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Morphometric estimation of pulmonary diffusion capacity
MORPHOMETRIC ESTIMATION OF PULMONARY DIFFUSION CAPACITY VI. EFFECT OF VARYING POSITIVE PRESSURE INFLATION OF AIR SPACES’
EWALD R. WEIBEL, PETER UNTERSEE, JOAN GIL and MARTIN ZULAUF Anatomisches
Institut der Uniuersiriit Bern, cmd Biozentrum der Uniuersitiit Basel, Switzerland
Abstract. The changes
the free alveolar diffusion
capacity.
were studied
in lung volume
surface
area.
Lungs
by electron
perfusion
methods.
of the septa
beneath
Levels by gradual
on completely explained
It is concluded
available
diffusion
phometric
unfolded estimates
barrier
change that
capacity lungs.
at five points
portions,
volume
by as much
part
Iming layer.
parts
Part
of reversed
and
into the
to that
hysteresis;
measured this can be
the use of a constant
as compared
of the differences
of the exposed
being dislocated
as compared
in the level of lung inflation
as 50 to 75 percent
This may explain
thickness
surface
diagram
was reduced
Most of the tissue barrier
shows a pattern
in the free alveolar
the variations
the surface
surface
capillary
lead to a reduction
in the
to the values obtained
between
physiological
of
pulmonary
of the pressure-volume
the thicker
barrier
variation
this influences
The alveolar
of the septum.
the effective mean
lungs. The capillary
by the hysteretic
pressure. completely
of the thinnest
this reduces
unfolded
folding
shifted to deeper regions
consists
of the septum;
using
cause a hysteretic
by how much
stereological
becomes
depth
and dellation
in this study
fixed by vascular
capillary
to the free surface
to inflation
microscopy
at lower inflation network
related
It is examined
and
on mor-
of DL.
Alveolo-papillary
membrane
Lung inflation
Capillary
blood
Morphometry
Diffusion
capacity
Pulmonary
Electron
microscopy
of lung
hysteresis
Surface lining layer
The morphometric estimates of pulmonary diffusion capacity hitherto obtained (Weibel, 1970; Siegwart et al., 1971; Weibel, 1972) considerably exceed corresponding physiological estimates (Piiper et al., 1969; Bitterli et al., 1971; Ghinet, Micheli and Haab, 1972). Since the two models defining DL (Weibel, 1970) imply that both Accepted fir ~libl~e~ition 2 May 1973. i This work was supported by grants 3.5.68 and 3682.71 by the Sandoz
Stiftung. 285
of the Swiss National
Science Foundation
and
286
E. R. WEIBEL
et d.
approaches should yield comparable data, the reasons for this systematic disagreement need to be clarified. The present study was undertaken to demonstrate in how much variations in the degree of lung inflation may modify the morphometric estimates of DL. One of the fundamental assumptions of the morphometric model is that every single unit of the alveolar tissue surface participates in gas exchange in proportion to its “loading” with capillaries and in dependence of the local barrier thickness. In our earlier studies we have therefore strived for a complete unfolding of the alveolar surface by fixing the lungs by controlled instillation of fixatives into the airways. This approach is justified because the diffusion “capacity” should indicate the ~~~~~~1 ca~abiiit~ of the lung to exchange gases by diffusion and this should be proportional to the ~xi~ul exchanging surface found in a fully unfolded lung. Recent studies on size and curvature of the free surface of pulmonary air spaces in specimens fixed by vascular perfusion under controlled conditions of positive pressure inflation revealed that considerable fractions of the alveolar tissue surface were excluded from immediate contact with alveolar gas because of an apparent folding of interalveolar septa, and even because of a partial or total collapse of individual alveoli (Gil and Weibel, 1972). This finding suggested that the assumption oftotal participation of the alveolar tissue surface in gas exchange -though theoretically correct in defining our model - would not be fulfilled in the living lung. In the present study we have therefore performed a morphometric estimation of pulmonary di~usion capacity on rat lungs fixed at live different points of the hysteretic pressure-voIume curve in order to determine by how much the level of inflation could influence DL. Material and methods a) FIXATION
AND PROCESSING
The material used in this study was derived from the same rat lungs as those studied by Gil and Weibel (1972); we therefore refer to that paper for all technical details. The lungs were fixed in situ by sequential perfusion through the pulmonary vascular bed of Ringer, glutaraldehyde, osmium-tetroxide and uranyl-acetate solutions using a pressure controlled peristaltic pump. Three lungs were fixed at each of five different points on the pressure-volume curve: 7, 12, and 16 mm Hg on the inflation curve and 12 and 7 mm Hg on the deflation curve. Since we worked in the open chest, airway inflation was achieved by positive pressure applied through a tracheal cannula. The perfusion pressure was kept constant in all instances at about 35 mm Hg at the beginning of the catheter (Gil and Weibel, 1971) which amounted to a pulmonary arterial pressure of about 25 mm Hg. After removal of the lungs their volumes were determined by a water displacement method (Scherle, 1970). From each lung five blocks derived by stratified sampling from different areas were dehydrated with ethanol and embedded in Epon 812. Sections of 70@-900 A
DIFFUSION CAPACITY
AND INFLATION
287
thickness were cut on a Reichert or LKB ultramicrotome using a diamond knife. They were picked up on parlodion covered 300 mesh grids, stained with lead citrate (Reynolds, 1963) for 10 min, and examined in a Philips electron microscope EM 300. b)
MORPHOMETRIC EXAMINATION
From each of the five sections per animal fifteen random micrographs were recorded on 35 mm film providing a total of 75 micro~raphs per animal for morphometric analysis. The stereological procedures used have been previously reviewed in detail (Weibel, 1969, 1970). The following basic tiarameters were estimated using a multipurpose test system containing 84 test lines of 2 cm and 168 test points: vv, - Volume density of air spaces ~alveoli~alveolar ducts) - Volume density of surface lining layer Vv, - Volume density of tissue (epithelium + interstitium + endothelium) Vv, - Volume density of capillaries Vv, - Density of functional or free surface of alveoli Sv,, Surface density of capillaries Sv, Harmonic mean thickness of a~~lood-barrier (including surface lining %(r+s) layer). Absolute values were obtained by multiplying the relative data (densities) by the parenchymal lung volume, V,. This parameter was obtained from the measured lung volumes, V, by subtracting the non-par~nchymal volume, composed of conducting airways and blood vessels, and of connective tissue, making the following assumption: in the fully inflated lung 18% of the rat lung is non-parenchyma (Burri and Weibel, 1971); of this about half is tissue, the remaining half being the content of larger airways and blood vessels; whereas the tissue volume would remain constant, the air and blood volumes might depend on the level of inflation and must be calculated in proportion to the actually measured lung volume. After subtracting 9”/, of the maximal lung volume from the measured lung volume the resulting figure was multiplied by 0.91 to correct for air and blood in conducting channels. Calculation of DM and DL followed the previously described model (Weibel, 1970). Instead of alveolar tissue surface, S,, the free or functional air space surface, S,,, was introduced; for estimating harmonic mean barrier thickness the distance from the free surface to the nearest point on the capillary surface along the random test lines was measured. The surface lining layer was therefore not treated as a separate entity but rather as part of the tissue barrier. This appeared justified because (a) it was often rather difficult to recognise the tissue surface in regions where it was heavily folded; (b) m . such folds the two adjoining tissue surfaces were in such close contact that they could not be conceived as boundary between the tissue and the virtually inexistant extracellu~ar lining layer. The hematocrit and the harmonic mean thickness of the plasma layer could, of course, not be estimated in this study since blood had been removed; the‘values found by Burri and Weibel (1971) were therefore used. Statistical group comparisons were performed by aid of the two-sided t-test.
E. R. WEIBEL ef ut.
A
Fig. 1. Low power electron
micrograph
of folded septa between
three alveoli (A). Infoldings
of epithelial
surface marked by arrows. Surface smoothed by extracellular lining (LL) which contains an alveolar macrophage (M) in a broad niche. Note that majority of cell bodies is shifted to deeper regions leaving predominantly Key to ahhrrsiatiotzs A
Alveolus
BM Basement C
barrier
portions
at the free surface.
EP2 Alveolar membrane
Capillary
CF Collagen EN Capillary
Bbre endothelium
EP
epithelium
Alveolar
the thinnest
2700 x
used in figs. 1-7: epithelium
type II
FB
Fibroblast
LL M
Extracellular lining layer Alveolar macrophage
V
Venule
DIFFUSION
CAPACITY
AND INFLATION
289
Results 1. MORPHOLOGICAL
OBSERVATIONS
In studying changes in the curvature of alveoli (Gil and Weibel, 1972) we had noted that interalveolar septa become folded beneath the surface lining layer, thus leading to partial or complete collapse of alveoli. As a consequence, part of the capillaries become shifted to deeper regions of lung tissue. In the context of the present study on the modifications of the gas exchange apparatus occurring with different degrees of airway inflation it was necessary to have a closer look at the variations in the disposition of the air-blood barrier. The first striking observation was that by far the largest part of the free barrier, i.e. the barrier where air and capillary blood come into closest contact, was constituted of the thinnest barrier portions. This was the case as well when one sheet of capillaries was folded like bellows (fig. 1) as when two or more capillary sheets came to be superimposed due to the partial or total collapse of an alveolus. Barrier elements contributing a larger mass, such as connective tissue fibers or cell bodies of epithelial, endothelial or interstitial cells were mostly shifted into the depth of the septum; this was the case even at the highest levels of inflation where the plication of septa was not as marked as at the other points of the pressure-volume curve. Figures 2 to 5 show that the process of folding of capillaries and barrier is a gradual one. In the longitudinal section of a capillary channel in fig. 2 one may recognise three folds of different depth in the wall. The first is shown in greater detail in fig. 3 : a thin portion of the barrier, consisting of cytoplasmic epithelial and endothelial sheets and fused basement membranes is crumpled in such a way that the short indentation of the epithelial surface contains a very small amount of surface lining material. In the second fold a deeper and wider cleft is formed (fig. 4); this fold is associated with a collagen fiber and a fibroblast which lie at the deepest point. As shown elsewhere (Weibel, 1973) connective tissue fibers are interwoven with capillaries in such a fashion that a relaxation of tension on the fibers should shift the fibers toward the center of the septum. There is therefore a fundamental difference between
folds 1 and 2: the second
(and the third)
fold are due to the bellows-like
plication of the capillary, whereas the first one is due to a crumpling of the air-blood barrier in order to adapt its extent to the area available. Figure 2 reveals that in a fourth deeper pocket both types of folds can be combined. Very deep folds (fig. 5) can finally be formed when the bellows-like plication of the individual septa no longer suffices to reduce the surface to the space available so that the surfaces of folded septa collapse onto each other (figs. 1, 2, 5). The last step is collapse of an entire alveolus. The folding of the alveolar epithelial surface occurs beneath the surface lining layer. Over {he thin barrier portions it is usually extremely thin, as described previously; deeper pools are observed over deeper folds and sometimes in collapsed regions (figs. l-5).
290
E. R. WEIBEL et ill.
Fig. 2. Electron m~crograph of longitudinal section through lightly folded capillary channel (Cl ). Folds of barrier indicated by arrows: 1 invcives only minimal barrier, whereas 2 and 3 are related to connective tissue elements; 4 is a deep pocket due to coIlapse of the surfaces in contact with capillaries Cl and C2; asterisk indicates the presence of a fine fold in this deep pocket. Deep pools of lining layer (LL) are contained in some of the clefts. 8000 x
2. MORPHOMETRIC DATA Table 1 summarises the data obtained in these five groups of animak. As reported in detail in the previous paper (Gil and Weibel, 1972) the hmg volume, V,, shows a distinct pressure-volume hysteresis. This is due to the variations in air volume, V,,
DIFFUSION
Fig. 3. Higher
power
( CJ fig. 2) composed epithelium
of fold in thin barrier of cytoplasmic
(EP) and endothelium
of fused basement small amount
CAPACITY
membranes
sheets of (EN) and
(BM).
291
AND INFLATION
Fig. 4. Fold fibroblast
in barrier
(FB) is deeper
to collagen
fiber (CF)
and contains
larger
and pool
of lining layer (LL). 23000 x
Very
of lining layer. 23000 x
which increases on the inflation limb, and then decreases to a lesser degree upon deflation (fig. 6). The capillary blood volume, V,, also exhibits hysteretic changes (table 1, figs. 6 and 7) but the hysteresis appears partly reversed: decreasing on inflation and increasing to a greater degree on deflation. As shall be discussed in detail below this seemingly strange pattern is due to the use of changing positive airway pressure together with constant perfusion pressure. There appears to be some variations in the tissue volume, V,, but none of the points differ significantly from the others. The tissue volume amounts to only about 5 percent of total lung volume at the highest inflation level, so that the expected statistical error is fairly large in the analytical system employed. This holds even more for the extracellular lining layer which amounts to less than 1 percent.
292
E. R. WEIREL et a/.
Fig. 5. Folding
of interalveolar
form of deep and narrow
septum
due to partial
clefts (rows of double
to the same interalveolar
septum
arrows).
collapse
of alveolar
Capillaries
which is heavily
marked
folded (dashed
surface
from both
with asterisk
sides in
(C”) belong
line). 6400 x
Nevertheless, it appears that this lining layer is considerably reduced at the highest inflation level (16 mm Hg); this value is significantly different from the others, whereas the other points do not differ significantly from each other. The free alveolar surface area, S,,, shows a pressure surface hysteresis (fig. 8) which
293
DIFFUSION CAPACITY AND INFLATION
IO-
--I---
Q8”
t
7-
T
6-
2 25 3
x 4-
3
2
3-
“0 J4
2-
“t l-
vc 7t
r?2__ 71
12 t AIRWAY
VS
PRESSURE
Fig. 6. Volumes of air (V,), tissue (V,). capillary lumen (V,) and surface lining layer (V,) at the five points on the pressure-volume curve investigated.
closely follows the pressure-volume hysteresis of air spaces, as already demonstrated in the previous paper (Gil and Weibel, 1972). The capillary surface is of the same order of magnitude as the alveolar surface at the highest inflation level, but it is larger at all other points (table 1, fig. 8). It does not change significantly on the inflation limb, but it increases upon deflation; the capillary surface thus follows partially the pattern of (reversed) hysteresis described for the capillary volume, though to a lesser degree. The harmonic mean thickness of the air-blood barrier, comprising both tissue and alveolar lining layer, is at every point smaller than the values obtained on specimens fixed by instillation of fixatives into the airways (fig. 9). This is due to the fact that the free barrier comprises in general the very thin portions of the tissue, whereas those parts which contain nuclei, connective tissue elements etc. are almost invariably shifted to deeper regions of the folds (figs. l-5). The barrier becomes slightly thinner with increasing inflation; this is probably due to a gradual reduction in the pools of extracellular lining layer found in clefts and to an opening of some folds where two barrier layers are intercalated between air and blood. 3. ESTIMATION OF DIFFUSION CAPACITY Since it was not possible to separate the tissue and surface lining layers in estimating
E. R. WEIBEL et d.
294
“,
i--
AIRWAY
PRESSURE
Fig. 7. Change in capiilary volume as function of airway pressure (mean + 1 S.E.).
barrier thickness, these two layers had to be treated as one barrier. Its diffusion capacity was defined as:
We have used the free alveolar surface, S,,, as the sole determinant of gas exchange surface; the permeability coefficient for tissue was used because tissue made up more than 90 percent of the barrier. With respect to the plasma layer we used the measured capillary surface, S,, as determining its extent; since the thickness of the plasma could not be measured, owing to blood removal by perfusion fixation, we used the value zhp= 0.18 p as determined by Burri and Weibel(l971) for rat lungs. For the physical coefficients the maximal values were used (Weibel, 1970). IS, = 3.3. lo- 8cm2/min, mm Hg K, = 4.3 ’ lo-’ cmz/min. mm Hg @o,= 2.5 ml/ml. min. mm Hg
DIFFUSION CAPACITY
Saf
Functional
SC
Capillary
alveolar
AND INFLATION
surface
surface
295 t i . .
area
area
AV
m2 96
7
12 Airway
Fig. S. Change
in free alveolar
76 mmHg
pressure
surface area, S,,, and in capillary
surface
area, S,.
INSTILLATION
Tht
T
72t AIRWAY Fig. 9. harmonic layer.
mean thickness
For comparison
16t : PRESSURE
of total air biood
the value of the tissue lungs fixed by instillation
barrier
barrier
7t
comprising
thickness
into the airways
mm both
9
tissue and surface
as measured is also plotted.
in completely
lining
unfolded
296
E. R. WElBEL
et al.
The membrane diffusion capacity, DM, included the resistances offered by tissue, surface layer and blood plasma:
& = &- + $
(2)
tr+st
P
whereas the total lung diffusion capacity included in addition the erythrocyte ponent :
t3)
1
DL =
com-
D&+&+&. P
e
The last columns of table 1 and figs. 30 and I1 report the data for the diffusion capacities as calculated from the group means of the morphometric data. The figures include an indication of the range of values of DM and DL as calculated from measurements obtained on specimens fixed by instillation of glutaraldehyde into the airways thus exhibiting a fully unfolded tissue surface; to this end the data of Burri and Weibel (1971) obtained on young rats raised in Berne as controls were corrected to match the larger body weight (2.50 g) of the animals of the present study assuming a linear relationship between DL and W (Weibel, 1972; Siegwart et C&1971). It is evident from fig. 10 that DM shows a hysteresis which closely follows that exhibited by the air volume and the free air space surface (fig. 8). The largest values, found at 16 and at 121 are about 15 percent smaller than those obtained on instillation fixed specimens. In the lungs of the inflation limb DM amounts to 40 percent of the, TABLE Synopsis Group
Body weight
VL cm3
of morphometric v, cm’
V, cm3
parameters: V, cm3
1 group V, cm3
means
k
S
1 standard SC mr
n$
error rhCl+s) pm
g
7t
127
16f
121
71
240
248
261
252
262
5.09
2.36
0.507
0.648
0.063
0.222
0.439
0.3i3
+ 0.53
& 0.44
t 0.012
& 0.044
_+O.OiI
& 0.018
kO.014
* 0.022
7.74
4.88
0.366
+ I.05
+ 0.89
i O&16
0.691 IO.062
0.047
0.226
0.373
0.287
& 0.009
k 0.048
&O.Of8
kO.017
12.85
9.49
0.396
0.745
0.012
0.467
0.435
0.240
+ 0.30
_t 0.35
+ 0.006
* 0.083
kO.003
kO.019
+ 0.048
+ 0.018
11.28
7.66
0.606
0.850
0.097
0.454
0.568
0.258
+ 0.84
+ 0.82
* 0.052
+ 0.078
& 0.037
f 0.016
kO.015
* 0.020
9.30 *0.27
5.77 ,0.44
0.658 &0.055
0.944 +0.155
0.041 io.007
0.376 &O.OlI
0.508 io.055
0.287 kO.017
DMo,
Dk>, ml 0,
---min.mm
Hg
1.91
0.76
2.01
0.63
3.95
0.79
4.05
1.10
3.18
1.08
297
DIFFUSION CAPACITY AND INFLATION
nl.~i~‘.~~H~’
INSTILLATION
I
** Fig. 10. Membrane metric parameters
diffusion obtained
capacity
RATS -2509
12 76 mm Hg AIRWAY PRESSURE for oxygen as calculated from the group means
7
in this study is compared
to the value obtained
of the morpho-
on instillation-fixed
lungs.
value in instillation fixed lungs, whereas DM only falls to about 70 percent on deflation to 7 mm Hg. As expected, DL is greatly influenced (fig. 11) by the changes in capillary volume which had shown a reversed hysteresis, falling on inflation and rising on deflation. The largest values were therefore found on the deffation limb, where DL amounted to about 757; of the control value found in instillation fixed specimens. At maximal inflation and on the inflation limb DL appeared reduced to about 5Oyi. Since the changes in V, were due to the use of positive pressure in airway inflation - necessitated by the experiment -we have recalculated DL with a constant V,; in this case DL also shows the “normal” hysteresis (fig. 11).
1. CHANGES
IN MORPHOMETRIC
PARAMETERS
RELATED
TO DIFFERENT
DEGREES
OF
LUNG INFLATION
This study confirmed our previous finding (Gil and Weibel, 1972) that the free alveolar surface area depends on the degree of in~ation; when plotted against in-
E. R. WEIBEL et Ul.
298
RATS -2509
AV
measured Vc constant
DLO,
A
0
ml min. mmH‘4
I
1,
INSTILLATION
I i
v
v ____~_
v---
*‘\’ /
.A----_
l-
--+/
------
7 AIRWAY
a/’
,’
x 0.7:
/ ‘.
,A
M
I
12
16
-
mm Hg
PRESSURE
Fig. 11. Total lung diffusion capacity for oxygen as calculated from the present measurements (full triangles) compared to the standard value derived from instillation-~xcd completely unfolded lungs. The open triangles report the values obtained if a constant capillary volume of 0.5 mf is assumed.
flation pressure it shows a hysteresis which is superimposable with that of air volume. It should, however, be noted that the values for alveolar surface area here reported are larger by about 20% than those previously obtained on the same lungs (Gil and Weibel, 1972); the use of electron microscopy at comparatively high magnification, as compared to light microscopy in the previous study, allows more surface detail to be recognized. Such systematic differences depending on magnification are a common observation and will require a critical study of the exact reasons. Caution must be exercised in comparing light and electron microscopic data from uncontrolled studies. The barrier between air and blood is formed by the tissue layer and by the extracellular lining material (Gil and Weibel, 1969/70). It is noteworthy that the harmonic mean barrier thickness was smaller in the present material than in rat lungs fixed by airway instillation (Burri and Weibel, 1971). It is not easy to exclude all artefact related to the different route of application of the fixatives, or to the use of somewhat different solutions since we needed to adjust the oncotic pressure
DIFFUSION CAPACITY AND INFLATION
299
of the perfusate by means of dextran. However, it was most striking to observe a very characteristic distribution of thin and thick barrier portions: most thicker regions containing cell nuclei or connective tissue elements were shifted away from the free surface into deeper regions of folds, whereas those parts of the alveolo-capillary barrier which were immediately adjacent to the free alveolar surface were composed almost exclusively of thin barrier portions where endothelium and epithelium are reduced to thin cytoplasmic sheets and their basement membranes are fused. This surprising observation reveals a design of interalveolar septa which assures good gas exchange properties of the barrier even if the septum becomes folded; it can be explained by the disposition of fibers, cells and capillaries in the septa (cJ Weibel, 1973). The volume of the extracellular lining layer is of the order of 5 percent of alveolar tissue and amounts to about 0.1 ml/m2 of alveolar surface at the higher inflation levels. The capillary surface area and volume also show a hysteresis with inflation and deflation. On inflation the capillary surface varies very little, being of the order of magnitude of the alveolar surface at maximal inflation, or only slightly below that found in instillation fixed lungs. On deflation, however, we observed an increase; this is probably related to the drastic increase in capillary volume observed on the deflation limb, a point which requires special consideration. 2.
REVERSED HYSTERESIS OF CAPILLARY
VOLUME
One of the most surprising findings of this study is the reversed hysteresis of the capillary volume (fig. 7). It is to be suspected that this is due to the use of positive pressure inflation together with a constant perfusion pressure. The capillary volume must be governed by the capillary-alveolar pressure gradient: (4)
AP = PC-P,
and this is bound to vary appreciably in our experimental situation; assuming P, to be about 20 mm Hg, AP will vary between 4 and 13 mm Hg. Fung and Sobin (1!&72)and Sobin et al. (1972) have recently measured changes in alveolar capillary sheet thickness with AP; between 4 and 13 mm Hg their data indicate an increase in sheet thickness from about 5.1 to 7.2 pm, i.e. by a factor of 1.41. In the present study, the capillary volumes at 7 mm Hg were increased by factors of I ..; I(, I .7 with respect to 16 mm Hg; this is compatible with the data of Sobin et 111.(19172) and would thus appear to be due to a widening of capillaries due to increasing AP. This does, however, not explain the hysteretic pattern, i.e. the difference between V, at the same pressure gradient on the inflation and on the deflation limb. The explanation is found in the fact that V, is not only influenced by the pressure gradient, but also by the surface area over which this pressure gradient acts on the capillaries, and this must be related to the free alveolar surface S,,. As developed in the appendix it is found that (5)
V, = a-b.S,,(P,-P,).
300
E. R. WEIBEL et al.
r
\
\
\ \ \
0.7
x)Pc=2OmmHg
\
--
PC
q2lmmHg
PC =19mmHg
1
04 I-
.
-Tl -// Fig. 12. Four curves obtained a capillary
The coefficients
pressure
a and
j
I
I
12
16
AIRWAY PRESSURE by fitting eq. (5) to the data on capillary of 20 mm Hg describe
the reversed
b can be calculated
from
volume. The two curves based on
hysteresis
reasonably
two arbitrarily
well.
chosen
points,
assuming “reasonable” values for the pressure gradient. In fig. 12 a number of curves produced by this analysis has been plotted together with the original data on capillary volume. It is seen that they all describe the data reasonably well, at least in the sense that they all show an identical hysteretic pattern. The best fit was obtained by assuming capillary pressure to be 20 mm Hg and calculating a and b from the capillary volumes measured at 77 and 16 mm Hg alveolar pressure. We may conclude from this analysis that the observed variations in the alveolar capillary volume were due to the combined variations in the alveolar surface area and in the prevailing alveolo-capillary pressure gradient, the latter being caused essentially by the positive pressure inflation with constant perfusion pressure. It remains to be shown whether such variations are also observed in negative pressure inflation or not, in other words, whether this finding is an artefact of the experimental design or whether it bears some significance for the living lung. Studies on blood flow such as those of Roos et al. (1961) and Fung and Sobin (1972) would suggest
DIFFUSION
CAFACITY
AND
INFLATION
301
a different effect of positive versus negative pressure inflation on the pulmonary vascular bed; how much of this is due to changes in the capillary bed is not clear yet, however. We should further mention that the present analysis did not take into consideration the effect of possible changes in the surface tension occurring along the pressurevolume diagram, as was suggested from our previous study (Gil and Weibel, 1972). 3.
DEPENDENCE
OF DWFUSZON
CAPACITY
ON AIRWAY
INFLATION
is quite evident from the model that the free atveofar surface area is the main determinant of the so-called membrane diffusion capacity DM. ft is therefore not surprising that DM shows a hysteresis which is very similar to that of alveolar surface area. It is slightly modified by the changes in barrier thickness and capillary surface area. Compared to values of DM obtained on instillation fixed material, where the alveolar epithelial surface is, on purpose, completely unfolded, we find that the highest value at 16 mm Hg inflation pressure is reduced by some 17 percent. This is due to the fact that even at this pressure a small part of the tissue surface is folded beneath the lining layer and thus not availabie for gas exchange. At the lowest inflation levels DM may fall down to as little as 40 percent of the value in completely unfolded lungs. The total lung diffusion capacity DL is, however, greatly in~uen~ed by capillary blood volume. The observed reversed hysteresis in capillary volume therefore changes the hysteresis pattern of DL considerably (fig. 1I). The largest vaIues are 73 percent and the lowest values 50 percent of those estimated for instillation fixed control lungs. Since we cannot be certain that the observed changes in capillary volume bear resemblance to those occurring in the living lung inflated by negative pleural pressure these data must be interpreted with caution. If the capillary volume were to remain unaffected by the degree of inflation the variations in DL would be somewhat different, but there still would be a dependence on the level of inflation (fig. 11); the truth may he somewhere inbetween. The general conclusion from this study is that the diffusion capacity of the lung depends on the level of inflation. In the range of physiologi~l airway inRation it must therefore be smaller than the maximal values estimated for completely unfolded lungs, those values which are determined essentially by the stable tissue framework of lung parenchyma. This maximal diffusion capacity is able to adapt during development to alterations in oxygen requirement of the organism, or to changes in oxygen supply (Burri and Weibel, 1971; Geelhaar and Weibel, 1971; Weibel, 1970/71). The functionally available diffusion capacity is, however, smaller, and this explains part of the differences between morphometric and physiological estimates of DL (Siegwart et al., 1971; Chinet Edat., 1971; Piiper et crl., 1969). The increase of DL with inflation may pa&y explain the increase in Dt observed with exercise or increased Vo, (Riper et al., 1969; Bitterli et al., 1971f where airway ventilation is maintained at a higher inflation level thus exposing a greater part of the alveolar surface to alveolar gas.
It
E. R. WEIBEL
302
et Uf.
Appendix INTERPRETATION
OF HYSTERESIS
IN CAPILLARY
VOLUME
is to be investigated whether the observed reversed hysteresis of the capillary volume (fig. 7) can be explained by a combined effect of changing alveolo-capillary pressure gradient and the hysteresis of the free alveolar surface area in an inflationdeflation experiment. The model lung is assumed to be made up of air in alveoli (V,), air in ducts and relatively rigid airways (V,), practically incompressible tissue (V,), blood in capillaries (V,), and blood in larger relatively rigid blood vessels (V,), so that total lung volume is It
(6)
vt = V~~V~~~~~V~~V~.
In an inflation-deflation experiment using variable positive pressure in airways, P,, and constant pressure applied to the blood vessels, P,, V,(P,), V,(P,) and VC{PA)show a hysteresis, the pattern of the former two parameters being closely related, whereas that of capillary volume is different. The change in air volume V,(P,) is related to a change in alveolar surface, S,(P,), which also shows a hysteresis. The ratio S,/V, is constant (Gil and Weibel, 1972) which is related to the observation that the alveolar surface does not increase by stretching but rather by unfolding of folded parts of the surface. In the following analysis the mechanisms causing the hysteresis in V,(P,) and S&P,) are not further considered, however, the hysteresis in V, (PA) is treated as an induced effect. We now first assume that at each pressure, PA, part of the surface, s:i, of an individual alveoius i is free, i.e. exposed to air, whereas another part, siz, is shifted into folds (fig. 13). These surfaces are related to the (maximal) surface of the completely unfolded alveolus, ~6~~~.as follows (7)
s61(P,4) = st,,X-sL(PA)
*
This assumption
is supported by our previous findings (Gil and Weibel, 1972). It is further assumed that the alveolar surface is homogeneously lined by a sheet of capillaries (fig. 13). The area of contact, a’, of an individual alveolus with capillaries is hence proportional to the surface area of the alveolus: ai= a-sil . (8) This contact area only changes because sii changes with P,. We may assume on the basis of previous findings (Gil and Weibel, 1972) that the folded regions of the alveolar surface are likewise loaded with the same density of capillaries. The volume of capillaries belonging to this alveolus is now given by the contact area and the thickness of the sheet, d, whereby we make the provision that d, in the exposed sheet may vary independently from dz in the sheet connected with folds. The exposed volume is (9)
vii = a’ai.d, I = sdt.s;,
; &=ct.cd
DIF~SION
CAPACITY AND INFLATION
303
Fig. 13. Model of spherical alveolus with pleating of surface used for deriving eq. (5) in Appendix.
where LXis the loading of alveolar surface with capillaries and cx’ a shape coefficient; the volume of the capillaries in folds is accordingly (10)
vi2 = edp- &
and the total capillary volume of alveolus i is
(11)
vi,= vi1 +viz.
The total capillary volume of all alveoli must hence be
(12) In de~ning the papillary volumes v,r and vC2 we now must introduce a number of crucial assumptions on the behaviour of the system:
304
E. R. WEIBEL et Ul.
1. The capillaries at the alveolar surface are connected to a common pressure reservoir, the pressure applied to the pulmonary artery, P,. The conducting vessels which distribute the blood (or perfusate) into the capillary sheet reduce this pressure to the capillary pressure P,; they are relatively rigid tubes when compared to capillaries so that the resistance in these arterial vessels is not greatly influenced by variations in alveolar pressure, P,. Consequently the pressure in the capillary bed, P,, is independent of P,. 2. Consider a change AP, in the alveolar pressure P,. It will be assumed that the superficial capillaries in the sheet enveloping the free alveolar surface react differently on AP,., than the deep sheets associated with the folds: the first will be deformed, an effect that translates in a corresponding change Av:,; the deformation of the deep lying capillaries is neglected, therefore vi. is assumed not to be affected by APA. Since this assumption is crucial for the following calculations, we provide further justification. In an idealizing model the tissue can be regarded, as far as deformations are concerned, as an incompressible fluid: it transmits pressure, but not stress forces and torques. However, the capillary sheet enveloping the free alveolar surface, being at the boundary, is more likely to be described as an elastically deformable body. The pressure change APA acts as a tension force normal to the alveolar surface and leads to a change in the capillary volume. This can be visualised in a model
a
PC
,,., .,.,.,. .,.,.,.,..., .,.,.,., .;,..,., .,., .,. ,. /
Fig. 14. Alternative Diagram
model of capillary
d shows that pillars forming
sheet which is pleated
upon reduction
wall of deep capillary
segments
shift of large structures
of available
are relatively
into depth of septum (c_C figs. l-7).
surface (a-c).
thicker
due to the
DIFFUSION
CAPACITY
305
AND INFLATION
treatment in which the capillary is thought as being made of deformable, but nonstretchable and incompressible material. The stress force will then change the cross section, but not the circumference of the capillaries. Such deformations clearly lead to a change in On the other hand, the capillary sheet associated with the folds is
vi,r.
embedded in the tissue (figs. 1 and 5) and therefore feels APA not as a stress force, but as a pressure change of the “liquid milieu”. Since the capillary walls are incompressible, no change in v)~ results. Some morphological evidence can be given to support these assumptions. As shown schematically in fig. 14 the plication of the barrier results in the formation of some kind of “pillars” formed by two barriers (figs. 2 and 4); the pillars are hence at least twice as thick as the superficial capillary wall. This is further accentuated by the fact that the infolded barrier portions are thicker than the superficial ones (fig. 14d) and contain connective tissue elements. We can therefore conclude that the assumption on the different effect of AP, on vi, and vi, is ‘sufficiently justified. Let us now calculate the capillary volume in its dependence on the pressure gradient P, - P,, where PA is varied and P, is kept constant. The capillary sheet enveloping a given alveolus i was described by the surface sL1 and the thickness di. Let di have the value d, at “equilibrium” P, - PA = 0. If PC- P, # 0, the sheet will be deformed. The theory of elastic deformations (Landau and Lifshitz, 1959) describes the deformations in terms of a distortion tensor Bik and a stress tensor gik according to the formula
G is the torsion or shear modulus, m is Poisson’s contraction constant, 6i, the Kroneker symbol, Tr 0 stands for the trace. We approximate by disregarding the on the grounds that it is related to hydrostatic Poisson contraction (let m -co) compression
deformations
which
we have ignored.
Furthermore
we go over
to
the diagonalised form of eq. (14) which is justified if the minimal radius of curvature are 5 pm of the alveolus is much larger than d, ~ the actual orders of magnitude for d, and 50 pm for the alveolar mean curvature of rat lungs (Gil and Weibel, 1972). In this approximation the distortion tensor reduces to ljik+Adl/do, the relative change of the sheet thickness, and the stress tensor is simply the pressure difference, c~~-+P~-- PA, directed normal to the alveolar surface. We then have d,(P,)
+,(l-~j.
(15) If this is introduced
(16)
= d, (1- A&/d,)
v;,(PJ
in (9) we get =sdO
P -P, 1 - +
. wT4)
.
a.
306
R. WEIBEL
et
al.
In calculating the volume of deep capillaries we assume, in accordance with the above-given arguments, the corresponding sheet thickness to be constant at d,; to get rid of additional parameters we put in first approximation dz = do. Then (17)
viz = s.d&,,,-s;r(PJ)
Since according to eq. (12) the total capillary volume is the sum of all the volumes associated with individual alveoli we obtain:
P-9
Since c sLiWX = S,,,, L
the maximal and the free alveolar surface, it follows that
(19)
V, = e(dr -d&S,r+d,S,,,,
.
Substituting eq. (15) we obtain
(20) Equation (20) is of the form (21)
V,(P,)= a-b.SJPJ*(P,-PA) a = Ed,,. S,,,,
Note that ifs&P,) describes a hysteresis, then V,(P,) describes a reversed hysteresis, provided b < 0. The parameters detining the coefficients a and b are not known, except for S,,,, which could be assumed to be represented by S, determined on instillation fixed lungs. However, these parameters are, by definition, constants of the system and need therefore not be separated. The coefficients a and b can be determined from two arbitrarily chosen experimental points. The capillary pressure P, is not precisely known; it must, however, lie between the head pressure of about 25 mm Hg in the pulmonary artery and the maximal alveolar pressure of 16 mm Hg at which flow was still maintained. As shown on fig. 12 the best fit was obtained with PC=20 mm Hg, a reasonable value. If a and b were determined from points 7$and 16 their
DIF~SION
CAPACITY
307
AND INFLATION
values were found as a= 0.192 b = -0.109. It is shown in the discussion and in fig. 12 that with these coefficients eq. (21) provides a reasonable description of the observed reversed hysteresis of capillary volume in an inflation-deflation experiment using constant perfusion pressure and positive pressure airway inflation.
The authors gratefully acknowledge the skilfull collaboration of Miss Helgard Claassen, Mrs. Brigitte Gil-Sollereder, Mr. Karl Babl, and Miss Gertrud Reber. References Bitterli, J., H. Bachofen.
K. Kyd and M. Scherrer
diffusing capacity in man during graded ed. by M. Scherrer. Bern-Stuttgart-Vienna, Burri,
P. H. and
E. R. Weibel (1971).
Effect of Po, on the growing Respir. Physiol.
(1971).
Repeated
Morphometric
lung. Adaptation
estimation
by steady-state
methods. (1972).
Elasticity
perfusion.
diffusing
Improvements
sheet,
of pulmonary
waltzing
in demonstration
Circulation
diffusion
Res. 30:
capacity.
III.
mice. Respir, Physiol. 1 I: 3455366. of lining
layer
of lung alveoli
by
apparatus
for perfusion
fixation
with automatic
pressure
L. D. and E. M. Lifshitz (1959). Theory uptake
and R. Herbst
levels in anesthetized
determined
of Elasticity.
Pergamon
Press.
diffusing
capacity
at high
pH as an electron
and D. C. Prommas
and vascular
Scherle, W. F. (1970). A simple method 26: 57-60.
pressures.
IV. The normal
at basal and increased
for volumetry
(1961).
opaque
Pulmonary
stain
vascular
in electron resistance
as
J. Appl. Physiol. 16: 77-84.
of organs
in quantitative
B., P. Gehr, J. Gil and E. R. Weibel (1971). Morphometric
stereology.
estimation
Mikroskopie
of pulmonary
diffusion
dog lung. Respir. Physiol. 13: 141-159.
H. M. Tremer
and T. H. Rosenquist
(1972). Elasticity
microvascular sheet in the cat. Circularion Res. 30: 440450. Weibel, E. R. (1969). Stereological principles for morphometry Rea. Cyrol. 26: 235-302.
in rat lungs fixed
dogs. Respir. Physvsiol. 6: 219-232.
E. L. Nagel
by lung inflation
Sobin, S. S.. Y. C. Fung,
hysteresis
(1969). Pulmonary
Reynolds, E. S. (1963). The use of lead citrate microscopy. J. Cell Bid. 17: 208-211. Roos, A. L., L. J. Thomas,
study of pressure-volume
Respir. Physic& 15: 190.-213.
Piiper, J., A. Huch, D. Kotter
capacity.
II.
J. Microscopy 94: 241-244.
by vascular
Siegwart,
and CO pulmonary
alveolar
estimation
in Japanese
Gil, J. and E. R. Weibei (1972). Morphological
0,
capacity.
and hyperoxia.
Respir. Physiol. 8 : 13-36.
microscopy.
Gil, J. and E. R. Weibel (1971). An improved
Landau,
effects on 0,
of the pulmonary
oxygen consumption
Gil, J. and E. R. Weibel (1969/70).
control.
diffusion
rat lung to hypoxia
O,-
on Exercise,
Respir. Physiol. 13: l-22.
Theory.
A. and E. R. Weibel (1971). Morphometric
The effect of increased electron
of pulmonary Capacity
11: 2477264.
Fung, Y. C. and S. S. Sobin 451-469. Geelhaar,
Diffusing
of pulmonary
of the growing
Chine& A., J. L. Micheli and P. Haab (1971). Inhomogeneity capacity
measurements
exercise. In: Pulmonary Huber, pp. 139-149.
in electron
of the pulmonary microscopic
alveolar
cytology.
Iht.
308
E. R. WE~BEL
Weibel, E. R. (1970). Morphometric Respir.
PhJ&d.
estimation
of pulmonary
diffusion
capacity.
I. Model
and method
estimation
of pulmonary
diffusion
capacity.
V. Comparative
11 : 54. 75.
Weibel, E. R. (1972). Morphometric phometry
et ul.
of alveolar
lungs. Respir. Physinl.
Weibel, E. R. (1973). The structural
mor-
14: 2643.
basis of alveolo-capillary
gas exchange.
Physiol.
Recirws
53: 419495:
EWALD R. WEIBEL, PETER UNTERSEE, JOAN GIL and MARTIN ZULAUF Anatomisches
Institut der Uniuersiriit Bern, cmd Biozentrum der Uniuersitiit Basel, Switzerland
Abstract. The changes
the free alveolar diffusion
capacity.
were studied
in lung volume
surface
area.
Lungs
by electron
perfusion
methods.
of the septa
beneath
Levels by gradual
on completely explained
It is concluded
available
diffusion
phometric
unfolded estimates
barrier
change that
capacity lungs.
at five points
portions,
volume
by as much
part
Iming layer.
parts
Part
of reversed
and
into the
to that
hysteresis;
measured this can be
the use of a constant
as compared
of the differences
of the exposed
being dislocated
as compared
in the level of lung inflation
as 50 to 75 percent
This may explain
thickness
surface
diagram
was reduced
Most of the tissue barrier
shows a pattern
in the free alveolar
the variations
the surface
surface
capillary
lead to a reduction
in the
to the values obtained
between
physiological
of
pulmonary
of the pressure-volume
the thicker
barrier
variation
this influences
The alveolar
of the septum.
the effective mean
lungs. The capillary
by the hysteretic
pressure. completely
of the thinnest
this reduces
unfolded
folding
shifted to deeper regions
consists
of the septum;
using
cause a hysteretic
by how much
stereological
becomes
depth
and dellation
in this study
fixed by vascular
capillary
to the free surface
to inflation
microscopy
at lower inflation network
related
It is examined
and
on mor-
of DL.
Alveolo-papillary
membrane
Lung inflation
Capillary
blood
Morphometry
Diffusion
capacity
Pulmonary
Electron
microscopy
of lung
hysteresis
Surface lining layer
The morphometric estimates of pulmonary diffusion capacity hitherto obtained (Weibel, 1970; Siegwart et al., 1971; Weibel, 1972) considerably exceed corresponding physiological estimates (Piiper et al., 1969; Bitterli et al., 1971; Ghinet, Micheli and Haab, 1972). Since the two models defining DL (Weibel, 1970) imply that both Accepted fir ~libl~e~ition 2 May 1973. i This work was supported by grants 3.5.68 and 3682.71 by the Sandoz
Stiftung. 285
of the Swiss National
Science Foundation
and
286
E. R. WEIBEL
et d.
approaches should yield comparable data, the reasons for this systematic disagreement need to be clarified. The present study was undertaken to demonstrate in how much variations in the degree of lung inflation may modify the morphometric estimates of DL. One of the fundamental assumptions of the morphometric model is that every single unit of the alveolar tissue surface participates in gas exchange in proportion to its “loading” with capillaries and in dependence of the local barrier thickness. In our earlier studies we have therefore strived for a complete unfolding of the alveolar surface by fixing the lungs by controlled instillation of fixatives into the airways. This approach is justified because the diffusion “capacity” should indicate the ~~~~~~1 ca~abiiit~ of the lung to exchange gases by diffusion and this should be proportional to the ~xi~ul exchanging surface found in a fully unfolded lung. Recent studies on size and curvature of the free surface of pulmonary air spaces in specimens fixed by vascular perfusion under controlled conditions of positive pressure inflation revealed that considerable fractions of the alveolar tissue surface were excluded from immediate contact with alveolar gas because of an apparent folding of interalveolar septa, and even because of a partial or total collapse of individual alveoli (Gil and Weibel, 1972). This finding suggested that the assumption oftotal participation of the alveolar tissue surface in gas exchange -though theoretically correct in defining our model - would not be fulfilled in the living lung. In the present study we have therefore performed a morphometric estimation of pulmonary di~usion capacity on rat lungs fixed at live different points of the hysteretic pressure-voIume curve in order to determine by how much the level of inflation could influence DL. Material and methods a) FIXATION
AND PROCESSING
The material used in this study was derived from the same rat lungs as those studied by Gil and Weibel (1972); we therefore refer to that paper for all technical details. The lungs were fixed in situ by sequential perfusion through the pulmonary vascular bed of Ringer, glutaraldehyde, osmium-tetroxide and uranyl-acetate solutions using a pressure controlled peristaltic pump. Three lungs were fixed at each of five different points on the pressure-volume curve: 7, 12, and 16 mm Hg on the inflation curve and 12 and 7 mm Hg on the deflation curve. Since we worked in the open chest, airway inflation was achieved by positive pressure applied through a tracheal cannula. The perfusion pressure was kept constant in all instances at about 35 mm Hg at the beginning of the catheter (Gil and Weibel, 1971) which amounted to a pulmonary arterial pressure of about 25 mm Hg. After removal of the lungs their volumes were determined by a water displacement method (Scherle, 1970). From each lung five blocks derived by stratified sampling from different areas were dehydrated with ethanol and embedded in Epon 812. Sections of 70@-900 A
DIFFUSION CAPACITY
AND INFLATION
287
thickness were cut on a Reichert or LKB ultramicrotome using a diamond knife. They were picked up on parlodion covered 300 mesh grids, stained with lead citrate (Reynolds, 1963) for 10 min, and examined in a Philips electron microscope EM 300. b)
MORPHOMETRIC EXAMINATION
From each of the five sections per animal fifteen random micrographs were recorded on 35 mm film providing a total of 75 micro~raphs per animal for morphometric analysis. The stereological procedures used have been previously reviewed in detail (Weibel, 1969, 1970). The following basic tiarameters were estimated using a multipurpose test system containing 84 test lines of 2 cm and 168 test points: vv, - Volume density of air spaces ~alveoli~alveolar ducts) - Volume density of surface lining layer Vv, - Volume density of tissue (epithelium + interstitium + endothelium) Vv, - Volume density of capillaries Vv, - Density of functional or free surface of alveoli Sv,, Surface density of capillaries Sv, Harmonic mean thickness of a~~lood-barrier (including surface lining %(r+s) layer). Absolute values were obtained by multiplying the relative data (densities) by the parenchymal lung volume, V,. This parameter was obtained from the measured lung volumes, V, by subtracting the non-par~nchymal volume, composed of conducting airways and blood vessels, and of connective tissue, making the following assumption: in the fully inflated lung 18% of the rat lung is non-parenchyma (Burri and Weibel, 1971); of this about half is tissue, the remaining half being the content of larger airways and blood vessels; whereas the tissue volume would remain constant, the air and blood volumes might depend on the level of inflation and must be calculated in proportion to the actually measured lung volume. After subtracting 9”/, of the maximal lung volume from the measured lung volume the resulting figure was multiplied by 0.91 to correct for air and blood in conducting channels. Calculation of DM and DL followed the previously described model (Weibel, 1970). Instead of alveolar tissue surface, S,, the free or functional air space surface, S,,, was introduced; for estimating harmonic mean barrier thickness the distance from the free surface to the nearest point on the capillary surface along the random test lines was measured. The surface lining layer was therefore not treated as a separate entity but rather as part of the tissue barrier. This appeared justified because (a) it was often rather difficult to recognise the tissue surface in regions where it was heavily folded; (b) m . such folds the two adjoining tissue surfaces were in such close contact that they could not be conceived as boundary between the tissue and the virtually inexistant extracellu~ar lining layer. The hematocrit and the harmonic mean thickness of the plasma layer could, of course, not be estimated in this study since blood had been removed; the‘values found by Burri and Weibel (1971) were therefore used. Statistical group comparisons were performed by aid of the two-sided t-test.
E. R. WEIBEL ef ut.
A
Fig. 1. Low power electron
micrograph
of folded septa between
three alveoli (A). Infoldings
of epithelial
surface marked by arrows. Surface smoothed by extracellular lining (LL) which contains an alveolar macrophage (M) in a broad niche. Note that majority of cell bodies is shifted to deeper regions leaving predominantly Key to ahhrrsiatiotzs A
Alveolus
BM Basement C
barrier
portions
at the free surface.
EP2 Alveolar membrane
Capillary
CF Collagen EN Capillary
Bbre endothelium
EP
epithelium
Alveolar
the thinnest
2700 x
used in figs. 1-7: epithelium
type II
FB
Fibroblast
LL M
Extracellular lining layer Alveolar macrophage
V
Venule
DIFFUSION
CAPACITY
AND INFLATION
289
Results 1. MORPHOLOGICAL
OBSERVATIONS
In studying changes in the curvature of alveoli (Gil and Weibel, 1972) we had noted that interalveolar septa become folded beneath the surface lining layer, thus leading to partial or complete collapse of alveoli. As a consequence, part of the capillaries become shifted to deeper regions of lung tissue. In the context of the present study on the modifications of the gas exchange apparatus occurring with different degrees of airway inflation it was necessary to have a closer look at the variations in the disposition of the air-blood barrier. The first striking observation was that by far the largest part of the free barrier, i.e. the barrier where air and capillary blood come into closest contact, was constituted of the thinnest barrier portions. This was the case as well when one sheet of capillaries was folded like bellows (fig. 1) as when two or more capillary sheets came to be superimposed due to the partial or total collapse of an alveolus. Barrier elements contributing a larger mass, such as connective tissue fibers or cell bodies of epithelial, endothelial or interstitial cells were mostly shifted into the depth of the septum; this was the case even at the highest levels of inflation where the plication of septa was not as marked as at the other points of the pressure-volume curve. Figures 2 to 5 show that the process of folding of capillaries and barrier is a gradual one. In the longitudinal section of a capillary channel in fig. 2 one may recognise three folds of different depth in the wall. The first is shown in greater detail in fig. 3 : a thin portion of the barrier, consisting of cytoplasmic epithelial and endothelial sheets and fused basement membranes is crumpled in such a way that the short indentation of the epithelial surface contains a very small amount of surface lining material. In the second fold a deeper and wider cleft is formed (fig. 4); this fold is associated with a collagen fiber and a fibroblast which lie at the deepest point. As shown elsewhere (Weibel, 1973) connective tissue fibers are interwoven with capillaries in such a fashion that a relaxation of tension on the fibers should shift the fibers toward the center of the septum. There is therefore a fundamental difference between
folds 1 and 2: the second
(and the third)
fold are due to the bellows-like
plication of the capillary, whereas the first one is due to a crumpling of the air-blood barrier in order to adapt its extent to the area available. Figure 2 reveals that in a fourth deeper pocket both types of folds can be combined. Very deep folds (fig. 5) can finally be formed when the bellows-like plication of the individual septa no longer suffices to reduce the surface to the space available so that the surfaces of folded septa collapse onto each other (figs. 1, 2, 5). The last step is collapse of an entire alveolus. The folding of the alveolar epithelial surface occurs beneath the surface lining layer. Over {he thin barrier portions it is usually extremely thin, as described previously; deeper pools are observed over deeper folds and sometimes in collapsed regions (figs. l-5).
290
E. R. WEIBEL et ill.
Fig. 2. Electron m~crograph of longitudinal section through lightly folded capillary channel (Cl ). Folds of barrier indicated by arrows: 1 invcives only minimal barrier, whereas 2 and 3 are related to connective tissue elements; 4 is a deep pocket due to coIlapse of the surfaces in contact with capillaries Cl and C2; asterisk indicates the presence of a fine fold in this deep pocket. Deep pools of lining layer (LL) are contained in some of the clefts. 8000 x
2. MORPHOMETRIC DATA Table 1 summarises the data obtained in these five groups of animak. As reported in detail in the previous paper (Gil and Weibel, 1972) the hmg volume, V,, shows a distinct pressure-volume hysteresis. This is due to the variations in air volume, V,,
DIFFUSION
Fig. 3. Higher
power
( CJ fig. 2) composed epithelium
of fold in thin barrier of cytoplasmic
(EP) and endothelium
of fused basement small amount
CAPACITY
membranes
sheets of (EN) and
(BM).
291
AND INFLATION
Fig. 4. Fold fibroblast
in barrier
(FB) is deeper
to collagen
fiber (CF)
and contains
larger
and pool
of lining layer (LL). 23000 x
Very
of lining layer. 23000 x
which increases on the inflation limb, and then decreases to a lesser degree upon deflation (fig. 6). The capillary blood volume, V,, also exhibits hysteretic changes (table 1, figs. 6 and 7) but the hysteresis appears partly reversed: decreasing on inflation and increasing to a greater degree on deflation. As shall be discussed in detail below this seemingly strange pattern is due to the use of changing positive airway pressure together with constant perfusion pressure. There appears to be some variations in the tissue volume, V,, but none of the points differ significantly from the others. The tissue volume amounts to only about 5 percent of total lung volume at the highest inflation level, so that the expected statistical error is fairly large in the analytical system employed. This holds even more for the extracellular lining layer which amounts to less than 1 percent.
292
E. R. WEIREL et a/.
Fig. 5. Folding
of interalveolar
form of deep and narrow
septum
due to partial
clefts (rows of double
to the same interalveolar
septum
arrows).
collapse
of alveolar
Capillaries
which is heavily
marked
folded (dashed
surface
from both
with asterisk
sides in
(C”) belong
line). 6400 x
Nevertheless, it appears that this lining layer is considerably reduced at the highest inflation level (16 mm Hg); this value is significantly different from the others, whereas the other points do not differ significantly from each other. The free alveolar surface area, S,,, shows a pressure surface hysteresis (fig. 8) which
293
DIFFUSION CAPACITY AND INFLATION
IO-
--I---
Q8”
t
7-
T
6-
2 25 3
x 4-
3
2
3-
“0 J4
2-
“t l-
vc 7t
r?2__ 71
12 t AIRWAY
VS
PRESSURE
Fig. 6. Volumes of air (V,), tissue (V,). capillary lumen (V,) and surface lining layer (V,) at the five points on the pressure-volume curve investigated.
closely follows the pressure-volume hysteresis of air spaces, as already demonstrated in the previous paper (Gil and Weibel, 1972). The capillary surface is of the same order of magnitude as the alveolar surface at the highest inflation level, but it is larger at all other points (table 1, fig. 8). It does not change significantly on the inflation limb, but it increases upon deflation; the capillary surface thus follows partially the pattern of (reversed) hysteresis described for the capillary volume, though to a lesser degree. The harmonic mean thickness of the air-blood barrier, comprising both tissue and alveolar lining layer, is at every point smaller than the values obtained on specimens fixed by instillation of fixatives into the airways (fig. 9). This is due to the fact that the free barrier comprises in general the very thin portions of the tissue, whereas those parts which contain nuclei, connective tissue elements etc. are almost invariably shifted to deeper regions of the folds (figs. l-5). The barrier becomes slightly thinner with increasing inflation; this is probably due to a gradual reduction in the pools of extracellular lining layer found in clefts and to an opening of some folds where two barrier layers are intercalated between air and blood. 3. ESTIMATION OF DIFFUSION CAPACITY Since it was not possible to separate the tissue and surface lining layers in estimating
E. R. WEIBEL et d.
294
“,
i--
AIRWAY
PRESSURE
Fig. 7. Change in capiilary volume as function of airway pressure (mean + 1 S.E.).
barrier thickness, these two layers had to be treated as one barrier. Its diffusion capacity was defined as:
We have used the free alveolar surface, S,,, as the sole determinant of gas exchange surface; the permeability coefficient for tissue was used because tissue made up more than 90 percent of the barrier. With respect to the plasma layer we used the measured capillary surface, S,, as determining its extent; since the thickness of the plasma could not be measured, owing to blood removal by perfusion fixation, we used the value zhp= 0.18 p as determined by Burri and Weibel(l971) for rat lungs. For the physical coefficients the maximal values were used (Weibel, 1970). IS, = 3.3. lo- 8cm2/min, mm Hg K, = 4.3 ’ lo-’ cmz/min. mm Hg @o,= 2.5 ml/ml. min. mm Hg
DIFFUSION CAPACITY
Saf
Functional
SC
Capillary
alveolar
AND INFLATION
surface
surface
295 t i . .
area
area
AV
m2 96
7
12 Airway
Fig. S. Change
in free alveolar
76 mmHg
pressure
surface area, S,,, and in capillary
surface
area, S,.
INSTILLATION
Tht
T
72t AIRWAY Fig. 9. harmonic layer.
mean thickness
For comparison
16t : PRESSURE
of total air biood
the value of the tissue lungs fixed by instillation
barrier
barrier
7t
comprising
thickness
into the airways
mm both
9
tissue and surface
as measured is also plotted.
in completely
lining
unfolded
296
E. R. WElBEL
et al.
The membrane diffusion capacity, DM, included the resistances offered by tissue, surface layer and blood plasma:
& = &- + $
(2)
tr+st
P
whereas the total lung diffusion capacity included in addition the erythrocyte ponent :
t3)
1
DL =
com-
D&+&+&. P
e
The last columns of table 1 and figs. 30 and I1 report the data for the diffusion capacities as calculated from the group means of the morphometric data. The figures include an indication of the range of values of DM and DL as calculated from measurements obtained on specimens fixed by instillation of glutaraldehyde into the airways thus exhibiting a fully unfolded tissue surface; to this end the data of Burri and Weibel (1971) obtained on young rats raised in Berne as controls were corrected to match the larger body weight (2.50 g) of the animals of the present study assuming a linear relationship between DL and W (Weibel, 1972; Siegwart et C&1971). It is evident from fig. 10 that DM shows a hysteresis which closely follows that exhibited by the air volume and the free air space surface (fig. 8). The largest values, found at 16 and at 121 are about 15 percent smaller than those obtained on instillation fixed specimens. In the lungs of the inflation limb DM amounts to 40 percent of the, TABLE Synopsis Group
Body weight
VL cm3
of morphometric v, cm’
V, cm3
parameters: V, cm3
1 group V, cm3
means
k
S
1 standard SC mr
n$
error rhCl+s) pm
g
7t
127
16f
121
71
240
248
261
252
262
5.09
2.36
0.507
0.648
0.063
0.222
0.439
0.3i3
+ 0.53
& 0.44
t 0.012
& 0.044
_+O.OiI
& 0.018
kO.014
* 0.022
7.74
4.88
0.366
+ I.05
+ 0.89
i O&16
0.691 IO.062
0.047
0.226
0.373
0.287
& 0.009
k 0.048
&O.Of8
kO.017
12.85
9.49
0.396
0.745
0.012
0.467
0.435
0.240
+ 0.30
_t 0.35
+ 0.006
* 0.083
kO.003
kO.019
+ 0.048
+ 0.018
11.28
7.66
0.606
0.850
0.097
0.454
0.568
0.258
+ 0.84
+ 0.82
* 0.052
+ 0.078
& 0.037
f 0.016
kO.015
* 0.020
9.30 *0.27
5.77 ,0.44
0.658 &0.055
0.944 +0.155
0.041 io.007
0.376 &O.OlI
0.508 io.055
0.287 kO.017
DMo,
Dk>, ml 0,
---min.mm
Hg
1.91
0.76
2.01
0.63
3.95
0.79
4.05
1.10
3.18
1.08
297
DIFFUSION CAPACITY AND INFLATION
nl.~i~‘.~~H~’
INSTILLATION
I
** Fig. 10. Membrane metric parameters
diffusion obtained
capacity
RATS -2509
12 76 mm Hg AIRWAY PRESSURE for oxygen as calculated from the group means
7
in this study is compared
to the value obtained
of the morpho-
on instillation-fixed
lungs.
value in instillation fixed lungs, whereas DM only falls to about 70 percent on deflation to 7 mm Hg. As expected, DL is greatly influenced (fig. 11) by the changes in capillary volume which had shown a reversed hysteresis, falling on inflation and rising on deflation. The largest values were therefore found on the deffation limb, where DL amounted to about 757; of the control value found in instillation fixed specimens. At maximal inflation and on the inflation limb DL appeared reduced to about 5Oyi. Since the changes in V, were due to the use of positive pressure in airway inflation - necessitated by the experiment -we have recalculated DL with a constant V,; in this case DL also shows the “normal” hysteresis (fig. 11).
1. CHANGES
IN MORPHOMETRIC
PARAMETERS
RELATED
TO DIFFERENT
DEGREES
OF
LUNG INFLATION
This study confirmed our previous finding (Gil and Weibel, 1972) that the free alveolar surface area depends on the degree of in~ation; when plotted against in-
E. R. WEIBEL et Ul.
298
RATS -2509
AV
measured Vc constant
DLO,
A
0
ml min. mmH‘4
I
1,
INSTILLATION
I i
v
v ____~_
v---
*‘\’ /
.A----_
l-
--+/
------
7 AIRWAY
a/’
,’
x 0.7:
/ ‘.
,A
M
I
12
16
-
mm Hg
PRESSURE
Fig. 11. Total lung diffusion capacity for oxygen as calculated from the present measurements (full triangles) compared to the standard value derived from instillation-~xcd completely unfolded lungs. The open triangles report the values obtained if a constant capillary volume of 0.5 mf is assumed.
flation pressure it shows a hysteresis which is superimposable with that of air volume. It should, however, be noted that the values for alveolar surface area here reported are larger by about 20% than those previously obtained on the same lungs (Gil and Weibel, 1972); the use of electron microscopy at comparatively high magnification, as compared to light microscopy in the previous study, allows more surface detail to be recognized. Such systematic differences depending on magnification are a common observation and will require a critical study of the exact reasons. Caution must be exercised in comparing light and electron microscopic data from uncontrolled studies. The barrier between air and blood is formed by the tissue layer and by the extracellular lining material (Gil and Weibel, 1969/70). It is noteworthy that the harmonic mean barrier thickness was smaller in the present material than in rat lungs fixed by airway instillation (Burri and Weibel, 1971). It is not easy to exclude all artefact related to the different route of application of the fixatives, or to the use of somewhat different solutions since we needed to adjust the oncotic pressure
DIFFUSION CAPACITY AND INFLATION
299
of the perfusate by means of dextran. However, it was most striking to observe a very characteristic distribution of thin and thick barrier portions: most thicker regions containing cell nuclei or connective tissue elements were shifted away from the free surface into deeper regions of folds, whereas those parts of the alveolo-capillary barrier which were immediately adjacent to the free alveolar surface were composed almost exclusively of thin barrier portions where endothelium and epithelium are reduced to thin cytoplasmic sheets and their basement membranes are fused. This surprising observation reveals a design of interalveolar septa which assures good gas exchange properties of the barrier even if the septum becomes folded; it can be explained by the disposition of fibers, cells and capillaries in the septa (cJ Weibel, 1973). The volume of the extracellular lining layer is of the order of 5 percent of alveolar tissue and amounts to about 0.1 ml/m2 of alveolar surface at the higher inflation levels. The capillary surface area and volume also show a hysteresis with inflation and deflation. On inflation the capillary surface varies very little, being of the order of magnitude of the alveolar surface at maximal inflation, or only slightly below that found in instillation fixed lungs. On deflation, however, we observed an increase; this is probably related to the drastic increase in capillary volume observed on the deflation limb, a point which requires special consideration. 2.
REVERSED HYSTERESIS OF CAPILLARY
VOLUME
One of the most surprising findings of this study is the reversed hysteresis of the capillary volume (fig. 7). It is to be suspected that this is due to the use of positive pressure inflation together with a constant perfusion pressure. The capillary volume must be governed by the capillary-alveolar pressure gradient: (4)
AP = PC-P,
and this is bound to vary appreciably in our experimental situation; assuming P, to be about 20 mm Hg, AP will vary between 4 and 13 mm Hg. Fung and Sobin (1!&72)and Sobin et al. (1972) have recently measured changes in alveolar capillary sheet thickness with AP; between 4 and 13 mm Hg their data indicate an increase in sheet thickness from about 5.1 to 7.2 pm, i.e. by a factor of 1.41. In the present study, the capillary volumes at 7 mm Hg were increased by factors of I ..; I(, I .7 with respect to 16 mm Hg; this is compatible with the data of Sobin et 111.(19172) and would thus appear to be due to a widening of capillaries due to increasing AP. This does, however, not explain the hysteretic pattern, i.e. the difference between V, at the same pressure gradient on the inflation and on the deflation limb. The explanation is found in the fact that V, is not only influenced by the pressure gradient, but also by the surface area over which this pressure gradient acts on the capillaries, and this must be related to the free alveolar surface S,,. As developed in the appendix it is found that (5)
V, = a-b.S,,(P,-P,).
300
E. R. WEIBEL et al.
r
\
\
\ \ \
0.7
x)Pc=2OmmHg
\
--
PC
q2lmmHg
PC =19mmHg
1
04 I-
.
-Tl -// Fig. 12. Four curves obtained a capillary
The coefficients
pressure
a and
j
I
I
12
16
AIRWAY PRESSURE by fitting eq. (5) to the data on capillary of 20 mm Hg describe
the reversed
b can be calculated
from
volume. The two curves based on
hysteresis
reasonably
two arbitrarily
well.
chosen
points,
assuming “reasonable” values for the pressure gradient. In fig. 12 a number of curves produced by this analysis has been plotted together with the original data on capillary volume. It is seen that they all describe the data reasonably well, at least in the sense that they all show an identical hysteretic pattern. The best fit was obtained by assuming capillary pressure to be 20 mm Hg and calculating a and b from the capillary volumes measured at 77 and 16 mm Hg alveolar pressure. We may conclude from this analysis that the observed variations in the alveolar capillary volume were due to the combined variations in the alveolar surface area and in the prevailing alveolo-capillary pressure gradient, the latter being caused essentially by the positive pressure inflation with constant perfusion pressure. It remains to be shown whether such variations are also observed in negative pressure inflation or not, in other words, whether this finding is an artefact of the experimental design or whether it bears some significance for the living lung. Studies on blood flow such as those of Roos et al. (1961) and Fung and Sobin (1972) would suggest
DIFFUSION
CAFACITY
AND
INFLATION
301
a different effect of positive versus negative pressure inflation on the pulmonary vascular bed; how much of this is due to changes in the capillary bed is not clear yet, however. We should further mention that the present analysis did not take into consideration the effect of possible changes in the surface tension occurring along the pressurevolume diagram, as was suggested from our previous study (Gil and Weibel, 1972). 3.
DEPENDENCE
OF DWFUSZON
CAPACITY
ON AIRWAY
INFLATION
is quite evident from the model that the free atveofar surface area is the main determinant of the so-called membrane diffusion capacity DM. ft is therefore not surprising that DM shows a hysteresis which is very similar to that of alveolar surface area. It is slightly modified by the changes in barrier thickness and capillary surface area. Compared to values of DM obtained on instillation fixed material, where the alveolar epithelial surface is, on purpose, completely unfolded, we find that the highest value at 16 mm Hg inflation pressure is reduced by some 17 percent. This is due to the fact that even at this pressure a small part of the tissue surface is folded beneath the lining layer and thus not availabie for gas exchange. At the lowest inflation levels DM may fall down to as little as 40 percent of the value in completely unfolded lungs. The total lung diffusion capacity DL is, however, greatly in~uen~ed by capillary blood volume. The observed reversed hysteresis in capillary volume therefore changes the hysteresis pattern of DL considerably (fig. 1I). The largest vaIues are 73 percent and the lowest values 50 percent of those estimated for instillation fixed control lungs. Since we cannot be certain that the observed changes in capillary volume bear resemblance to those occurring in the living lung inflated by negative pleural pressure these data must be interpreted with caution. If the capillary volume were to remain unaffected by the degree of inflation the variations in DL would be somewhat different, but there still would be a dependence on the level of inflation (fig. 11); the truth may he somewhere inbetween. The general conclusion from this study is that the diffusion capacity of the lung depends on the level of inflation. In the range of physiologi~l airway inRation it must therefore be smaller than the maximal values estimated for completely unfolded lungs, those values which are determined essentially by the stable tissue framework of lung parenchyma. This maximal diffusion capacity is able to adapt during development to alterations in oxygen requirement of the organism, or to changes in oxygen supply (Burri and Weibel, 1971; Geelhaar and Weibel, 1971; Weibel, 1970/71). The functionally available diffusion capacity is, however, smaller, and this explains part of the differences between morphometric and physiological estimates of DL (Siegwart et al., 1971; Chinet Edat., 1971; Piiper et crl., 1969). The increase of DL with inflation may pa&y explain the increase in Dt observed with exercise or increased Vo, (Riper et al., 1969; Bitterli et al., 1971f where airway ventilation is maintained at a higher inflation level thus exposing a greater part of the alveolar surface to alveolar gas.
It
E. R. WEIBEL
302
et Uf.
Appendix INTERPRETATION
OF HYSTERESIS
IN CAPILLARY
VOLUME
is to be investigated whether the observed reversed hysteresis of the capillary volume (fig. 7) can be explained by a combined effect of changing alveolo-capillary pressure gradient and the hysteresis of the free alveolar surface area in an inflationdeflation experiment. The model lung is assumed to be made up of air in alveoli (V,), air in ducts and relatively rigid airways (V,), practically incompressible tissue (V,), blood in capillaries (V,), and blood in larger relatively rigid blood vessels (V,), so that total lung volume is It
(6)
vt = V~~V~~~~~V~~V~.
In an inflation-deflation experiment using variable positive pressure in airways, P,, and constant pressure applied to the blood vessels, P,, V,(P,), V,(P,) and VC{PA)show a hysteresis, the pattern of the former two parameters being closely related, whereas that of capillary volume is different. The change in air volume V,(P,) is related to a change in alveolar surface, S,(P,), which also shows a hysteresis. The ratio S,/V, is constant (Gil and Weibel, 1972) which is related to the observation that the alveolar surface does not increase by stretching but rather by unfolding of folded parts of the surface. In the following analysis the mechanisms causing the hysteresis in V,(P,) and S&P,) are not further considered, however, the hysteresis in V, (PA) is treated as an induced effect. We now first assume that at each pressure, PA, part of the surface, s:i, of an individual alveoius i is free, i.e. exposed to air, whereas another part, siz, is shifted into folds (fig. 13). These surfaces are related to the (maximal) surface of the completely unfolded alveolus, ~6~~~.as follows (7)
s61(P,4) = st,,X-sL(PA)
*
This assumption
is supported by our previous findings (Gil and Weibel, 1972). It is further assumed that the alveolar surface is homogeneously lined by a sheet of capillaries (fig. 13). The area of contact, a’, of an individual alveolus with capillaries is hence proportional to the surface area of the alveolus: ai= a-sil . (8) This contact area only changes because sii changes with P,. We may assume on the basis of previous findings (Gil and Weibel, 1972) that the folded regions of the alveolar surface are likewise loaded with the same density of capillaries. The volume of capillaries belonging to this alveolus is now given by the contact area and the thickness of the sheet, d, whereby we make the provision that d, in the exposed sheet may vary independently from dz in the sheet connected with folds. The exposed volume is (9)
vii = a’ai.d, I = sdt.s;,
; &=ct.cd
DIF~SION
CAPACITY AND INFLATION
303
Fig. 13. Model of spherical alveolus with pleating of surface used for deriving eq. (5) in Appendix.
where LXis the loading of alveolar surface with capillaries and cx’ a shape coefficient; the volume of the capillaries in folds is accordingly (10)
vi2 = edp- &
and the total capillary volume of alveolus i is
(11)
vi,= vi1 +viz.
The total capillary volume of all alveoli must hence be
(12) In de~ning the papillary volumes v,r and vC2 we now must introduce a number of crucial assumptions on the behaviour of the system:
304
E. R. WEIBEL et Ul.
1. The capillaries at the alveolar surface are connected to a common pressure reservoir, the pressure applied to the pulmonary artery, P,. The conducting vessels which distribute the blood (or perfusate) into the capillary sheet reduce this pressure to the capillary pressure P,; they are relatively rigid tubes when compared to capillaries so that the resistance in these arterial vessels is not greatly influenced by variations in alveolar pressure, P,. Consequently the pressure in the capillary bed, P,, is independent of P,. 2. Consider a change AP, in the alveolar pressure P,. It will be assumed that the superficial capillaries in the sheet enveloping the free alveolar surface react differently on AP,., than the deep sheets associated with the folds: the first will be deformed, an effect that translates in a corresponding change Av:,; the deformation of the deep lying capillaries is neglected, therefore vi. is assumed not to be affected by APA. Since this assumption is crucial for the following calculations, we provide further justification. In an idealizing model the tissue can be regarded, as far as deformations are concerned, as an incompressible fluid: it transmits pressure, but not stress forces and torques. However, the capillary sheet enveloping the free alveolar surface, being at the boundary, is more likely to be described as an elastically deformable body. The pressure change APA acts as a tension force normal to the alveolar surface and leads to a change in the capillary volume. This can be visualised in a model
a
PC
,,., .,.,.,. .,.,.,.,..., .,.,.,., .;,..,., .,., .,. ,. /
Fig. 14. Alternative Diagram
model of capillary
d shows that pillars forming
sheet which is pleated
upon reduction
wall of deep capillary
segments
shift of large structures
of available
are relatively
into depth of septum (c_C figs. l-7).
surface (a-c).
thicker
due to the
DIFFUSION
CAPACITY
305
AND INFLATION
treatment in which the capillary is thought as being made of deformable, but nonstretchable and incompressible material. The stress force will then change the cross section, but not the circumference of the capillaries. Such deformations clearly lead to a change in On the other hand, the capillary sheet associated with the folds is
vi,r.
embedded in the tissue (figs. 1 and 5) and therefore feels APA not as a stress force, but as a pressure change of the “liquid milieu”. Since the capillary walls are incompressible, no change in v)~ results. Some morphological evidence can be given to support these assumptions. As shown schematically in fig. 14 the plication of the barrier results in the formation of some kind of “pillars” formed by two barriers (figs. 2 and 4); the pillars are hence at least twice as thick as the superficial capillary wall. This is further accentuated by the fact that the infolded barrier portions are thicker than the superficial ones (fig. 14d) and contain connective tissue elements. We can therefore conclude that the assumption on the different effect of AP, on vi, and vi, is ‘sufficiently justified. Let us now calculate the capillary volume in its dependence on the pressure gradient P, - P,, where PA is varied and P, is kept constant. The capillary sheet enveloping a given alveolus i was described by the surface sL1 and the thickness di. Let di have the value d, at “equilibrium” P, - PA = 0. If PC- P, # 0, the sheet will be deformed. The theory of elastic deformations (Landau and Lifshitz, 1959) describes the deformations in terms of a distortion tensor Bik and a stress tensor gik according to the formula
G is the torsion or shear modulus, m is Poisson’s contraction constant, 6i, the Kroneker symbol, Tr 0 stands for the trace. We approximate by disregarding the on the grounds that it is related to hydrostatic Poisson contraction (let m -co) compression
deformations
which
we have ignored.
Furthermore
we go over
to
the diagonalised form of eq. (14) which is justified if the minimal radius of curvature are 5 pm of the alveolus is much larger than d, ~ the actual orders of magnitude for d, and 50 pm for the alveolar mean curvature of rat lungs (Gil and Weibel, 1972). In this approximation the distortion tensor reduces to ljik+Adl/do, the relative change of the sheet thickness, and the stress tensor is simply the pressure difference, c~~-+P~-- PA, directed normal to the alveolar surface. We then have d,(P,)
+,(l-~j.
(15) If this is introduced
(16)
= d, (1- A&/d,)
v;,(PJ
in (9) we get =sdO
P -P, 1 - +
. wT4)
.
a.
306
R. WEIBEL
et
al.
In calculating the volume of deep capillaries we assume, in accordance with the above-given arguments, the corresponding sheet thickness to be constant at d,; to get rid of additional parameters we put in first approximation dz = do. Then (17)
viz = s.d&,,,-s;r(PJ)
Since according to eq. (12) the total capillary volume is the sum of all the volumes associated with individual alveoli we obtain:
P-9
Since c sLiWX = S,,,, L
the maximal and the free alveolar surface, it follows that
(19)
V, = e(dr -d&S,r+d,S,,,,
.
Substituting eq. (15) we obtain
(20) Equation (20) is of the form (21)
V,(P,)= a-b.SJPJ*(P,-PA) a = Ed,,. S,,,,
Note that ifs&P,) describes a hysteresis, then V,(P,) describes a reversed hysteresis, provided b < 0. The parameters detining the coefficients a and b are not known, except for S,,,, which could be assumed to be represented by S, determined on instillation fixed lungs. However, these parameters are, by definition, constants of the system and need therefore not be separated. The coefficients a and b can be determined from two arbitrarily chosen experimental points. The capillary pressure P, is not precisely known; it must, however, lie between the head pressure of about 25 mm Hg in the pulmonary artery and the maximal alveolar pressure of 16 mm Hg at which flow was still maintained. As shown on fig. 12 the best fit was obtained with PC=20 mm Hg, a reasonable value. If a and b were determined from points 7$and 16 their
DIF~SION
CAPACITY
307
AND INFLATION
values were found as a= 0.192 b = -0.109. It is shown in the discussion and in fig. 12 that with these coefficients eq. (21) provides a reasonable description of the observed reversed hysteresis of capillary volume in an inflation-deflation experiment using constant perfusion pressure and positive pressure airway inflation.
The authors gratefully acknowledge the skilfull collaboration of Miss Helgard Claassen, Mrs. Brigitte Gil-Sollereder, Mr. Karl Babl, and Miss Gertrud Reber. References Bitterli, J., H. Bachofen.
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