Patency and compliance of pulmonary
veins when
airway pressure exceeds blood pressure
YUAN-CHENG
FUNG, SIDNEY
S. SOBIN, HERTA
TREMER,
MICHAEL
R. T. YEN, AND H. H. HO
Department
of AlWES/Bioengineering,
University
of California,
San Diego, La Jolla 92093; and
University of Southern California, American Heart Association Cardiovascular
Research
Laboratory,
Los Angeles, California 90033
treat this unique blood flow problem as a one-dimensional flow in a collapsible tube, whereas a few others
emphasize the three-dimensional features. However, no
one seems to have focused on the actual behavior of the
blood vessels. The popular approach treats the vessels as
an isolated elastic tubing, ignoring the tissues surrounding them. The majority consider only one single tube,
forgetting that the critical points where flow limitation
may occur are at the junctions of successive generations
of vessels.
The purpose of the present paper is to report on the
mechanical behavior of pulmonary veins subjected to
negative transmural pressure and the effect of this behavior on the flow limitation problem. We shall show
that at normal levels of airway, pleural, and blood pressures the pulmonary veins remain open (i.e., not collapsed) when PA exceeds Pv. Then we present data on
the elasticity of pulmonary veins when Pv changes from
a value greater than PA to values smaller than PA. We
shall show that even the smallest pulmonary venules are
patent at negative values of Pv - PA. On the other hand,
waterfall phenomena;
tethering; pulmonary circulation
we know that the capillary blood vessels are definitely
collapsed when Pv - PA is negative (see Refs. 9, 10, and
25). Consequently we can show that in the zone 2 conIT IS WELL
KNOWN
that in the so-called zone 2 region of dition the places where sluicing can occur are the juncthe lung, where the pulmonary venous pressure (Pv) is tions of the venules and capillary sheets. When this is
smaller than the alveolar gas pressure (PA), the blood made certain we can then calculate the pressure-flow
flow rate is subjected to limitation. In this region, for a relationship of the entire lung.
given arterial pressure, flow cannot be increased indefiThe patency of pulmonary veins is not unexpected
nitely by decreasing Pv. In fact, after a limit is reached, when one notices that these veins do not stand alone but
further decrease in Pv decreases the flow (22). Experiare connected to the interalveolar septa. We shall call
mental evidence was obtained by Banister and Torrance
this interconnection “tethering,” some details of which
(l), Permutt et al. (22), and others (6). The phenomenon will be presented below.
is known as the “vascular waterfall” or “sluicing” in
The three topics, proof of patency, measurements of
analogy with a natural waterfall whose flow rate does not blood vessel elasticity, and the evidence of tethering,
depend on how high the fall is, or sluicing in which the together form a foundation on which a theory of blood
collecting vat has no influence on the flow rate. It is flow in zone 2 condition rests, because in any theory one
known also as the “Starling resistor effect,” in reference must know the site of flow limitation and the compliance
to a device used by Knowlton and Starling (14).
of the blood vessels of all generations. These three topics,
Related phenomena are found in other fields, such as however, require three different methods, which are disthe effort-independent forced expiration (5, 17)) micturcussed sequentially in this paper.
ation in male and female urethra, Korotkof sound in
compressed arteries (32)) and peristaltic pumping (23). A PATENCY
OF PULMONARY
VESSELS
WHEN
ALVEOLAR
long series of studies has been done on this phenomenon GAS PRESSURE
EXCEEDS
LOCAL
BLOOD
PRESSURE
(see bibliography in Ref. 23). The intensity of research
of the Problem
has increased recently [(2, 3, 13, 16, 17, 19, 23); R. Collins Formulation
The pressure at a point in a pulmonary blood vessel is
and A. Tedgui, unpublished observations]. Most papers
S. SOBIN,
HERTA
TREMER,
H. H. HO. Patency and compliance
of pulmonary
veins when airway pressure exceeds Hood pressure. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol.
54(6): 153%1549,1983.-Our
measurements
on cat’s lung show
that pulmonary
veins and venules are not collapsible,
but
remain open when the alveolar gas pressure (PA) exceeds the
local blood pressure (Pv). Their compliance constants show no
discontinuity
as Pv falls below PA. The capillaries, however, do
collapse when PA > Pv. The explanation
of the patency of the
veins when PA > Pv is the pulling on the blood vessels by
tension in the interalveolar
septa. Photomicrographs
show that
each venule (or vein) is pulled radially
by three or more
interalveolar
septa. Capillary sheets, however, are exposed to
gas on the lateral sides and can readily collapse when PA > Pv.
These facts provide the key to the analysis of pulmonary blood
flow in zone 2. The “sluicing”
gate, i.e., the site of flow limitation, must be located at the junctions of capillary sheets and
the first generation of venules. Further, data on the branching
pattern and compliance
of small pulmonary
veins, which are
needed in quantitative
analysis of pulmonary
circulation,
are
presented.
FUNG,
MICHAEL
1538
YUAN-CHENG,
R. T. YEN,
SIDNEY
AND
0161-7567/83/0000-0000$01.50
Copyright
@
1983 the American
Physiological
Society
N~~~~LLAP~IBILITY
OF PULMONARY
VENULES
determined by the fullowing factors: the pressures at
pulmonary artery and left atrium, the height of the point
relative to th& heart, the volume rate of flow, the resistance to flow j in the vessels, and the frequency of the
p~sat~e component*
At a point in a vein the static
pressure is equal to the left atrial pressure minus the
product of the height of the vessel above the left atrium
and the specific weight of the blood, plus the pressure
head loss due to the flow from that point to the left
atrium, Because of the cavitations
head, Pv can become
if the vessel is located
negative (i.e., subatmospheric)
sufficiently high above the left atrium. Such negative
pressure tends to collapse the blood vessel.
We would like to answer the fo~owi~g question: when
Pv is smaller than PA, would the vein collapse or remain
patent? The following method is designed to answer this
question.
The method we use and the situation we study are
static. The result will help quantify only one term in the
equation describing dynamic events in the lung. However, as we have stated above, it helps to settle one
crucial question: when sluicing occurs in the lung, where
are the sluicing gates?
Method
The lung was prepared by the same method reported
by us earlier (26,30). Very briefly, eight healthy mongrel
male cats (3.1-5.9 kg) were anesthetized with pentobarbital sodium, and the trachea was exposed, cannulated,
and ventilated, A lethal dose of pentobarbital
sodium
was then given intravenously, and the chest was opened
by a midline thora~tomy. The airway pressure was then
held constant at 10 cmHz0 above the pleural (atmospheric) pressure. Through a cannula inserted into the
main pulmonary artery, lihe pulmonary blood vessels
were perfused with a low viscosity (25 cP) silicone elastomer (3% tin ~ctoate and 1.5% ethyl silicate h~dening
agent freshly added), The silicone was drained from a
previously inserted abdominal aortic cannula at the atmospheric pressure. After perfusing at an arterial pressure of 25 Torr for 20 min, the aortic cannula was closed
and the perfusion pressure was lowered to a desired level
and held constant. At this selected static condition the
silicone elastomer hardened. The course of hardening
and the flow behavior of the catalyzed fluid in the first 2
h are discussed in detail in the APPENDIX. The hardening
was so slow that 1 h after the flow stopped the viscosity
of the catalyzed elastomer was only 2.55 poise; hence
there was plenty of time for the fluid to respond to the
elastic forces in the blood vessel wall and to redistribute
itself as the ~onditiun of equilibrium requires,
The volumetric expansion of the silicone elastomer
during solidification was measured (30) to be less than
1%; hence the change in linear dimension is no more than
0.3%. After 2 h the animal was frozen for 2 wk or longer
to increase the strength of the silicone rubber. After
thawing the heart and lungs were removed and suspended in 10% KOH solution to corrode away the tissue.
In a period of 1 mo, frequent changes of the solution were
made until the cast was bare and clean. Then the arterial
tree was gently separated from the venous tree, and casts
of the two trees were obtained.
1539
Results
Patertt uessclrls.If a blood vessel is collapsed at a point
to such an extent that its internal cross-sectional area
vanishes, then after the process of tissue corrosion that
cross section will disappear from the tree. If there were
two occluded sections on a vessel, then after corrosion
Lhe segment between these two cross sections will be
dropped. For the lung prepared in the manner described
above, the capillary blood vessel sheets (inter~ve~l~
septa) disappeared when the transmur~ pressure (Pv PA) was sufficiently negative. If Pv is higher than PA, an
entangled mass of silicone was obtained. This is consistent with our previous result (8) that the thickness of the
capi~~y sheet is finite when Pv - PA > 0, but it becomes
zero if Pv - PA is sufficiently negative. According to
Fung, Sobin, et/ al. (8,10,26), the alveolar sheet thickness
of the cat lung is 4.3 pm when Pv = PA; it increases
linearly with increasing Pv - PA if Pv - PA > 0, at a rate
of 0.22 ~m/cmH~O but decreases rapidly when Pv - PA
< 0 and becomes zeru when Pv - PA < -1 cmHz0. These
results (8, 10, 26) were obtained by using the silicone
fluid and procedure described in the present paper, and
the fact that; the capillary blood vessels were readily
collapsed should add conf”lden~e to the methud~ i.e., that
which remained on the tree was due to patent vessels
and not to premature hardening of the polymer. Figure
1 shows a venous tree cast of a cat lung prepared with a
perfusion pressure (me~ured at the level of the left
atrium) 17 cmHzO lower than PA. Casts made at other
negative values of Pv - PA appears similar. Figure f
shows that the pulmonary veins do not collapse at these
negative transmural pressures. Although it is not shown
here, the arterial tree casts also look similar. But since
the patency problem is of interest only on the venous
side (unless reversed flow in the laboratory is considered),
data on the arterial tree will not be reported here.
SmaUe& open ueins, branchingpattern
of wnom3tree,
aid el~~ti~~t~ aid ~urn~l~~~~e eu~st~~t~ of the ~~~~le~.
A quantitative analysis of the flow limitation hinges on
knowing the location of the sluicing gate. In a theoretical
analysis, Fung and Sobin (8) conclude that the sluicing
gate must be located at the entry to the smallest vein
that can remain patent under negative transmur~ pressure. In our silicone rubber casts of the pulmonary venous
tree, the smallest veins that remained open under negative transmural pressure are those smallest twigs that
remained on the tree and did not fall off. Hence by
measuring the dimensions of these smallest twigs, we can
determine the dimensions of the vessels just beyond the
sluicing gate,
To measure these smallest open venules, branches
were cut at random from the trees and the diameters of
vessels were measured with a vide~dimensional
analyzer.’ The Strahler system of ordering (4) is used to
’ The word ‘kkuneter” is used here to mean the width of the vessels
memured with the video system without actually identifying the shape
of each cross section. Most of the cross sections appear somewhat
elliptical, hence the diameter data represent a collection of the major
axes, minor axes, and values in between, of the vessels measured. As
a reference to the meaning of diameter in this sense, the following
mathematical data may be helpful. If a circle is deformed into an etlipse
of the same circumferential length, then the ratio of the mean dia.-meter
of the ellipse, defined as the average of the major and minor axes, to
the diameter of the circk, is 0,998 when a/b = 1.25,0.976 when a/lr =
1540
FUNG
ET
AL.
FIG. 1. Silicone
elastomer
cast of venous tree of cat’s lung whose
veins are subjected
to pressure
difference
(Pv - PA) of -17 cmHzO.
Pleural pressure = 0 (atmospheric);
airway pressure
= 10 cmHz0,
blood
vessel pressure
pressure.
describe the vessels. In this system the smallest blood
vessel is said to be of order 1. When two vessels of order
1 meet, the next larger generation is called a vessel of
order 2. Two order 2 vessels meet to form a vessel of
order 3, etc. However, if an order 1 vessel meets an order
2 vessel, the order number remains at 2. If a vessel of
order 2 meets a vessel of order 3, the combined trunk’s
order remains at 3, and so on. If the branching pattern of
the vascular tree were that of “symmetrical”
bifurcation,
with every parent vessel yielding two equal daughters,
then the ratio of the number of vessels in order n to that
of n + 1 (the branching ratio) is 2. However, the pulmonary vascular tree does not bifurcate symmetrically,
and
the branching ratio is close to 3 for vessels of orders l-4
and 3.59 for vessels of orders 4-11. In this situation, the
Strahler system gives a more accurate description
of the
branching
pattern than the method of “symmetrized
asymmetric”
bifurcation
system used by Weibel (31).
Table 1 presents the results of the measurement.
At
Pv - PA = -2 cmHzO, Pv being measured at the level of
the left atrium, the data from the right lower lobe of two
cats are listed. At Pv - PA = -7 cmHPO the data are
from the left lower lobe of a cat. At Pv - PA = -17
cmHa0, the data from one cat are shown. The mean
values of the diameters
of the smallest open venules
(vessels of order 1) are 27 and 24 pm for the two cats at
1.75, and 0.965 when a/b = 2.0, where a is the major diameter
and b is
the minor diameter.
In other words, if an inextensible
circle is deformed
into an ellipse with the major axis twice as large as the minor axis, the
mean diameter
of the ellipse is only 3.5% smaller than that of the circle.
Therefore,
if the blood vessel cross sections were circular
originally
and
were deformed
into elliptical
shapes under a negative
transmural
pressure, then a collection
of random
samples of the projected
widths will
yield a mean diameter
quite close to the mean diameter
of the original
circular
vessels. The standard
deviation
will reflect
the degree of
deformation
as well as the variation
in the original
diameter.
= -7 cmHz0.
Pv, local
blood
pressure;
PA, alveolar
gas
NONCOLLAPSIBILITY
OF
PULMONARY
1541
VENULES
- PA = -2 cmHz0;
this decreases to 22 and 23 ,um
when Pv - PA is decreased to -7 and -17 cmHa0,
respectively.
If a linear regression is assumed the rate of
decrease of the diameter (compliance
constant)
is approximately
0.32 ,um/cmHzO, or 1.24%/cmHzO
based on
the average diameter at Pv - PA = -2.
We measured the diameters of the smallest noncapillary blood vessels in each photomicrograph of the cat’s
lung and found that these smallest vessels have mean
diameters of 14.5, 16.6, 17.0, 18.2, and 21.0 pm when Pv
- PA = +O, +3, +10.25, +17, and +23.75 cmHz0, respectively (28). The compliance constant is 0.274 pm/cmHaO
or 1.6l%/cmH20. This is quite consistent with the value
found above for the venules. Thus the compliance
changes rather moderately when Pv - PA varies in the
range -17 to +24 cmH20.
The remainder of Table 1 lists the ratio of the diameters of successive orders of vessels, the average length of
the vessels of successive orders, the length ratio, and the
branching ratio. The last quantity is obtained by plotting
the number of branches in successive orders on a semilog
paper and finding the slope. The regression line yields
PV
log (Ni/Ni+l)
= B
where Ni is the number of vessels of order i and B is a
constant. The branching ratio is then given by 10B. It is
seen that the branching ratio is about 3.0 for pulmonary
venules of orders l-4.
A typical histogram of the diameters of the venules is
shown in Fig. 2.
The structure of the venous tree was measured from
the right lungs of the five cats at Pv - PA = -7 cmHz0.
The pooled data of all lobes yield the results shown in
Table 2. The overall branching ratio from order 4 and up
is 3.59.
The venous trees of cats at Pv - PA = -2 and -17
cmHBO were used to count the number of orders in each
lung. All lungs have eleven orders (l-11) from the smallest venule to the vessel that is connected to the left
atrium. We conclude therefore that the structure of the
venous tree is not changed when Pv - PA varies from
-2 to -17 cmH20.
In the data presented above, the Pv - PA values are
nominal based on the pressure measured at the level of
the left atrium. The true values of Pv - PA can be
calculated by adding to the nominal values the distance
(in cm) from the left atrial level: positive downward,
negative upward. Preliminary trials to correlate the
smallest twig diameter with the height of the twig failed
to show significant correlation; hence for simplicity all
data were pooled to obtain the mean and standard deviation of the diameters.
The average diameter of the open venules lies in the
range 22-27 pm (Table 1) when Pv - PA is negative.
Earlier we have shown (28) that the smallest vessels in
CAT LUNG, CDJ
P, - Pa = -17cm
Hz0
n = 370
mean = 23.59
S. D. = 9.05
1. Diameter, length, and branch number
ratio of the first 3 orders of small pulmonary
veins subjected to negative values of Pv - PA
TABLE
PV
-
s
5
PA
s
-2
cmHnO
Diam*,
pm
Order 1
Order
Cat CFB
(RLL)
Cat CFK
N--U
Cat CET
uu
Cat CJG
NJ2
27.4
t10.1
42.8
77.6
t19.8
160.3
k39.5
1.80
24.2
t8.2
41.0
t9.1
73.9
k8.9
142.0
t33.9
1.80
22.2
t4.1
40.5
k7.3
67.7
k11.5
136.3
t44.7
1.84
23.6
t9.4
37.0
tll.1
71.0
U8.1
126.1
t25.7
1.77
0.59
to.27
1.57
kO.60
2.23
kl.58
1.94
0.56
to.42
1.47
k0.63
2.44
kO.77
2.08
0.50
kO.21
1.55
k1.11
2.38
AA.74
2.18
0.58
to.37
1.48
to.76
2.69
t1.75
2.15
t 10.0
3
Order
4
Diam ratio
Mean length*,
Order 3
Order
4
Order
5
Length
--I7
cmHnO
er
u
I
2
Order
-7
cmHs0
mm
ratio
Ni = B
logK
r+l
B
Correlation
coef
Branching
ratio
0.462
0.9976
2.90
0.465
0.9995
2.92
0.516
0.9991
3.27
0.487
0.9999
3.07
Pv, blood pressure in vein (variable
measured
at level of left atrium);
PA, alveolar
gas pressure
(10 cmHz0);
Ppl, pleural
pressure
(atmospheric);
RLL, right lower lobe; LLL, left lower lobe; Ni, no. of vessels of
order i; B, constant.
* Values are means t SD.
0
10
20
30
40
50
DIAMETEROF SMALLESTOPENVENULE,
pM
FIG.
2. Typical
histogram
of diameter
of smallest branches
of venous
tree of cat's lung subjected
to negative
Pv - PA. Pleural pressure
(Ppl)
Pressure
in veins is -7 cmHa0.
Pv, local blood
= O;PA
= 10 cmHs0.
pressure;
PA, alveolar
gas pressure.
2. Branching pattern of venous
tree of cat’s right lung according to
Strahler system of ordering
TABLE
Order
11
10
9
8
7
6
5
4
No. of
Branches
1
4
13
46
171
656
2,348
8,024
Diam,
4,600
3,080
1,767
1,063
665
448
264
136
pm
t 956
t 331
t 272
rfr 180
t 122
t 74
t 45
Length,
mm
19.24
15.12
7.61
4.95
3.81
2.38
1.55
t 10.81
t 9.17
t 4.28
t 3.73
t 3.34
t 1.74
t 1.12
Values
are means t SD. Branching
ratio = 3.59; Pv cmHn0;
Ppl = atmospheric;
PA = 10 cmHg0;
Pv = 3 cmHz0.
PA = -7
1542
FUNG
each photomicrograph
of lung tissue when Pv - PA is
positive lies in the range 14.5-21 pm. These smallest
vessels must be smaller than the average. Hence we
conclude that these open vessels are venules of the lowest
order. It is remarkable
that they remain open when Pv
is smaller than PA by as much as -17 cmHa0. In contrast,
the capillaries would collapse completely when Pv - PA
= -1 cmHzO, according to Fung and Sobin (8) and as
evidenced by the fact that the capillaries disappeared
from the casts when Pv - PA = -2. This difference in
behavior between capillaries and venules is important for
hemodynamics:
it is the basis of our conclusion that the
sluicing gates in zone 2 condition are located at the
junctions
of the capillaries
and venules-a
conclusion
whose theoretical
reasoning was presented earlier (Ref.
8, p. 473).
COMPLIANCE
NEGATIVE
OF PULMONARY
VEINS
TRANSMURAL
PRESSURE
UNDER
Results of the preceding section show that pulmonary
venules and veins do not collapse under a negative pressure difference (Pv - PA) as much as -17 cmHa0. How
do the diameters
of these vessels change with blood
pressure?
To answer this question we determine
the
compliance of cat’s pulmonary
veins under positive and
negative transmural
pressure. The data provide further
support to the results presented in the preceding section,
and they are important
for the analysis of blood flow in
the lung.
Method
The diameters of the pulmonary veins were measured
on the X-ray films of isolated lungs after perfusing it first
with saline and then with BaS04 suspension. The experimental setup and procedure have been presented earlier
(34)) and only the most salient points essential to the
understanding
of the results are mentioned below. Briefly
the lung was hung in a closed Lucite box. The left atrium
was connected to a reservoir,
and the trachea and pulmonary artery were left open to the atmosphere
via
connecting tubing. Pleural pressure (Ppl) was adjusted
using a vacuum source and monitored
with a water
manometer. The left atrial perfusion pressure was altered
by raising or lowering the reservoir and was measured by
determining
the height difference
between the liquid
level in the reservoir and the location of individual vessel
in the box. Conventional
radiographs
were taken, using
a special grid cassette.
All experiments
were carried out with freshly excised
lungs of cats weighing 2.5-3.5 kg, anesthetized with ketamine hydrochloride
(20 mg/kg iv), heparinized, and killed
with a minimal overdose of pentobarbital
sodium (Nembutal).
The vessels in the lung were purged of blood by perfusing normal saline (with 5% dextran) through the vessels. The lung was then perfused with a solution consisting of normal saline, 30% BaSO+ 10% glucose, and 0.75%
methyl cellulose. The preconditioning
procedure
consisted of inflating and deflating the lung 10 times by
varying Ppl. Then Ppl was fixed at a selected value (-5,
-10, -15, or -20 cmHzO), the pulmonary
artery was
ET
AL.
closed off, and the pressure in the veins and arteries was
allowed to be equilibrated
at selected levels. X-ray photographs were then taken. Because the BaS04 particles
were large enough that they could not pass through the
capillary blood vessels, the X-ray film showed only venular vessels. On these films we can locate a particular
blood vessel along the vascular tree at different perfusion
and pleural pressures.
The diameter of this vessel was
measured, and its dependence on perfusion and pleural
pressures
was determined.
Repetition
of this process
yielded the desired information.
In measuring the vessel diameter from the film, penumbra effect was accounted for as previously
described
(33). Our X-ray-film
reader consists of a microscope,
a
television camera and video amplifier, an electronic image rotator, an “image splitter,”
and an oscilloscope.
A
selected portion of the television image can be “sheared”
by the splitter, i.e., horizontally
displaced by an amount
proportional
to an adjustable voltage. To measure the
diameter a segment of a vessel is sheared in a direction
perpendicular
to its axis from one side of the blood vessel
to the other (i.e., one diameter). It is then calibrated and
displayed digitally.
Result:
Patency
and Compliance
of Pulmonary
Veins
Our results are shown in Fig. 3, in which the distensibility of vessels in the diameter range of 100-200, 200400, 400-800, and 800-1,200 pm, airway
pressure
0
cmHg0, and pleural pressures of -20, -15, -10, and -5
cmHz0
are presented.
On the ordinate
the percent
change in diameter normalized with respect to & (diam
at Ap = Pv - Ppl of 10 cmH20) is shown. This AP is the
difference between Pv and Ppl. The vessel diameter of
Pv - PPl = 10 cmHz0 is chosen as a standard to normalize the vessel size to avoid all the uncertainties
arising
from the possible elliptical shape of the vessel at transmural pressure of zero. At AP = 10 cmH20 the vessel is
effectively round [it is shown theoretically
(33) that any
deviation from roundness is reduced to 5% of its initial
value at AP of about 1 cmHzO]. The ranges (e.g., 100-200
pm) denote all vessels whose diameters
fall in these
ranges when AP = 10 cmHz0. At other AP the same
vessels were followed. It appears from Fig. 3 that a linear
relationship
between pressure and diameter change exists
for all these vessels in the ranges tested. In these figures,
the vertical bars indicate the scatter (SD) of the D/D10
of the vessels studied, whereas the horizontal bars indicate the SD of the pressure difference Pv - PA in these
vessels. The scatter of Pv - PA was caused mostly by
the effect of gravity on the different
heights of the
branches, which resulted in different hydrostatic
pressures in the vessels.
A linear regression line is assumed for each group of
vessels (in a given diameter range), and the slope and
intercept
of the regression
line are determined
by the
method of least squares using the mean values of D/D10
and Pv - PA. These regression lines are plotted in Fig. 3.
Their slopes are called the compliance coefficients and
are listed in Table 3. The unit of the compliance coefficient is the percent change in diameter per cmHz0 AP,
or inverse Pascal. The table shows that smal.ler veins of
the cat are more compliant than larger veins. Further-
NONCOLLAPSIBILITY
OF
PULMONARY
PPl = -5 cm H’O p98
l
100-200 pm
4 200-400 pm
0 4OO-8001m
A 800-1200 brn
MEAN
1543
VENULES
ppr
=-15
Pa)
cm h’20
p 98 Pa)
100-200 pm
A 200400 pm
0 400-800 pm
A 800-1200 pm
l
MEAN ,+ SO.
+ S.O.
AP=P,-
I
PA cm H,O (98 Pa)
AP=Pv
-10
ppr=- 10 cm 40
- PA cm Hz0 (98 Pa)
0
Ppl= -20
(x 98 Pa)
cm H20
10
p 98 Pa)
pm
A 2004OOp m
0 400-8OOpm
A 800- 12OOp m
l
100-200 pm
A 200400 pm
0 400-800 pm
A 800-1200 pm
l
100-200
MEAN
MEAN + S.O.
+ S.O.
I
-15
10
0
-10
M=P,-
-10
PA cm HI0 (98 Pa)
0
10
AP = P, - PA cm H20 (98 Pa)
are classified
according
to their
See text for further
explanation.
more for smaller veins (100-400 pm) inflation to a higher
lung volume results in higher compliance coefficient initially until Ppl of -15 cmH20 is reached, whereas further
increase in lung volume decreases compliance. For larger
veins (400-1,200 pm) the compliance coefficients are
smaller and their variation with the degree of inflation is
not as significant.
These results complement those previously described
used effectively for vessels smaller than 100 pm in diameter. The information on the smallest vessels that
remain patent is best obtained by the former method.
It is a common observation in radiology that the apical
pulmonary vein (where the transmural pressure is negative) does not collapse. Lai-Fook (15) and Smith and
Mitzner (24) have obtained curves similar to those of Fig.
3 for large pulmonary veins of the dog. Our data show
the uniformity of this behavior for all pulmonary veins,
down to venules.
(see
section
ALVEOLAR
PATENCY
GAS
PRESSURE
OF
PULMONARY
EXCEEDS
VESSELS
LOCAL
BLOOD
WHEN
PRES-
three ways. I) Whereas the former method
proves the patency of the veins under negative values of
Pv - PA by catalytically hardening a liquid, the present
method proves the patency by observing the vessel while
it is perfused by a liquid. 2) Whereas in the former
method each cast yields only one point on the pressurediameter curve of a given vessel, the present method can
yield the whole curve. 3) The present method cannot be
SURE)
in
TETHERING
FOR
PATENCY
BY
ALVEOLAR
OF
PULMONARY
diameters
WALLS
VENULES wHEN pv - PA < o
at Pv - Ppl
AS
VEINS
THE
=
10 cmHn0.
FIG. 3. Distensibility
of pulmonary
veins subjected
to positive
and
negative
Pv - PA. Vessel diameter
is normalized
against its value when
Pv - Ppl = 10 cmHaO at which vessel cross section is circular.
Points
REASON
AND
The results presented in the preceding sections may
be explained by the pull provided by the tension in the
interalveolar septa on the veins, and in this section we
shall clarify some details of the tethering.
1544
FUNG
TABLE 3. Compliance coefficient
veins when Pv - PA is negative
Vessel Diam Range, gm
100-200
200-400
400-800
800-1,200
Pv, local blood pressure;
pressure.
Airway
pressure
is
slope of linear regression
line
determined
for each group of
change of diameter
per cmHz0
Ppl, cmH~0
-5
-10
-15
-20
-5
-10
-15
-20
-5
-10
-15
-20
-5
-10
-15
-20
of cat’s pulmonary
Compliance
Coef
1.98
2.05
2.79
2.44
1.83
1.44
2.01
1.60
0.98
1.08
1.16
0.93
0.79
0.71
0.57
0.58
PA, alveolar
gas pressure;
Ppl, pleural
0 (atmospheric).
Compliance
constant
is
over range -10 < Pv - PA < 10 cmHn0
vessels. Compliance
coeffkient
is percent
change in Pv - PA.
To clarify the anatomic relationship
between the pulmonary blood vessels and the inter-alveolar
septa, we
developed a special method of particulate
polymer cast
of the vascular tree and several criteria to decide whether
a noncapillary
vessel is arterial or venous, and we made
casts from four cats. The details of this method and
criteria have been reported earlier by Sobin et al. (25) in
connection with a study of the topology of pulmonary
arterioles
and venules in the cat, and only the most
pertinent points are briefly mentioned here. Three kinds
of silicone elastomer were used for casting: 1) a clear
colorless preparation
(General Electric compound 88017);
(2) a pale yellow-orange-colored
“reground”
GE RTV-60,
which passes through the capillary bed ‘and contains
some red iron oxide particles; and 3) a “resuspended”
GE
RTV-60 containing iron oxide particles large enough not
to pass through the capillary bed. Tin octoate (3%) and
ethyl silicate (5%) were used for catalytic polymerization
of the silicone liquid to a solid. The animal preparation
was similar to that described by Sobin et al. (25,30). The
lungs were perfused either in normal direction
or in
retrograde direction, each with the fluid (1) first and then
with either (2) or (3) named above. After pressure equilibration and hardening of the elastomer, the lung tissue
was fixed by 10% Formalin instilled into the trachea at
20 cmHpO pressure and so maintained. Histological
sections were then cut and stained for observation.
The identification
of arteries and veins is done according to three criteria. I) By the iron oxide particles: these
particles are hydrophilic
and adhere to the blood vessel
wall. Therefore in lungs perfused in the normal direction
the arterial tree is more heavily filled with iron oxide
particles and is darker red, whereas the venous tree is
pale yellow. In lungs perfused in retrograde direction the
veins are darker. 2) By ,smooth muscle cells: the pulmonary arterioles
in mature animals have some vascular
smooth muscle cells (though not in thick layer) (27, 29);
the venules do not. 3) By the differences,jn
the relationship of the terminal pulmonary arterioles and venules to
ET
AL.
the alveolar capillary bed described by Sobin and Tremer
(29): pulmonary
arterioles pass in the intersecting
planes
of interalveolar
walls; the pulmonary
venules fan out
from the flat portion of the interalveolar
wall. An illustration of the latter is shown in Fig. 4, which shows a
venule draining an alveolar wall, i.e., an inter-alveolar
septum, about 90% of which is the vascular sheet of
capillary blood vessels. Arterioles
have not been seen in
such a configuration.
The microscopic
examination
of a single vessel is insufficient to distinguish
between small pulmonary
arteries (arterioles)
and veins (venules). Without using these
criteria, the arterioles and venules cannnot be told apart.
From such preparations
we made large montages of
photomicrographs
of cat’s lung showing the relationship
between arteries, arterioles, venules, and veins and the
capillaries
in the interalveolar
septa. An example is
shown in Fig. 5A, whereas an enlargement of a portion of
it is shown in Fig. 5B. In these figures the tethering of a
pulmonary
venule of diameter about 25 pm by three
interalveolar
septa is clearly seen.
The picture shown in Fig. 5 is typical of small vessels,
as can be seen from a large montage (Fig. 6). Larger
vessels may be pulling and pulled by four or more interalveolar septa. A few appear to be tethered by only two
septa. We have never seen an isolated untethered vessel
in the lung.
The interalveolar
septa that tether the blood vessels
will affect the compliance of the vessel and help keep the
FIG. 4. Venule draining
alveolar
wah from lateral
tion and away from alveolar
opening.
Cat lung, ~155.
by permission.
and anterior
From Sobin
por(29),
NONCOLLAPSIBILITY
OF
PULMONARY
VENULES
FIG. 5. A: montage
of photomicrographs
of silicone elastomer-filled
cat lung showing
2 venules in central portion
of figure, each tethered
by 3 interalveolar
septa. Another
venule, which was cut lengthwise,
is
seen at lower right corner. All noncapillary
vessels are venous. Gelatinembedded
preparation.
Cresyl
violet stain. W-pm-thick
sections.
B:
enlargement
of a portion
of A, showing
tethering
of venule
by 3
interalveolar
septa. A and B are enlargements
of a small portion
of
montage
presented
by Sobin et al (25), in upper right corner of their
Fig. 3 near “a.” Dark shadows
at left border of A are marks of arterial
regions as explained
in Ref. 25.
FIG. 6. Map made from montage
of individual
photomicrographs
of
thick histological
section af cat lung. Every noncapillary
blood vessel is
marked.
Veins and venules
are marked
as bull’s eyes; arteries
and
arterioles
are marked
as white dots. Branches
of pulmonary
vessels
from 15 to 100 pm diam were individually
identified
as explained
in
text. Domains
of pulmonary
arteries
are made darker
by overlay
of
area with blue transparent
fihn. Individual
alveoli and branching
vessels
are clearly
seen in plane of photomicrograph.
Lines of demarcation
between
arterial and venous zones were drawn at roughly
equal distance
between
neighboring
arteries
and veins. Pulmonary
arterial
domains
are seen to be discontinuous,
whereas
pulmonary
venous
areas are
continuous,
showing
that arterial
areas are islands immersed
in an
ocean of pulmonary
veins.
1546
FUNG ET AL.
vessel patent. Tensile stressesprevail in the interalveolar
septa as long as the lung is inflated and the alveoli are
open, and they tend to distend the blood vessel. Between
the successive septa the vessel wall is subjected to the
pressure of the blood (Pv) in the inside and alveolar gas
pressure (PA) on the outside; the net pressure acting
outward is Pv - PA. When Pv - PA is negative the
pressure force tends to bend the wall inward. To analyze
the resulting deformation of the vessel, we must take into
account not only the tension in the tethered septa and
the bending of the wall, but also the nonlinear stressstrain relationship of the blood vessel wall material in
which the stresses are exponential functions of the strain
(see Ref. 7, chapt. 8). Theoretical analysis (unpublished
observation) shows that the stability of the vessel when
Pv - PA is negative is due to the tethering and the
nonlinear stress-strain relationship and not because of a
large intrinsic bending rigidity. If a vessel is not tethered
by the interalveolar septa, a theoretical estimate of critical buckling pressure based on the bending rigidity of
the wall is about 1 cmH20.
Theoretically, in the interalveolar septa, the tension is
equal to the transpulmonary pressure (PA - Ppl) divided
by the total length of the septa per unit cross-sectional
area of the lung, as long as the septa are not in the
immediate neighborhood of a blood vessel or bronchus.
The average of the tensile forces in the interalveolar
septa per unit cross-sectional area of the lung is the
parenchymal stress. By considering the equilibrium of an
element of the pleura (see, e.g., Fig. 4 of Ref. 34), one
concludes that the parenchymal stress balances the
transpulmonary pressure (if the product of the curvature
of the pleura and the tension in the pleura is neglected).
In the neighborhood of blood vessels that are tethered
by interalveolar septa, the tension in the septa is influenced by the distensibility of the blood vessels. For large
blood vessels, the effect of this interaction is that the
parenchymal stress in the immediate neighborhood of
the blood vessel is a fraction of PA - Ppl (see Refs. 15
and 24).
In the neighborhood of small pulmonary blood vessels
(arterioles and venules) whose diameters are smaller
than those of the alveoli, the use of the parenchymal
stress is no longer appropriate because the cross-sectional
area needed for its definition must be many times larger
than that of the blood vessel. For these small vessels the
mechanics are much clearer if we think of them as
subjected to pressures Pv and PA and tension in the
septa.
SUMMARY,
CONCLUSIONS,
AND
HISTORICAL
REMARKS
We conclude that in the normal range of pressures in
the zone 2 condition the pulmonary veins, including
venules, will not collapse. The elasticity of the blood
vessels is such that the slope of the diameter vs. Pv - PA
curve remains almost constant for Pv - PA as negative
as -17 cmHzO. The reason for this patency is the tension
exerted on the vessels by the interalveolar septa which
are attache Id to the outer walls of the vessels. Although
this conclusion is based on cat lung, it should be applicable to other mammalian lungs because their basic
structures are similar.
With this observation, we recall the theoretical conclusion (8) that if sluicing occurs, the sluicing gate would be
located at the junction of the collapsible and noncollapsible parts of the blood vessel system. It follows that the
sluicing gates must be located at the junction of the
capillary sheets and the venules.
We can now construct a theoretical analysis of pulmonary blood flow based on the compliance data presented above. Compared with other theories, our theory
is pleasantly simple because the sluicing gate is definitely
known. One of the popular methods of analysis of flow in
a collapsible tube uses one-dimensional approximation
and an analogue with the flow of a compressible fluid in
a rigid tube; and the flow limitation is interpreted as due
to the development of a sonic throat at which the speed
of the flow becomes equal to the speed of harmonic
progressive waves [see Dawson and Elliott (5) and Shapiro (23)]. However, the shock recovery part is not analogous to the gas dynamic case, and it is necessary to
consider three-dimensional effects. For this reason many
recent investigators have turned to numerical solutions
of axisymmetric transient flow in a flexible tube, and the
calculations become rather formidable. In contrast, we
can show that the flow on both sides of the sluicing gate
is subsonic and the shock recovery problem does not
arise.
Besides determining the site of flow limitation in the
pulmonary circulation in zone 2, this paper offers data
on the branching pattern and compliance of the small
pulmonary veins and venules. These data are required in
any quantitative analysis of pulmonary blood flow.
A perspective of the contributions presented in this
paper may be obtained by a review of literature that
follows.
Historical
Remarks
In technical language, what we have shown is that the
so-called “tube law” (23) of the pulmonary venules and
veins is very different from that of an isolated vena cava
or a rubber tube. The classical “elastic buckling phenomenon” does not occur. As a consequence, all the theoretical analyses in the literature [(3,13,16,19,23); R. Collins
and A. Tedgui, unpublished observations; and earlier
papers], as well as model experiments [(2) and earlier
papers] have to be revised when applied to the lung.
We are, of course, not the first to have seen open blood
vessels in the lung where alveolar pressure (PA) exceeds
the local blood pressure (Pv). In a paper by Glazier et al.
(11) photomicrographs of rapidly frozen lung in zone 1
and zone 2 conditions are shown in which there are open
“corner” vessels, i.e., vessels at the junction of three
interalveolar septa. There is, however, no way to identify
in their photographs whether these vessels are arterioles
or venules, nor to obtain the compliance (the pressurediameter relationship) of these vessels. Thus our conclusion that the venules are open when PA - Pv is as large
as 17 cmHzO and that the compliance is continuous when
Pv - PA changes sign from positive to negative cannot
be deduced from their photographs. We show further
that these open venules are connected continuously to
the venous tree that is patent everywhere.
The compliance of large pulmonary extra-alveolar ves-
NONCOLLAPSIBILITY
OF
PULMONARY
1547
VENULES
sels has been measured by Patel, Schilder, and Mallos;
Frasher and Sobin, Attinger, Caro, and Saffman; and
Maloney, Rooholamini, and Wexler in the 1960s (see
bibliography, Ref. 33) and recently by Lai-Fook (15).
None of these has dealt with pulmonary vessels smaller
than 800 pm in diameter, nor with negative Pv - PA.
Sobin et al. (28) measured the compliance of the smallest
extra-alveolar vessels in the cat’s lung, but Pv - PA was
positive and arterioles and venules were not differentiated. The results reported in this paper, covering pulmonary veins with diameters in the range 100 pm and
up, are therefore new as far as we know.
For large pulmonary vessels their patency under negative Pv - PA is well known. The first observation was
made by Howell et al. (12) who, following Macklin (18),
filled the vessels of excised lungs with kerosene and
showed that the volume of the larger vessels increased as
the lungs were inflated, whereas the volume of the small
vessels unfilled by kerosene decreased as the lungs were
inflated by positive airway pressure. In one experiment
the arterial and venous cannulas were connected to the
top of a vertical tube 30 cm long that stood in a beaker
of saline. When the lung was expanded with a positive
pressure of 30 cmHz0, liquid was drawn up the tube into
the pulmonary vessels. This showed that some of the
lung vessels were increasing in volume while the pressure
in the lumen was 30 cmH20 below atmospheric pressure.
Mead and Whittenberger (20) explained this phenomenon by the tension (tissue and surface tension) in the
interalveolar septa acting on the outside of the vessel
wall. They called this tension “perivascular interstitial
pressure, ” since the vessels are surrounded by interstitial
tissue. They called the larger vessels “extra-alveolar”
to
distinguish them from the smaller vessels exposed to
alveolar pressure. This is an operational definition, and
Mead and Whittenberger (20) did not specify the distinction in anatomic terms. We agree with their explanation,
and our results show that only the capillary blood vessels
in the interalveo lar septa qualify for the term “ahe olar”
vessels, whereas venules and veins, arterioles and arteries, are all “extra-alveolar.”
Permutt (21) measured the changes in perivascular
interstitial pressure when the blood volume was kept
constant while the lung was inflated, by attaching burettes to the artery and vein and moving the burettes UP
and down to keep the vascular volume constant. In
current terminology he measured the parenchymal tissue
stress (including surface tension) as the lung volume was
increased while the vascular volume was constant. In
terms of stresses and strains many new papers have been
published since 1970 [see Lai-Fook (15), whose predictions for large blood vessels are compatible with the
results of the present paper]. Small vessels such as venules are beyond the scope of Lai-Fook’s (15) theory.
Smith and Mitzner (24) measured the total vascular
volume of either the arteries or the veins as a function of
the transpulmonary pressure and the blood pressure.
Whether the venules were open or collapsed at negative
values of Pv - PA cannot be determined by their method,
and they did not discuss this question. With our results,
however, we can assert that all their vessels were open,
except the capillaries, when Pv - PA < 0. They analyzed
the interdependence theoretically with the methods of
Lai-Fook (15), which is applicable only when the size of
the blood vessel 1s large compared with the alveolar
dimension.
In summary, our results confirm the fact that pulmonary veins remain patent when PA > Pv, and sharpen it
to say that the venules remain patent as well as the veins,
at least up to PA - Pv = 17~cmHa0. This sharpening
then puts-the “sluicing” gates squarely at the junctions
of the capillary sheets and the venules. The knowledge
of this location has a crucial significance with respect to
the hemodynamics in zone 2 condition.
APPENDIX
Fluidity and Hardening Process of the SiZicone Polymer. The
question
is raised whether
the silicone
polymer,
after mixing
with
catalysts
and used in perfusing
the lung for 20 min, will become
so
hardened
that it will no longer be able to flow in response to changing
pressure
distribution.
Specifically,
when the perfusion
is stopped
and
the external
perfusing
pressure
gradient
is removed,
will the silicone
material
be able to redistribute
itself throughout
the vasculature
in
such a way that the pressure becomes equal everywhere
and in equilibrium with the elastic stresses in the vessel wall? The cast can represent
the shape of the blood vessel only if the silicone still behaves as a fluid
when the flow stops. The fluid being viscous, the question
is evidently
one of the ratio of the time constant
for fluid movement
(in response to
vessel shape change)
to the time constant
for the hardening
of the
material.
To answer the question
we measured
the change of the viscoelasticity of the catalyzed
polymer
with time. We then fiied a vein with this
material
and demonstrated
the ability
of the vein to respond
to static
pressure
changes in the polymerto collapse
under negative
transmural pressure
and to reinflate
under positive
transmural
pressurehours after the compound
was catalyzed.
These results are described
briefly
below.
The silicone
polymer
we used (compound
88017, General Electric
Silicone Products)
was catalyzed
by tinbctoate
and ethyl silicate. The
were
change of viscosity
of the mixture
with time after the catalysts
added was measured
with a Brookfield
viscometer.
The results are
shown in Fig. 7. It is seen that the rate of change of the viscosity
The concentrations
we
depends on the concentrations
of the catalysts.
normally
use are 3% tin octoate and 1.5% ethyl silicate, corresponding
to curve 3 in Fig. 7. We may add that every batch of commercially
available
silicone polymer
and catalysts
is somewhat
different
and the
CATALYZED TRIMER
4OOr
0
I
I
I
I
I
I
I
I
I
20
40
60
80
100
120
140
160
TIME (min)
7. Change
of viscosity
of silicone
polymer
with time after
addition
of catalysts.
Percents
by weight of catalysts,
tin octoate
and
ethyl silicate, are, respectively,
for curve 1, 5 and 2.5; curve 2, 4 and 2;
curve 3, 3 and 1.5; curve 4, 3 and 1.0; and curve 5, 3 and 0.
FIG.
1548
FUNG
ET
AL.
A
C
E
G
I
FIG. 8. Demonstration
of fluidity
and hardening
process of silicone
polymer
in inferior
vena cava of rabbit.
At time zero, polymer
liquid
was mixed with 3% tin octoate
and 1.5% ethyl silicate and was used
immediately
to perfuse vena cava for 5 min. Then outflow
was stopped
by tying off right atrium.
At 10 mm pressure
was decreased
to -12.5
cmH*O.
Vein collapsed,
and photograph
was taken (shown in A). At 11
min pressure
was increased
to +17.0 cmHz0.
B, vein at 12 min: it was
again patent.
Then pressure was decreased
to -12.5 cmH&
C, vein at
20 min; D, at 21 min after pressure
(P) was returned
to 17.0 cmHp0 for
1 min, E, P = -12.5 cmHz0
at 40 min, F, P = 17.0 cmHx0 at 41 min, G,
P = -12.5 cmHz0
at 42 min, H, P = 17.0 cmHs0 at 62 min; I, P = -12.5
cmHz0
at 92 min; and J, P = 17.0 cmH20 at 93 min.
exact quantities
of the catalysts
to be used must be determined
by
experiment.
We routinely
measure
the hardening
history,
as shown in
Fig. 7, whenever
new (or old). bottles of chemicals
are used.
Our catalyzed
polymer
mixture
has no static elasticity
within
3 h of
mixing. Liquid in open tubes will drain itself completely
under gravity.
Hence its dynamic
modulus
of elasticity
vanishes
at zero frequency.
Therefore
for our problem
the mixture
may be treated as a viscous fluid
within 3 h.
To demonstrate
the ability
of a vein filled with the mixture
to
respond
to the change of pressure,
we perfused
the inferior
vena cava
of the rabbit with a freshly mixed catalyzed
polymer,
and then the flow
was stopped. At specified
times the pressure was changed to either 17.0
or -12.5 cmHz0.
After 1 min of each change a photograph
was taken,
and the results are shown in Fig. 8. The vein was patent under positive
transmural
pressure and collapsed
under negative transmural
pressure.
Within
the first 40 min of catalysis,
the time required
to change the
NONCOLLAPSIBILITY
OF
PULMONARY
1549
VENULES
vessel shape into the new equilibrium
configuration
is less than 1 min.
After 60 min of catalysis,
however,
1 min is no longer
sufficient
to
completely
inflate the vessel, as can be seen in Fig. 8, H and J. The
sequence after (J) is not shown, but we can still inflate and collapse the
vein at 2 h.
This experiment
shows that the hardening
process of the silicone
polymer
did not prevent
elastic deformation
of the blood vessel in at
least the 1st h. In our experiment
on the pulmonary
vein, a static
condition
was imposed at 20 min after catalysis.
Although
a direct proof
is not available,
it seems reasonable
to believe that sufficient
time is
available
hydrostatic
for the polymer
pressure
before
liquid
to equilibrate
itself
the material
is solidified.
into
a uniform
This work was supported
by National
Institutes
of Health
Grants
HL-11152
and NOl-HR-6-2910.
S. S. Sobin was the recipient
of Research Career Award 5K06-HL-07064.
Y. C. Fung was the recipient
of
National
Heart,
Lung, and Blood Institute
Grants
HL-26647
and HL07089 and National
Science Foundation
Grant CME-79-10560.
Received
13 October
1981; accepted
in final
form
27 December
1982.
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