INTERNATIONAL JOURNAL OF
OCCUPATIONAL SAFETY AND ERGONOMICS 1996, VOL. 2, NO. 2, 137-147
Alveolar Macrophage (AM) Mobility Reduction
as a Result of Long-Term Exposure to High Dust
Concentration in Inhaled Air
Leon Gradori
Albert Podgorski
Warsaw University of Technology, Poland
The influence o f high concentration of insoluble particles in inhaled air on the alveolar m acro­
phage (AM) m o b ility is analyzed. Kinetics o f phagocytosis and the m o b ility o f AM as a function of
overloading is proposed. Three patterns o f AM displacem ent on the surface o f alveolus are
distinguished depending on the loading o f the surface w ith insoluble deposits, namely, directional
being a result o f surfactant activity, directional w ith a chem otactic bias, and purely random . The
exit tim e o f AM from alveolus under overloading is calculated.
particle
deposition
clearance
chem otaxis
loading
1. INTRODUCTION
Solid and liquid aerosols in the atmosphere originate from both natural and industrial sources.
Inhalation of these aerosols from the ambient air results in the introduction and deposition of
various particulate substances in the human respiratory tract, creating a potential health
hazard. The assessment of this hazard and appropriate countermeasures to be taken require
an understanding and estimation of the local and regional deposition of inhaled particles in
the respiratory tract.
The human organism is supplied with a system of natural defense mechanisms, which
accelerate the removal and clearance of foreign bodies deposited in the lungs. Knowledge of
the residence time of inhaled particles in the lungs can provide valuable insight into the
etiology of many diseases such as pneumoconiosis, emphysema, and carcinogenesis. Perhaps
the most valuable tool that describes the variation of deposited mass in the lungs with time is
the retention curve, whose characteristics are governed by the kinetics of the deposition and
clearance processes. Recent years have witnessed not only increased interest in the experimen­
tal investigation of the retention curve, but also the development of the theoretical models that
attempt to duplicate and generalize experimental results. In addition, retention curves can be
used for a variety of medical purposes, such as optimizing the administration of drugs through
inhalation. To find a quantitative description of the retention, residence time of deposits in a
particular region of the respirator system should be known.
This work was supported by the European Community under Grant No. FI3P-CT92-0064
Correspondence and requests for reprints should be sent to Leon Gradori, Department of Chemical and Process
Engineering, Warsaw University o f Technology, 00-645 Warszawa, Waryriskiego 1, Poland.
137
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L. GRADON AND A. PODGORSKI
2. ALVEOLAR MACROPHAGES (AM) A N D THEIR ROLE
IN THE CLEARANCE PROCESS
Alveolar macrophages are part of a family of mononuclear phagocytic cells. They originate
from bone marrow precursor cells and are carried as monocytes to the lung, where they can
mature and multiply in the lung interstitium (Brain, 1986; Hunnighake, Gadek, Szapiel, &
Strumpf, 1980). The primary function of AM is to keep the alveolar surfaces of the lung sterile
and free of debris. AM may metabolize various potentially carcinogenic compounds that are
present in some inhaled particles. Many animal studies have shown that alveolar macrophages
have the capacity to ingest a variety of inorganic and organic particles. Some of them are
cytoxic for these cells. In addition to the clearance of foreign particles, AM may also participate
in removing of endogenous substances, such as surfactant, a-antitrypsin and neutrophil, and
neutrophil elastase, from the alveolar surfaces.
According to Atherley (1978), phagocytosis consists of several stages:
• Chemotaxis of the phagocytic cell (AM) by the deposited particle or substance.
• Adhesion of the particle to the phagocytic cell.
• Ingestion of the particle by ameboid movement of the phagocyte.
• The intracellular inclusion of the particle attracts a lysosome (the lysosome discharges the
enzymes into the space surrounding the particle and makes the so-called phagosome).
• The enzyme may chemically digest the particle (alternatively, the phagocytic cell may
deposit the residue of phagosome in its wake).
• AM may be killed by a particle.
Recent publications show that the process of phagocytosis is even more complex than
mentioned. Phagocitosing foreign debris and bacteria, for example, is accompanied by the
production of superoxide anions, on the surface of the plasma membrane (Di Gregorio,
Cilento, & Lantz, 1989). The presence of these active anions destroys surfactant and decreases
its activity for passive clearance from the alveolar region of the lung.
Different responses of AM were observed for particles of different chemical composition
delivered to the pulmonary region (Vincent & Donaldson, 1990). These authors explained how
the chemical composition of particles affects the clearance rate. Morrow (1988) drew attention
to the role of the pulmonary macrophage in the overloading phenomenon and to how it might
vary for different kinds of inhaled matter.
As has been mentioned (Figure 1), there are a few possible pathways for AM from alveolus.
The most clearly documented pathway is for macrophages laden with particles to move toward
the conducting airways where mucociliary clearance operates. Another pathway is for AM to
migrate toward specialized epithelium with overlaying bronchus associated with lymphoid
tissue. Macrophages loaded with particles penetrate the alveolar epithelia and migrate through
the membrane transport directly to the lymph nodes. The first pathway was deducted from
many experimental measurements. The data are consistent and reliable. Analysis of AM
displacement along this pathway is the subject of our further considerations.
3. CHEMOTAXIS OF ALVEOLAR MACROPHAGES
Chemotaxis is a complex movement in which the net direction of cell movement depends on
the concentration gradient of some chemical substances. The substance is chemoattractant of
the net cell movement in the direction of higher concentration of the substance. It is called a
repellant if the movement of a cell is toward lower concentration of the substance. Recent
studies have demonstrated that normal human alveolar macrophages are capable of respond­
ing to various chemotactic stimuli (Hunnighake et al., 1980). Immunological factors (opsonins)
are of great importance in promoting the attachment of an alveolar macrophage to particles
MACROPHAGE MOBILITY REDUCTION UNDER DUST OVERLOADING
139
MUCOCILIARY ESCALATOR
Figure 1.
Pathways of deposits in th e alveolar region. Note. K is th e rate of particle deposit
and X is th e perm eability coefficient.
and micro-organisms. It was found that human AM have receptors for the IgG and C3b
fragments of the complement (Reynolds, Fulner, & Kazimierowski, 1972), and both of these
opsonins are found on the epithelial surface of a normal human lung (Reynolds & Newball,
1974).
Also, deposits in the human alveoli stimulate the releasing of a chemoattractant for alveolar
macrophages (Kaelin, Center, & Bernardoy, 1983; Kagan, Oghiso, & Hartman, 1983). The first
step in the chemotactic movement of AM is the perception of the chemoattractant by the cell,
140
L. GRADON AND A. PODGORSKI
and the movement of the cell (Koshland, 1979). It consists of a few stages: chemoattractantreceptor binding, signal transducing, and activation of motility (Figure 2).
For cells like AM or neutrophil, the motor response is stimulated by a change of the
structure of the cortical network and, finally, because of different hydrodynamical and tension
effects, the ameboidal displacement of the whole cell takes place. The macrophage moves with
velocity VCH in the direction of a chemoattractant gradient (Figure 3). The exact mechanism
is unknown. A critical description of the models of cell displacement was given by Tranquillo
(1990). The orientation bias of the cell will depend on many factors, such as gradient steepness,
viscosity of the surrounding liquid, mechanical properties of the cortical network, and many
others.
For the purpose of this article only, the estimation of the cell velocity in the chemotactic
displacement is necessary. If we assume that the attractant concentration gradient is suffi­
ciently small, the net directional velocity of macrophage VCH is proportional to the gradient
v ch
= X’V i
(1)
where % is the chemotaxis coefficient, s is the chemoattractant concentration, and Vs is the
gradient of chemoattractant concentration.
The chemotaxis coefficient, describes the intrinsic ability of the macrophage to bias its
direction of movement in the chemoattractant gradient (Laufenburger, 1983; Tranquillo,
Zigmond, & Laufenburger, 1988). In general, the chemotaxis coefficient will depend on the
CHEMOATTRACTANT
Figure 2.
Com ponents of chemotaxis for alveolar macrophages.
MACROPHAGE MOBILITY REDUCTION UNDER DUST OVERLOADING
141
Figure 3. Cell response to th e chem oattractant gradient. Note. VCH is th e net directional
velocity of macrophage.
individual properties of a cell, like the random motility and the individual velocity of the cell,
attachment of the macrophage to the epithelial surface, and, finally, the kinetics and equilib­
rium of the dissociation of the chemoattractant and the cell. Such data are not available, so
VCH can be estimated from systematic experimental data for human leukocyte and neutrophil
with formyl-norleucyl-phenylamine (FNLLP) acting as chemoattractant and taken as a
parameter for further modeling. The estimated values were given by Stickle, Laufenburger, and
Zigmond (1984), Tranquillo et al. (1988), Stickle, Laufenburger, and Damiele (1985),
Laufenburger (1983), Maher, Martell, and Brantley (1984), and Zigmond and Hirsch (1973).
We realize that for AM, VCH will depend on the particular chemoattractant and the individual
properties of AM, including loading of the cell.
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L. GRADON AND A. PODGORSKI
To calculate the residence time of AM for different models, the random mobility coefficient
D ch of the macrophage on the surface of alveolar epithelium was calculated from the equation
D ch
(2)
(V c h )2T
where D CH is the random mobility coefficient, VCH is the net directional velocity of macro­
phage, and T is the persistent (relaxation) time of the cell.
The estimated values of VCH and D ch were taken for further calculation.
4. ALVEOLAR MOBILITY AS A RESULT OF
OVERLOADING EFFECT
A substantial number of experimental observations have lead to the general concept of dust
overloading of the lungs. Long-term exposure to relatively high dust concentrations leads to
excessive pulmonary lung burdens whereby the pulmonary clearance of persistently retained
particles by alveolar macrophages becomes progressively reduced until it essentially ceases
(Morrow, 1988). Dust overloading in the lungs is caused and perpetuated by loss in the mobility
of the alveolar macrophage. In these circumstances, the volume, not the mass of the phagocitosed particles was considered crucial. According to measurements, the critical volume of
ingested particles that reduce AM ’s mobility is 60 (xm3. The maximum volume of particles that
can be ingested was estimated at 600 jam3. On the basis of these data, the following equation
describing alveolar macrophage mobility as a function of loading effect is proposed:
—60^
(3)
/
V
where D CH is the random mobility coefficient, DC°H is the mobility of “fresh” macrophage,
calculated from Equation 2, and ving is the actual volume of ingested particles.
Equation 3 means that AM that ingested less than 60 (im3 of particles has uniform mobility
D ^ h - Because the volume of ingested particles passes the volume of 60 fim3, the mobility of
the macrophage is linearly reduced to the value of zero when the ingested volume exceeds 600
|am3. A graphical interpretation of this phenomenon is shown in Figure 4. The value of alveolar
macrophage mobility strongly affects the residence time of the phagocitosed material in the
pulmonary region of the human lungs. In order to calculate the residence time of the AM, a
model of a process will be formulated. The second equation, necessary to compute AM exit
time, is a relation between ving(t) and residence time of AM on the surface of alveolar
epithelium, t. It depends on many parameters; for example, on the surface concentration of
deposits, their size, and properties. The influence of these parameters may be summarized by
means of two average times of reaching and ingestion of deposits by AM. This time seems to
be of the order of several minutes. In this study, the following form of the function vmg(t) is
proposed:
(4)
V
//
where ving is the volume of phagocitosed particles, vmax is the maximum volume of phagoci­
tosed particles, t is time, f0 is the critical time, and vmax is assumed to equal 600 (am3, according
to the analysis by Morrow (1988).
The analytical Equation 4 was derived on the basis of the hypothesis that the process of
phagocitosing is controlled by the enzymatic reaction, so the kinetics should be analogical to
that described by the Michaelis-Menten reaction. A geometrical interpretation of Equation 4
is shown in Figure 5
to
t
Figure 4. The effect of volum e of ingested deposits on alveolar macrophage chem otactic
mobility. N ote. ving is th e volum e of phagocitosed particles, vmax is th e m axim um value of
ingested particles, t is th e tim e, and t0 is th e critical tim e.
Figure 5. Variations of ingested volum e of deposits in tim e. Note. DCH is th e random m obility
coefficient, ving is th e volum e of phagocitosed particles, vmax is th e m axim um value of ingested
particles, v* is th e ingested volum e for critical loading, and D * CH is th e displacem ent coeffi­
cient for critical loading.
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L. GRADON AND A. PODGORSKI
5. RESIDENCE TIME OF AM IN ALVEOLUS
For a quantitative analysis of the displacement of AM loaded with ingested particles, estab­
lishing the alveolar geometry is necessary. Our considerations will be limited to the case of a
single alveolus, which is a part of a sphere with a radius R (Figure 6). It has a circular
connection to the alveolar duct with a radius a.
During breathing, the surface area of the alveolus periodically increases and decreases. It is
accompanied by periodical changes of the thickness of the lining layer covering the epithelium
(hypophase) of the surface concentration of surfactant, T, placed at the air-hypophase inter­
face, and of the surface tension. Relaxation phenomena in the viscoelastic system (hypophase
+ interfacial film of surfactant) result in the dynamical gradient of the surface tension along
an alveolus circumference and, hence, in the net outflow of the lining fluid from the alveoli per
each respiratory cycle. The mathematical description and numerical analysis of these phenom­
ena was given by Gradon and Podgorski (1989) and Podgorski and Gradori (1990,1993). A
similar mechanism of fluid flow in small, nonciliated bronchioles is also postulated and the
mathematical model was presented Podgorski and Gradori (1991).
From the aforementioned description, the average velocity of the hypophase can be calcu­
lated Depending on the relation of the AM to the surface of epithelia and the interaction of
the macrophage with the hypophase, the velocity of the directional movement of AM can be
also calculated. According to our calculations for the suspended macrophages, the directional
velocity of the AM only slightly differs from the velocity of the hypophase. Going back to our
geometry (Figure 6a), AM moves to the exit from the alveolus along a particular meridian of
the sphere with velocity V. When no deposits exist and only natural chemoattractants are
present (opsonize effect), their gradient follows the gradient of surface tension and the chemotactic movement overlaps the hydrodynamical displacement of the macrophage. The residence
time of AM in the alveolus can be calculated from the equation
where L is the length of the meridian of the part of sphere (alveolus; see Figure 6a) and VD is
the velocity of a macrophage.
What will happen when the chemotactic movement is activated, for instance, by the presence
of deposits? The directional movement of the macrophage will be affected by the presence of
deposits and the releasing of the chemoattractant around any deposits. Now we have a new
element of displacement—a stochastic one—due to the chemotaxis of AM. The “stochasticity”
of the movements will depend on the activation of the “side” chemotaxis, which is a function of
the deposition pattern. The stochastic motion only slightly affects the directional movement of
AM. It takes place for a small amount of deposits on the surface of the alveolus. Information
oncoming to the macrophage only slightly changes its directional trajectory (Figure 6b). For this
case, the equation of AM motion loses its deterministic character, and becomes stochastic. The
process of displacement X -> X£ (stochastic) with small noise of stochastic is defined by a small
parameter e. That parameter is a function of the deposition rate, r: e = e(r).
The exit time of the macrophage from the alveolus is a function of surfactant activity; that
is, the directional displacement given by velocity V and the active motion of AM due to
chemotactic movement described by coefficient DCH (Equation 2). The contribution of chemo­
taxis in the displacement is measured by parameter 8.
The analytical form of x for that case has the form (Gradori & Podgorski, 1995)
T=
k [i + e2pe ~i(e - pe*-2 -
1)]
(6)
where the dimensionless parameter Pe = VL/D CH, V is velocity, L is length, DCH is the
displacement coefficient, and e is the stochastic parameter.
Let us consider a case in which the passive transport of macrophages determined by velocity
V vanishes and AM moves on the surface of an alveolus by chemotaxis only. Signals come to
MACROPHAGE MOBILITY REDUCTION UNDER DUST OVERLOADING
145
a)
c)
Figure 6. Possible mechanisms of alveolar macrophage (AM) exit from a single alveolus: (a)
passive m otion of A M w ith directional flo w of hypophase due to th e surface tension gradient;
(b) passive m otion, influenced by stochastic "w h ite noise" due to chemotaxis; (c) com pletely
"random w alk" of A M as a model of chemotactic m otion. Note. R is the radius o f the alveolus
and a is the radius o f the alveolus opening.
AM from different places (sites and deposits) and the macrophage makes its random walk. The
exit time, based on Einstein’s concept, can be calculated from the equation (Einstein, 1956)
L2
T = 25^
-
(7)
where L is the length and D CH is the displacement coefficient.
6. RESULTS A ND DISCUSSION
As discussed in the previous section, the overloading of AM affects the exit time of AM from
the alveolus only through changing the AM mobility. When passive transport dominates,
irrespective of whether AM is overloaded or not, the exit time depends only on the velocity of
the hypophase V.
To make a comparison of the proposed description of directional, directional with small
random deviation, and purely random displacement of AM, the calculation of residence times
146
L. GRADON AND A. PODGORSKI
(exit times) and half-clearance time for assumed and calculated parameters of the model
should be performed.
1. Geometry. Taking average values from morphological data we assume the radius of single
alveolus to be R = 150 jxm and the radius of circular exit to alveolar duct to be a = 100
jim. The initial position of the macrophage is assumed at the point P, then total distance
for the directional displacement along the sphere meridian to the exit of the sphere is L ~
361.8 nm.
2. The mobility coefficient of the alveolar macrophage D CH can be calculated from the
analysis described earlier. For the particular case of AM, many physicochemical data are
unknown, and there is a wide variety of chemoattractants. Our estimation of D ^H has been
based on experiments with human neutrophil. Some modifications were connected with
the size of macrophage. Generally, D CH can be treated as a parameter of the model. For
those particular calculations we assumed
= 6 X 10-7 cm2/s.
3. The surfactant activity parameter for the hydrodynamics described earlier was T = 0.95r0,
where r o is the saturation concentration of surfactant, the viscosity of hypophase \i = 12
mPas, the thickness of the hypophase h = 0.05 jam, assuming a symmetrical 4-s cycle of
breathing.
DgH
For given data, the linear average directional velocity of macrophage was V = 9.6 jim/min.
The exit times of AM—with loading below 60 nm3—from the single alveolus are the following:
• Directional movement (Equation 5), x = L/V = 361.8/9.6 ~ 37 min 42 s.
• Directional movement with small ( e = 0.1) stochastic noise (Equation 5), xe = 37 min 18 s.
• Random walk (Equation 6), x = 18 min 11 s.
It can be seen from these calculations that for macrophages with small loading, chemotaxis
significantly decreases the residence time.
For overloaded AMs with deposit volume above 600 nm3, chemotaxis decreases to zero.
Macrophage is removed from the alveolus only by active transport. Equations 5 and 6 con­
verge and residence time has the value x = L /V = 37 min 42 s. If, in addition to overloading,
the passive transport decays, the residence time of phagocitosed deposits tends to infinity.
The model just presented can be useful for an analysis of the influence of different phenom­
ena on the clearance and retention of deposited and phagocitosed particles in the lung. It has
to be emphasized that exit times in this article were calculated for a single alveolus.
The exit time of AM from the alveolar sac, because of its complex composition of single
alveoli, will be much longer, on the order of hundreds of hours.
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