Morphometric Basis of the Sheet-Flow
Concept of the Pulmonary Alveolar
Microcirculation in the Cat
By Sidney S. Sobin, M.D., Ph.D., Herto M . Tremer, Ph.D.,
and Y. C. Fung, Ph.D.
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ABSTRACT
The purpose of this study was to describe quantitatively the geometric
organization of the pulmonary alveolar capillary bed. Conventional representation of these vessels as a tight network of circular cylindrical tubes (tube-flow
model) was contrasted with a suggested alternative of a continuous sheet
bounded on two sides by endothelium held apart by connective tissue and
cellular posts (sheet-flow model). A vascular space-tissue ratio, VSTR, is
defined as the ratio of vascular lumen volume to the circumscribing tissue
volume. The VSTR was obtained by planimetric measurements. Formulas were
developed to relate VSTR to the geometric models. Cat lungs were perfused in
situ with liquid silicone elastomer at 25 mm Hg, and the liquid elastomer was
allowed to catalyze at 15 or 25 mm Hg static pressure while the airway
pressure was maintained at 10 cm H 2 O. After the silicone became solid, the
lungs were fixed with formalin-steam, and morphometric analysis was carried
out on photographs of frozen sections. The mean values of VSTR of each cat
(six lobes) were 0.91 to 0.92, irrespective of intracapillary pressure. These data
are consistent with a sheet-flow model. Sheet thickness then becomes a
significant variable.
pulmonary capillaries
capillary bed
ADDITIONAL KEY WORDS
microvascular geometry
lung circulation
microcirculation models
silicone elastomer
blood vessel perfusion
alveolar wall circulation
capillary flow model
• Understanding the regulatory physiological mechanisms of any microcirculation requires knowledge of the hydrodynamics and
rheological behavior of blood in those microscopic vessels and ultimately must be based on
an accurate description of microvascular
From the Los Angeles County Heart AssociationUniversity of Southern California Cardiovascular Research Laboratory, Los Angeles County-University of
Southern California Medical Center, Los Angeles, California 90033.
This investigation was supported in part at the
Cardiovascular Research Laboratory by U. S. Public
Health Service Research Grant HE 1152 from the
National Heart Institute and at the University of
California San Diego by the United States Air Force
Office of Scientific Research Grant 1186-67 and the
National Science Foundation Grant GK-1415.
Dr. Sobin is a Career Awardee of the U. S. Public
Health Service, National Institutes of Health.
Received May 13, 1969. Accepted for publication
January 28, 1970.
CircmUiwt Roivncb,
Vol. XXVI, March 1970
geometry. A comprehensive and elegant study
of the microscopic blood vessels of the human
lung has been carried out by Weibel (1). This
served as the reference from which we
attempted to understand the dynamics of
pulmonary microcirculatory flow. Ultimately,
what must be known is how a red blood cell
flows through the alveolar capillary bed. The
relation between function (red cell movement) and structure (vascular channel) may
be understood when the geometry of these
channels is clearly defined. This paper develops the morphometric basis for considering
that the alveolar capillary bed is arranged as a
microvascular sheet. Theoretical treatment of
alveolar sheet flow has been carried out
separately by Fung and Sobin (2).
Malpigbi's observations on the anastomoses
between arteries and veins were made in the
living frog lung in which he described a
397
398
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network of vessels through which blood
moved m a manner "which escape(s) description by the pen" (3). He speculated that the
same vascular anastomoses existed in the
mammalian lung. In recent times the living
microcirculation of the mammalian lung surface has been extensively studied by visual
observation (4) and photography (5) through
the intact thorax. A serious limitation of this
method is that the microcirculation of the
pleural surface is not representative of the
respiratory alveoli of the bulk of the lung
which are inaccessible to the examining
microscope (6,7).
The organization of alveolar capillaries into
a network of variable mesh density was clearly
demonstrated by Miller (6) with the gelatin
infusion technique. The relative simplicity of
the method and the beauty of the preparations
led to repeated demonstrations of Miller's
observation (8, 9) but not to microvascular
measurements. Faithful retention of the living
state was achieved by quick-freezing the lung
surface, which resulted in rapid arrest of the
pulmonary circulation (10), although studies
of the geometry of the alveolar microcirculation apparently have not been done with this
preparation. The first rigorous analytic treatment of the geometry of the alveolar capillary
network was carried out by Weibel (1) on
formal in-steam-fixed human lungs in which
the basement membrane of capillaries was
stained by the periodic acid-Schiff, PAS,
reaction. For analytic purposes Weibel treated
vascular segments as wedged cylinders and
the network as a series of interconnected
cylindrical tubes. Our proposal of a microvaseular sheet is in direct contrast to this.
Three-dimensional geometry of the microcirculation can be obtained by a •: '
elastomer microvascular casting (injection)
method and subsequent histological processing of the tissue (11). Perfusion of these
silicone materials under physiological pressures without prior wash-out of blood results
in filling of vessels open at the moment of
perfusion and retention of that filling pattern
(see Discussion, Critique of Methods). By
these methods any portion of the vascular bed
SOB IN, TREMER, FUNG
of an organ can be studied and the geometry
determined. Our initial preparations of cat
lung showed a much closer or tighter mesh of
the alveolar capillary bed than we had
anticipated (Fig. 1). All subsequent preparations confirmed these initial observations. We
believe that this tight mesh may be described
as a sheet in which the two vascular
endothelial surfaces are essentially parallel
and held together by cells and connective
tissue which act as posts (7). We shall call
this a sheet model. Compared with the
conventional model of the pulmonary capillary bed as composed of a network of circular
cylindrical tubes, the tube or cylinder model,
the sheet model described above offers certain
simplification of hemodynamics. The difference between these two models may be
clarified by considering the space seen by the
red cell as it enters the interalveolar septum:
the capillaries of the tube model would be
seen as cylindrical tunnels which branch
Cat lung. Flat view of interalveolar wall with the
microcirculation filled with a silicone elastomer. This
corresponds to a "whole membrane preparation" of
Weibel (1). This photomicrograph illustrates the tight
mesh or network of the extensively filled capillary bed.
The circular or elliptical enclosures are basement membrane stained with cresyl violet and are the nonvascular posts. Frozen section from gelatin-embedded tissue;
glycerol-gelatin mount.
Cirml&ittt Rtltarcb. Vol. XXVI, March 1970
SHEET-FLOW IN PULMONARY MICROCIRCULATION
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repeatedly. On the other hand, the space in
the sheet model would appear as a parking
garage with floor, ceiling, and intervening
support posts. The sheet model simplifies the
geometry since the tube model is inherently
complex at the junctions where different
cylindrical tunnels meet. The simplification
permits us to introduce the thickness of the
sheet as an independent parameter. The
variation in thickness of the alveolar sheet has
great physiological significance because it
determines, in part, the blood pressure-velocity relation and the interaction between red
cells and capillary wall.
The material that follows will provide a
mathematical analysis of the models, describe
experimental preparations and methods and
present data in support of the sheet-flow
concept.
Geometric Model Analysis
The geometric model for sheet-flow is
c j..,.-,s£
FIGURE 2
Sheet-flow model. A: Plan view. B: Cross section
through X
X of A. The clear rectangular spaces
are the nonvascular posts. The stippled areas indicate
the flow channels. For orientation only, T = top and
B — bottom. Sheet thickness = h. C and D = contact
of posts with endothelial surface at T and B. See text
for details.
CircutttioB Research, Vol. XXVI, March
1970
399
illustrated in Figure 2. In the plan view (A)
this is a sheet with regularly arranged
obstructions. The plane may be divided into a
network of hexagons, with a circular post at
the center of each hexagon. The sheet-flow
model is therefore characterized by three parameters: I, the length of each side of the
hexagon; h, the height or thickness of the
sheet; e, the diameter of the posts.
In the plan view, the sheet-flow model does
not differ very much from die cylindrical rube
model. However, in elevation they are different. In Figure 2B a certain cross section X—X
of the sheet model shows a rectangular channel
of flow, whereas in Figure 3B a particular
cross section X—X shows a circular channel.
The cross-sectional geometry varies, of course,
with the direction of cut. The height h is an
independent parameter to be determined in
the sheet model, whereas it must be set equal
to the diameter, d, in the circular-cylindricaltube model. In reality, the vascular channel
would not appear exactly rectangular even if
the natural configuration were so, because the
elastic deformation of the vascular wall under
blood pressure would cause the walls to be
curved. Under a large transmural pressure, a
membranous structure would be so inflated
as to appear rounded. The real cross section
configuration of the alveolar capillary network
is somewhere between these two models.
The largest error in the cylindrical tube
model occurs at the junction of the "tubes," as
at point A in Figure 3A. In the neighborhood
of this point, the real vascular wall under an
internal pressure must be a smooth surface of
nearly uniform curvature. This is well approximated by the sheet-flow model, but poorly
approximated by the tube model, which
requires a complex, wrinkled surface in this
region. On the other hand, the largest error in
the sheet-flow model occurs at the junction of
the posts to the floor and ceiling, as at the
corners C and D in Figure 2B. The lung
probably does not have a sharp corner here.
Microscopically, the vascular cross section
usually appears in a rather irregular shape, the
most reasonable description of which is a
rectangle with rounded corners (Fig. 4).
SOBIN, TREMER, FUNG
400
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Tube-flow model. A: Plan view. B: Cross section through X
X of A. The vascular
network is stippled and completely fills the interalveolar space with a thickness equal to the
tube diameter (d). The clear spaces are the posts. See text for details.
It is possible to choose between these two
models on the basis of morphometric data.
Accordingly, we shall define a "vascular spacetissue ratio," VSTR, as the ratio of the
vascular lumen volume to the circumscribing
tissue volume.1 For the cylindrical tube model,
Figure 3A, the VSTR of the hexagonal tube
AB . . . F is the indicated part of the volume
of the tubes of diameter d divided by the
volume of a circumscribing hexagon with
height d. Let I be the length of a side of the
hexagon, then:
The volume of the hexagonal body AB . . . F
of height d = 6
y^Fd.
*As illustrated in Figure 2B, the circumscribing
volume is that enclosed between surfaces T and B.
The tissues (epithelial, interstitial and endothelial)
external to the surfaces T and B are excluded. Thus,
VSTR does not represent the volumetric fraction of
the total interalveolai septum occupied by blood.
The volume of a wedge (30°) at the corner
..^y-Y.
of a cylinder =
The volume of the tubes (blood volume) =
2x12/ d
2
4
Hence for the cylindrical tube model:
VSTR=
,„ ,-rr
2M3
V3
I
On the other hand, for the sheet model,
Figure 2, the VSTR is independent of the
CircmUiion Rtsurcb,
Vol. XXVI, Mtrcb
1970
401
SHEET-FLOW IN PULMONARY MICROCIRCULATION
VSTR of the sheet-flow model is higher than
that of the tube model. For the purpose of
comparison, we have, from Weibel's data for
human lung (1, p. 82), a d-l ratio varying
from 0.633 to 0.776. A substitution into
equation 1 leads to cylindrical tube VSTR
varying from 0.485 to 0.570, respectively.
The corresponding sheet-flow model dimensions may be calculated as follows:
From Figure 3A, the area of the central hexaDownloaded from http://circres.ahajournals.org/ by guest on July 31, 2017
Equating this with IT — , we obtain
4
(3)
~~ik)'
Substitution of the right side terms of equation
3 into equation 2 results in:
VSTR = l - (
1-^=).
LOO
FIGURE 4
Cat lung. Capillary bed filled with silicone elastomer.
Cross section of interalveolar septum. This photomicrograph taken to show "rectangles with rounded corners"
in the capillary bed (X). The post showing a slanting
angle through the sheet also has straight and parallel
surfaces in cross section (Y). Section 12n thick; cresyl
violet stain; intracapuTary pressure, 15 mm Hg. Oil
immersion objective 100x, NA 1.25.
UJ
^—•
0.75 -
O 0.50 -
SHEET
MODEL
v \
TUBE
height h and is equal to the percent of the
area occupied by blood in the plane cross
section. From Figure 2A, we have,
(4)
\
MODEL
0.25 -
The area of a hexagon = -¥— P.
/
The area of circle = TT —
4
Hence for the sheet-flow model,
1
L0
0.5
d/L
(2)
If the obstructing post of the sheet-flow
model has the same cross-sectional area as the
central hexagon of the tube model, then the
Circidition Rtnatch, Vol. XXVI, Mtrcb 1970
FIGURE 5
Comparison of the vascular space-tissue ratios (VSTR)
of the sheet-flow and tube-flow models as a function of
d/l (or e/l through equation 3; see text.) There are
no possible values of d/L greater than 0.90 for the
tube model.
SOBIN, TREMER, FUNG
402
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This expresses the VSTR for the sheet-flow
model in terms of diameter and length of the
cylindrical tube model. A substitution into
equation 4 with d/l varying from 0.633 to
0.776 yields a ratio for the sheet-flow model,
based on Weibel's data for human lung,
varying from 0.597 to 0.695, respectively. Thus
the VSTR of the sheet-flow model is 23S
higher than that of the cylindrical tube model
if bodi were evaluated on the basis of an
average d-l ratio.
Figure 5 shows a comparison of the
theoretical VSTR at various values of d/l or
e/i (connected by equation 3) according to
these two models. The sheet-flow model gives
a consistently higher ratio. By plotting observed ratios of d/l or e/l and VSTR on this
figure, a discrimination between these two
models is possible.
In actual practice, it is difficult to measure
and evaluate d/l or e/l from microscopic
preparations because of the random irregularities in the geometric appearance of the
specimens. The VSTR, however, can be
determined with greater confidence by planimetry and random sampling. The dimension
of the obstructing posts (e) can be calculated
from equation 2 by determining VSTR, and
measurement of 3i indicated in Figure 2A.
€
_
/6V3
(1-VSTR).
(5)
Experimental Methods
Silicone Microvascular Preparation.—A
complete description of the general procedure
has been published, including rationale, technical details, and validation of the method
(11). The silicone polymers used prior to this
study were highly viscous elastomers and
required a silicone diluent to decrease viscosity to approximately 25 centipoise (cP). The
silicone polymer material2 used in these
experiments had a natural viscosity of 19.5 cP
at 37°C, was nonvolatile and catalytically
cross-linked at room temperature. In the fluid
state, with the addition of the catalyst tin
2
Compd. 88017. Silicone Products Dept, General
Electric Corporation, Waterford, N. Y.
octoate to 3% concentration, this material
readily passed through the capillary bed
under physiological perfusion pressure. The
viscosity increased to 45 to 50 cP at 20
minutes. At two hours, the silicone was
firm.8
Animal Preparation.—Studies were carried
out on male cats weighing 3-5 kg that were
anesthetized with sodium pentobarbital, 30
mg/kg ip. The trachea was exposed and
cannulated for subsequent mechanical ventilation with a Bird respirator. A laparotomy was
performed and the abdominal aorta was
cannulated with thin-wall stainless steel tubing previously filled with heparin and saline
and closed with a stopcock. A lethal dose of
sodium pentobarbital was given intravenously,
and in rapid succession the chest was opened
in midline, the pulmonary artery dissected
free from the aorta and two loose ligatures
applied to the pulmonary artery. The thorax
was then filled with saline to prevent entrance
of air into the pulmonary artery at the time of
cannulation. The pulmonary artery was ligated at its base, incised just beyond the
ligature, cannulated with a thin-wall stainless
steel cannula filled with heparin and saline
and the cannula secured with the distal
ligature. The perfusion system was filled with
silicone polymer catalyzed immediately before
pouring and connected to the pulmonary
artery cannula while the saline was removed
from the thorax and the lungs mechanically
ventilated. The time elapsed between killing
the animal and start of silicone perfusion
averaged 30 minutes.
Both aortic and pulmonary artery tubing
had side connections for continuous recording
of pressure at the blood vessel level. Reservoir
s
The shrinkage or expansion of the silicone elastomer
in the process of solidification was measured by filling
pipettes to a measured value with the precatalyzed
liquid silicone, which was then allowed to solidify.
With the system employed, which was accurate to 1%
of the total volume, no measurable change in volume
was found- The linear dimension of a silicone cast,
therefore, does not change more than 0.3% and the
cross-sectional area does not change more than 0.655.
The effect of catalyzed polymerization of the silicone
on the VSTR is, accordingly, less than 0.6%. The data
in Tables 1-3 were presented without this correction.
Circtlnkm Resetrcb, Vol. XXVI, March 1970
SHEET-FLOW IN PULMONARY MICROCIRCULATION
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pressure was adjusted to provide the desired
hydraulic pressure at the pulmonary artery.
Zero reference pressure was at the level of the
cannula in the pulmonary artery. Pressure in
the aorta was maintained at zero mm Hg by
adjustment of the level of the drain tubing.
Perfusion of the silicone polymer into the
pulmonary artery was accompanied by removal of the stopcock from the aortic tubing
to provide the least obstruction to flow from
the pulmonary artery, through the lung and
left heart, to the aortic drain site. Perfusion
(flow) was continued for 20 minutes at 25
mm Hg pressure during which 200 to 400 ml
of silicone was perfused. This was followed by
reduction of pressure to 15 mm Hg, after
which the aortic drain was closed in one group
of animals, and maintenance of pressure at 25
mm Hg with closure of the aortic drain in the
other group. Pulmonary artery pressure was
then maintained at the preselected level for an
additional 90 minutes while the polymer
hardened.
Following closure of the aortic drain,
pressure in the aortic cannula rose from zero
to 15 mm Hg in one group and from zero to
25 mm Hg in the other group within 1 minute,
where it remained for 30 to 60 minutes.
Pressure subsequently fell parallel with the
pulmonary artery pressure during hardening
of the silicone.
During the period of perfusion of the
pulmonary vasculature, tracheal pressure was
maintained at 3 cm H2O, which was just
sufficient to partially distend the lung, and at
intervals of 1 to 2 minutes the lung was given
several "deep breaths" by overinflation up to
17 cm H2O, and then returned to 3 cm H2O
pressure. It was found by trial and error that
this technique was the most effective in
preventing atelectasis and facilitating displacement of blood by the silicone. Approximately 3 minutes before the aortic cannula
was closed, the airway pressure was set at 10
cm H2O to distend the lung normally and
maintained at that level throughout the
balance of the procedure.
From the above, two separate periods of
Rtluuh, Vol. XXVI, March 1970
403
pressure on the pulmonary vascular system are
identified: (1) the period of perfusion (flow)
with a pressure drop from 25 mm Hg at the
pulmonary artery cannula to zero at the aortic
drain site while silicone polymer viscosity was
low, to displace the contained blood; and (2)
the period of static pressure (no flow) of 15
mm Hg or 25 mm Hg throughout the vascular
bed of the lung before and during catalysis. In
period 1, the lung was ventilated sufficiently
to facilitate silicone perfusion of the pulmonary circulation. Subsequently, in period 2,
during static intravascular pressure, constant
airway pressure maintained the lung in
apparently normal distention.
Eight animals prepared by the combination
of silicone elastomer perfusion and formalinsteam fixation had airway and vascular
pressures described above. Two were technically unsatisfactory and the remaining six
were used for morphometric studies. Three of
the six had 15 mm Hg static intracapillary
pressure (low pressure) and three had 25 mm
Hg static intracapillary pressure (high pressure ); the airway pressure in both was 10 cm
H2O. It will be shown later that the
intracapillary pressure has little effect on the
VSTR, but it is expected to have an influence
on the thickness of the alveolar vascular
sheet.
Tissue Preparation.-Two hours after beginning perfusion, the various catheters were
disconnected, the carcass below the thorax
was removed and discarded, the thoracic skin
and diaphragm were removed, and the split
sternal edges approximated with towel clips.
The lung was then fixed by the formalin-steam
technique of Weibel and Vidone (12), modified to give positive pressure in the formalinsteam line without simultaneous negative
pressure on the outside of the lung, and kept
under direct observation from the diaphragmatic surface until fully fixed. Throughout the
dissection and other necessary maneuvers,
airway pressure was carefully kept at 10 cm
H2O to preserve the geometry of the lung,
until the tracheal cannula was connected to
the formalin-steam line also set at 10 cm H2O
404
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pressure.4 The time necessary for complete
fixation averaged 4 hours and was indicated
by a change in normal lung color to a uniform
gray. After complete fixation, the lung did not
collapse when disconnected from the formalinsteam line. The retained carcass was stored in
a freezer until used.
Histological preparations were made from
blocks of lung removed while still frozen from
comparable sites in six lobes of each animal,
right and left upper, middle and lower lobes.
Transverse slices of tissue 5 mm thick were
removed from the upper and middle lobes at
approximately the midpoint of the long axis of
each lobe; these slices were cut completely
across the lobe. Longitudinal slices 5 mm thick
were removed from the lower lobes at
approximately the lateral midpoint of the
transverse axis; these were cut half way across
and up the lobe. Each block was washed with
0.9% saline to remove free formalin and
embedded in 10% gelatin in 0.9% saline at 50°C
under vacuum sufficient to remove trapped
air. This was done under direct observation.
Without this precaution to remove air bubbles
from the lung, focal compression of these
unsupported areas occurred during tissue
sectioning. Tissue sections were cut with a
refrigerated microtome (International Equipment Co.), from the pleural surface in, stained
with cresyl violet, and mounted in a glycerolgelatin medium. The tissue sections were cut
serially as follows: three at lOfi., four at 75/t,
and three at 10/A. Histological materials were
analyzed for VSTR on the 75/i.-thick sections,
excluding the 1-mm region immediately below
the pleural surface.5
4
By maintaining airway pressure at the same value
as during silicone perfusion and solidification, the
geometry of the lung was kept the same shape as during solidification, and the elastomer was not stretched.
Since the silicone elastomer is effectively incompressible
(with its bulk modulus many orders of magnitude
larger than the Young's modulus of the lung tissue),
any stress change in the capillary wall and adjacent
tissue caused by the formalin-steam would have no
effect on the volume of the elastomer. The measured
ratio b unaffected by the formalin treatment.
6
These 75M-thick sections were examined by the
method described by Weibel (1, p. 47) as "whole
membrane preparations" of interalveolar septa and
cut by him from 50 to 150/* thick. The rationale of
SOB IN, TREMER, FUNG
0
21A.
Tracing made from photomicrograph in Figure 1 for
planimetry. The position of the perimeter line for
planimetry should be especially noted: it is halfway
between adjacent posts. The VSTR of the tracing —
0.81. This photograph was taken from an immediate
subpleural region of the lung to demonstrate the
technique used in planimetry which would have been
obscured in a bed with a high ratio.
Prior study of the silicone polymer-filled
microvascular bed of the lung quickly demonstrated the difficulty inherent in photographing the capillary bed of alveolar walls that are
randomly oriented in space. The microscopic
optical resolution necessary for this study
precluded a significant optical depth of field
and therefore eliminated all but the rare
alveolar wall oriented essentially at right
angles to the optical axis of the microscope.
Therefore, a microscope stage was constructed
with two tilting axes and horizontal rotation.
This enabled us to select many alveolar walls
for study that could not be examined on the
fixed horizontal stage of the microscope.
Histological preparations stained with cresyl
whole membrane preparations, including tissue thickness, was given by Weibel (1).
CitcuUtio* Rtsurcb, Vol. XXVI, March 1970
405
SHEET-FLOW IN PULMONARY MICROCIRCULATION
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violet showed a sharp blue-black line around
injected capillaries. This line appeared identical to the basement membrane stained with
the PAS reaction (1) in control lung sections.
It was not seen in unstained sections. The
cytoplasm of the endothelial cell was not
separately seen in stained preparations. By
selective optical filtration techniques it was
shown that the margin of the silicone injection
mass was indistinguishable from the blueblack cresyl violet-stained line demarcating
the inside of the capillary walL Therefore, the
intravascular edge of the basement membrane
stained with cresyl violet was used as the
limiting line of the inside of the capillary.
Photomicrography and Planimetry—Photomicrographs were taken of randomly selected
fields on Polaroid 4" X 5" Land film, type 55
P/N, with a continuous xenon light source
filtered by a yellow filter, Schott No. GG 148,
absorption maximum at 4950A. This combination remarkably enhanced the contrast of the
basement membrane. The microscope was a
Leitz Ortholux-Aristophot combination modified by installation of a photometer at the film
plane to obtain reproducibility of photomicrograph density. The optical system comprised
two Leitz 22X oil/water objectives NA 0.65
used as an objective-condenser pair, a 10X
Leitz Periplan eyepiece, and sufficient bellows
extension to give 500 magnification at the film
plane. The 4" X 5" negatives were in turn
photographed on 35-mm fine-grain positive
film and projected at a magnification of 2000
times the original histological material. Tracings were made from this projected image for
subsequent planimetry (Fig. 6).
The original inked tracing was retained as a
"master" and Xerox copies of the original were
used for analysis. There was no measurable
difference between planimetric measurements
of the original tracing and a copy. An area on
the tracing was arbitrarily demarcated by
various straight lines to enclose the area for
planimetry, and drawn halfway between
adjacent posts (Fig. 6). Not infrequently, due
to unevenness in the "flat" field of the capillary
6
Fish-Schunnan, New Rochelle, N. Y.
CircuUlion Rttttrcb, Vol. XXVI, Mtrcb 1970
bed, a number of areas were outlined on a
single tracing.
The validity of planimetric measurement
was determined as follows. The projected
image was traced and demarcated by different
persons and planimetered by them and others.
The results in all cases were essentially
identical.
Morphometric Analysis
Vascular Space-Tissue Rafro.-The VSTR
was obtained from two planimetric measurements of the tracing (Fig. 6): the total surface
area A8 of a demarcated area of the alveolar
wall and the surface area of all the pasts AP
within that area.
The vascular area Av of the total area:
AV = AS — Ap, and the vascular space-tissue
ratio: VSTR = AF/AS. This quantity was obtained without consideration of the actual
dimensions (magnification) of the projected
image.
Sheet Dimensions.—Additional information
was computed by converting the planimeter
measurements to actual dimension (microns).
The conversion factor was determined by
planimetry of a square of known dimension,
the sides of which were made from a Leitz
stage micrometer scale photographed and
projected under identical conditions used for
the interalveolar capillary bed.
The total demarcated surface area as
indicated in Figure 6 can be visualized as a
series of individual hexagons A, of equal size,
each containing a single post (Fig. 7).
No. of posts -"*•
Area A, can be considered as the "domain" of
each post. Then, for a hexagon with side I, the
area
1=
3V3
The center-to-center distance of adjacent
hexagons = l\j~3 (Fig. 2), and
SOB IN, TREMER, FUNG
406
ZV3 =
PfV3.
The area occupied by each individual post
Sheet thickness.—The derivation of equation 2 for the VSTR of the sheet-flow model
specifically excluded "h" or sheet thickness
(Fig. 2). This independent parameter is,
however, essential in considering the hemody-
. _ AP area occupied by all the posts (by planimetry)
"~
No. of posts
=
TT[ — ] where e is post diameter, and
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e = 2-
The interpost distance (the distance between post edges) = ?V 3 — e. This is the smallest distance for free passage of the red cell in
the plane of the alveolar wall.
The information necessary for this computation is obtained from the planimetry measurements converted to actual dimension and the
number of posts in the area considered.
Representation of these dimensions in microns provides a more objective view of the
total picture of the capillary bed of the
alveolar wall than can be arrived at by direct
and individual measurements, which are made
difficult by irregularity in local geometry.
namics of the alveolar capillary bed (2). Sheet
thickness was obtained by the technique of
optical sectioning7 (13). It was measured in
thick histological sections in alveolar walls
that could be positioned by the tilting stage
exactly parallel to the optical axis of the
microscope. Under these conditions the
"sheet" on edge was not displaced from the
7
The statistical analysis of randomly cut thin sections of septa (1, 14) was found to be an unsatisfactory
alternative to the optical sectioning technique for
thickness determination for this study. With paraffin
block sections l/i thick and attendant processing artifact, measurement would still be on the basis of an
optical cross section in the light microscope. Sections
cut thinner than the optical depth of field would have
to be cut from Epon-embedded material, also with
processing artifact, and these sections could not be
stained to demonstrate the basement membrane for
light microscopy. In addition, the silicone elastomers
are incompatible with the solvents used in tissue processing for Epon or paraffin.
Semtperspective view of sheet-flow model. The hexagon arrangement is a necessary geometric
configuration for theoretical analysis and does not represent a flow channel. See text for details.
trch, Vol. XXVI, M.rcb
1970
SHEET-FLOW IN PULMONARY MICROCIRCULATION
Downloaded from http://circres.ahajournals.org/ by guest on July 31, 2017
optical axis on changing microscope focus.
Sheet thickness was taken as the average
distance between the opposing stained capillary walls (basement membrane) at 5/A steps
through a 25/A vertical travel. It was measured
with a Leitz filar eyepiece standardized
against a stage micrometer and expressed in
microns. The microscope optics were a Leitz
63X objective, achromat, NA 0.85, with a
computed depth of field of 0.3/x and a Leitz
aperture diaphragm condenser with aplanatic
oil top element, NA 1.25. The condenser
illumination was reduced to 9/10 cone of light
in the rear focal plane of the objective. This
combination of optical system and a 75/u. thick
section will increase the depth of field to a
maximum of 0.5/x.
Results
The data obtained from the measurements
and computations carried out on the cat lung
perfused with silicone elastomer are presented
in tabular form. The VSTR for each individual
lobe in all three animals of both the low (15
mm Hg) (Table 1) and high (25 mm Hg)
(Table 2) pressure groups are essentially the
same. This striking similarity in ratio values
within each group is also seen between the
two groups with different intravascular pressures: 0.9143 at 15 mm Hg and 0.9178 at 25
mm Hg. These data simply indicate that in the
plane of the interalveolar wall, the capillary
bed can occupy between 91 and 92% of the
area it circumscribes. Furthermore, in the
planar dimension the vascular space is not
significantly changed by altering intravascular
pressure from 15 to 25 mm Hg.
No attempt was made to separate the fields
studied by anatomical location except to avoid
alveoli noted by Miller to have capillary beds
with a "coarse" mesh, such as pleural,
peribronchial, perivascular, and abutting connective tissue septae (6). Size, configuration
and number of posts in the planimetered areas
differed considerably. The number of posts in
each total area is an indication of the overall
size of each planimetered area. The hexagon
area is obtained by subdividing the total
planimetered area into "post domain" areas
(A,): it is a computed value and not directly
CucuUiio* Rtiurcb, Vol. XXVI, Mtrcb 1970
407
measured. The considerable variation in the
hexagon areas is seen in both Tables 1 and 2
and is accompanied by an equivalent change
in post area, which is consistent with the
unvarying ratios. This is clearly demonstrated
in the individual lobe values of post diameter
and VSTR in animal 5 (Table 2) as well as
the general trend when these mean values for
each animal are compared. Similarly, the
interpost distance will vary in the same
manner. The post center-to-center distance is
not entered in the tabular data. It can be
obtained by adding the interpost distance and
one post diameter, although, as noted in the
section on Morphometric Analysis, the interpost distance was obtained by subtraction of
the post diameter from the center-to-center
distance of the hexagon.
The mean value of the measured thickness
of the sheet at low and high intravascular
pressures was 7.4 and 7.8/i, respectively.
The data presented in Table 3 were
obtained from an analysis of cat lungs
prepared before the use of the formalin-steam
fixation method to ensure a controlled experimental preparation. These included lungs
prepared by liquid formalin fixation and
distention (inflation) and subsequent gelatin
instillation into the airways. The striking thing
about these data is the high VSTR's between
0.85 and 0.90 with a relatively small standard
deviation, and values for hexagon area, post
diameter, and interpost distance not remarkably different from those obtained with the
controlled formalin-steam method.
Discussion
Geometric Model.—The experimental data
obtained from the cat lung perfused with
silicone elastomer support the sheet-flow
model of the pulmonary alveolar microcirculation in the areas selected for study. By
contrast, they are not consistent with a
circular cylindrical tube model composed of
interconnecting wedged circular cylindrical
segments. The VSTR is the starting point for
the morphometric analysis of the contrasted
sheet-flow and cylindrical tube models. The
VSTR is relatively insensitive to small geometric irregularities, therefore measurement errors
RUL
RML
RLL
LUL
LML
LLL
Total lungt
LML
LLL
Total lungf
LUL
RUL
RML
RLL
Total lungt
RUL
RML
RLL
LUL
LML
LLL
Lobe
1.62
0.94
1.21
0.81
1.98
1.61
1.82
1.21
1.69
1.37
1.52
0.76
1.70
1.75
± 0.88
=t 1.66
•*= 0.94
* 1.06
± 2.02
± 0.93
=±= 1.39
±
±
±
±
±
±
±
*
±
*
±
±
±
±
8.3
9.1
9.1
10.0
7.7
10.6
92
9.2
9.5
10.6
9.0
10.5
10.6
9.8
7.9
11.1
10.0
9.4
9.3
8.3
9.5
No. pottt
per field
7.54
21.20
23.43
31.86
31.64
30.46
29.20
± 20.96
* 34.63
* 58.80
=•= 29.37
± 30.39
± 39.39
± 44.17
="= 17.77
± 12.55
± 26.10
± 29.39
=•= 63.39
± 31.52
=•= 34.51
±
±
*
±
±
±
•*=
163.66 ± 37.11
158.18
170.80
205.87
139.49
163.99
150.58
166.15
167.63
177.14
188.54
169.44
184.37
170.78
175.38
137.87
137.58
148.91
158.76
154.02
177.44
151.99
Hexagon
ire* (B)
0.')
Hg)
TABLE 1
Lung: Low Pressure (15 mm
±
±
±
±
±
±
±
±
±
±
±
±
±
=*=
±
±
±
±
±
±
*
0.20
0.56
0.78
0.60
0.83
0.64
0.72
0.47
0.29
0.52
0.47
1.28
0.67
0.75
0.24
0.48
0.50
0.66
0.55
0.78
0.67
4.19 ± 0.79
4.35
4.42
4.92
4.07
4.43
3.91
4.36
4.61
4.65
5.04
4.02
4.45
4.75
4.56
3.36
3.77
3.50
3.97
3.53
4.51
3.76
w
Post
Ala.m
0.47
0.73
0.76
0.75
0.72
0.51
0.75
±
±
±
*
±
±
=t
0.68
1.10
1.27
0.65
0.57
0.91
1.04
=*» 0.55
± 0.36
± 0.58
* 0.72
=•= 1.08
=•= 0.65
=t 0.74
±
="=
*
±
±
±
±
9.13 ± 0.85
8.79
9.20
9.96
8.23
8.92
8.88
9.03
8.92
9.28
9.28
9.59
9.57
8.88
9.24
8.98
8.49
9.28
9.19
9.47
9.39
9.12
(M)
IntorpMt
distance*
160
9
7
7
8
46
7
8
10
8
7
10
8
9
52
7
13
13
7
12
10
62
Mo. fleldi
analyzed
7.4
8.9
7.1
7.4
7.4
7.4
7.5
7.7
7.2
7.5
7.7
7.0
7.2
7.3
7.3
7.0
7.8
6.7
8.2
7.1
7.8
7.4
Sheet
thiaknoH
00
RUL = right upper lobe; RML = right middle lobe; RLL = right lower lobe; LUL = left upper lobe; L M L = left middle lobe; L L L = left lower lobe.
VSTR = vascular space-tissue ratio expressed in % ( V S T R x l O O ) . Values are means ± SD.
*Distance between post edges. fValues for each total lung and each total series based on individual values for the set.
91.43 =* 1.91
90.52
90.80
90.58
90.62
90.52
91.95
90.84
89.96
90.40
89.34
92.45
91.53
89.54
90.59
93.48
91.73
93.41
92.14
93.63
90.94
92.57
VSTB
of Data for Silicone Elastomer-Filled
All low-f>i•assure lungat
3
2
1
Cat
no.
Summary
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2
»Z
H
B-
f
£
Vol.
o
I
S
—
-
Downloaded from http://circres.ahajournals.org/ by guest on July 31, 2017
TABLE 2
± 1.48
* 1.06
=* 0.60
* 0.96
± 0.93
± 1.28
* 1.47
92.77
92 94
93.89
93.49
92.31
90.73
92.70
RUL
RML
RLL
LUL
LML
LLL
Total lungt
See footnote to Table 1.
91.78 * 1.95
1.28
1.73
0.84
0.76
0.93
0.75
1.38
±
*
±
±
=t
«t
±
91.44
92.92
93.10
92.88
94.0S
92.17
92.64
RUL
RML
RLL
LUL
LML
LLL
Total lungt
1.98
1.52
1.31
1.19
1.56
2.02
1.86
±
±
*
±
±
*
±
V8TR
90.14
89.97
89.31
91.16
91.86
90.06
90.44
Lobe
RUL
RML
RLL
LUL
LML
LLL
Total lungt
All high-presaure lungst
6
5
4
Oat
no.
9.6
11.3
9.6
11.9
13.6
16.7
12.0
14.7
12.7
7.4
8.3
8.5
8.7
10.3
14.6
11.2
11.3
7.2
10.5
15.3
11.9
No. posts
per field
±
±
±
±
±
±
*
24.49
24.21
21.61
29.13
30.05
13.64
25.75
26.57
25.04
32.35
35.17
10.50
15.90
33.97
22.53
25.19
33.72
12.98
19.48
35.49
28.17
142.06 * 31.70
155.30 ±
144.24 ±
146.55 ±
145.84 =•=
167.76 =<=
147.63 ±
151.00 ±
121.62 =•=
116.10 ±
170.15 ±
118.22 ±
98.03 *
114.22 ±
123.58 *
164.34
138.24
161.22
144.43
145.72
141.10
148.91
Hexagon
area(s)
Summary of Data for Silicone Elastomer-Filled Lung: High Pressure (25 mm Hg)
± 0.46
=fc 0.40
=*= 0.32
* 0.31
± 0.41
* 0.41
± 0.49
3.82 •*• 0.70
3.75
3.57
3.36
3.44
4.03
4.17
3.71
± 0.59
* 0.68
=*= 0.58
± 0.61
± 0.26
± 0.21
•t 0.63
3.63
3.22
3.86
3.25
2.71
3.36
3.37
0.66
0.67
0.53
0.28
0.46
0.77
0.65
±
±
*
±
±
*
t
4.52
4.20
4.65
4.01
3.86
4.19
4.23
0»)
Post
± 0.80
± 0.71
=t 0.64
± 1.00
=fa 0.83
* 0.37
± 0.80
=•= 0.66
± 0.63
* 0.69
* 0.97
± 0.43
± 0.60
* 0.95
* 0.58
*= 0.45
± 0.92
=t 0.51
± 0.65
± 0.88
* 0.75
8.61 =t 0.90
9.30
9.00
9.34
9.20
9.52
8.54
9.14
7.87
8.04
9.78
8.05
7.70
7.83
8.20
8.87
8.06
8.55
8.57
8.78
8.16
8.49
Inteipost
distance*
M
149
8
9
7
7
7
7
45
10
6
7
8
6
7
44
10
9
9
9
11
12
60
No. fields
analyzed
7.8
7.0
7.2
7.4
7.5
8.0
7.6
7.4
8.3
8.1
7.9
8.4
8.3
7.1
8.0
8.2
8.0
8.1
8.1
7.8
7.6
8.0
Sheot
thickness
GO
z
—
oo
n
35
o
?
70
o
c
Z
IEET- FLOW
410
SOBIN, TREMER, FUNG
TABLE 3
Summary of Data for Silicone Elastomer-Filled Lung: Miscellaneous Preparations
Cat
7
8
9
VSTE
90.59 ± 2.42
84.96 ± 3.91
85.48 ="= 4.01
No . potts
pe r field
12.4
6.8
7.4
Hexagon
area(»)
W
151.68 * 39.27
109.68 ± 34.36
163.07 ± 34.35
Fott
dlam
Interpost
distance*
W
4.22 =•= 0.91
4.53 ± 1.10
5.44 ± 1.12
W
No. fields
analysed
8.59 ± 0.95
6.26 ± 0.72
7.78 ± 0.78
27
28
18
See footnote to Table 1.
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are reduced when this ratio is planimetrically
determined. From the graphic data in Figure
5, it is clear that the larger the ratio the more
likely the geometric model will conform to the
sheet-flow model. For a VSTR of 0.68 the
vascular network would have cylindrical units
equal in length and diameter, and with an
increasing ratio, length becomes less than
diameter to the point where, for the ratio of
0.90 or more found in these experiments, there
is no meaningful circular cylindrical tube
length-diameter ratio.
The consistently high values for the ratios
are especially surprising when experimental
preparations include two different pulmonary
interalveolar vascular pressures (15 and 25 mm
Hg) and experimental preparations of different types. These data indicate that throughout
the lung the relation between the vascular and
nonvascular space in random plane sections of
the wall tends to remain constant in such a
manner that the interpost and post dimensions
vary equally.
The unresponsiveness of the capillary bed in
the plane of the septum to altered intracapillary pressure has also been seen in the coldblooded lung. Maloney and Castle (15), in a
report on work with frogs (Rana catesbiana),
have shown a beautiful photograph of an
alveolar septum which bears a close resemblance to our Figure 1 for the cat. They found
that in the plane of the septum the capillaries
occupied 79.1 ±5.3? (SD) of the frog alveolar
septum at low intracapillary (1 cm H2O)
pressure and 80.5 ±4.4% (SD) at higher
intracapillary pressure (27 cm H 2 O). This
result is similar to ours, although numerically
the VSTR is lower for the frog (80*) than for
the cat (91%).
The detailed dimensions of the sheet
(nonvascular posts and interpost distances)
computed from the VSTR, under the assumption of a regular hexagonal pattern in plan
view and uniform thickness in cross section,
were sufficiently close to those obtained by
sample direct measurement to exclude the
prohibitively time-consuming direct measurement.
Critique of Methods.—Since the silicone
method is the basis of this study, a discussion
of its applicability and limitations to define
the pulmonary capillary bed morphologically is warranted, especially in comparison to
other techniques available. There are a
number of advantages of the silicone method.
Since the entire lung is perfused, the microcirculation at any depth can be studied. The
vascular space, and therefore the vascular
dimension, is not altered, either by the change
in silicone from fluid to solid or by subsequent
tissue processing. This silicone material is inert
with respect to the vascular endothelium, as
indicated by the ability of the kidney to form
urine when reperfused with blood after
silicone perfusion (16). It is probably inert
with respect to vascular smooth muscle, as
indicated by (1) retention of vasoconstriction
of the epinephrine or cold-constricted rabbit
ear, compared to the contralateral control ear,
and (2) extensive fining of the microvasculature of reactive hyperemic muscle compared
to its contralateral control (11). The obvious
disadvantage of the method is that the sample
is not taken from a live, blood-filled lung.
There are at least three additional methods
used to define the pulmonary microcirculation
morphologically. (1) The quick-freezing technique pioneered by Staub and co-workers
OrcmUiion Rtstarcb,
Vol. XXVI, M*rcb
1970
SHEET-FLOW IN PULMONARY MICROCIRCULATION
Downloaded from http://circres.ahajournals.org/ by guest on July 31, 2017
(10) has the great advantage of rapidly
arresting and capturing the circulation in its
physiological state, or closely approximating
it. The only obvious disadvantages of the
method are that structures away from the
surface are frozen more slowly and that tissue
processing by either (a) freeze-substitution or
(b) freeze-drying and subsequent fixation still
results in distortion artifacts of both tissues
and vascular lumen by an amount difficult to
determine. (2) The value and limitations of
direct microscopical studies of the living lung
through thoracic windows by modern recording techniques were noted in the introduction
to this paper. (3) The study of post-mortem
lungs specially prepared by the formalinsteam technique of Weibel and Vidone (12)
has been discussed. The advantage of the
method to make available material which
would otherwise be lost must be carefully
weighed against the obvious distortion artifacts.
All methods obviously have advantages and
disadvantages and the choice of one to be
used must be determined by the objectives of
the investigation. For the present at least, the
artifacts associated with tissue preparation cannot be avoided. It probably is not valid to
assume that the measured overall shrinkage or
swelling involves all tissue elements to the
same degree. The silicone technique, despite
its other limitations, sets the vascular lumen
dimension before tissue processing.
The low flow rate of the silicone perfusion
at 25 mm Hg pressure through the lung
should be noted: it is approximately 1/10 to
1/20 of the cardiac output of the open-chest
cat (100 ml/kg/min). This is due to (1) the
higher viscosity of the silicone—approximately
five times that of blood-and (2) the
interracial surface tension between the hydrophobic silicone fluid (20.8 dynes/cm at 25°C)
and blood (average 73 dynes/cm), and the
blood vessel wall. The movement of the
interface along the capillary vessel wall
dissipates energy and increases vascular flow
resistance, and at a constant pressure gradient
the flow rate is decreased. The surface tension
effect diminishes as blood is displaced from
Rtitrrcb, Vol. XXVI, M,rcb 1970
411
the capillary bed so that the ratio of final flow
rate of silicone to that of blood is approximately the ratio of their viscosities.
The possible effect of biological materials
on catalytic hardening of the silicone must be
considered. Prolongation of hardening time
will not interfere with the experimental
procedure. Shortening of hardening time
could lead to premature hardening of the
silicone in the capillary bed, so that the
pressure in the capillary bed would not be
identical to that in the pulmonary artery and
the aorta, but would be transmitted across the
lung through pathways other than the capillary
bed. The fact that this is not so was verified
by prior experiments in which the airway
pressure was raised above the static pressure
in the pulmonary artery and the aorta at the
beginning of the static pressure period (after
20 min) : the interalveolar capillary bed was
always compressed and the measured interalveolar vascular sheet thickness was essentially
zero.
Although the silicone elastomer microvascular injection method has been increasingly
used to study the functional geometry of the
microvasculature of various organs (17, 18,
19), it had to be determined whether the
characteristics of the alveolar capillary bed
could conceivably result in excessive or
abnormal microvascular filling with silicone
polymer. Therefore, the vascular perfusion of
the cat lung described for the silicone
technique was repeated, using both heparinized cat blood and plasma which remained
under 15 mm Hg pressure while being fixed
by formalin-steam at 10 cm H 2 O pressure.
Blocks of tissue were processed for paraffin
embedding and sections were stained by the
PAS method used by Weibel (1) to demonstrate the pulmonary capillary basement
membrane. The VSTR from a preparation of a
whole blood-perfused lung is 0.914. Due to
uncontrolled tissue shrinkage that occurs
during formalin-steam fixation and subsequent
wax embedding, morphometric analysis was
not done on these plasma and blood preparations. Although shrinkage could be measured,
an assumption that all tissue elements would
412
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shrink in proportion to overall shrinkage is not
valid. Blood and plasma preparations were
done primarily to establish the similarity of
the microvascular pattern when natural and
artificial materials were perfused.
The extent and type of artifact resulting
from tissue processing was not determined in
these preparations. Every attempt was made
to minimize artifacts, and for this reason
gelatin embedding and frozen sections were
used to avoid shrinkage that would have
resulted from paraffin preparations. The
shrinkage accompanying formalin-steam fixation in freely hung post-mortem human lung
was determined by Weibel (18% in linear
dimension). Our specimens were not freely
hung and any blanket correction for the extent
of shrinkage by this value is undoubtedly
inappropriate for our preparations, since the
microvascular bed was filled with an incompressible material that solidified prior to
formalin-steam fixation and therefore was not
affected by it. In other words, the vascular
space was already fixed when formalin was
applied. The tendency for the tissue to shrink
merely imposes compression on the solidified
elastomer without sensibly changing its dimensions. A residual stress would be introduced in the tissue when it contacts formalin
steam, but the dimensions and the VSTR
cannot be affected.
By the same token, the pressure in the fluid
silicone during catalytic hardening does not
affect the VSTR. Fluid silicone is effectively
incompressible. When the lungs were perfused, the geometry of the vascular space was
determined by the pressure in the silicone
fluid and the airway pressure. Before catalyzing, these pressures were carefully controlled.
The perfusion system was then shut off, and
the volume of trapped fluid silicone was not
permitted to change any further. Therefore
the vascular volume was fixed.
The only remaining factor is the shrinkage
or expansion of the polymer upon solidification. As remarked earlier, this amounts to less
than 1% in volume. This requires a correction
in VSTR of less than 0.66%. This small
SOBIN, TREMER, FUNG
correction was ignored in preparing Tables 1
through 3.
Physiological Significance.--What is the
physiological significance of the high VSTR of
the interalveolar septum? In its entire extent,
that capillary bed can be considered to
be an interalveolar endothelium-lined vascular
space, with a variable reservoir capacity,
which plays a not clearly defined role in the
changing pulmonary blood flow in varying
physiological states. The sheet-flow concept
simply defines the limits of that anatomical
space and does not consider the use or
participation of that space in physiological
regulation of blood flow through the lung, nor
in the related problem of the changing extent
of the diffusing membrane of the lung. A
theoretical analysis of the details of alveolar
sheet-flow by Fung and Sobin (2) may
provide the basis for further understanding of
blood flow in the pulmonary microcirculation.
The potential space occupied by the alveolar microvascular bed in man is demonstrated
in a photograph by Loosli illustrating extensive capillary filling when the pulmonary
arteries and veins were ligated (shortly after
sudden death) to prevent dislocation of blood
from the lungs by the endotracheal fixation
(20). The VSTR measured from this photograph was 0.894.
How appropriate is the sheet-flow model to
the living pulmonary alveolar microcircularion, based as it is on a bistological analysis of
the nonliving lung perfused with an intravascular "casting" material prior to tissue death?
The perfused microvasculature invariably reveals an open capillary network, which is
consistent with the preparations and data of
Weibel on the human lung (1). The lungs in
his study were removed at autopsy, expanded
by appropriate vacuum and subsequently
fixed by formalin-steam. Measurements were
made on the flat aspect of the alveolar septum
in which the PAS-stained basement membrane
delineated a microscopically identified capillary space. The basis of Weibel's observations
is a patent network of capillaries (1, p. 48).
The fact that the capillary network is seen
Grc*Ul«m Rtst+rcb, Vol. XXVI, M.tib 1970
SHEET-FLOW
IN PULMONARY
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open in the appropriately fixed lung may
indicate that closed pulmonary capillaries may
be the exception rather than the rule.
An essential point in the sheet-flow model is
that the VSTR is independent of sheet
thickness (equation 2). Sheet thickness is
therefore an independent parameter. Since the
ratio was insensitive to an increase in the
intravascular pressure from 15 to 25 mm Hg, it
was anticipated that sheet thickness would
increase with increasing pressure. There is a
measured increase in sheet thickness or width
of 0.4//. for 10 mm Hg pressure increase. From
the graphic data of Glazier et al. (21), it is
possible to extrapolate capillary width measurements in the isolated quick-frozen upright
greyhound lung: at 10 cm H2O airway
pressure, capillary width increases by approximately 0.86/A and 0.76/x in zones II and III,
respectively, for each 10 mm Hg (13.54 cm
H 2 O) pressure increase. Although the sheet
thickness in the present experiments increases
by only 50? of that found by Glazier et al.
(21), this is surprisingly close, especially when
lung position is considered in the dorsal
recumbent cat and the upright greyhound. It
will be necessary to explore both the lower
and higher ranges of pressure to characterize
fully the response of the sheet thickness to
changing pressure in the context of the sheetflow concept.
The detailed geometry of the pulmonary
pleural microcirculation and blood flow
through it cannot be used as criteria for
geometry and flow in the deeper lung
structures. Thus conclusions reached from
study of the pleural vessels should be applied
to the latter with caution. It is unfortunate
that the anatomy and physiology of the lung
preclude extrapolation of observations made
on the surface.
The limitations on the application of
Poiseuille's law to pulmonary blood flow have
been well stated by Caro (22). As a result of
the studies reported here, it seems more
appropriate to consider the resistance imposed
by a vascular sheet with interspersed posts.
This has physical significance and can be
Circulation Rtstorcb,
413
MICROCIRCULATION
Vol. XXVI, March 1970
handled theoretically and by modeling (2,
23).
The organization of the alveolar microcirculation into a vascular sheet rather than a
cylindrical network indicates that the question
of "capillary" distensibility should, for the
lung, be replaced by the question of sheet
distensibility. That the alveolar vascular sheet
is extensible and probably distensible is seen
from studies of others on the effect of pressure
on capillary filling (21). Red cell packing of
distended alveolar capillaries in heart disease
in man is not uncommon. The elastic or
distensible behavior of the sheet and the
factors which modify it need to be further
characterized.
Acknowledgment
The technical assistance of Miss Millicent Bortle,
Miss Elizabeth Cogswell, Mr. George Rathbun, Mr.
Russell Packard and Mr. Lawrence Lenz is gratefully
acknowledged. Dr. Ewald R. Weibel has kindly provided us with the details of the PAS methods used by
him.
References
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SOBIN, TREMER, FUNG
414
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CircuUtion Rositnb, Vol. XXVI, M~cb 1970
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Morphometric Basis of the Sheet-Flow Concept of the Pulmonary
Alveolar Microcirculation in the Cat
SIDNEY S. SOBIN, HERTA M. TREMER and Y. C. FUNG
Circ Res. 1970;26:397-414
doi: 10.1161/01.RES.26.3.397
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Permissions: Requests for permissions to reproduce figures, tables, or portions of
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