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-Actin: disposition, quantities, and estimated effects
on lung recoil and compliance
1 Departments of Medicine and Pathology, Memorial Hospital of Rhode Island and Brown University, Pawtucket, Rhode Island 02860; 2 Biomedical and X-ray Physics, Royal Institute of Technology, Stockholm, SE-10044 Sweden; and 3 Physiology Program, Harvard School of Public Health, Boston, Massachusetts 02114
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
MODEL
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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We have investigated the basis and
implications of pneumoconstriction by measuring disposition and
quantities of 
-smooth muscle actin in rat and guinea pig lungs and
modeling its effects on lung recoil and compliance. A robust marker of
contractility, -smooth muscle actin appears in smooth muscle or
myofibroblast-like cells in pleura, airways, blood vessels, and
alveolar ductal tissues. In each site, we measured its transected area
by immunofluorescent staining and frequency-modulated scanning confocal
microscopy. We incorporated these data in a model of the parenchyma
consisting of an extensive elastic network with embedded contractile
structures. We conclude that contraction at any one of these sites
alone can decrease parenchymal compliance by 20-30% during tidal
breathing. This is due mostly to the stiffness of activated contractile
elements undergoing passive cycling; constant muscle tension would have little effect. The magnitude of the effect corresponds with known responses of the lung to hypocapnia, consistent with a homeostatic function in which gas exchange is defended by redistributing
ventilation away from overventilated units.
alveolar duct; intensity-modulated multiple-wavelength scanning confocal microscopy; lung compliance; ventilation-perfusion ratio; hypocapnia
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
MODEL
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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A VARIETY OF CONSTRICTING AGENTS can increase the lung's elastic recoil pressure and elastance (3, 6, 7, 25, 30, 42), and conversely relaxing agents can decrease its elastic recoil pressure (9). The static and passive dynamic properties of strips cut from lung parenchyma are influenced by smooth muscle agonists (10, 17, 32, 38, 50). Hypocapnia can reduce the lung's dynamic compliance on the order of 30% (1, 18, 41, 43, 48, 49), and this may represent a mechanism for control of ventilation (6, 18).
The source of this contractility, however, is unclear. Structural considerations suggest that contractile elements in the airways, blood vessels, or alveolar ducts can draw in on the surrounding parenchyma, thereby increasing its tensions. Contractile interstitial cells located within the alveolar walls themselves might increase the tensions of the alveolar parenchyma (19, 50). Airways acting alone may have an effect, because selective pharmacological constriction of conducting airways substantially reduces quasi-static and dynamic lung compliances (30). Other locations may also have independent effects, because agonists can change tissue dynamic properties independently of airway resistance (17). Furthermore, it has been argued that the contractility observed in subpleural strips of lung parenchyma may not be due to vascular or airway smooth muscle contraction (10, 19, 38).
We thought that some insight might be gained from knowing more about
the contractile material in each location and estimating the effects of
each on lung recoil and compliance. Accordingly, we chose -smooth
muscle actin as a major marker of contractile capability, and we
applied a variety of microscopic techniques to sections of rat and
guinea pig lungs to characterize the cells that contained it and to
determine its locations and quantities in the lung parenchyma. We then
modeled its effects by considering the lung parenchyma as an elastic
network with embedded contractile elements. In the model, the elastic
network was given the known elastic properties of relaxed lung, and the
contractile elements were given the plastoelastic properties of
passively cycled, activated smooth muscle. This model, incorporating
the anatomical data from the first part of the study, estimates the
effects of activation of the contractile elements in each location on
regional parenchymal recoil and compliance during tidal breathing.
Our results show, in the two species examined, that any one of
the locations alone has sufficient contractile material to account for
modest but significant reduction of parenchymal compliance under
dynamic conditions. This is consistent with the hypothesis that this
mechanism, locally responsive to carbon dioxide levels, defends the
overall efficiency of gas exchange by modulating local ventilation-perfusion (
/
) ratios.
Glossary
Primary symbols
Forces
| F | force |
| T | tension (force per length) |
| P | pressure (force per area) |
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nominal stress (force per area at lo) |
| A | area |
| V | volume |
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density of embedded structure in the lung unit |
| TLC | maximal physiological lung unit volume |
| FRC | relaxed physiological lung unit volume |
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bulk modulus |
| µ | shear modulus |
| lo | length for maximal muscle stress |
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angle of muscle fiber to the axis of airway cylinder or equator of ductal sphere |
| a | radius of sphere or cylinder |
| u | displacement of a boundary |
Modifiers
Geometry
| ax | axial |
| circ | circumferential |
| tm | transmural |
| 1 | inner radius of surrounding (thick-walled) parenchyma, or equivalently outer radius of (thin-walled) duct or airway |
| 2 | outer radius of lung unit |
| ce | contractile element |
| tiss | tissue |
| L | lung |
| duct | alveolar duct |
| aw | airway |
| par | parenchyma |
| pl | pleura |
| active | contractile elements activated |
| passive | contractile elements relaxed |
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
MODEL
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Immunostaining
We used a monoclonal antibody to mark-smooth muscle actin
(44). It is highly specific, having been raised against
the highly conserved amino terminal 10 amino acids of the smooth muscle isoform of -actin. It is nonetheless very broad in its species reactivity, including human, rat, and chicken (44), cow,
frog, goat, guinea pig, mouse, rabbit, dog, sheep, and snake (Sigma Chemical), and hamster and pig (personal observations of an author, C. Kuhn III).
The antibody was visualized by three different techniques.
1) To determine the disposition of -smooth muscle actin
on large sections with moderately well preserved septal configuration, we examined frozen sections by transmission light microscopy with the
antibody made visible by diaminobenzidine-horseradish peroxidase (DAB-HRP). 2) To quantify -smooth muscle actin in various
sites over large fields of view, we prepared paraffin sections and used intensity-modulated multiple-wavelength scanning confocal microscopy (IMS) to measure the areas of fluorescence of Cy-3 linked to the antibody and to obtain anatomical context from fluorescent images of
BODIPY-SE (Molecular Probes, Eugene, OR) staining lung tissue generally. 3) To determine the subcellular patterns
and concentrations of -smooth muscle actin, we examined epoxy
sections by transmission electron microscopy with the antibody
visualized by immunogold.
Organ Isolation, Fixation, and Sample Preparation
Experimental animals comprised six female, viral antigen-free Sprague-Dawley rats (241-348 g) and three guinea pigs (423-523 g). Each was briefly sedated with carbon dioxide (dry ice vapor in a desiccator) and then anesthetized with pentobarbital sodium (30-41.5 mg/kg body wt im). Tracheal intubation was immediately performed, and the animal was maintained on a ventilator until the heart and lungs could be rapidly removed en bloc.Transmission light microscopy.
Rat lungs were filled with a 1:1 mixture of cryostabilizing compound
(Tissue-Tek OCT compound; Sakura Finetek, Torrance, CA) and saline.
Blocks of tissue were placed in pools of OCT compound on copper chucks
and frozen by immersion in 2-methyl butane cooled in dry ice. Frozen
sections were prepared on a cryotome with section thickness of 6 µm.
Sections were thaw-mounted on silanized slides and dried for 30-60
min. After fixation for 5 min in 80% ethanol, the sections were
hydrated in phosphate buffered saline-horse serum albumin-horse serum
and incubated with anti--smooth muscle actin antibody 1:1,000 for
1 h. The bound antibody was visualized by an immunoperoxidase
reaction by using the avidin-biotin complex method with commercial kits
(Vectastain, Vector Laboratories, Burlingame, CA).
3,3'-Diaminobenzidine was used as a chromogen.
Confocal fluorescence light microscopy.
Rat and guinea pig lungs were degassed under vacuum, filled with
fixative of methanol-chloroform-glacial acetic acid 60:30:10 by volume
(29), and submerged in a bath of the same fixative for
2 h, with the meniscus of the liquid column continuous with the
trachea maintained at 25 cm above the bath, which we consider to be
close to maximal physiological volume (total lung capacity; TLC). The
left (unlobated) lung was sliced transversely into three to eight
slices ~2-3 mm thick, dehydrated in absolute ethanol, embedded
in paraffin, cut ~7 µm thick, deparaffinized by standard techniques, and affixed to slides. For fluorescent staining of -smooth muscle actin, slides were incubated in 0.1% Triton X-100 in
0.1 M Tris-buffered saline (TBS, pH 7.6) for 10 min, washed in
TBS-bovine serum albumin (TBS-BSA) three times for 10 min each, incubated in TBS-BSA containing 1% horse serum for 30 min, incubated in mouse anti-human -smooth muscle actin antibody (1:100 dilution in
TBS-BSA, containing 1% horse serum and 0.1% Tween 20, Sigma Chemical,
St. Louis, MO) overnight at 4°C, washed with TBS three times for 10 min each, incubated with biotinylated goat anti-mouse IgG (1:100
dilution with PBS-BSA-HS; Sigma Chemical) for 2 h, washed in PBS
three times for 10 min each, incubated in the dark with ExtraAvidin
Cy-3 complex (1:100 dilution with 0.1 M PBS, pH 8.2; Sigma Chemical)
for 1 h, and washed in distilled water two times for 5 min each.
For fluorescent counterstaining of tissue in general, slides were
incubated in 1:40,000 dilution of BODIPY-SE in 0.1 M NaHCO3
(Molecular Probes) for 30 min and washed in distilled water two times
for 5 min each.
Transmission electron microscopy.
Rat lungs were similarly prepared, except that the intratracheal
fixative was 2% paraformaldehyde, 0.1% glutaraldehyde in 0.1 M
cacodylate buffer, pH 7.4. The slices, after dehydration in absolute
ethanol, were embedded in LR white resin (Polysciences; Warrenton, PA).
Ultrathin sections were cut and mounted on gold grids (Polaron
Equipment; Watford, UK). Grids were incubated overnight with -smooth
muscle actin antibody as described above, washed, incubated with goat
anti-mouse IgG gold (1:40 dilution with the same diluent as used for
the primary antibody, Sigma Chemical) for 2 h, washed with TBS-BSA
two times for 5 min and then with distilled water two times for 5 min;
air-dried overnight; and finally counterstained with uranyl acetate and
then lead nitrate.
Imaging and Field of View Selection
Transmission light microscopy. Sections were viewed with a Zeiss Photomicroscope I with ×25 objective, 1.25 intermediate lens. A Dage-MTI CCD video camera fed a signal to a Sony Trinitron monitor and Sony Video Printer. The images on the monitor were ×375 final magnification. Forty-two contiguous, nonoverlapping fields of view covering the entire usable area of the section were acquired.
Confocal fluorescence light microscopy. Sections were examined with ×63 (rat) or ×100 (guinea pig) objectives. The optimal pinhole size in the confocal detection unit was selected so as to collect as much light as possible while still obtaining nearly maximal depth resolution. This depends on the ratio of magnification to numerical aperture. It corresponded to a diameter of 20 µm (rat) or 40 µm (guinea pig) in the image plane of the objective. Cy-3 was excited by a laser light beam at 568-nm wavelength and detected at 620 ± 30 nm (red). BODIPY-SE was excited at 488 nm and detected at 525 ± 25 nm (green). Because of overlap between the Cy-3 and BODIPY-SE images, we used a recently developed adaptation of IMS and morphology-based image processing (see DISCUSSION). The energies and intensity modulations of the two excitation beams were monitored before imaging of each sample. Pixels represented areas 0.32 µm on a side for the rat and 0.2 µm for the guinea pig.
As seen in the raw 620-nm images (Fig. 1A), Cy-3 stained large masses of-smooth muscle actin in the smooth muscle bands in walls of
airways and blood vessels and smaller groupings of -smooth muscle
actin in the alveolar ductal structures. Images were processed with the
sequence of morphological operations "2× dilate, 4× convex hull
creation, 2× erode, and 1× isolated pixel removal" to remove
isolated pixels and to collect pixels enfolded by a group of -smooth
muscle actin pixels or between two or more neighboring groups
(35). Those pixels preserved after thresholding and image
processing were considered -smooth muscle actin (Fig. 1B). As seen on the raw 525-nm images (Fig. 1C),
BODIPY-SE stained all tissue, including -smooth muscle
actin-containing structures. Tissue was readily distinguished from
generally dimmer air and lumen pixels by thresholding at an
interactively chosen intensity. The same sequence of morphological
operations that separated -smooth muscle actin from tissue on the
620-nm images was also effective on the 525-nm images in smoothing the
edges of tissue profiles, filling internal holes due to noise, and
repairing occasional gaps in thin capillary wall profiles. Small
capillary lumens were also filled, although lumens of arterioles and
venules were not, in general. The pixels preserved after this operation
(both -smooth muscle actin- and non--smooth muscle
actin-containing) were considered tissue (Fig. 1D). Each
animal generated three to five lung slices. Systematic sampling was
performed on a rectilinear grid with constant spacing and random
starting point; 2.7 and 1.5% of the areas of the sections of rat and
guinea pig lung, respectively, were recorded.
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Transmission electron microscopy. Micrographs of sections stained with immunogold were viewed at an instrumental magnification of ×20,000 and were printed at a final magnification of ×68,000. All micrographs from a single animal were of tissue sections stained under the same conditions. Gold particles decorated smooth muscle cells in all airway and blood vessel walls and were very rare in airspaces or vessel lumens, indicating adequate sensitivity and specificity.
Quantifying -Smooth Muscle Actin in Anatomical Context
-smooth
muscle actin among three sites: blood vessels, airways, and alveolar structures. On the confocal fluorescence light micrographs, we identified all airways (terminal bronchioles and larger) on each field-of-view's original image pair by referring principally to the
525-nm channel's images, but also to the 620-nm channel's images for
clarification of smooth muscle morphology. A polygon was drawn closely
around the airway, and the tissue within was categorized as airway.
Analogous images were produced for blood vessel (arterioles, venules,
and larger) and unknown regions (recognizable as airway or blood vessel
but not further classifiable). All remaining tissue was considered
alveolar. All pixels selected as -smooth muscle actin or
non--smooth muscle actin in each of these anatomic locations were
registered from 790 image pairs from the rats and 240 from the guinea
pigs. Areal densities of -smooth muscle actin or tissue were
calculated from the fractions of pixels of each category in each
location. For example, the areal density of airway contractile elements
(Ace) at TLC
[(Aceaw/AL)TLC]
is the product of the morphometrically observed ratio of the number of
pixels recording -smooth muscle actin in airways to the number of
pixels recording lung tissue and the areal density of tissue in the
fully distended lung. The latter, being stereologically identical with the corresponding volumetric density, was obtained as the mass density
of the lung at TLC divided by the mass density of lung tissue, with the
assumptions of 0.067 and 1 g/ml, respectively. The use of summed
intensities instead of summed areas did not materially affect the
estimates of the quantitative distribution of -smooth muscle actin.
Our measurements of the fraction of muscle in the airway wall by the
immunofluorescent IMS technique (0.53/6.9 = 8%; see Table 2) were
similar to previous measurements obtained by tracing relevant areas on
digitized light micrographs (Table 1 of Ref. 15). This
tends to validate our quantitative approach, although the species were
not the same.
We next addressed the prevalence of -smooth muscle actin among
alveolar structures. We examined transmission light micrographs using a
Richards surgical microscope at four locations of particular mechanical
significance (see DISCUSSION). These are 1) the
border of an alveolar septum that abuts two other septa, appearing on section as a three-way septal junction; 2) the border of an
alveolar septum that abuts one other septum, forming a ridge between
the two septa and appearing on section as a distinct bend of the septal trace; 3) the free border of an alveolar septum, as at an
alveolar entrance ring, appearing on section as the free end of a
septal trace; and 4) the alveolar septum away from its
borders. We identified and circled all the septal ends and bends on
each transmission micrograph (the other two locations turned out to
have no identifiable -smooth muscle actin), and recorded each as
showing -smooth muscle actin stain or no stain. When we applied a
similar approach to the confocal light micrographs, we obtained data
for the septal ends, but could not obtain satisfactory data for the
septal bends, because their characteristic configuration was not well
enough preserved in these paraffin preparations for secure identification.
To quantify the distribution of -smooth muscle actin among the
septal ends, we examined confocal fluorescence light micrographs from
three rats. A polygon was drawn closely around every septal end on each
section studied. The transected areas of -smooth muscle actin in
each of 350 septal ends were obtained from the number of -smooth
muscle actin pixels.
The subcellular concentration and configuration of -smooth muscle
actin were studied on transmission electron micrographs of rat lungs.
Fields-of-view centering on -smooth muscle actin-containing material
were collected from airway smooth muscle, blood vessel smooth muscle,
and septal ends (36, 35, and 33 fields-of-view, respectively). The
outlines of all cells tagged with gold particles were emphasized with a
fine-pointed marker. Each micrograph was overlaid with a transparent
grid with lines spaced at distances equivalent to 0.4 µm. The number
of gold particles visible in each grid square was recorded on the grid,
and the mean densities (particles per grid square) were calculated.
For examining the visceral pleura, we abandoned the approach of random
sampling because of the discreteness of the pleural structure and the
frequent stripping of pleura from sections. On two sections of guinea
pig lung, we measured pleural thicknesses, -actin layer thicknesses,
and lung slice perimeters, using calipers on light micrographs. From
these we calculated the transected areas of pleural tissue, pleural
-smooth muscle actin, and lung.
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MODEL |
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TOP
ABSTRACT
INTRODUCTION
METHODS
MODEL
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Overview
Our goal was to predict how activation of the contractile elements in each site affects lung distensibility during periodic breathing, specifically the effects on constriction, elastic recoil, and compliance. Our approach was to model a region of lung as an extensive network of elastic elements within which are embedded various contractile structures, namely airways, blood vessels, and alveolar ducts. During breathing, the entire region is cyclically extended and released, and the lengths and tensions of its elastic and contractile components are cycled according to their mechanical properties and their mechanical linkage.The model respects the important distinction between elasticity and plastoelasticity. We assume that the lung behaves reasonably elastically, i.e., its stress-strain relationship is single valued. By contrast, the activated contractile elements are plastoelastic, i.e., they can change their stress-strain relationship substantially, e.g., after being stretched (11, 14, 39, 42). Although the two systems have this fundamental difference, they are each reasonably predictable.
The model also respects fundamental differences in the mechanical linkage of the elastic and contractile elements. When two elements are linked in parallel, i.e., side by side, their lengths are the same, whereas the net tension is the sum of their individual tensions. By contrast, when they are linked in series, i.e., end to end, their tensions are the same, whereas their lengths sum to the net length. The present context suggests both models. The anatomies of the contractile elements of the pleura and of the axially oriented elements in the airways and blood vessels suggest mechanically parallel linkages with the elastic network of the lung. Because the dimensions of both elastic and contractile components depend only on lung volume, the contributions of each component to lung recoil can be predicted from its characteristic mechanical properties, the level of activation, and lung volume, lung volume excursions, and timing. Their contributions can be simply summed. By contrast, although the circumferentially oriented elastic and contractile elements of the ducts, airways, and blood vessels are mechanically in parallel with each other, they in turn are linked mechanically in series with the surrounding alveolar parenchyma. Because of the series linkage, the activated contractile elements at any given lung volume are shorter; the duct, airway, or vessel is narrower; and the surrounding alveolar parenchyma is drawn in. The governing constraint here is that the additional radial tension due to the contractile element matches the net increase in opposing radial tensions in the elastic structures, i.e., in the surrounding parenchyma and the passive elastic elements of the duct, airway, or blood vessel. Calculations for serial linkage are more complex than for parallel linkage, because the elastic solution must include the distortion from contraction of the embedded structures, and the dimensions and tensions of elastic and contractile components must be resolved to be compatible with each other, with each following its respective properties.
Responses of the Elastic Structure to Internal Contractile Stress
The major assumptions are: 1) that the noncontractile structure of the lung is linearly elastic over the range of distortion under consideration (22), which includes the airways, blood vessels, and alveolar ducts as well as the network of alveolar septa that surrounds them and does not separate the properties of their different tension-bearing components; 2) that, for serial linkage, predictions of small deformation elasticity theory are reasonable approximations for the magnitude of deformation of concern; and 3) that constriction of the alveolar duct is reasonably spherical and that of airways or blood vessels reasonably cylindrical.Spherical model for constriction of the alveolar duct.
Consider a spherical ventilatory unit, comprising a spherical alveolar
duct and its associated alveoli. The structural elements of the duct
consist of a net of connective tissue "cables" and their
accompanying contractile elements. In the model, we replace that
spherical net by a thin-walled spherical shell with the same mechanical
properties as the net, and we express the radial stress at the
interface as a stress jump across the wall of the shell. The
contribution of the activated contractile elements to that transmural
stress jump (Ptmactive) is obtained from the
Laplace relationship, in which the contractile tensions are those of
passively cycled, activated smooth muscle and the stereologically
determined density of -smooth muscle actin in the unit. The
contribution of the passive elements (Ptmpassive), is
taken, for computational purposes, at the radial stress at the surface
of a solid spherical elastic continuum that has the same bulk modulus
as that of the whole lung (22).
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(1) |
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(2) |
Cylindrical model for constriction of the airway or blood vessel. The analysis for the cylindrical structures differs from the above in two ways. First, there is an axial linkage to consider. We assume that, because of the treelike structure of the airways and blood vessels, the lengths of airway and blood vessel segments are absolutely constrained by lung volume and vary closely with its cube root, regardless of activation. The linear linkage of the segments suggests that axial tensions can be transmitted along the branches of the trees, independent of the tensions in the alveolar parenchyma. The axial components, thus, are mechanically in parallel with the parenchyma. Second, there is an asymmetry to the serial linkage because at a fixed lung volume the segments can narrow without changing length by drawing in on the surrounding alveolar network. Absent an elastic solution for such a deformation, we take the approach of an earlier report from this laboratory (45) and consider the effects of radial constriction at fixed lung unit volume as a volumetric constriction within an extensive elastic medium.
We consider the effects of circumferential and axial tensions separately. As developed in the APPENDIX, radial constriction of the airway (or blood vessel)1 is a function of the shear modulus and the increment of circumferential tension
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(3) |
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(4) |
Incorporation of stereologic data.
The increment of ductal tension is a function of the volume reference
for scaling the normal stress of the contractile element, the
fractional volume of the lung relative to that at maximal physiological
volume, the density of the embedded structures in the lung, and the
stereological densities of contractile material.
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(5) |
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(6) |
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(7) |
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(8) |
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(9) |
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(10) |
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(11) |
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(12) |
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Pleural model.
In the guinea pig, there is abundant -smooth muscle actin in the
pleura. To estimate its maximal effect on net recoil, we consider a
spherical pleura with contractile elements uniformly distributed with
regard to location and orientation. As shown in the
APPENDIX, pleural tension is the same as is given by
Eq. 5 with = 1, and the effect on lung recoil,
then, is the same as that given by Eq. 9.
Properties of Passively Cycled, Activated Contractile Element
Like the elastic elements, the contractile element is predictable, although it differs in its substantial plasticity. When activated smooth muscle is cycled, the stress-strain relationship departs dramatically from the classical isometric stress-strain curve depending on the timing and sequence of forces imposed on it. For example, when trachealis muscle is activated maximally at a constant length in vitro, stress rises to a plateau over several minutes. Such plateau values, obtained at different lengths, generate the familiar maximum isometric contraction curve (MICC; Fig. 2, solid curve). If the muscle is forcibly stretched after reaching the plateau tension, stress generally yields along this curve. If it is then shortened rapidly, stress falls sharply away from the MICC. If it is cycled with a frequency and amplitude typical of tidal breathing, it forms a stable, narrow, stress-strain loop that peaks near the MICC but that is much stiffer than the MICC (examples in Fig. 2A, dashed and solid loops) (11, 39, 42). Such loops can be generated anywhere along the length axis, creating an infinite array of parallel, narrow, stiff loops.
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End-Inspiratory and End-Expiratory Points
For parallel linkage, the lengths follow the cube root of lung volume, the stresses follow the elastic and plastoelastic descriptions, and the recoil is simply the sum of those stresses applied to the appropriate areas. For serial linkage, compatible solutions are required for the elastic and plastoelastic components. In tidal breathing, the elastic structure lies at end-inspiration on its linear function for that volume (Eqs. 8 or 10), and the contractile element lies on the MICC. Their intersection identifies the end-inspiratory point. At end-expiration, the elastic structure lies on the linear function for that volume, and the contractile element lies on a curve that comes down from the particular end-inspiratory point of the tidal breath, following the general trajectory of nadirs of such loops (11). Their intersection identifies the end-expiratory point. Applying Eqs. 9, 11, and 12, we obtained the effects on lung recoil. From these data, we can calculate the specific compliances and fractional changes of compliance.Incorporation of Specific Anatomic and Functional Data
Compatible solutions were found by numerical analysis on a spread sheet (Excel) using Eqs. 8-12 and curves fitted to the data for volume/pressure, MICC, and the general trajectory of nadirs of repeated loops of activated smooth muscle.Elastic structure.
The isovolume elastic solutions for radius of the airway, vessel or
duct, are obtained as
(fVLTLC)
, is derived from a generalized lung pressure-volume curve
(37) and human pressure-volume data (12), and
the shear modulus, µ, is derived from lung distortion properties
(22) (See APPENDIX). We take fractional FRC
(FRC/TLC) as 0.5, and the volumetric densities of the spherical
alveolar duct and of the cylindrical airway within their ventilatory
units, , as 
Contractile elements.
The MICC is adapted from a generalized curve (Fig. 1, Ref.
47) with maximum stress set at 2.88 × 106 dynes cm2 at lo
(15), and with lo of the relaxed
muscle set at FRC. We assume that the length of the relaxed muscle
varies as VL
Orientation and closure.
The orientation of the contractile elements in the airways is nearly
circumferential (23), thus favoring circumferential over
axial tension. We modeled the airway with a single (77° to the
axis of the airway) because the observed distribution is narrow. We did
not have information regarding the distribution of in the blood
vessels, but predictions made with the assumption of uniform
distribution of (not shown) are not very different. When the airway
closes, i.e., when the outside radius falls to ~0.48 of its initial
radius (26), any excess of 
Tcirc over that
needed for closure has no additional effect on the surrounding parenchyma. We therefore limit the effects of Tcirc on
recoil (Eq. 11) to that threshold. Nonetheless, the full
Tax can still be transmitted along the closed airway tree.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
MODEL
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Anatomic Observations
Location.
-Smooth muscle actin appears in the walls of all conducting airways,
in the walls of all blood vessels larger than capillaries, and in two
of four sites of particular mechanical significance, namely the septal
ends and bends, where elastin- and collagen-rich cables are located
(34). It is present in about three-quarters of the ends
and half of the bends (Fig. 3, Table
1). No -smooth muscle actin was
detected in the septa away from the ends and bends, nor in the
three-way septal junctions. -Smooth muscle actin is present in the
visceral pleura of the guinea pig, but not in that of the rat.
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Quantities.
The amounts of -smooth muscle actin and tissue in the various sites
are given in Table 2 and are of roughly
similar magnitude in the two species, with the exception of the rat
pleura. The rat has slightly less -smooth muscle actin in
the alveolar duct than in either the airways or blood vessels, whereas
the guinea pig has more. The rat has more -smooth muscle actin in
its airways and blood vessels than does the guinea pig, but less in the
ducts. In addition, the guinea pig has substantial -smooth muscle
actin in the pleura, almost as much as in the parenchyma.
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-smooth muscle actin at cable
sites as seen on section are mostly 1 µm2 or less (Fig.
4). The variation of areas is only partly
due to tangential sectioning-random sectioning of uniform linear
bundles would produce fewer large areas than we saw. It is our
impression from the transmission light micrographs that heavier clumps
of -smooth muscle actin are present in clusters of septal ends
associated with larger alveolar ducts. In an attempt to confirm this
impression, we looked for visual evidence of a gradient of heavy
staining from hilum to pleura but were unable to draw a conclusion.
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Fine distribution and concentrations.
At the cellular level, the rat shows distinct differences between the
smooth muscle of the airways and blood vessels and the -smooth
muscle actin-containing cells in the cable sites of the alveolar
parenchyma. As shown in Fig.
5A, the -smooth muscle actin-containing cells of blood vessels and bronchioles have the well-known morphologic features of smooth muscle: their outline is
unbranched, compatible with a fusiform shape; their cytoplasm is
nearly filled with electron-dense filamentous material that binds the
gold particles; and caveolae are numerous along the cell periphery. The
basal lamina in these preparations is not consistently visible, owing
to low contrast, but an unfilled gap of several tenths of a micrometer
is present between the periphery of neighboring cells or between cells
and interstitial fibrils. By contrast, the immunogold-tagged cells in
the septal ends (Fig. 5B) are represented by profiles of
fine cell processes that sometimes branch. The gold particles are bound
to packets of electron-dense, filamentous material that occupy a
relatively small portion of the profile, the remainder being electron
lucent with occasional mitochondria or sacs of endoplasmic reticulum.
Caveolae are few, and interstitial fibrils abut the cell periphery,
indicating the absence of an intervening basal lamina. These cells
indeed resemble the myofibroblasts in other portions of the alveolar
wall save for the actin isoform expressed. On the other hand, within
the portions of the cells that do contain -smooth muscle actin, over regions of similar size to the confocal pixels, the concentrations of
-smooth muscle actin (immunogold particles per overlay square) are
similar among the ends (1.98) and the smooth muscles of the airways
(1.84) and blood vessels (2.02). So, although these cells seem to be
myofibroblasts, they appear to have hefty contractile machinery
comparable to smooth muscle.
|
Predictions From Modeling
The end-inspiratory and end-expiratory radii and contractile element stresses during tidal breathing are shown in Fig. 6, A and B. When relaxed, radii of ducts, airways, and vessels vary simply as the cube root of lung volume, but with activation, the structures are narrower. The degree of narrowing 1) during a given tidal breath is greater at end-inspiration than at end-expiration by up to 150%, reflecting the greater contractile stress at end-inspiration; 2) is generally greater in tidal breaths taken at lower lung volumes, reflecting less opposing tension in the elastic structures; 3) is greater if the density of-smooth muscle actin is
greater, e.g., the ducts of the guinea pig compared with those of the
rat; and 4) is greater for the airways than for the ducts,
reflecting the higher local concentration of -smooth muscle actin.
Maximally activated airways are predicted to close at mid-range lung
volumes. Contractile stresses are much lower at end-expiration than at end-inspiration, reflecting the characteristic dynamic stiffness of the
activated contractile element. Lung recoil (Fig. 6C) is increased modestly, e.g., rat ductal constriction increases recoil by
<1 cmH2O, although this reaches 20% of relaxed recoil at
lowest lung volumes. At high lung volumes, the airways have greater
effects on recoil than do the ducts. Most of this (about
three-quarters, data not shown) is due to circumferential tensions. At
lower lung volumes, where the airways close, the contribution of
circumferential tension falls off, while that of axial tension
increases, reversing the ratio. Specific compliance (Fig. 6,
D and E) is reduced by up to 20-30% with
constriction in any one site alone. The effects of pleural activation
(guinea pig) on recoil (not shown) were somewhat less than that of
ductal activation, but its effects on specific compliance were ~50%
greater (Fig. 6E).
|
| |
DISCUSSION |
|---|
|
TOP
ABSTRACT
INTRODUCTION
METHODS
MODEL
RESULTS
DISCUSSION
APPENDIX
REFERENCES
|
|---|
The main findings of this study are 1) that the amounts of contractile material do not vary widely between the alveolar ducts, airways, and blood vessels of the lung parenchyma, 2) that estimated effects on lung recoil are small, and 3) that there is the potential for modest but physiologically significant control of regional compliance.
Methodology
We chose-smooth muscle actin as a marker of contractile
capability, as have others (8). Although the most
plentiful isoforms of actin in lung are nonsmooth muscle
(24), such isoforms are generally involved in processes
(e.g., cell migration, phagocytosis, secretion, and translocation of
organelles within the cytoplasm) that do not involve deformation of the
tissue external to the actin-containing cell. By contrast, the smooth
muscle isoforms are found in cells such as fibroblasts during the
contraction of wounds, the myoepithelial cells of gland ducts, and
smooth muscle itself, i.e., in sites or circumstances where cells put tension on the surrounding tissue. In addition, the force generated by
smooth muscle cells is ~10-fold that generated by contraction of
cells such as endothelium and chick embryo fibroblasts with nonmuscle
actin (20). We recognize that, in limiting ourselves to
the -smooth muscle isoform, we may have underestimated the intrinsic
contractile capability of the alveolar parenchyma. We are not likely,
however, to have overestimated it.
We needed images identifying -smooth muscle actin-containing pixels
in anatomical context to quantify contractile elements in the several
sites. We had tried several approaches before settling on the described
techniques. We failed to obtain reliable immunostaining of -smooth
muscle actin for light microscopy with a number of plastic embedding
materials, combined on occasion with etching and removal techniques.
Paraffin-embedding provided excellent immunostaining, but DAB-HRP stain
deposits were neither well localized nor opaque enough to allow the
video microscopic images to be segmented cleanly into -smooth muscle
actin, tissue, and air regions. We then tried combinations of
immunofluorescent staining of -smooth muscle actin and absorptive or
fluorescent staining of tissue, but the thickness of the sections
(7-12 µm) meant that portions of the section above and below the
plane of focus contributed to both the -smooth muscle actin and
tissue signals, making their separation unreliable. This problem was
partly overcome by the use of confocal laser scanning microscopy to
look at optical sections that are a fraction of the thickness of the
section itself (<1 µm out of 7 µm or more). Nonetheless, even with
emission spectra as well separated as those of BODIPY-SE and Cy-3,
there was enough cross talk between the two detected signals that
separating them quantitatively was insecure. This final limitation was
largely overcome by the use of the novel IMS technique (5)
in which two lasers are used, each tuned to a suitable excitation
wavelength of one of the dyes. The intensities of the two exciting
wavelengths are modulated at different frequencies in the megahertz
region. As a result, the intensities of the light from the
different dyes have different frequencies and can be distinguished by
lock-in amplifiers, each tuned to one of the exciting frequencies,
rejecting in each case the out-of-frequency signal contaminating that
channel. This approach gave us two superimposable images, one showing
the -smooth muscle actin-containing pixels and the other showing lung tissue for context.
The images were further clarified by morphology-based image processing.
On the 620-nm image (-smooth muscle actin), there were individual
pixels that appeared to be out of anatomical context. There were two
reasons for this. First, tissue pixels are subject to a certain random
noise. This is photon quantum noise with a broad frequency spectrum and
random signal level proportional to the square root of the signal level
of the rejected (525 nm) signal. It randomly increases or decreases the
intensity of all tissue pixels, whether -smooth muscle actin
containing or not, creating enough of an overlap of intensity that
simple intensity thresholding of the 620-nm channel does not clear it
of the noise from the 525-nm channel. Because the noise is random,
however, the severely affected pixels tend to occur in isolation, e.g., isolated low-intensity pixels within typical patches of -smooth muscle actin and isolated high-intensity pixels in regions of non--smooth muscle actin-containing tissue. Second, there were many
pixels of equivocal intensity at the borders of patches of -smooth
muscle actin, where many pixels lie partly over -smooth muscle
actin-containing tissue and partly over non--smooth muscle actin-containing tissue. These two features (isolation and edges) lend
themselves to morphology-based image processing.
Contractile Cells
-Smooth muscle actin appears not only in classical smooth
muscle cells, but also, in the rat, in myofibroblast-like cells (Fig.
5). One of us (C. Kuhn III) has previously found similar cells in the
septal ends of mice and hamsters. These cells have concentrations of
-smooth muscle actin at the pixel scale that are comparable to those
in smooth muscle. They lie in the same site (alveolar ducts) as do
classical smooth muscle cells in the guinea pig, human, and other
species (Fig. 3). It seems likely, then, that this cell in this
location has a primary contractile function.
Mechanical Linkage-Anatomic Basis
The effect of activation of contractile elements on lung recoil depends on how the contractile and elastic structures of the lung are linked (see MODEL). The outer boundaries of the airway and blood vessel trees deform nearly exactly with the pleural surface, because the relative volume of lung that might be mechanically in series with the trees is a subpleural rim several hundred micrometers in depth, and this is negligible compared with the volume of lung encompassed by the trees. The inner portions of the trees most likely remain shape stable. To the extent that the trees are tensed, branching structures, supported in space by terminal branches, the angles at each branch point are determined by the ratios of axial tensions in the branches and will not change if the axial tensions are changed proportionally during change of lung volume or change in tone. Furthermore, the alveolar parenchyma, within which the tree is embedded, is itself inherently shape stable. Indeed, airways in situ generally change length as the cube root of lung volume, which is completely compatible with shape stability. We conclude that the trees most likely provide a pervasive network that is generally shape stable either with lung volume change or with uniform changes of axial tension in its branches, that the linkage of its axial elements with the lung parenchyma is mechanically in parallel, and that lung recoil is directly changed by changes of axial tensions.The lengths of the pleural contractile elements (guinea pig only) appear to be tied to lung volume, independent of the elastic elements of the lung, and are thus also in a parallel linkage.
Circumferential elements of the airways, blood vessels, and alveolar ducts, on the other hand, appear anatomically to be linked in series with the elastic structures of the lung. They are situated where they can shorten the elastic elements of the airway or blood vessel at fixed lung volume, drawing in radially on the surrounding alveolar septa, expanding their surfaces and deforming their elastic structures. In particular, the alveolar ductal contractile elements accompany most of the connective tissue "cables" (Table 1), and we presume that their mechanical action is similar. These cables are linear condensations of elastin-rich connective tissue that are positioned to support the free (end) and tented (bend) septal borders by their tensions and curvatures (34, 36) and are not found in the alveolar septa away from the cabled borders or in the three-way septal junctions, where the configurations are simply compatible with locally uniform septal tensions (33). The contractile elements of the duct, then, are positioned to both relieve the elastic elements of the duct and tense the surrounding alveolar network. Presumably this is the mechanism of the dramatic radial constriction of alveolar ducts reported by Nadel et al. (31) in cat lung fixed after barium sulfate embolism. Unfortunately, to date there have been no systematic measurements of the degree and circumstances of such deformation in situ. The tensions of the activated contractile elements in this series linkage goes in part to distort the elastic network and in part to increase the lung recoil. Figure 6, A and C, shows quantitative predictions of narrowing and change of recoil.
Importance of Incorporating the Dynamic Contractile Properties and the Series Linkage in the Model
The predictions of the model would be very different if we were to ignore the dynamic properties of activated contractile elements and assume instead that the stresses remain high throughout the breathing cycle. In particular, if the stresses in activated rat alveolar ductal elements were to lie on the MICC at end-expiration as well as at end-inspiration, parenchymal compliance would actually increase slightly with activation of the contractile elements (Fig. 7, curve b), an unexpected result that relates to the volume-related terms in Eqs. 9 and 11. Reduction of parenchymal compliance, then, is largely due to the substantial stiffness shown by the activated contractile element when it is stretched and released at typical breathing frequencies.
|
The predictions of the model are also different for serial and parallel
linkages. For example, a model in which the duct is linked in parallel
with the surrounding parenchyma (Fig. 7, curve a) predicts
greater effects on compliance than our model in which the linkage is
serial (Fig. 7, curve c). There are two reasons for this.
First, in a serial linkage, the relatively stiff activated contractile
element has less excursions of length than the excursions required in a
parallel linkage (compare the slopes of the four serial linkage curves
in Fig. 6A with the solid curve which varies as
V
Effects of Activation on Lung Parenchymal Recoil and Compliance
The estimated effects on recoil of activation at each of the sites are generally small (Fig. 6C). We were particularly interested, however, in the effects on compliance because of the functional implications to the distribution of ventilation. Contractile stresses are much higher at end-inspiration than at end-expiration (Fig. 6B), because of the remarkable stiffness of activated contractile elements when they are length-cycled at typical breathing frequencies (Fig. 2), and, largely for this reason, parenchymal compliance in this dynamic setting is significantly reduced (Fig. 6, D and E).Comparison With Previous Theoretical Estimates
A much earlier study from our laboratory had estimated that constriction of the smaller airways could increase lung recoil by as much as 10-20% and had speculated that constriction of more peripheral contractile elements, at the level of the alveolar duct, might have an even greater effect (45). The current report moves well beyond that study in several ways. The earlier estimates, unencumbered by data, were based on an assumption about the fractional narrowing of the airways, whereas we can now base our estimates on measured amounts of contractile material. The earlier study did not attempt to quantify the effects of contraction at the level of the alveolar ducts. It did not address the effects on parenchymal compliance, which is of considerable interest because of its role in distributing ventilation (27) and therefore in modulating gas exchange efficiency (9). Finally, it did not incorporate the stiffness of passively cycled, activated smooth muscle, which turns out in our model to be almost solely responsible for the predicted effects on parenchymal compliance.Comparison With Experimental Data
Pneumoconstriction has been studied experimentally for decades under a range of experimental conditions: operating lung volumes, volume excursions, frequencies, agents, species, routes of stimulation, and preparations. With major constriction of the conducting airways, the overall dynamic elastance of the lung can increase manyfold (3, 25). Our study finds insufficient contractile material for stiffening the lung parenchyma to that degree and therefore indirectly supports the interpretation that the mechanism of the reported major changes of elastance in those experiments is nonuniformity of airway constriction. Pseudostatic volume/pressure curves, presumably more directly reflective of parenchymal properties, show modest decreases of compliance when agonist is delivered specifically to the bronchi of sheep (30). The magnitudes of these changes are consistent with our predictions for the effects on lung parenchymal compliance. Direct measurements of lung tissue tension in lung tissue strips show contractile behavior with modest increases of tension (7-29%) and changes of dynamic properties that are again generally consistent with the densities of contractile material that we find.Functional Implications
In the pulmonary vasculature, the accepted role of the smooth muscle is homeostatic redistribution of pulmonary blood flow away from units of low ventilation-perfusion ratio (/). Our analysis suggests an additional effect, which is that narrowing of the
vessels would at the same time draw in on the parenchyma, reducing its
compliance and redistributing ventilation away from such units. Such an
effect would oppose the accepted homeostatic role of pulmonary
vasoconstriction on low / units. This contrary effect,
however, is probably very small compared with the homeostatic effect on
perfusion because of the exquisite sensitivity of vascular resistance
to blood vessel radius.
In the airways, as in the blood vessels, constriction changes flow resistance. In the normal subject, breathing quietly and with minor changes of airway diameter, the changes of flow resistance may do little to the distribution of ventilation because the local time constants are short relative to the period of a breath and therefore the distribution of ventilation is governed primarily by local parenchymal compliance (27). We find sufficient contractile material in the airways or alveolar ducts to bring about significant changes in local parenchymal compliance. This is consistent with the early proposal of Colebatch (6) that alveolar duct constriction enables local control of the distribution of ventilation. The wide distribution of contractile material in the ducts (Table 1) suggests that it could affect relatively small units of lung. To the extent that alveolar ductal elements can be activated independently of the conducting airways, the distribution of ventilation can be modulated without interfering with other airway functions. Alveolar ductal constriction is predicted to change parenchymal compliance by 20-30% in the volume ranges of quiet breathing (Fig. 6E). In healthy humans, lung recoil is reduced and nonuniformity of ventilation is increased after intravenous atropine, suggesting that there is tone in the airways and/or the ducts, defending uniformity of ventilation at baseline (9).
Our predictions for pleural activation represent a maximal effect in that they assume uniform contraction. Such a contraction would seem physiologically disadvantageous given that it would serve only to impose a load (albeit minor) on the muscles of respiration. On the other hand, nonuniform contraction might restrict expansion on one side of a lobe and redistribute ventilation by this means. We can say no more because we have not looked carefully into the distribution and orientation of the pleural elements.
We should caution that our predictions may well overestimate the effect on local lung distensibility because we have not factored in mechanical interdependence of abutting or interconnected lung regions (28). If, on the other hand, several sites were activated at the same time, the effects should be additive. As illustration, Fig. 6E shows that, when both airways and alveolar ductal contractile elements are activated at low and mid ranges of lung volume (0.3-0.4 and 0.5-0.6 fVLTLC), parenchymal compliance is reduced by 30% or more.
Perspective
We have applied novel technology to make measurements at a level of lung structure that is very difficult to access for physiological measurements. We find substantial amounts of contractile material in the alveolar duct (where it has long been a structure in search of a function), similar to the amounts in the airways. We estimate that contractile elements in either location could significantly affect parenchymal compliance, and we find that the effect depends almost entirely on the characteristic stiffness of the activated contractile element when it is passively length-cycled at typical breathing frequencies. The reductions in compliance predicted for maximal activation are in the range reported for unilateral pulmonary artery occlusion in dogs and humans. As proposed by Colebatch (6), such local reduction of compliance would benefit gas exchange by reducing the ventilation in high/ regions. Indeed, the response to unilateral pulmonary artery occlusion has been
shown to be mediated by hypocapnia, which is an appropriate marker of
high / units. Such hypocapnic lung stiffening has an
appealing symmetry with hypoxic pulmonary vasoconstriction in that both
poles of the / spectrum are modulated; i.e., hypoxic pulmonary vasoconstriction increases the
/ of low / units, whereas
hypocapnic lung stiffening decreases the / of
the high / units.
| |
APPENDIX |
|---|
|
TOP
ABSTRACT
INTRODUCTION
METHODS
MODEL
RESULTS
DISCUSSION
APPENDIX
REFERENCES
|
|---|
Spherical Model
To determine radial constriction of the duct, we start with the constraint that the radial stresses must exactly match at the interface between the duct (thin-walled shell) and the surrounding alveolar parenchyma (thick-walled shell)
|
(A1) |
Ppar is the change of normal stress at the interface
due to the local elastic recoil of the surrounding alveolar parenchyma and Ptmpassive and Ptmactive are the
changes of transmural stress across the thin-walled shell due to the
elastic and contractile tensions in the ductal structures. Ppar can
be evaluated from the known relations of radial stresses and
displacements of the inner and outer boundaries of a thick-walled
spherical elastic medium (46). For a fixed outer radius
|
(A2) |
|
(A3) |
|
(A4) |
|
(A5) |
|
(A6) |
= (a1/a2)3.
Combining this with Eqs. A5 and A6
|
(A7) |
Cylindrical Model
The analysis for circumferential constriction of the airway (or blood vessel) is parallel to that given above for the spherical model. The change in the radial stress of the surrounding alveolar parenchyma where the outer boundary is remote, i.e., a2 is large, is given (21) by
|
(A8) |
|
(A9) |
|
(A10) |
Tcirc is the increment in active circumferential wall
tension. By combination of Eqs. A1, A8, A9, and
A10
|
(A11) |
|
(A12) |
F/A, where F is the axial force and Aaw is the cross-sectional area of the
airway (45). By geometry, F/A = 2(Tax/a1). Combining, we obtain
the effect of axial tensions
|
(A13) |
|
(A14) |
|
Application of Stereological Data
First, the spherical case, i.e., the alveolar duct. The contractile elements are modeled as an equivalent thin-walled shell. The incremental active wall tension,Tduct, is, from
geometrical considerations at an equatorial section, the normal
component of the force divided by the length of the equator,
2
a1. For fibers that lie at an angle, ,
relative to the normal at the equator, the normal component of force is
the integral of the normal component of the muscle stress, cos
ce,duct, times the fiber cross-sectional area.
This area is equal to cos times the area of fibers observed on the
equatorial sectioning plane, Ace,duct. Let () be the fractional probability that a contractile element in the wall lies at
. Its likelihood of being sectioned varies as cos , and its area
seen on the sectioning plane varies as 1/cos . The fraction of the
total area seen on section that represents elements lying at is
thus simply ()d. For uniform distribution of orientation of
the fibers in the plane of the wall, () = 2/. From these
relationships, Tduct = 2
a1 
cos2
Ace,duct ce,duct. Integrating over 0 to
/2 and dividing by a1, we obtain
Tduct/a1 = [Ace,duct/(4a
ce,duct.
We can evaluate Aceduct from our stereological data.
It is the product of the perimeter of the sphere at its equator,
2a1, and its thickness, which in turn is the
volume of the wall, Vce,duct, divided by its surface area,
4aa
(a
The radii in this expression depend on the volumetric density of
the relaxed embedded structure, , and the fractional volume of the
lung unit relative to that at maximal physiological inflation, fVLTLC. We take the appropriate
reference lung volume for the dimensions of the relaxed smooth muscle
as FRC. We restrict the reference dimensions of the contractile element
to the relaxed state (designated by the asterisk) in order that we may
use published values for nominal stresses developed by smooth muscle.
Thus a1 = fVLTLC
|
(A15) |
|
For a spherical pleura investing the lung, the Laplace relationship
gives the incremental contribution to the transmural pressure as
2Tpl/a, where a is the radius. Because the
volume contained by the pleura and the lung are the same,
Tpl/a is the same as Tduct/a
given by Eq. A15 with set at 1.
The cylindrical case for the airways (or blood vessels) parallels
the spherical case with the following exceptions. First, whereas we
could assume that the contractile elements in the alveolar duct were
uniformly distributed in the plane of the network, the smooth muscle in
the airways are known to be preferentially oriented. Axial and
circumferential tensions, then, vary with cos and sin, respectively. Second, circumferential tension is the normal force at a
sagittal section of an airway segment divided by the length of the
segment, l, so that
Tcirc/a1 = [Ace,aw/(la1)]sin
ce,aw. Axial tension is the normal force on a
transverse section divided by its perimeter, such that
Tax/a1 = [Ace,aw/(2a1)]cos
ce,aw. By geometry, Aceaw
is the volume of the contractile elements in the wall divided by the
perimeter of the cylinder,
Vce,aw/(2a1). The volumetric and
areal densities are again identical, but this time the volume of the
lung unit is
la
1/2 (rather than 1/2a2,TLC,
and a1/2a2,TLC.
From these equivalencies, the incremental active circumferential and
axial tensions are
|
(A16) |
|
|
(A17) |
|
Elastic Moduli
We invoke the general expression for pressure-volume relationship, V = Vmax (Vmax Vo)eKP, where
Vmax is the asymptotic volume, K is a shape
constant, and Vo is the extrapolated volume at zero
pressure (37). The bulk modulus, , is the normalized
inverse slope of this curve, dP/(dV/V), and, with Vmax set
to 1, is simply V/[K(1 V)]. We take K = 0.102 (cmH2O)1, and Vo = 0.095 (12). The shear modulus, µ, is 0.7 P
(22).
| |
ACKNOWLEDGEMENTS |
|---|
This study was supported by National Heart, Lung, and Blood Institute Grant HL-26863 and by the Swedish Research Council for Engineering Sciences.
| |
FOOTNOTES |
|---|
Address for reprint requests and other correspondence: F. G. Hoppin, Jr., Division of Pulmonary and Critical Care Medicine, Memorial Hospital of Rhode Island, 111 Brewster St., Pawtucket, RI 02860 (E-mail: frederic_hoppin_jr{at}brown.edu).
1 Parenchymal compliance or inertance in this paper refers to a property directly attributable to tensions in the lung and not to overall behavior that may include important effects due to airway or parenchymal nonuniformities (3, 25).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 2 June 2000; accepted in final form 7 February 2001.
| |
REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
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MODEL
RESULTS
DISCUSSION
APPENDIX
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) and
end-expiratory (
) points for tidal breaths between 0.3 and 0.4, 0.5 and 0.6, 0.7 and 0.8, and 0.9 and 1.0 fVLTLC are identified by the
intersections of the contractile curves with the isovolume elastic
curves as described in the text.
, rat airways; dot-dashed lines and
,
guinea pig airways; 
, guinea pig pleura. See
text.
