Am J Physiol Lung Cell Mol Physiol 301: L625–L635, 2011.
First published August 26, 2011; doi:10.1152/ajplung.00105.2011.
Review
What do we know about mechanical strain in lung alveoli?
Esra Roan1 and Christopher M. Waters2
1
Departments of Biomedical Engineering and Mechanical Engineering, University of Memphis, and 2Department of
Physiology, University of Tennessee Health Science Center, University of Tennessee, Memphis, Tennessee
Submitted 31 March 2011; accepted in final form 23 August 2011
lung injury; mechanotransduction; distension; stretch
THE ALVEOLUS, the location of gas exchange in the lung, has a
complex three-dimensional structure that is composed of an
epithelial cell-lined air space and endothelial cell-lined capillaries separated by a thin basement membrane and interstitial
space. The basement membrane, composed of extracellular
matrix (ECM) proteins including collagen and elastin (54, 70,
80), provides support for the alveolar epithelial cells, which
include both type I (AEI) and type II (AEII) cells.
During normal tidal breathing, the alveolus undergoes volume fluctuations that have been estimated to cause 4% linear
distension of the basement membrane (28, 29, 58). The alveolar distension, experienced by the alveolar basement membrane and alveolar epithelial cells, is described as a “mechanical stretch load.” In an injured lung, changes in structure and
mechanical properties can lead to changes in the magnitude of
stretch experienced by the alveolus compared with a healthy
lung. For example, in the case of acute lung injury, fluid
leakage into the interstitium and into the alveoli causes changes
in the properties of the tissue, loss or dilution of surfactant, and
changes in the inflation of non-fluid-filled regions. This causes
changes in the overall compliance of the lung that will affect
not only gas exchange locally, but also the distension of the
tissue in both injured and noninjured parts of the lung (91). It
has become increasingly apparent over the last two decades
that the levels of mechanical stress influence the biological
function and signaling of alveolar epithelial cells (82, 85, 99).
For example, mechanical stretch of cultured type II cells was
shown to stimulate changes in surfactant secretion (25, 72, 99),
Address for reprint requests and other correspondence: C. M. Waters, Dept.
of Physiology, The Univ. of Tennessee Health Science Center, 894 Union
Ave., Rm. 426, Memphis, TN 38163-0001 (e-mail: [email protected]).
http://www.ajplung.org
cell injury or death (3, 36, 84), permeability (12, 14), and cell
migration (22).
From the clinical perspective, a study by the ARDSNet
demonstrated a significant reduction in mortality when acute
respiratory distress syndrome (ARDS) patients were ventilated
with lower tidal volumes (1, 50, 74, 88). Since the lower tidal
volume is thought to correlate with lower distension of the
lung, the outcome of the ARDSNet trial provides strong
evidence that alterations in lung mechanics can significantly
impact both the basic biology of the lung as well as clinical
outcomes. However, because of the complexities of lung mechanics and limitations in imaging capabilities, our knowledge
of the micromechanics of the individual alveolus is limited.
One aim of this article is to summarize the previous studies of
alveolar mechanics and to extrapolate quantitative information
about the alveolar strain field.
Mechanical Determinants of the Alveolus
When examining the mechanical environment of the alveolus,
we often consider factors either at the level of the whole organ
(macroscale) or at the level of the alveolus (microscale), but these
considerations across scale are interrelated (see Fig. 1). We can
think of the lung as a prestressed network structure whose
overall response to a mechanical stimulus depends not only on
the properties of the network elements (alveolar structures) but
also on how those elements are connected to one another. The
mechanical properties, composition, and geometry of underlying constituents, the mechanical loads, and the edge displacement conditions (boundary conditions) are all factors that are
known to contribute directly or indirectly to the mechanical
response of the alveolus. Therefore, it is convenient to depict
two length scales for discussion of the important factors that
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Roan E, Waters CM. What do we know about mechanical strain in lung
alveoli? Am J Physiol Lung Cell Mol Physiol 301: L625–L635, 2011. First
published August 26, 2011; doi:10.1152/ajplung.00105.2011.—The pulmonary
alveolus, terminal gas-exchange unit of the lung, is composed of alveolar epithelial
and endothelial cells separated by a thin basement membrane and interstitial space.
These cells participate in the maintenance of a delicate system regulated not only
by biological factors but also by the mechanical environment of the lung, which
undergoes dynamic deformation during breathing. Clinical and animal studies as
well as cell culture studies point toward a strong influence of mechanical forces on
lung cells and tissues including effects on growth and repair, surfactant release,
injury, and inflammation. However, despite substantial advances in our understanding of lung mechanics over the last half century, there are still many unanswered
questions regarding the micromechanics of the alveolus and how it deforms during
lung inflation. Therefore, the aims of this review are to draw a multidisciplinary
account of the mechanics of the alveolus on the basis of its structure, biology, and
chemistry and to compare estimates of alveolar deformation from previous studies.
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regulate lung mechanics, with the understanding that there is a
strong communication between these two scales.
The major determinants of lung mechanics during normal
tidal breathing are depicted at two length scales in Fig. 1. The
loads at the organ level include alveolar pressure (PALV),
pleural pressure (PPL), elastic recoil, and gravity. PPL is regulated by changes in the volume of the thoracic cage primarily
controlled by its elastic recoil and contraction of the diaphragm. The difference between the pressure levels in the
alveolus (PALV) and in the pleural space (PPL), the transpulmonary pressure (PT), determines the volume of the lung,
whereas the difference between atmospheric pressure and PALV
drives air flow into and out of the lungs. An increase in PT
causes the lungs to expand, and air flows into the lungs when
alveolar pressure is less than the pressure at the mouth. At the
alveolar level, the surface tension of the air-fluid interface, the
elastic recoil of the tissue, interdependence, and the PALV are
the predominant loads. As described by Mead et al. (53), PALV
will be the same in all alveoli, and there will be no pressure
differences across the walls except at the pleural surface. Thus
the forces that distend air spaces are derived from tissue
attachments that transmit stresses due to the PT. One boundary
condition of the lung tissue is the volumetric limitation provided by the relatively more rigid tissue of the rib cage.
Intercostal muscles (not shown in the illustration) help in the
expansion of the rib cage during forced inspiration; thus the
boundary conditions of the lung tissue are not static. Moreover,
since the lung is not attached to the rib cage or the diaphragm,
it slides against these surfaces during breathing with low
frictional resistance due to the presence of a thin layer of
pleural fluid (18, 90).
At the microscale level, the key structure of the lung parenchyma is the alveolus, which has a three-dimensional structure
resembling an octahedron with an approximate diameter on the
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order of 100 ␮m at physiological pressure levels (6, 35, 42, 55,
58, 83). A cross-sectional illustration of a group of alveoli is
depicted in Fig. 1B in a partially inflated configuration. Because alveoli share structural walls with neighboring alveoli,
there is an interdependence in which neighboring units resist
the collapse of one another and also allow for uniform expansion (53). The space that separates an alveolus from its adjacent neighbor is referred to as the alveolar septum, which is
composed of a layer of epithelial cells on the surfaces in
contact with air, endothelial cells that line the capillaries that
allow blood flow through the septal tissue, and matrix materials
that comprise the basement membrane and interstitial space.
The alveolar epithelial cells include AEI and AEII cells, of
which the AEI cells cover ⬃93% of the alveolar surface area
(17), whereas the AEII cells tend to reside near the cornerlike
areas of the alveolus. Alveolar epithelial cells form a relatively
impermeable barrier that is dependent on the formation and
maintenance of tight junctions. Typically, macrophages reside
in the alveolar air space, but other immune cells can also be
recruited into the interstitial space or into the air space. Although epithelial cells, endothelial cells, and fibroblasts are
abundant within the lung parenchyma, their direct contribution
to the mechanical strength of the lung parenchyma is generally
considered to be small (5, 11); we will consider this topic
further below. However, epithelial cells and fibroblasts do
contribute to the mechanical properties of the alveolus by
synthesizing and secreting ECM proteins that form the basement membrane (16). For example, dysregulated repair of
alveolar epithelial cells following injury has been suggested to
induce epithelial-mesenchymal transition (EMT), resulting in
excessive matrix production and fibrosis (69, 96, 97). It has
also been suggested that changes in the mechanical environment might promote EMT or that fibrosis itself alters the
mechanical environment (37).
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Fig. 1. A: mechanical determinants of the lung
include loads, tissue properties, and boundary
conditions at 2 length scales. B: close-up, 2D
cross-section of a group of alveoli. Alveoli are
separated by the alveolar septa, which are composed of alveolar basement membrane, capillaries, and alveolar epithelial cells. This illustration is representative of an inflated, but not
an overdistended alveolus. The outline of the
alveoli was adapted by tracing one of the microscopic images of rat lungs found in Ref. 64
corresponding to 5 cmH2O inflation pressure.
PALV, alveolar pressure; AEI and AEII, type I
and II alveolar epithelial cells, respectively.
The schematic is not to scale for illustration
purposes. C: pressure-volume (P-V) curve.
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Despite this limitation in our capability for measuring the
strength of connections between cells similar to the in vivo
loading of alveolar epithelial cells, there are a number of
studies using techniques that measure a variety of mechanical
responses of cells (4, 27, 45, 89). In general, studies utilizing
beads (micrometers in diameter), translated or rotated with
either magnetic or optical forces, result in measurements that
yield an elastic modulus on the order of 1 kPa or less (27, 45).
In comparison, the elastic moduli of cultured alveolar epithelial
cells and A549 cells (an adenocarcinoma-derived human lung
epithelial cell line) were measured to be 2.5 ⫾ 1.0 kPa (4) and
0.91 ⫾ 0.47 kPa (71), respectively, using an AFM in indentation mode. Although these two measurement approaches resulted in comparable elastic moduli, each technique measures
different aspects of the mechanical response of cells. The
microbead tests apply a load to move a bead that is tethered to
the cytoskeleton, resulting mainly in a tensile load on the
cytoskeletal proteins. If the bead is not fully immersed, the
measurement is more of an indication of the cellular response
near the plasma membrane. With AFM indentation, the contact
between the AFM cantilever tip and the cell can generate an
indentation of up to a few micrometers, reaching a level that is
a significant proportion of the cell height. Therefore, AFM
indentation is capable of measuring the contribution of the
underlying cytoplasmic constituents, including the nucleus,
which has been shown to have a significantly higher elastic
modulus (9, 51).
Although these techniques are informative, none of them are
capable of providing information regarding the tensile strength
of an epithelial sheet that experiences a stretch loading in a
direction parallel to the substrate. In other words, it is important to note that none of the current microscale techniques have
been adapted to apply a tensile load in a way that can measure
the strength of cell-to-cell contacts. Moreover, most of our
measurements of cell mechanical responses are conducted on
substrates that are relatively more rigid than lung tissue (such
as plastic), and evidence in the literature suggests that the
mechanical response of cells is dependent on the stiffness of
the substrate (41, 77). In addition, cell stiffness has been shown
to respond to mechanical stretch (82), and this may also impact
how cells contribute to the overall mechanical properties of the
lung. Because of these limitations, we do not have an accurate
assessment of the contribution of cells to overall lung mechanics.
Nevertheless, the measurements of alveolar epithelial cell
mechanical response indicate that isolated cells have an elastic
modulus that is less than but of the same order of magnitude as
the lung tissue strips. The elastic modulus of the alveolar wall
estimated from the extension of lung tissue strips was ⬃5 kPa
(11). In this study by Cavalcante et al. (11), the contractile cells
of the lung parenchyma were assumed to be inactive at the time
of experiments. Interestingly, three recent studies demonstrated
that the scaffold material of decellularized rat or mouse lungs
had significantly lower compliance than native lungs (59, 67,
68), suggesting that the presence of the cells made the lungs
less stiff. This could potentially be due to the lack of surfactant
in the decellularized lungs, since lungs with repopulated cells
capable of producing surfactant had increased compliance
(albeit lower than native lungs). However, the decellularization
process may have affected the structure and content of the
matrix, and the potential presence of fluid or foam in the air
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The alveolar basement membrane supports the epithelial
cells; is composed of collagen, elastin, proteoglycans, and
other ECM proteins (54, 92, 93); and is regulated by matrix
metalloproteinases (60, 61). The relatively higher strength
collagen is generally considered to be the load-bearing protein,
because it resists loads induced by large distension, whereas
elastin allows the lung parenchyma to return to its original
shape following deformation (80). A recent study by Cavalcante et al. (11) examined lung slices to demonstrate that
proteoglycans contribute significantly to the mechanical structure of lung tissue, since they act as connectors between
various load-bearing proteins. The overall elastic recoil of the
lungs is also greatly dependent on the ratio of these underlying
constituents found elsewhere in the lung, such as the airways,
blood vessels, and parenchymal tissue (26, 54, 70, 79, 80).
Both compliance and elastic recoil can be affected by lung
disease that alters the underlying composition of the alveolar
constituents. For example, the destruction of alveolar units and
loss of elastic tissue in emphysema results in increased compliance and decreased elastic recoil (15, 52), and bleomycininduced fibrosis increased the local tissue elasticity by sixfold
measured with atomic force microscopy (AFM) in indentation
mode (47).
In addition to the role of material properties in regulating
alveolar mechanics, alveolar deformation is also determined by
interactions between levels of prestress, the stiffness of individual wall components, and resistance to changes in alveolar
geometry. Because PT balances the elastic recoil of the lungs
and keeps the air spaces open at the end of exhalation, tension
is maintained in the alveolar walls, and there is resistance to
changes in the geometry of the structures due to the interdependence between neighboring units. Stiffness is a term that
describes the mechanical response of a material to deforming
stress inclusive of the geometric factors. Thus the overall
mechanical response to changes in distending pressure is complex and involves multiple factors.
Are epithelial and endothelial cells mechanical determinants of the alveolar strain field? In examining the mechanics
of the alveolus, the composition of the alveolar basement
membrane and the interfacial forces at the air-liquid interface
are considered to be major determinants of the mechanical
response to normal breathing loads (26, 79). However, the
potential contribution of epithelial and endothelial cells at
the micromechanics scale has not been clearly defined.
There are two potential reasons why epithelial cells in
particular may be contributors of the overall mechanical
response of the lung: 1) the mechanical properties of alveolar epithelial cells have been measured to be of the same order
of magnitude as the measured mechanical response of lung
tissue slices, and 2) the epithelial cells are loaded parallel to
their surface, which implies loading of the cell-to-cell connections in tension that are known to form strong connections
between cells. Using a continuum mechanics framework, an
indirect estimate of the strength of cell-to-cell junctions could
be computed using information regarding cell mechanical
properties, morphology of tight junctions, and a measured
strain level at which confluent monolayers begin to form
intercellular gaps. However, at this time we lack direct quantitative mechanical measurements of the tensile strength of the
cell-to-cell connections of epithelial cells.
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Alveolar Strain Field: How Do Alveoli Expand?
Tissue deformation is often expressed in terms of mechanical strain, which is described as the change in a linear
dimension over its initial or reference value. For most bodies
undergoing deformations, the linear change in length can be
linked to a change in area or volume. The strain levels in soft
tissue are usually distributed nonuniformly; thus such a tissue
is considered to experience a nonuniform strain field. In the
case of lung tissue, because the deformation often involves
positive changes in dimension, the term stretch or distension is
often used in place of strain. Compression is also used to
describe negative changes in dimension, for example, during
constriction of airways. There have been several studies focusing on the magnitude and distribution of strain within the
alveolus, and these are summarized in the next section.
Morphometric assessments of alveolar inflation. Early attempts to determine lung distension were based on the assumption of isotropic expansion of the lung upon inflation, and
estimates of linear mechanical strain of the alveoli were made
on the basis of changes in lung volume (6, 28, 42, 55, 58, 78,
87). Many studies have used morphometric measurements of
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isolated lung tissue fixed at varying pressure levels or fractions
of the total lung capacity (TLC) to determine surface area,
volume, surface tension, and pressure relationships. [It is
important to recognize that TLC in humans is defined as the
volume at maximal inspiratory effort, whereas in studies with
whole animals or isolated lungs TLC is often based on specific
criteria (pressure) that might vary from study to study.] Perfusion fixation was a common method in these studies, but
freeze-drying techniques were also utilized in some studies
(42). In these studies, the lungs were excised and the P-V
curves were determined to identify the volumes at TLC. Lungs
were then fixed during either inflation or deflation portions of
the P-V curves. This is important to note because the overall
mechanical response of the lung exhibits a strong hysteresis
due to the presence of the surface tension (as discussed above).
In these studies, animal models also varied between cat, rabbit,
rat, and guinea pig.
Examination of lung microstructure using isolated fixed
tissue was popular in obtaining morphological information
during the earlier stages of lung biomechanics. In 1929, Macklin (49) suggested that the alveoli were merely static terminal
structures and that the airways experienced the volume
changes. Later, many challenged this view with studies involving alveolar duct and alveolar measurements, questioning
whether the alveoli experienced major alterations in shape
during inflation or whether their shape remained nearly constant with an increase in surface area (24, 28, 78). Storey and
Staub (78) provided evidence toward the latter by showing that
the mean alveolar diameter increased with inflation pressure in
cats. In 1967, Dunnill provided data in dogs indicating that the
relationship between alveolar surface area (SA) and volume (V)
was approximated by SA⬀V2/3, which would suggest that the
alveolar shape remains constant and that there was expansion
rather than recruitment of previously collapsed alveoli. In
contrast, Forrest (28) found that total alveolar surface area
increased linearly as a function of the total lung volume,
suggesting recruitment. Macklem (48) later suggested that both
relationships fit the data well, probably because of the limited
sensitivity of the morphometric techniques. The reader is
referred to this discussion by Macklem for a more extensive
analysis of this relationship (48). However, it is worth noting
that the question of whether the alveolar surface area increases
as SA ⬀ V or SA ⬀ V2/3 still remains unresolved because of
challenges in obtaining dynamic in vivo measurements. Particularly important for this review is the fact that direct measurement of alveolar strain was not possible in these earlier
studies because a single alveolus could not be imaged at
varying pressures.
On the basis of these and other early morphological studies
using fixed tissue, discussion arose regarding the mechanism of
lung volume expansion: were alveoli recruited and derecruited
by opening and closing of units, did they expand by an
accordion-like change in shape, or did they expand from a
prestressed state like a balloon (23) to account for the volumetric increase of the lungs? Klingele and Staub (42) concluded that the alveolar walls became unfolded with inflation
on the basis of their experimental observations of fixed tissue.
Later, Gil et al. (35) outlined four mechanisms by which the
lung could inflate and deflate (illustrated in Fig. 2): 1) recruitment and derecruitment of alveoli SA ⬀ V; 2) balloonlike
increases and decreases in volume with SA ⬀ V2/3; 3) equal
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space may have affected the measurements. More experimental
studies will be required to examine the possibility of epithelial
and endothelial cells contributing to the overall mechanical
properties of the lung. A combination of experimental approaches, imaging studies, and computational models may be
necessary to determine whether the epithelial or endothelial
cells contribute to the overall lung mechanical response.
Surface tension. The alveolar epithelial cells, basement
membrane, and endothelial cells form a barrier that allows the
efficient transport of gas molecules and prevents the leakage of
fluids into the air space. At the interface between the air space
and the epithelial cells, a thin layer of fluid covers the epithelial
cells. The surface tension of this air-fluid interface results in
significant forces that tend to collapse the alveolus. Although
the magnitude of the surface tension varies with the inflation of
the alveolus (and thus the pressure), a maximum surface
tension value was measured to be 30 mN/m in rabbit lungs (7,
29). The magnitude of the surface tension is reduced by
surfactant produced and released by AEII cells, which prevents
the collapse of the alveolar walls at low pressures (5, 8, 76).
Inadequate surfactant production in premature infants (38) or
surfactant depletion in acute lung injury (95) and other diseases
can result in increased surface tension and difficulty in inflation
of alveoli. Although surface tension plays an important role in
the balance of forces involved in individual alveolar inflation,
the considerable size of the alveolar surface area dictates that
surface tension impacts overall lung mechanics, for which
pressure-volume (P-V) curves similar to the one in Fig. 1C
serve as an indication or a measurement.
In summary, because of spatially and temporally nonuniform loading and edge conditions, the lung is a complex organ
in which changes in mechanical strains have been shown to be
critical determinants of biological function. As described in the
next section, the alveolar strain field, the microscale representation of the bulk and alveolar lung mechanical environment, is
challenging to describe because of the complex structure and
limited imaging modalities that can measure alveolar deformation as a function of volume or pressure.
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alveolar volumetric change accompanied by a shape change,
from a truncated octahedron to a sphere; and 4) accordion-like
“crumpling” of the alveolar walls.
The same authors proposed that these different mechanisms
may regulate the alveolar geometry with varying significance
as a function of inflation volume (35). They suggested that the
alveoli experience volume changes due to folding and unfolding of the alveolar septa (termed pleating) at low pressures as
shown in Fig. 2B. Figure 2 is a schematic indicating how
alveolar structures may change at different inflation pressures.
The size of the cells is somewhat exaggerated to distinguish the
changes in basement membrane. Figure 2B shows an alveolus
at a moderate level of inflation (⬃5 cmH2O). The dashed line
indicates the alveolar surface area. Figure 2B also shows a
diagram of a septal wall at low inflation pressure (⬃0 cmH2O),
indicating septal wall folding. However, many investigators
questioned whether the images of septal wall folding from the
earlier studies were artifacts of the fixation process (57, 58,
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64). In 1991, Oldmixon and Hoppin (58) systematically addressed this possibility by examining fixed lungs using light
and electron microscopy. They defined septal folding according to the appearance of apposition of epithelial surfaces on
electron microscopy, or by capillary bunching within septal
tissue that separated two air spaces (as indicated in Fig. 2B), or
rounding of air space profiles observed by light microscopy.
They suggested that folding occurred only at lower PT values
in excised lungs and was unlikely to occur in vivo. Although
they could not absolutely rule out folding and unfolding, they
concluded that there was a “reasonable possibility” that this
proposed mechanism was an artifact of the ex vivo approach.
In 1999, Tschumperlin and Margulies (84) examined the question of whether or not there were changes in epithelial basement membrane (and thus deformation of epithelial cells) at
different levels of inflation in isolated rat lungs. Because
Oldmixon and Hoppin had shown that alveolar folding was
highly dependent on the volume history of the lungs prior to
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Fig. 2. Illustration of how alveolar structure
changes with different inflation pressures (P).
A: 4 mechanisms by which the lung expands
according to Gil et al. (5). Alveoli close or
collapse at low volumes in recruitment
(mechanism 1). In the case of mechanisms 2
and 3, the alveoli grow in an isotropic manner, but rounding of the alveolar wall is a
characteristic of the third mechanism only. In
the case of crumpling (mechanism 4) the
walls fold in an accordion-like fashion, maintaining the total number of alveoli the same.
B: an alveolus with a moderate inflation pressure (⬃5 cmH2O) at the bottom and depictions of the most significant effects of
changes in pressure in the alveolar walls for
each mechanism. Isotropic expansion thins
the walls, whereas recruitment results from
opening of previously collapsed alveolar
walls. The alveolar surface area would be
estimated from the dashed line indicated in B.
The alveolar wall crumpling illustration
shows a septal wall in an alveolus at low
inflation pressure (⬃0 cmH2O), indicating
septal wall folding. In this case the epithelial
basement membrane surface area would be
estimated by the solid dark lines.
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another study, Perlman et al. (65) utilized the same technique
to image adjacent air filled and fluid-filled alveoli. The liquidfilled alveoli tended to shrink, causing the adjacent air-filled
alveoli to expand. Their observation of increased distension
with pressure and the lack of collapse and reopening agreed
with the findings of Mertens et al. (56), who used OCT to
visualize alveolar dynamics in normal and acid-injured mouse
lungs without immobilizing the pleural surface. They concluded that alveolar overdistension could occur in injured lungs
owing to redistribution of volume from small alveolar clusters
with reduced compliance to larger alveoli. These observations
are important because they may indicate one source of overdistension injury that is commonly accompanied by lung edema.
Although how alveoli change volume still remains a controversial topic, the cumulative weight of evidence suggests that
alveoli expand in vivo in a manner best represented by a
combination of mechanisms involving isotropic expansion and
shape change as summarized above. Because physiological
levels of pressure do not normally allow deflation below the
residual volume, accordion-like crumpling seems unlikely during tidal breathing. However, it is likely that alveoli in injured
lungs will undergo heterogeneous levels of expansion in different regions of the lungs. CT imaging suggests that regions of
the lung also become recruited and derecruited due to regional
variations in compliance and changes in fluid accumulation and
distribution, but direct visualization remains elusive. It is also
plausible that alveolar wall crumpling could occur in an injured
lung due to nonuniform compliance and fluid distribution, but
this has not been directly visualized either.
Interpretation of subpleural alveolar imaging. Although
recent studies involving images of alveoli in situ or ex vivo
have reported new techniques capable of tracking subpleural
alveoli during volumetric evolution, there are limitations to
these approaches. The use of suction pressure to fix the microscope objective to the surface of the lung may affect the
deformation of the tissue and result in a significant deviation
from in vivo conditions. However, even if the in vivo conditions were fully achieved, from the mechanics perspective, the
alveoli near the pleura that are constrained by a glass coverslip
with or without suction pressure are likely to have a mechanical environment that is significantly different from the lung
interior.
To expand this point, a simple finite element (FE) model of
a spherical structure with an encapsulation was generated (see
Fig. 3) using ABAQUS (Simulia, Providence, RI). In this
model, the internal sphere represents the lung, whereas the
outer structure represents the collective response of the rib cage
and tissue level boundary conditions (see Fig. 3A). A twodimensional model (Fig. 3B) of the spherical assembly was
generated to accurately implement the axisymmetric boundary
conditions and reduce the computational cost. As an initial
approximation, the sphere (material 1) and the cover (material
2) were assigned elastic moduli of E1 ⫽ 5 kPa (11) and E2 ⫽
10 kPa, respectively. A circular opening with 60-mm diameter
was created such that material 1 is exposed on the right-hand
side of the sphere. A rigid structure, resembling a glass coverslip was modeled to fit this opening. All interfaces were
allowed to slide against each other in a frictionless manner.
Two analyses were conducted using this model with and
without the suction pressure applied near the glass slide.
During the first analysis, a 250-Pa (2.55 cmH2O) uniform
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fixation, Tschumperlin and Margulies fixed the lungs during
deflation following three cycles of inflation at high lung volume (10 –25 cmH2O). On the basis of measurements of epithelial basement membrane from electron microscopy, they
concluded that the alveolar expansion in isolated rat lungs at
low volumes was by septal folding and unfolding but that
stretching of septal tissue occurred at higher lung volumes.
Imaging approaches. Because of the limitations of morphometric measurements from fixed tissue, several investigators
have developed imaging approaches for the measurement of
alveolar shape change as a function of volume and pressure in
situ or ex vivo. In 1983, Smaldone et al. (75) measured the
deposition of aerosol without flow on excised dog lungs and
suggested that alveolar diameters remained unchanged for
most of the deflation from TLC. Later, Carney et al. (10) used
intravital microscopy to examine the subpleural alveoli of
porcine lungs and concluded that lung volumetric changes
occurred by recruitment-derecruitment (RD) of the alveoli
since they did not observe alveolar shape change up to 80%
TLC upon inflation from a (nonphysiological) degassed state.
Other studies by this group supported RD of the alveoli and
suggested that the folding and unfolding of alveolar septa was
the mechanism in which unstable alveoli change volume (62)
and that the alveolar recruitment was dependent on the magnitude of the recruiting pressure and its duration (2).
Volumetric change of the lungs by RD has been suggested
by studies involving ARDS patients, which may provide clues
related to how alveoli expand in one diseased condition (13,
31–33, 63). Using computed tomography (CT), this group
showed the heterogeneous nature of injured lungs suggesting
the existence of fluid and air filled regions of the lung that are
unrecruitable and recruitable. A discussion provided by Hubmayr (40) raises concerns regarding three underlying assumptions of the CT studies of injured lungs: 1) the strong dependence of lung volumetric change on the weight of the tissue,
2) the nature of the relationship between the alveolar volume
change and CT scan grayscale, and 3) the dependence of the
change in the P-V curves in ARDS patients predominantly on
the alveolar recruitment. A partial dependence of lung mechanics on the gravitational forces within the lung and the existence
of many mechanical contributors of the P-V curves raise
concerns about the use of CT scan data to deduce lung stress
and strain levels. Although CT scan analyses are useful in the
clinical setting for assessing regional heterogeneity and recruitment of air spaces, it is important to understand their limitations in measuring stress and strain levels in the lung. It is
unlikely that alveolar level information can be obtained from
gross CT scan grayscale measurements of injured lungs.
Recent developments in real-time fluorescence microscopy
and optical coherence tomography (OCT) of the lung have
provided an opportunity to monitor the volumetric evolution of
a given alveolus as a function of pressure (44, 56). Perlman and
Bhattacharya (64) combined real-time laser scanning confocal
fluorescence microscopy with optical sectioning to measure
length changes of the alveolar perimeter in subpleural alveoli
following changes in alveolar pressure in isolated lungs. They
concluded that alveolar strain was heterogeneous both within a
particular alveolus and throughout the lung. They observed that
the AEI cells experienced greater strains than AEII cells. In
images with alveolar pressures ranging from 5 to 20 cmH2O,
they reported no evidence of recruitment and derecruitment. In
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STRAIN IN THE ALVEOLUS
pressure load (P1) was applied on the outer surface of the
sphere as a net distending pressure. The vacuum pressure load
(P2) was selectively raised to 500 Pa (5.1 cmH2O) near the
outer surface of the inner sphere that was in contact with the
rigid glass slide. The magnitude of the vacuum pressure load is
right at the lower end of suction pressure that was applied in
Carney et al. (10) near the glass slide. Material 1 falling within
region C was prohibited from moving in the y-direction to
stabilize the FE model in a way that is similar to the lung; i.e.,
the connection between the large airways and parenchyma
stabilizes the lung.
A contour plot of the averaged strain in a plane that is
normal to the glass coverslip, is shown in Fig. 3C. Although
the majority of the strain levels in the sphere were positive or
tensile, indicating stretch, the strain levels near the coverslip
(region A) were negative, indicating compressive strain in the
alveoli beneath the coverslip. In this model, the compressiveto-tensile transition of the strains occurred at 34.3 mm away
from the glass slide, which is 11.4% of the diameter of the
inner sphere. Moreover, the tensile strain parallel to the perimeter of the sphere, as indicated in Fig. 3B, is significantly lower
for region A relative to region B. In summary, this simplified
FE analysis indicates an increased compression and a reduced
tension (opening) near the subpleural alveoli adjacent to the
glass coverslip. This indicates that both the glass slide and a
suction pressure can affect the localized mechanical response
of the lung and result in a unique response in the region of
interest. Certainly, the presence of the suction pressure amplifies the magnitude of the compressive stress.
This FE model of the lung at the macroscale is simplistic
because it does not include all of the mechanical determinants
of the lung as shown in Fig. 1. However, it does indicate some
of the potential artifacts that can result from this approach for
imaging alveoli. The presence of compressive strain near the
coverslip may encourage movement of alveoli toward the surface.
AJP-Lung Cell Mol Physiol • VOL
Moreover, the reduced tensile strain parallel to the surface of the
coverslip may indicate a lack of change in surface area with a
given pressure relative to an unconstrained area. These are both
consistent with findings indicating lack of alveolar volume
increase of subpleural alveoli and the increase in the number of
alveoli beneath the coverslip (2, 10). This FE model shows
how subpleural alveoli are constrained by the presence of a
glass coverslip and how these alveoli experience a mechanical
environment that is significantly different from other subpleural regions and internal or parenchymal environment. This
underlines the importance of further consideration when extending subpleural findings to the remainder of the lung parenchyma when the actual measurements are conducted near a
region in which the mechanical environment is greatly modified.
Estimates of change in tensile strain in the alveolus. In
addition to addressing fundamental questions regarding the
mechanisms of lung volumetric increase, previous studies have
provided data that can be utilized to calculate the change in
tensile strains experienced in the lung during tidal or TLC
inflation/deflation. A summary of the change in strain levels
estimated from the literature is presented in Table 1. These
articles were selected on the basis of providing specific numerical information about surface area or diameter of the alveoli at
either a specific pressure level or at a fraction of total lung
capacity (TLC). The majority of the studies reported changes
in surface area (⌬SA), and we either listed the reported surface
area strain (or distension) or calculated the strain by ⌬SA ⫽
(SAf ⫺ SAo)/SAo where ⌬SA is the area strain for a particular
change in lung volume from an initial (o) and final (f) pressure.
To compare the area strain with the linear strain
ε ⫽ 共1 ⫹ ⌬SA兲1⁄2 ⫺ 1
where
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Fig. 3. A simple finite element (FE) model
showing the effect of additional suction pressure near a glass slide placed on the surface
of a spherical lung. A: full geometry of the
composite spherical assembly. B: FE model
of the simplified geometry with pressure
loads and the coverslip. All structures are
allowed to slide freely against each other.
C: contour plot of the strains in the y-direction showing a close-up of the compressive
strains near the subpleural region closest to
the coverslip (with and without suction pressure). A total of 12,646 2D elements were
utilized to discretize this assembly.
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STRAIN IN THE ALVEOLUS
Table 1. Alveolar strain at physiological pressure levels calculated from previously published morphometric data
Reference No.
6
Species
Surface Area Distension ⌬SA, %
Fixation Method/Imaging
Vascular perfusion, EM
28
Guinea pig
Rapid freezing and vascular perfusion, LM
35
Rabbit
Vascular perfusion, EM
42
Cat
Rapid freezing and freeze drying, LM
55
Rat
Vascular perfusion, EM
83–85
Rat
Vascular perfusion, EM
In situ
66
Rat
Laser scanning fluorescence microscopy
Initial/Final, %TLC
9.8(I)–7.9(D)
33.9(I)–10.4(D)
28.2(I)
5.5(I)
9.6(I)
21.7(I)
4.7(D)*
11.2(I)–9.9(D)*
4.2(D)*
2.5(I)–4.1(D)
14.4(I)
55.8(I)–30.0(D)
10.3(D)
3.5(D)
2.2(D)
7.2(D)
5.7(D)
15.4(D)
80N100
40N80
40)75.7
28.5)40
40)80
80)100
75(100
50N75
37(50
95.8N100
73.2)95.8
24.8N95.8
82(100
42(82
24(40
24(60
24(82
24(100
20.6(I) ⫺15.2(D)
79.2(I)–19.8(D)
64.4(I)
11.3(I)
20.2(I)
48.1(I)
n/a
n/a
n/a
5.1(I)–8.0(D)
30.8(I)
142.6(I)–51.0(D)
19.5(D)
7.0(D)
4.4(D)
13.8(D)12(D)†
11.1(D)25(D)†
28.5(D)37(D)†
n/a
14
5)20 cmH2O
(82%TLC)
Our values are computed with (SAf ⫺ SAo)/SAo. %TLCf⬎%TLCo for inflation and %TLCf⬍%TLCo for deflation. SA, alveolar surface area; TLC, total lung
capacity; subscript o, initial value; subscript f, final value; LM, light microscopy; EM, electron microscopy; (I), inflation; (D), deflation. *Linear strain (ε) is
computed from change in diameter. †⌬SA values of 12, 25, and 37% were obtained from the synthesis of a series of studies in which an empirical equation was
derived from experimental data. The reported data is shown in the first column under ⌬SA, and estimates from the empirical equation are shown in the second
column. We report these values (12, 25, and 37%) since they have been used extensively in other studies.
ε ⫽ 共Lf ⫺ Lo兲 ⁄ Lo ⫽ ␭ ⫺ 1.
␭ is the stretch ratio, and Lf and Li represent the initial and final
lengths (or alveolar diameters).
We selected only limited measurements from each study for
comparison. For example, 40% TLC is the initial and 80%
TLC is the final configuration for many of the measurements
recorded during inflation because of the physiological relevance of this particular range. It is important to recognize that
strain values can vary greatly depending on the selection of the
initial starting point. Ideally, we would estimate changes in
strain based on an initial unstressed state, but that is difficult to
define in a lung in vivo. Therefore, we referred to strain levels
as % distension to account for the possibility of different
reference lengths within the studies. Furthermore, as described
above, the deformation of the lung differs during inflation and
deflation, and inflation causes positive changes in dimensions
(stretch) whereas deflation causes negative changes (compression or relaxation). In this table, those measurements corresponding to lungs that were fixed during the deflationary stage
have a final condition (f) that was at a lower %TLC value than
the initial one, i.e., lower surface area. Instead of denoting the
change in surface area for these measurements with only a
negative sign, we marked these deflationary distension and
⌬SA values with (D), and we indicated inflationary ones with
(I). We also reported the initial and final configurations corresponding to the computed distension values with arrows indicating the direction of the pressure change. It is also important
to recognize that the type of distension that may be of interest
will depend on the perspective of the reader: if one is concerned with cellular mechanotransduction, then levels of linear
distension are important, whereas those concerned with gas
exchange and organ level physiology may be more interested
in changes in surface area.
AJP-Lung Cell Mol Physiol • VOL
Among the studies presented in the table, Tschumperlin and
Margulies (84) and Bachofen et al. (6) measured the epithelial
basement membrane surface area (EBMSA), which measures
area based on the basement membrane including the alveolar
folds, whereas other studies reported alveolar surface area. The
difference between the EBMSA and alveolar surface area is
indicated in Fig. 2, where the EBMSA was calculated by using
the perimeter of the alveolus from two-dimensional images
including basement membrane folds, as seen in the close-up
image of the alveolar wall in this figure. The alveolar basement
membrane folds were excluded when the alveolar surface area
was calculated. Therefore, the EBMSA are inherently larger
than the alveolar surface area and may be less sensitive to
changes in pressure, because the unfolding of these features
will precede an increase in surface area. As discussed above, it
is unclear whether these folds exist in an in vivo lung in the
same way as an excised lung (58). Therefore, although
Bachofen et al. measured both EBMSA and total surface area,
we calculated the change in distension utilizing only the total
surface area.
A number of the studies shown in Table 1 reported morphometric information comparing deformation from ⬃40 to 80%
TLC during inflation. Estimates of linear distension values
range from 9.6 to 33.9% during inflation from 40 to 80% TLC.
The change in linear distension was substantially lower during
deflation in this range with estimates ranging from 3.5 to
10.4%. The lower estimate may reflect differences in measurements of EBMSA vs. total surface area since Bachofen et al.
(6) showed differences in strain dependent on the use of the
EBMSA or alveolar surface area in the computation of strain.
To examine changes in alveolar dimensions directly, Perlman and Bhattacharya (64) utilized optical sectioning methods
(OSM) with confocal fluorescence microscopy to image iso-
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Rabbit
Linear Distension ε, %
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AJP-Lung Cell Mol Physiol • VOL
behavior of the lung. Denny and Schroter (21) later used their
repeat unit truncated octahedron model to conclude that the
large deformation and anisotropic behavior of the lung parenchyma were not negligible when the aim was to capture the
nonuniformity of the distortions in the lung.
A number of targeted computational models have been
generated to predict the contribution of the alveolar interaction
to lung mechanics (73) and the mechanics of lungs with
emphysema (34, 79). Gefen et al. (34) utilized scanning electron microscopic images in the generation of the “alveolar sac”
geometry and concluded that emphysemic lungs experienced
higher strains than normal lungs at a given pressure. However,
it should be recognized that their results were based on a
two-dimensional FE model without the surface tension loading
condition. Although mechanical models such as these are
useful for examining the complexities of lung mechanics, they
have not yet provided a detailed description of the alveolar
strain field.
One aspect of recent multiscale, multidisciplinary computational models is the incorporation of patient-specific data into
the models, which is coupled with one type of global imaging
modality. Werner et al. (94) concluded that in patients with
lung tumors the overall lung deformation can be estimated
using FE models of four-dimensional patient CT scans. Their
study was aimed at improving the image-guided radiation
therapy outcomes by controlling the dose distribution. In another study, Sundaresan et al. (81) utilized a mechanical model
of the lung to capture the “recruitment status of lung units” to
determine the optimal positive end-expiratory pressure. This
type of progress in patient-specific modeling in the lungs is in
line with the overall progress made in this field, which is still
in its early stages and necessitates substantial clinical validation and usability tests (56a).
In general, computational mechanics approaches to determine function in a healthy or diseased lung have proven to be
useful in explaining or measuring observations that are not
captured by imaging modalities. However, for these models to
fully explain complex physiological mechanical events, appropriate mechanical properties, boundary conditions, and mechanical loads must be identified. Moreover, validation of such
computational models, which is an essential component of any
computational mechanics approach, remains to be a challenge
in the analysis of soft tissue mechanics.
Concluding Remarks
The extent of mechanical deformation in the alveolus affects
the functionality of the alveolus in a number of critical ways,
including by controlling surfactant release, permeability, inflammation, and cell injury and repair. Lung injury and disease
can result in substantial alterations of the alveolar mechanical
environment, which is then transmitted to the cells through
changes in the strain field. Despite substantial progress, there
are still many unanswered questions about this mechanical
environment. This limitation is based mostly on the complexity
of the lung tissue, which is composed of a relatively soft ECM
and cells that are continuously undergoing large deformations.
The complexity of experimental and theoretical analysis of the
soft tissue mechanics coupled with the lack of imaging techniques
to fully describe the lung shape at each inflation pressure contributes greatly to our lack of understanding. In this review, we
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lated lungs, and focused on a single alveolus to measure its
volumetric evolution in situ. Their results reflect the strain of a
single segment in the alveolar perimeter, which was shown to
vary between 5% and 25% with an average of 14% at 82%
TLC or ⌬15 cmH2O. This is the first study to directly measure
the alveolar wall deformation in an intact lung. It provides
direct evidence that the alveolar walls experience a nonuniform
strain throughout.
Establishing a consensus for the magnitude of strain in the
alveolus at different levels of inflation based on the morphometric measurements is challenging. To determine the actual
(or physiological) distension level, stress (normalized force)
and strain relationships in alveolar walls must be described. It
is not currently possible to measure the alveolar wall stress in
situ. As discussed above, it is also difficult to establish a
reference or equilibrium condition for in vivo lungs by which
to describe subsequent changes. Some studies have determined
the stress-free volume in ex vivo lungs (86). Although informative, such ex vivo studies are limited in capturing this
reference condition in vivo. Once the lungs are removed from
the thoracic cavity and fixed, a number of critical mechanical
determinants, such as the rib cage volumetric limitation and the
PPL, are eliminated from the overall mechanical system. Therefore, the excised lung, without any compensating increase in
PT, is more inclined to exhibit a configuration in which the
alveolar walls may fold or collapse, potentially indicating a
stress- and strain-free condition. As discussed in detail in
Oldmixon and Hoppin (58), the inflation-deflation cycling of
the excised lungs may result in atelectasis when pressures cycle
below 3 cmH2O. It should also be pointed out that many of the
studies summarized in the table utilized different standards for
volume cycling and fixation, and this makes it more difficult to
compare results directly (39). In addition, TLC is often defined
by using an arbitrary pressure that may vary in different species
or models. The majority of the studies shown in Table 1
inflated the lungs to 25 to 30 cmH2O and referenced percent
inflation relative to this.
Nevertheless, the morphometric measurements have provided invaluable estimates of the alveolar strain field. However, given the many caveats discussed above, we must be
careful in our interpretation of these estimates. On the basis of
the various studies to date, we estimate that normal tidal
breathing results in linear distension in the range of 0 to 5%,
whereas inflation from functional residual capacity to TLC
likely causes more variation in strain ranging from ⬃15 to
⬃40% (and potentially higher). We expect that there will be
much greater variation in injured or diseased lungs, but little
information is available. A final note of caution is that none of
the morphometric or imaging studies have provided direct
estimates of alveolar strain in human lungs.
Computational models. Computational models have been
used extensively in an attempt to describe the mechanics of
lung parenchyma and alveoli. Initial models were developed in
an attempt to interpret pressure-volume loops measured in vivo
(19, 20, 43, 98). In a number of these studies, a mathematical
analog of the alveolus was generated with the use of a truncated octahedron (19, 30). Utilizing this three-dimensional
analog as a repeat unit, Denny and Schroter (20) generated a
model of the lung alveolar duct and concluded that the alveolar
duct must be included in the mechanical analysis of the lung
parenchyma to accurately describe the overall mechanical
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STRAIN IN THE ALVEOLUS
attempted to unify some of the key findings over many years of
mechanics studies in the literature and to summarize some of the
key measurements and studies. Sophisticated experimental, computational, and theoretical approaches combining biology, chemistry, mechanics, and imaging will be necessary to fully describe
the alveolar mechanical environment and its effects on alveolar
cells.
ACKNOWLEDGMENTS
We thank Dr. Kaushik Parthasarathi and Dr. Scott Sinclair for helpful
discussions regarding this manuscript.
GRANTS
DISCLOSURES
No conflicts of interest, financial or otherwise, are declared by the author(s).
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