Journal of Biomechanics 32 (1999) 891}897
Analysis of stress distribution in the alveolar septa of
normal and simulated emphysematic lungs
A. Gefen , D. Elad *, R.J. Shiner
Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
Department of Clinical Respiratory Physiology, The H. Sheba Medical Center, Tel Hashomer 52621, Faculty of Medicine, Tel Aviv University, Israel
Received 15 April 1999
Abstract
The alveolar septum consists of a skeleton of "ne collagen and elastin "bers, which are interlaced with a capillary network. Its
mechanical characteristics play an important role in the overall performance of the lung. An alveolar sac model was developed for
numerical analysis of the internal stress distribution and septal displacements within the alveoli of both normal and emphysematic
saline-"lled lungs. A scanning electron micrograph of the parenchyma was digitized to yield a geometric replica of a typical
two-dimensional alveolar sac. The stress-strain relationship of the alveolar tissue was adopted from experimental data. The model was
solved by using commercial "nite-element software for quasi-static loading of alveolar pressure. Investigation of the state of stresses
and displacements in a healthy lung simulation yielded values that compared well with experimentally reported data. Alteration of the
mechanical characteristics of the alveolar septa to simulate elastin destruction in the emphysematic model induced signi"cant stress
concentrations (e.g., at a lung volume of 60% total capacity, tensions at certain parts in an emphysematic lung were up to 6 times
higher than those in a normal lung). The combination of highly elevated stress sites together with the cyclic loading of breathing may
explain the observed progressive damage to elastin "bers in emphysematic patients. 1999 Elsevier Science Ltd. All rights reserved.
Keywords: Lung parenchyma; Alveolar wall; Finite element method
1. Introduction
The alveolar septum is a very thin structural framework that ensures a minimal barrier between air and
blood, while a relatively enormous surface of contact is
maintained for e$cient gas exchange (Fung and Sobin,
1972). It consists of a skeleton of "ne collagen and elastin
"bers which are interlaced with the capillary network
(Weibel, 1970,1983). The structural organization which
comprises extensible elastin "bers, woven in nonextensible collagen networks, allows the lung to in#ate within
the normal range, and also provides support and a high
level of sti!ness at limiting volumes (Mead, 1961). Alteration of the distribution and relative densities of these
"bers results in redistribution of stresses and displacements in the lung micro structures, which may consequently induce pathological changes in alveoli as seen in
di!erent lung diseases (Vawter et al., 1975; Denny and
Schroter, 1995).
* Corresponding author. Tel.: #972-3-640-8476; fax: #972-3-6407939.
E-mail address: [email protected] (D. Elad)
The role of the relative content of collagen and elastin
in lung pathologies has been clearly demonstrated in
emphysema, a condition which is characterized by abnormal permanent enlargement of air spaces distal to the
terminal bronchioles, accompanied by destruction of
their walls due to degradation of elastin "bers (Saetta et
al., 1985a,b; Snider et al., 1985; Nagai et al., 1991). Simulation of emphysema states in animal lungs by elastase or
collagenase treatment showed that the initial reduction
in elastin density after application of the enzyme subsequently led to the breakdown of many more elastin
"bers during the following 12 weeks (Sugihara and Martin, 1975; Mercer and Crapo, 1992).
Recent models of the lung parenchyma have used
various geometrical bodies (e.g. truncated octahedrons,
dodecahedrons or a combination of cones, spheroids and
ellipsoids) to describe the volumetric structure of the
alveolar region (Dale et al., 1980; Fung, 1988; Kimmel
and Budianski, 1990; Denny and Schroter, 1995). These
models successfully described the mechanical characteristics of the whole lung and provided information on its
gross mechanical behavior. However, they were not designed to study the internal distribution of stresses within
0021-9290/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved.
PII: S 0 0 2 1 - 9 2 9 0 ( 9 9 ) 0 0 0 9 2 - 5
892
A. Gefen et al. / Journal of Biomechanics 32 (1999) 891}897
alveolar walls. The present model was developed to study
the stresses within the parenchymal microstructure in
order to facilitate better understanding of the mechanical
factors at work in lung disease. For example, analysis of
the mechanical aspects of elastin breakdown in the alveolar septa during the development of emphysema.
2. Methods
2.1. Rationale
The overall performance of the lung is controlled by
the mechanics of its microstructure. However, the
alveolar sac structure is too small to allow direct
stress}strain measurements. On the other hand, a great
deal of understanding of its mechanical behavior has
been gained from experiments with samples of lung parenchyma (Hoppin et al., 1975; Yager et al., 1992), from
detailed micrographs of the alveolar region (Weibel,
1983) and from model simulations of the parenchymal
structure (Dale et al., 1980; Kimmel et al., 1987; Fung,
1988; Denny and Schroter, 1995). It is generally accepted
that the relative content of elastin and collagen in the
alveolar walls determines the gross mechanics of the
lung, but the "ber organization and the precise stress
distribution within the septal walls of normal and pathological lungs are unknown. Accordingly, the goal of this
study was to investigate the stress distribution within the
septal walls of a simpli"ed two-dimensional (2D) model
of an alveolar sac, which is based on a realistic anatomical structure and available experimental data.
2.2. Microscopic model of the parenchyma
The microscopic structure of the lung parenchyma
may be represented by a respiratory unit (the acinus)
which is composed of alveolar ducts that branch o!
a terminal bronchiole and terminate at common chambers of multiple individual alveoli, called alveolar sacs
(Fig. 1). Each lung comprises abundant alveoli (about
150;10), which are distributed within the pleural membrane and constitute the open space for respiratory gases.
When the lung is in#ated to a volume of < due to
*
a transpulmonary pressure, P "P !P (P * al
veolar pressure, P * pleural pressure), the alveolar
septa of all the alveoli that "ll the parenchymal space are
stretched by forces (¹) that maintain an open lung under
quasi-steady equilibrium (Mead et al., 1970; Wilson,
1972; Mead, 1973; Elad et al., 1988).
In this study we have developed a 2D model of a typical alveolar sac structure (Fig. 1), whose geometry is
taken from a scanning electron microscope image. In the
absence of experimental data on the forces ¹ transmit
ted from the pleural membrane to the outer walls of
a single alveolar sac, it is assumed for modeling purposes
Fig. 1. Schematic description of the lung parenchyma microstructure.
The lung is in#ated due to a transpulmonary pressure P "P !P
(P * alveolar pressure, P * pleural pressure). The alveolar septa are
stretched by traction forces ¹ that maintain an open lung under steady
equilibrium.
that these forces are due to uniformly distributed stresses
(p ) within the neighboring septa. The present model was
developed for a saline-"lled lung, thus the issue of surface
tension due to the liquid lining on the septal walls was
not addressed.
The traction stresses (p ) at di!erent lung volumes were
approximated by a global analysis of internal stresses
within the septal walls. The neutral state of the lung is
assumed to be at < "35% of the total lung capacity
*
(TLC) at which the lung is in#ated with open alveolar
spaces, but with zero stresses within the alveolar septa
and bronchial tree (Wilson and Bachofen, 1982; Elad et
al., 1988). Accordingly, the characteristic stretch ratio (j)
of any alveolar wall at a given lung volume (< ) can be
*
approximated by using the generally accepted relationship (Hoppin et al., 1975),
j"¸/¸ "(A/A )"(< /< ),
(1)
* *
where ¸ and A are typical length and area, respectively.
The experimental pressure}volume data obtained from
a saline-"lled rabbit lung (Gil et al., 1979) can be used to
approximate j from Eq. (1) for any < as determined by
*
P . The traction stresses on the external boundaries of
the alveolar sac model were determined from experimental stress-stretch data of human lung samples
(Sugihara et al., 1971), and are given in Table 1.
2.3. Geometry of an alveolar sac
The geometry of a typical alveolar sac was extracted from a scanning electron micrograph of a mouse's
A. Gefen et al. / Journal of Biomechanics 32 (1999) 891}897
893
Table 1
Alveolar pressures (P ) and traction stresses (p ) at di!erent lung
volumes (< ). The values of P vs. < are taken from Gil et al. (1979),
*
*
the values of j are computed from Eq. (1), and the corresponding p are
taken from Eq. (2) which was "tted to the data of Sugihara et al. (1971)
P
(cm H O)
<
*
(%TLC)
j
p
(KPa)
3
3.5
4
5
6
7.5
10
12
35
40
45
60
70
90
95
100
1
1.046
1.088
1.197
1.260
1.370
1.395
1.419
0
0.1
0.25
1
2
5
6
7
Fig. 3. Two-dimensional model of a typical alveolar sac subjected to
biaxial loading due to uniformly distributed stresses (p ) in the neigh
boring septal walls. The constraints at the two edges of the sac's
`moutha are marked by triangles.
Fig. 2. A scanning electron micrograph (180;) of a mouse lung parenchyma (Lawrence Berkley Laboratories, USA; http://www-itg.lbl.gov).
The white circle marks the region from which the geometry for the
alveolar sac model was extracted.
parenchymal tissue (Fig. 2) which was "xed by inspiration of glutaraldehyde and instantly coated with gold
and platinum to maintain its realistic geometry (Lawrence Berkley Laboratories, USA; http:/www-itg.lbl.gov).
Utilization of data from the mouse parenchyma is justi"ed since the general shape of septal structures is common to all mammals, although alveolar dimensions do
di!er between species (Weibel, 1983; Mercer et al., 1994;
Fung, 1988). The latter was taken into consideration by
appropriate scaling of the data.
The alveolar zone is composed of numerous alveolar
sacs of an almost in"nite number of geometrical shapes.
However, all the alveoli perform the same function of gas
transfer, and their overall dimensions (e.g. volumes and
wall thickness) are of the same order of magnitude.
Therefore, we selected a typical geometry for the model
from the region marked by the white circle on the parenchymal image in Fig. 2. The region of interest was pro-
cessed using edge-detecting algorithms (e.g., sharpen,
edge enhancement, posterize and median image "lters) to
de"ne the alveolar septa geometry for the 2D model. The
contours of the alveolar walls were digitized and scaled
to ensure an averaged human septal thickness of 8 lm
(Sugihara et al., 1971; Mercer et al., 1994). The inner and
outer contours of the septal walls were digitized by 265
points at a resolution of approximately 1 lm. A movingaverage "lter was utilized to reduce errors during digitization and to produce smooth contours without loss of
signi"cant information (Fig. 3).
2.4. Constitutive law of the parenchymal tissue
The septal tissue is assumed to be an isotropic nonlinear elastic material. Its mechanical characteristics were
taken from Sugihara et al. (1971) who conducted uniaxial
length-tension measurements on healthy and diseased
human lungs. Sugihara's data from a normal, healthy
human lung were "tted to the following expression (Elad
et al., 1988)
p"jL!j\L,
(2)
where p is the stress in KPa, j is the stretch ratio (Eq. (1))
and the best "t was obtained for the coe$cients n "8
and n "!6.4 (Fig. 4). The instantaneous tissue sti!
ness is given by
dp
E(j)" "n jL\#n j\L\.
dj
(3)
894
A. Gefen et al. / Journal of Biomechanics 32 (1999) 891}897
Fig. 4. Stress-strain curves of uniaxial tension of the lung parenchyma
tissue: (䊏) data from a healthy human lung specimen (Sugihara et al.,
1971), (solid line) regression curve to the data of a healthy lung, (dashed
line) curve for the early stage of emphysema.
Assuming that lung tissue exhibits a linear behavior in
the vicinity of any instantaneous deformation, the shear
modulus can be obtained from the length-tension curve
(Eq. (2)) as follows:
E(j)
n jL\#n j\L\
G(j)"
" ,
2(1#l)
2(1#l)
(4)
where the Poisson ratio was taken to be l"0.4 (LaiFook, 1981). At the neutral state (< "35% TLC),
*
E(j"1)"n #n "4 cm H O (or 0.39 KPa) which is
similar to the results of indentation measurements in
saline-"lled rabbit lungs (Stamenovic and Yager, 1988).
It is generally accepted that the volumetric densities of
elastin and collagen are nearly the same in the septal
walls of healthy lungs (Matsuda et al., 1987; Mercer and
Crapo, 1990), while in emphysema there is a signi"cant
reduction in relative volume density of elastin (Sugihara
and Martin, 1975; Mercer and Crapo, 1992; Cardoso et
al., 1993). Sugihara et al. (1971) obtained signi"cantly
higher slopes in the force}extension curves of all the
emphysematic lungs as compared to normals, regardless
of tissue age. Similarly, conversion of pressure}volume
curves of normal and emphysematic lungs (Comroe,
1974) to pressure}strain relationships using Eq. (1) shows
material sti!ening during the progress of emphysema.
For example, an emphysematic specimen was found to
bear four times greater forces than those carried by
a normal specimen, for the same extensions j in the range
of 1}1.4 (Sugihara et al., 1971). Here, we assumed that for
the early stages of emphysema, the stresses required to
induce a given deformation are twice as large as in
normal lungs (Fig. 4).
2.5. Numerical method
The data specifying the contours of the alveolar sac
geometry were transferred to the ANSYS 5.0 commercial
"nite-element software package in order to determine the
quasi-steady stress distribution and displacements of the
alveolar sac model for given lung volumes. Automatic
Fig. 5. The mesh of the alveolar sac model (Fig. 3) for the "nite-element
solver.
meshing was used to generate 513 quadrilateral and
triangular elements that describe the alveolar sac walls
(Fig. 5). Each of the selected elements has eight nodes
which are well suited for curved boundaries and allow for
large displacements. Each node has two degrees of freedom, i.e., translation in the x and y directions, a state
which is compatible with compound stresses.
The boundary conditions at each lung volume included the corresponding alveolar pressure (P ), external
traction stresses from neighboring septal walls (p ), and
constraints on the two edges of the alveolar sac `moutha,
which allowed only rotation (but not translation in the
x and y directions). Releasing each of the constraints for
translation in the x direction caused no signi"cant changes in the resulting stress distribution. Similarly, allowing for stress gradients as traction forces on the external
boundaries (0.75p }1.25p ) did not reveal any signi"cant
di!erences in both location and values of stress concentrations.
The computational procedure started at < . The
*
alveolar pressure P was then incrementally increased as
shown in Table 1, while the corresponding traction stresses p and the resulted distribution of stresses within the
septal walls were calculated for each new P . For every
lung volume, the general equilibrium equations were
solved for planar stresses within approximately 10 min
on a Pentium 200MMX CPU.
3. Results
The model was utilized to study stress distributions
within the septal walls. The distributions of principal
A. Gefen et al. / Journal of Biomechanics 32 (1999) 891}897
895
Fig. 7. (a) The predicted displacement of the alveolar sac at < "45%
*
TLC with respect to its shape at < , (b) Area vs. Pressure of the
*
alveolar sac at di!erent lung volumes. (Solid line) model predictions,
(dashed line) experimental data of Hoppin et al. (1975).
Fig. 6. Predicted distributions of principal tension stresses (in KPa) in
(a) normal and (b) emphysematic alveolar septa at < "45% TLC
*
(P "4 cm H O).
tension stresses (which align with the local curvature of
the septum) in normal and emphysematic alveolar sacs at
< "45% TLC that corresponds to P "4 cm H O
*
(391.92 Pa), are shown in Fig. 6. The walls of the normal
alveolar sac withstand average tension values of 0.6 KPa,
but the tension increases to more than 15 KPa around
sharp edges or curves. In contrast, the tension stresses
within internal walls shared by adjacent alveoli, are nearly zero (Fung, 1988). The predicted shape of the alveolar
sac at < "45% TLC, in comparison with the neutral
*
state at < , is shown in Fig. 7a. This drawing clearly
*
shows that the alveolar sac wall deformation is not uniform. The alveolar sac mouth opens toward the interior
aspect as the whole structure expands. The predicted
displacements were used to calculate the area of the 2D
geometry of the alveolar sac at any < that corresponds
*
to the range of P from 0}12 cm H O in order to evalu
ate area changes (A/A ). Evaluation of the area change
for each di!erent < enabled us to construct a pressure*
area curve, similar to the experimental data of Hoppin et
al. (1975). In order to compare experimental data of
volume versus pressure, we transformed volumes into
areas using Eq. (1). Fig. 7b depicts the theoretical and
experimental curves that are nearly the same, thus
validating our model.
Regions of highly intensi"ed stress in the emphysematic model (Fig. 6b) were circled for clearer identi"cation. Two representative sections at the septal wall (A}A
and B}B in Fig. 6b) were delineated in order to compare
the stress distributions across them in the normal and
pathologic lung models. The comparison is shown in
Fig. 8 for three di!erent lung volumes. As shown graphically in the above "gures, local highly elevated compound
stresses are developed around sharp edges and curves.
4. Discussion
The new model of the alveolar sac presented in this
study is capable of predicting the distribution of tension
896
A. Gefen et al. / Journal of Biomechanics 32 (1999) 891}897
stresses and pressures within alveolar walls, thereby, offering a new perspective on the micromechanical behavior of parenchymal tissue in healthy and diseased lungs.
The 2D geometry of a typical alveolar sac was taken from
a micrograph image of a real lung parenchyma, whereas
the mechanical characteristics of the septal material
were determined from published experimental data.
Accordingly, the model can be utilized to simulate lung
volume-dependent stress distributions in the parenchymal microstructure in di!erent pathological states.
The predictions of the present model were compared
with the pressure}area experimental data of Hoppin et al.
(1975), and the agreement between the theoretical and
experimental values appears to be good (Fig. 7b). The
minor di!erences ((5%) may be due to the 2D simpli"cation of the present model, the particular stress}strain
relationship which may di!er from that of the experimental specimen, and the absence of surface tension
e!ects in the present model.
The present model has the ability to simulate the
re-distribution of sepal stresses by altering the non-linear
stress-strain characteristics of parenchymal tissue. The
results for a normal parenchyma indicated that signi"cant stress concentrations are developed near curved
regions, where elevated tension values may be as high as
20 times that of the average stresses (Fig. 6a). These sites
become most vulnerable in cases of emphysema, wherein
changes in the content and distribution of elastin and
collagen "bers have been observed (Mercer and Crapo,
1992). The impact of elastin breakdown on the mechanical behavior of the lung microstructures in emphysema
is also observed in Fig. 8, which shows signi"cantly
higher stresses in the emphysematic lung (e.g. 6 times
more at < "60% TLC). Thus, it is reasonable to as*
sume that during breathing, while the lung is subjected to
cyclic loading/unloading maneuvers, additional elastin
"ber breakdown occur at sites of a highly elevated compound stresses. This increased damage to septal walls
further reduces the `elastic recoila properties of the parenchymal tissue, and may be followed by septal destruction which eventually leads to enlargement of alveolar
sac walls (Saetta et al., 1985a,b; Cosio et al., 1986; Mercer
and Crapo, 1992; Nagai et al., 1994). Similarly, Denny
and Schroter (1995) suggested that tissue properties may
contribute to the formation of alveolar shapes. Further
damage to parenchymal tissue may arise when the capillary walls mechanically fail due to regionally elevated
stresses, as shown by Fu et al. (1992) and West et al.
(1974,1991), who observed breaks in the capillary endothelial layer and alveolar epithelial layer when in#ating
anaesthetized rabbit lungs to a transpulmonary pressure
of 20 cm H O.
In an in vivo air-"lled lung at 50% TLC and higher,
P is signi"cantly larger than in a saline-"lled lung due to
the contribution of pleural pressure P . For example, at
< "60% TLC the alveoli in an in vivo air-"lled lung
*
Fig. 8. Distribution of principal tension stresses in cross sections A}A
and B}B (Fig. 6) in normal and emphysematic alveolar sacs for three
di!erent lung volumes.
will withstand P "10 cm H O, while alveoli in an ex
cised saline-"lled lung in#ated to the same volume will
only be subjected to P "5 cm H O (Mines, 1986). Con
sequently, the predicted stresses within the normal alveolar walls in the living body are 4}5 times higher, and
accordingly, the e!ect of increased structural stresses
may be more pronounced in emphysematic tissue.
The complexity of structures and material properties
characterizing the lung parenchyma have so far prevented accurate modeling of stress distribution within the
alveolar septa. The basic aim of this study was to develop
a 2D mechanical model that resembles as nearly as possible a typical real 2D cross section of an alveolar sac.
Nevertheless, the present 2D model cannot take into
account the e!ect of out-of-plane tissue resistance to
expansion, which may induce greater tension stresses in
the inner septa that link between alveolar mouths and the
outer sac septa. Moreover, scanning electron micrographs of the alveolar sac as used here rarely represent
a truly planar cross section. The lung parenchyma was
assumed to be non-linear isotropic in order to allow for
a "rst analysis of the stress distribution within the alveolar septa even though it is a highly anisotropic material, as demonstrated experimentally (Hoppin et al., 1975;
A. Gefen et al. / Journal of Biomechanics 32 (1999) 891}897
Vawter et al., 1978). Nevertheless, the major result of
increased stress concentrations at locations of small curvatures are also expected in an anisotropic material due
to tissue sti!ening. In view of these and other limitations
of the present 2D approach, we consider this work to be
a "rst step towards a more complex three-dimensional
simulation of the mechanics of a lung parenchyma unit.
Finally, our "ndings had demonstrated that the internal stress distribution in parenchymal microstructures
can be solved using a numerical model by integrating two
powerful techniques: scanning electron microscopy and
"nite-element analysis. This approach should be further
modi"ed to study the mechanical behavior of normal and
pathological biological microstructures of the parenchyma by adding heat and mass transfer e!ects, to simulate the cardinal function of the human lung-gas
exchange.
References
Cardoso, W.V., Sekhon, H.S., Dallas, M.H., Thurlbeck, W.M., 1993.
Collagen and elastin in human pulmonary emphysema. American
Review of Respiratory Diseases 147, 975}981.
Comroe, J.H., 1974. In: Physiology of Respiration. Year Book Medical
Publishers, Chicago.
Cosio, M.G., Shiner, R.J., Saetta, M., Wang, N.S., King, M., Ghezzo, H.,
Angus, E., 1986. Alveolar fenestrae in smokers: relationship with
light microscopic and functional abnormalities. American Review of
Respiratory Diseases 133, 126}131.
Dale, P.J., Matthews, F.L., Schroter, R.C., 1980. Finite-element analysis
of lung alveolus. Journal of Biomechanics 13, 865}873.
Denny, E., Schroter, R.C., 1995. The mechanical behavior of a mammalian lung alveolar duct model. Journal of Biomechanical Engineering 117, 254}261.
Elad, D., Kamm, R.D., Shapiro, A.H., 1988. Tube law for the interpulmonary airway. Journal of Applied Physiology 65, 7}13.
Fu, Z., Costello, M.L., Tsukimoto, K., Prediletto, R., Elliott, A.R.,
Mathieu-Costello, O., West, J.B., 1992. High lung volume increases
stress failure in pulmonary capillaries. Journal of Applied Physiology 73, 123}133.
Fung, Y.C., Sobin, S.S., 1972. Elasticity of the pulmonary alveolar sheet.
Circulation Research 30, 451}469.
Fung, Y.C., 1988. A model of the lung structure and its validation.
Journal of Applied Physiology 64, 2132}2141.
Gil, J., Bachofen, H., Gehr, P., Weibel, E.R., 1979. Alveolar volumesurface area relation in air- and saline-"lled lungs "xed by vascular
perfusion. Journal of Applied Physiology 47, 990}1001.
Hoppin, F.G., Lee, G.C., Dawson, S.V., 1975. Properties of lung parenchyma in distortion. Journal of Applied Physiology 39, 742}751.
Kimmel, E., Budianski, B., 1990. Surface tension and the dodecahedron
model for lung elasticity. Journal of Biomechanical Engineering
112, 160}167.
Lai-Fook, S.J., 1981. Elasticity of lung deformation problems. Annals of
Biomedical Engineering 9, 451}462.
Matsuda, M., Fung, Y.C., Sobin, S., 1987. Collagen and elastin "bers in
human pulmonary alveolar mouths and ducts. Journal of Applied
Physiology 63, 1185}1194.
Mead, J., 1961. Mechanical properties of the lung. Physiological Review
41, 281}328.
897
Mead, J., Takishima, T., Leith, D., 1970. Stress distribution in lungs:
A model of pulmonary elasticity. Journal of Applied Physiology 28,
596}608.
Mead, J., 1973. Respiration: pulmonary mechanics. Annu. Rev. Physiol.
35, 169}192.
Mercer, R.R., Crapo, J.D., 1990. Spatial distribution of collagen
and elastin "bers in the lungs. Journal of Applied Physiology 69,
756}765.
Mercer, R.R., Crapo, J.D., 1992. Structural changes in elastic "bers after
pancreatic elastase administration in hamsters. Journal of Applied
Physiology 72, 1473}1479.
Mercer, R.R., Russeli, M.L., Crapo, J.D., 1994. Alveolar septal structure
in di!erent species. Journal of Applied Physiology 77, 1060}1066.
Mines, A.H., 1986. In: Respiratory Physiology. Raven Press, New York.
Nagai, A., Yamawaki, I., Takizawa, T., Thurlbeck, W.M., 1991.
Alveolar attachment in emphysema of human lungs. American
Review of Respiratory Diseases 144, 888}891.
Nagai, A., Inano, H., Matsuba, K., Thurlbeck, W.M., 1994. Scanning
electronmicroscopic morphometry of emphysema in humans.
American Journal of Respiration Critical Care Medicine 150,
1411}1415.
Saetta, M., Ghezzo, H., Kim, W.D., King, M., Angus, G.E., Wang, N.S.,
Cosio, M.G., 1985a. Loss of alveolar attachments in smokers.
American Review of Respiratory Diseases 132, 894}900.
Saetta, M., Shiner, R.J., Angus, E., Kim, W.D., Wang, N.S., King, M.,
Ghezzo, H., Cosio, M.G., 1985b. Destructive index: A measurement
of lung parenchymal destruction in smokers. American Review of
Respiratory Diseases 131, 764}769.
Snider, G.L., Kleinerman, J., Thurlbeck, W.M., Bengali, Z.H., 1985. The
de"nition of emphysema: Report of a national lung and blood
institute division of lung disease workshop. American Review of
Respiratory Diseases 132, 182}185.
Stamenovic, D., Yager, D., 1988. Elastic properties of air- and liquid"lled lung parenchyma. Journal of Applied Physiology 65,
2565}2570.
Sugihara, T., Martin, C.J., Hilderbrandt, J., 1971. Length-tension properties of alveolar wall in man. Journal of Applied Physiology 30,
875}878.
Sugihara, T., Martin, C.J., 1975. Simulation of lung tissue properties in
age and irreversible obstructive syndromes using and Aldehyde.
Journal of Clinical Investigations 56, 23}29.
Vawter, D.L., Matthews, F.L., West, J.B., 1975. E!ect of shape and size
of lung and chest wall on stresses in the lung. Journal of Applied
Physiology 39, 9}17.
Vawter, D.L., Fung, Y.C., West, J.B., 1978. Elasticity of excised dog lung
parenchyma. Journal of Applied Physiology 45, 261}269.
Weibel, E.R., 1970. Functional morphology of the growing lung.
Respiration 27, 27}35.
Weibel, E.R., 1983. How does lung structure a!ect gas exchange. Chest
83, 657}665.
West, J.B., 1974. Regional distribution of mechanical stresses in the
lung. Scandinavian Journal of Respiratory Diseases Supplementum
85, 7}16.
West, J.B., Tsukimoto, K., Mathiue-Costello, O., Prediletto, R., 1991.
Stress failure in pulmonary capillaries. Journal of Applied Physiology 70, 1731}1742.
Wilson, T.A., 1972. A continuum analysis of a two-dimensional mechanical model of the lung parenchyma. Journal of Applied Physiology 33, 472}478.
Wilson, T.A., Bachofen, H., 1982. A model for the mechanical structure
of the alveolar Duct. Journal of Applied Physiology 52, 1064}1070.
Yager, D., Feldman, H., Fung, Y.C., 1992. Microscopic vs. macroscopic
deformation of the pulmonary alveolar duct. Journal of Applied
Physiology 72, 1348}1354.