-45
78-80 ppm O3
4.03
20.1
1.05
3.07
0.747
2.07
0.70 0.0044
0.660
0.52 0.665
0.884
0.49 0.732
0.902
3.17
2.42
0.340
0.822
0.260
0.687
a Frank et al. (1969).
b Yokoyama and Frank (1972).
OCR for page 357
James S. Ultman
Lit 1.0
cr
6 ~
To
I O 0.50
cr
_ ~
6 Al
I
S02(1) \ ~' 03(1)
\ //
~ SO2(E) .
o
10-2 10-1 1 10 1o2
INLET CONCENTRATION (ppm)
1n2
Figure 22. The concentration dependence of SO2 penetration (Strandberg 1964) in
rabbits and O3 penetration (Vaughan et al. 1969) in dogs. Both inspiratory (I) and
expiratory (E) samples were obtained in the trachea.
lures from a reservoir into the nose and
through the upper airways (Vaughan et al.
1969~. Tracheal concentration was deter-
mined by sampling from a tracheostomy
tube while the dog breathed spontaneously
through the caudal portion of the tracheos-
tomy.
These data reveal that penetration of SO2
through the upper airways is inversely re-
lated to its inlet concentration, but penetra-
tion of O3 is directly related to concentra-
tion. It is possible to attribute the behavior
of O3 to a saturation limitation in chemical
reaction rate as concentration increases.
Such reaction kinetics are common for a
variety of biochemical reactions and are
often described by the Michaelis-Menten
equation (Mahler and Cordes 1968, p. 153~.
It is difficult to conceive of a purely phys-
ical explanation for the concentration de-
pendence of SO2 penetration. Rather, it has
been postulated that short exposures to
high levels of SO2 stimulate mucus secre-
tion, thereby reducing penetration as com-
pared to exposures at low concentrations
(Brain 1970~.
Far less information is available for ab-
sorption in the lower airways than for
uptake in the upper airways. In experi-
ments where the lower airways of dogs
were surgically isolated from the upper
airways, penetration of O3 to the respira-
tory airspaces estimated as the ratio of
expired-to-inspired partial pressures was
357
~n3
from 0.15 to 0.20, depending on the me-
chanical ventilation rate and the inlet con-
centration (Yokoyama and Frank 1972~.
And in free-breathing rabbits (figure 22),
the analogous ratio for SO2 was from 0.2 to
0.4. Because of the naturally reversing res-
piratory flow in the latter experiments,
some Resorption of pollutant may have
occurred during expiration, as pollutant-
depleted air from distal airways passed over
the pollutant-rich tissue and mucus in more
proximal airways. Therefore, the expira
. . . . . . .
t1on-to-1nsp1rat1on partial pressure ratios
may be somewhat larger than the actual
lower airway penetrations.
An important factor to consider in the
design of uptake experiments is exposure
time of the animal to the pollutant.
Whereas an acute exposure results in data
relevant to transport in a healthy animal
lung, chronic exposure can result in ana-
tomic and functional derangements that
further affect the absorption process. All
the investigations cited above utilized short
exposures, usually less than an hour. How-
ever, Moorman et al. (1973) measured O3
absorption into the upper airways of dogs
that were chronically exposed for 8 to 24
hr. and compared the results with data
from acutely exposed dogs. Their results
show that in dogs, penetration through the
nasotracheal path is generally greater dur-
ing chronic exposure than during acute
exposure. These investigators hypothesized
OCR for page 358
358
Transport and Uptake of Inhaled Gases
that decreased mucus flow due to chronic
exposure was responsible for the increased
penetration.
· Recommendation 4. Using a consistent
experimental protocol, total uptake of se-
lected pollutants should be measured in
different animal species and then used to
develop basic rules of extrapolation.
In Vivo Human Subject Studies
Extensive research into the transport of
foreign gases in the human lung has been
directed toward the development of non-
invasive tests of pulmonary function. To a
large extent, progress in this area has been
stimulated by the development of reliable
fast-responding gas analyzers. Literature on
the use of inert insoluble gases for the
characterization of gas mixing and distribu-
tion is extensive (Engel and Paiva 1985~.
One of the most widely used lung func-
tion tests employing inert insoluble gas is
the multibreath wash-out (Fowler et al.
1952~. In this measurement, the end-ex-
pired nitrogen fraction is recorded for a
series of regular breaths following a change
. . . . ,~ .
in 1nsplrec . gas mixture trom room air to
pure oxygen. If the lungs behaved in ac-
cordance with the static Bohr model, then a
semilogarithmic plot of expired nitrogen
fraction versus breath number would be a
straight line having a slope and intercept
from which dead space and alveolar vol-
ume could be determined. However, for
patients with diseased lungs, this plot is far
from linear, and even in normal subjects,
expired nitrogen fraction exhibits multiex-
ponential rather than single-exponential
decay. Such nonideal behavior has been
successfully simulated using multicompart-
ment models with ventilation inhomoge-
neities between parallel regions (Robertson
et al. 1950~.
Most research on reactive foreign gases
has been devoted to the uptake of CO.
Because the absorption of this species is
limited by diffusion through the alveolar
membranes, decreased CO uptake can
serve as an indicator of parenchymal tissue
abnormalities. In the single-breath method,
CO diffusing capacity is computed from
the ratio of final-to-initial alveolar con-
centration measured during a series of
breath-holding periods of known duration
(Apthorp and Marshall 1961~. The diffu-
sion-limited form of equation 27 (that is,
Bo = 0) is appropriate for this calculation,
and it predicts that a semilogarithmic plot
of alveolar concentration ratio versus breath-
holding time has a slope proportional to
KmS. Roughton and Forster (1957) recog-
nized that pulmonary diffusing capacity is
composed of a true membrane-diffusing
capacity and a hemoglobin reaction capac-
ity that is proportional to capillary blood
volume (eq. 25~. Moreover, they devel-
oped a method of estimating the capillary
blood volume by measuring the change in
reaction capacity at different levels of in-
spired O2. Although the method is fraught
with difficulties, primarily because a unique
value of alveolar concentration must be in-
ferred from expired gas analysis, the single-
breath CO uptake procedure as standardized
by Ogilvie et al. (1957) is still in use.
There has also been considerable interest
in soluble nonreactive gases such as acety-
lene. Since the absorption of acetylene is
perfusion-limited, it can be used as an
indicator of pulmonary blood flow, Q.
Acetylene uptake has been measured by the
same breath-holding procedure developed
for CO, and the data were then analyzed
with equation 27. For a moderately soluble
gas, the Bo parameter is large enough that a
semilogarithmic plot of expired alveolar
concentration versus breath-holding time
should have a slope proportional to Q. To
study in detail the influence of solubility on
uptake, Cander and Forster (1959) per-
formed single-breath experiments using
five different nonreactive gases including
acetylene. Their results depart from the
theory in two important ways, particularly
for the most soluble gases, ethyl ether and
acetone (figure 23~.
First, the "percent of initial alveolar con-
centration" does not extrapolate to the ex-
pected value of 100 percent at zero breath-
holding time. This was attributed to an
initially rapid absorption of the foreign gas
into parenchymal tissue, thereby causing an
instantaneous drop in alveolar partial pres-
sure. By extending the mathematical model
OCR for page 359
James S. Ultman
359
~ ' 30
u,
oh
~5
:~
._
~ 0
F ID
A: ~
~ c
~ g
A: ~
~ ~ 3
100 ~ h.
50 _
10
5
b
_~
W~
_ 04,
_
1 _
~v
-~ N2`J
-
-
o
. _
1
0 1 0 20 30 40 50
BREATH-HOLDING TIME (see)
Figure 23. Breath-holding uptake data for five inert
gases of increasing solubility obtained in a series of
single breaths. (Adapted with permission from
Cander and Forster 1959, p. 544, and from the Amer
ican Physiological Society.)
to account for this, Cander and Forster
were able to estimate reasonable values of
the tissue volume. Second, the semiloga-
rithmic plots are not linear. Instead, as
breath-holding time increases, the alveolar
concentration data become progressively
larger than expected from a linear extrapo-
lation of the initial data. Cander and Forster
attributed this result to the contamination
of expired alveolar gas with foreign gas that
was initially absorbed into conducting air-
way tissues. Although no formal model
was proposed, this behavior could un-
doubtedly be predicted by a multicompart-
ment simulation that accommodates de-
sorption processes during expiration.
By combining individual measurements
into one multiple-gas test, it is possible to
simultaneously estimate several transport
parameters for the same subject. Moreover,
since the parameters are measured under a
single set of conditions, their values and the
relations among their values may be more
reliable than if each was measured under
conditions that must necessarily differ,
even if only slightly. An example of such
an approach is the work of Sackner et al.
(1975) who performed a series of breath-
holding experiments on subjects inspiring a
gas mixture containing helium (to assess
alveolar volume), CO (to evaluate mem
brane-diffusing capacity and capillary
blood volume), and acetylene (to determine
blood flow). Whereas Sackner's study used
a single-compartment static model to ana-
lyze the uptake data, Saidel et al. (1973)
used a more sophisticated multicompart-
ment model to elucidate both ventilation
distribution and uptake dynamics.
These investigators carried out parame
. . . .
ter estimation experiments in two stages.
They first performed multibreath wash-out
measurements in which uptake of the ni-
trogen test gas is negligible. By matching
simulations (eq. 28) to these data, flow
fraction parameters, Ok, governing distri-
bution of volume and ventilation among
the four distensible lower-airway compart-
ments (figure 12a) could be evaluated for
each subject. Then, the subjects were ad-
ministered a steady-state uptake test in
which a dilute CO-air mixture was in-
spired and the end-tidal concentration and
uptake of CO was measured during con-
secutive breaths. By using the fkj ventila-
tion parameters already established from
the nitrogen wash-out data, simulations of
CO uptake data could be performed to
estimate the parenchymal diffusion param-
eters, KmS.
In humans as in animals, it is also possi-
ble to study uptake in the upper airways
independent of the lower airways. For ex-
ample, Speizer and Frank (1966) described
an experiment in which cooperating sub-
jects inhaled a 15-ppm mixture of SO2-air
into the nose, while inspiratory and expi-
ratory samples were automatically with-
drawn through a nasal sampling tube just
inside the nares and a pharyngeal sampling
tube was inserted through the mouth. By
comparing concentrations between the
nose and pharynx, it was clear that SO2
penetration beyond the upper airways was
only 1 percent during inspiration. And be-
cause the pharyngeal concentration was on
the order of 0.4 ppm during both inspiration
and expiration, it appears that the lower
airways neither absorbed nor desorbed a de-
tectable quantity of SO2. However, the ex-
pired nasal concentration was 2 ppm, five
times larger than the pharyngeal value, indi-
cating that Resorption from the nasal pas-
sages was promoted during expiration
OCR for page 360
360
Transport and Uptake of Inhaled Gases
by the flow calf air that had horn strinn~H of
SO2 during inspiration. This temporal
countercurrent exchange process enhances
the protective capability of the upper air-
ways. That is, in addition to preventing
pollutants from reaching lower airways,
countercurrent exchange reduces pollutant
loading in the upper airway mucosa.
Up to this point, the discussion has fo-
cused on physicochemical problems,
namely, absorption rates and internal con-
centration distributions of foreign gases.
From a medical point of view, however,
these physicochemical descriptions are use-
ful only if they correspond to functional
abnormalities. The connection between
characterization of local dose on the one
hand, and graded response of lung function
on the other, has clearly been established
for SO2. In particular, it is well known that
acute exposure to SO2 leads to a reversible
increase in airway flow resistance because
of bronchoconstriction mediated by neural
chemical sensors (Frank 1970~. Because
these sensors are particularly abundant near
the larynx and carina, it should be possible
to correlate local dose at these sites with
airway resistance. Amdur (1966) used pub-
lished SO2 penetration values obtained by
Strandberg (1964) on free-breathing rabbits
in conjunction with her own airway flow-
resistance values measured in guinea pigs
and graphed the logarithm of airway resis-
tance increase versus the logarithm of tra-
cheal concentration. This local dose/re-
sponse plot was linear with a slope of 0.6,
corresponding to an approximate square
root dependence of airway resistance in-
crease on tracheal SO2 concentration.
Going one step further, Kleinman (1984)
hypothesized that if changes in airway re-
sistance are directly related to the dose of
SO2 reaching the postpharyngeal airways,
then apparent differences in response that
have been observed during rest, exercise,
free breathing, and breathing through a
mouthpiece (figure 24a) can be explained
by the dependence of upper airway pene-
tration on flow rate and on the point of air
access. Kleinman presented a quantitative
analysis in which equation 32 was used to
convert the inhaled dose rate, Vpx, of the
nine data points in figure 24a into their
Is
a)
o
Q
x
a)
A 200
o
c
a)
C`7
LU
oh
CO
UJ
An:
-
CO
As
llJ
of
I
200 400 600 800
POSTPHARYNGEAL DOSE RATE, VpxO(~g/min)
Figure 24. Dose/response data for increased airway
resistance following exposure to SO2. A: Correlation
with respect to inhaled dose. B: Improved correlation
with respect to postpharyngeal dose. (Adapted with
permission from Kleinman 1084, pp. 33, 35, and from
the Air Pollution Control Association.)
400
300
100
400
300
200
100
A
Mouth breathing
(exercise)
/ Mouth breathing
(rest) I_
g ~ ~ Natural breathing
(exercise)
I I I ~ I 1 1 1 1 1 1 1
200 400 600 800 1000 1200
INHALFn nORF RATE An. (,,~lmin]
~ ~Xj~-~ ~
B
/
/ o
corresponding postpharyngeal dose rate,
Vpx. The flow fraction entering the nose,
In, Divas evaluated as a function of airflow by
assembling available human subject data;
and the nasotracheal penetration, (PxO/Px)n'
and orotracheal penetration, (PxO/Px'jm'
were both modeled by a formula similar to
equation 34, with separate values of KmS
for the nose and for the mouth estimated on
the basis of mixed data from dogs and man.
When the change in airway resistance is
replotted against the predicted values of
postpharyngeal dose (figure 24b), the dose/
response correlation is considerably im-
proved relative to the use of inhaled dose
(figure 24a).
Oulrey et al. (1983) performed a similar
analysis of SO2 dose/response, but used a
larger data set composed of 23 grouped
measurements of airway resistance. They
concluded that the increase in specific air
OCR for page 361
lames S. Ultman
361
way resistance is best correlated with the
square of postpharyngeal penetration.
· Recommendation 5. Noninvasive pul-
monary function tests such as the CO
uptake method should be extended to the
evaluation of pollutant transport in hu-
mans.
Summary
Mathematical models can serve several pur-
poses in the analysis of pollutant gas up-
take. In order of increasing importance, a
model can be used to correlate experimen-
tal measurements made under differing en-
vironmental or respiratory conditions; to
extrapolate data obtained on laboratory an-
imals to those values expected in humans;
and to estimate sites and rates of uptake
under conditions for which no data are
available. There is no single model that best
serves all these tasks. Rather, there may be
a different model appropriate to each. For
example, in data correlation and in extrap-
olation, a compartment model can incor-
porate important physiologic phenomena
(for example, geometric asymmetry, air-
flow nonuniformities, ventilation/perfu-
sion inequalities) within a mathematical
framework that requires little detailed in-
formation for its development and only
modest computational power for its imple-
mentation. On the other hand, a distribut-
ed-parameter model, which requires more
elaborate input and more complex numer-
ical algorithms to solve, is capable of pre-
dicting outcomes from first principles.
Whatever the nature of the model se-
lected, it is assembled from four basic
building blocks. First, an idealized geome-
try accounting for the structure of the
airways, tissue, and blood spaces must be
decided upon. Then material balance equa-
tions describing the time-dependent and
possibly spatially distributed transport of
pollutant are formulated. At the foundation
of these material balances are the basic
thermodynamic equilibrium, diffusional
flux, and chemical reaction rate equations.
Finally, using a specified set of pulmonary
function parameters as forcing functions
(for example, respiratory and pulmonary
blood flows), the material balance equa-
tions are solved to provide a numerical
simulation of pollutant uptake.
Experimental measurements are neces-
sary to provide the geometric and physico-
chemical data required as inputs to a model
and also to validate predictions by the
model. Ideally, this is accomplished by a
combination of separate experiments. For
example, basic thermodynamic and reac-
tion rate data can be obtained from in vitro
systems such as isolated perfused lungs or
excised tissue samples, whereas predicted
uptake rates might be verified with nonin-
vasive measurements in human subjects or
invasive measurements in intact anlma s.
Clearly, an adequate quantification of
pollutant gas transport and uptake is an
interdisciplinary problem. Its solution re-
quires the modeling skills of engineers and
physicists, as well as the biological exper-
tise of biochemists, toxicologists, and
physiologists. And if some scientists should
choose to straddle two or more disciplines,
then so much the better!
Summary of Research Recommendations
Recommendation 1 Objective. There is a critical need to quantify the chemical
Basic Property Data interaction of specific pollutants with mucus, tissue, and blood.
Besides determining solubility and Dyson coed~c~ents, it Is
essential to determine the coefficients in reaction rate equations.
The difficulty of this task is complicated by the fact that the
associated thermodynamics are undoubtedly nonideal, and nonlin
ear concentration effects are likely.
OCR for page 362
362
Transport and Uptake of Inhaled Gases
Motivation. The descriptions of pollutant chemistry that are con-
tained in this chapter were intended to be illustrative of quantitative
methods, but were not completely accurate. In particular, physical
properties in biological media were represented by aqueous values,
and in the absence of chemical rate data, it was necessary to assume
either instantaneous reaction or first-order kinetics.
To develop reliable mathematical models and provide sound
interpretation of absorption data, basic property data remain to be
established, even for the most common pollutants. For example,
the explanation of concentration effects in O3 and SO2 uptake data
is still somewhat speculative, largely because of our ignorance of
the underlying chemistry.
Approaches. The use of isolated tissue preparations, such as
tissue cultures or excised organ segments, could provide more
direct measurements of biochemical properties than are possible in
the entire organ. For example, by incorporating such a preparation
into a flow-through or batch reactor, it is possible to determine a
reaction rate expression using the well-established engineering
principles of reactor design.
Recommendation 2 Objective. A serious effort is needed to analyze mass transport
Individual Mass through individual diffusion barriers, particularly the mucous
Transfer Coefficients layer, the bronchial wall, and the alveolar capillary network.
Undoubtedly, the sparsely perfused bronchial wall will require
different mass transfer theory than the richly perfused plate-and
post structure of the alveolar walls. And the analysis of diffusion
through the mucous blanket, because it may have a discontinuous
dynamically changing conformation, poses unique challenges.
Motivation. At the core of any mathematical model of pollutant
uptake are the individual mass transfer coefficients for the diffusion
barriers. The values of mass transfer coefficients presented in this
chapter were merely estimates. Considerable refinement is neces
sary.
Approaches. Although some physical modeling may be appro
priate, it is also possible to perform computations based on existing
geometric and hydrodynamic data. DuBois and Rogers (1968) have
illustrated the application of diffusion theory to the bronchial wall;
mechanical engineers have reported methods for analyzing trans
port in interrupted flows similar to those in the pulmonary
circulation (Wieting 1975~; and chemical engineers have developed
a surface renewal theory to deal with dynamically changing inter
faces such as the gas/mucus boundary (Astarita 1967~.
Recommendation 3 Objective. To analyze total uptake of pollutants and to predict
Ventilation and dose distribution, mathematical models that account for ventilation
Perfusion Effects and perfusion limitations, including their regional distribution,
should be developed and validated.
Motivation. It is clear that there is a nonuniform distribution of
ventilation and perfusion, even in a normal lung. And the possi
bility of diffusion and perfusion limitations exists for all pollutant
gases. These interrelated phenomena have not been systematically
investigated for pollutant gases, and yet it seems likely that they
will have an impact on uptake distribution.
OCR for page 363
.Iames S. Ultman
363
Approaches. A combination of measurement and mathematical
modeling is necessary. The use of isolated perfused lung prepara-
tions could allow the measurement of total uptake under conditions
where the overall ventilation/perfusion ratio is controlled. More-
over, intravascular tracer methods previously developed for deter-
mining ventilation/perfusion ratios in humans (Wagner 1981)
might also be applied to an isolated lung. In analyzing data,
distributed-param eter models may be unnecessarily complicated.
Multicompartment lumped-parameter models are probably more
appropriate.
Recommendation 4 Objective. Using a consistent experimental protocol, total up
Extrapolation take of select pollutants should be measured in different animal
Modeling species and then used to develop basic rules of extrapolation. More
specifically, these uptake data could be correlated using known
interspecies differences in lung volume, surface area, breathing rate,
and rate-limiting mass transfer coefficients within the framework
of an appropriate mathematical model.
Motivation. There is virtually no information in the literature
that allows prediction of uptake by the human lung from data
obtained in smaller laboratory animals. This represents a critical
problem in setting air quality standards in cases where measure
ments on humans do not exist or cannot be taken.
Approaches. Yokoyama (1984) described an enclosure, similar
to a closed-circuit metabolic chamber, in which the total O3 uptake
by a free-breathing rat could be monitored, without the need to
anesthetize the animal. Using such a device, or possibly several
chambers of different sizes, it would be possible to amass total
uptake data on a series of different animal species. This data base
could be analyzed with a simple compartment model that treats the
animal and the chamber as two separate subsystems.
Recommendation 5 Objective. Noninvasive pulmonary function tests such as the CO
Noninvasive uptake method should be extended to the evaluation of pollutant gas
Methods transport in humans. The data from such experiments, particularly
when several indicator gases are used simultaneously, can be analyzed
with an appropriate mathematical model to extract considerable
information about regional inhomogeneities in uptake rate and dose.
Motivation. To date, most pollutant uptake data have been
obtained in animals using protocols that required heavy sedation,
and in some cases, extreme surgical procedures. Moreover, these
measurements were made in the absence of complementary tests
that characterize other important functional features such as the
distribution of ventilation.
Approaches. It would be useful to extend the methodology of
Saidel et al. (1973) to soluble and reactive pollutants. Naturally, the
multicompartment model used by these investigators to simulate
CO uptake must be generalized to include absorption into the
upper airway and conducting airway compartments. Also, because
of limitations in gas analyzer response and the potential health
hazard during continual exposure, it may not be practical to use the
steady-state uptake technique; the single-breath, breath-holding
method may be a better choice.
OCR for page 364
364
Acknowledgment
This work was supported in part by Na-
tional Institutes of Health Grant HL-20347.
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Representative terms from entire chapter:
upper airways
