Vol. 89, Issue 1, 163-168, July 2000
Effects of age on elastic moduli of human lungs
Stephen J.
Lai-Fook1 and
Robert E.
Hyatt2
1 Center for Biomedical Engineering, University of Kentucky,
Lexington, Kentucky 40506; and 2 Mayo Clinic and Foundation,
Rochester, Minnesota 55905
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ABSTRACT |
The model of
the lung as an elastic continuum undergoing small distortions from a
uniformly inflated state has been used to describe many lung
deformation problems. Lung stress-strain material properties needed for
this model are described by two elastic moduli: the bulk modulus, which
describes a uniform inflation, and the shear modulus, which describes
an isovolume deformation. In this study we measured the bulk modulus
and shear modulus of human lungs obtained at autopsy at several fixed
transpulmonary pressures (Ptp). The bulk modulus was obtained from
small pressure-volume perturbations on different points of the
deflation pressure-volume curve. The shear modulus was obtained from
indentation tests on the lung surface. The results indicated that, at a
constant Ptp, both bulk and shear moduli increased with age, and the
increase was greater at higher Ptp values. The micromechanical basis
for these changes remains to be elucidated.
elastic properties; lung mechanics; interdependence
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INTRODUCTION |
PROBLEMS OF NONUNIFORM
LUNG deformation have been studied by using elasticity theory.
Such problems include the gravitational effects on the vertical
gradient of lung expansion (3, 6, 16, 29) and the interaction between the lung
parenchyma and pulmonary blood vessel (14). In these
studies, the lung is described as an elastic continuum undergoing small
distortions from a state of uniform inflation (19). This
approach requires only two elastic moduli that are functions of
transpulmonary pressure (Ptp) to describe the stress-strain material
properties of the lung parenchyma. One elastic modulus, the bulk
modulus (reciprocal of specific lung compliance; K) describes the lung
behavior during a uniform inflation and is measured by a
pressure-volume (P-V) test. To describe nonuniform lung behavior
requires the knowledge of another constant such as the shear modulus
(µ), which has been measured by indentation tests (9,
15). These elastic moduli describe only the macroscopic
behavior of the lung in which stresses and strains are averaged over
several alveoli. Models of the lung microstructure at the alveolar
level have been developed to elucidate the contribution of alveolar
tissue and surface forces to the macroscopic lung properties
(11, 25, 30).
The effects of aging on the mechanical behavior of the human lung have
been well described in relation to its P-V behavior (for review, see
Refs. 5 and 13). Morphometric studies in human (12,
27) and dog (10) lungs showed that alveolar
mean linear intercept (or alveolar diameter) increases, whereas
alveolar surface area decreases with age. This behavior is associated
with an increase in lung tissue elastin and little change in collagen content (21, 22). Studies relating K and µ to age have been carried out in pig lungs with ages from 5 to 95 days
(18). K decreased whereas µ remained constant with age.
This behavior is associated with pig lung development from neonatal to
the early adult stage, in which alveolar size is reduced with age, a
behavior opposite to that observed for the adult human.
Accordingly, in this study we measured the effects of age on K and µ at Ptp between 4 and 16 cmH2O in isolated adult human lungs
obtained at autopsy. We showed that, in general, both bulk and shear
moduli increased with age. These changes might be associated with
surface forces induced by the increase in alveolar diameter with age
and with tissue forces induced by the increase in elastin content with age.
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METHODS |
The left lungs from 20 human cadavers (7 female, 13 male) were
obtained at autopsy from the pathology department of the Mayo Clinic.
Lungs from subjects who had a known history of lung disease were
excluded from the study. Also excluded were lungs that showed on post
mortem examination any gross evidence of pathology, such as pulmonary
edema, and any evidence of a smoking history.
Each lung was cannulated and inflated to check for air leaks from the
pleural surface by immersion in saline. Any air leak was eliminated by
deflating the lung and tying off the lung area surrounding the leak
with string. After degassing in a vacuum jar, the leak-free lung was
inflated with a syringe to total lung capacity (TLC), defined as the
volume at 25 cmH2O Ptp (airway pressure relative to pleural
pressure that was atmospheric). Static deflation P-V curves were
measured by deflating the lung stepwise to deflation pressures of 16, 12, 8, 6, 4, 2, and 0 cmH2O Ptp. The collapsed lung at 0 Ptp was weighed and displaced in water to determine its residual
volume. The total lung volume (air plus tissue volume) was calculated
at each Ptp value.
The following procedure was used to determine K and µ (15). We measured K from incremental changes in Ptp and
lung volume. Small P-V loops were performed around deflation Ptp values
of 16, 12, 8, and 4 cmH2O. The increment in Ptp of these
loops was ~2-3 cmH2O. To determine the µ,
indentation tests were performed at deflation Ptp values of 16, 12, 8, and 4 cmH2O. In brief, the lung was held at a constant
deflation Ptp. The middorsal surface of the lung was indented with the
flat surface of a 3-cm-diameter cylindrical rod. The applied load
(L) required to displace the rod incrementally into the lung
surface was measured. The increment in displacement (w) was
2 mm and the maximum w was limited to 1 cm to ensure a
linear w-L curve. Between each indentation test, the lung was inflated to TLC before deflating to the test Ptp to
eliminate any distortion of the parenchyma caused by the indentation.
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RESULTS |
Pressure-volume behavior.
Table 1 summarizes age, gender, TLC, and
left lung weight of the subjects. Figure
1 shows lung volume as percent TLC
(volume at 25 cmH2O Ptp) vs. age at different Ptp values of
0, 2, 4, 6, 8, 12, and 16 cmH2O. Linear regression analyses
showed that volume increased significantly (P < 0.05)
with age at all Ptp values except 0 cmH2O (residual volume,
P > 0.05). This indicated that the residual volume
expressed as a fraction of TLC was invariant with age. The increased
volume with age was a reflection of the changes in shape of the P-V
curve with age as shown in Fig. 2. This
figure shows the mean P-V curves at ages of 20, 40, and 60 yr obtained
from the regression equations shown in Fig. 1. Note in Fig. 2 the shift
of the P-V curve with increasing age toward a greater lung compliance
(
V/P) at the lower Ptp values, a characteristic of an
emphysematic lung (17). The ratio of TLC (ml) to lung mass
(M; g) was not significantly related to age by linear regression analysis: TLC/M = 10.7 
0.066 age,
r2 = 0.109, n = 18, P = 0.1. This indicated that the change in
shape of the P-V curve was not caused by an increase in TLC with age. Also, lung residual volume as a fraction of TLC was uncorrelated with
age (Fig. 1, Ptp = 0 cmH2O). This suggests that the
material properties that were responsible for residual volume and TLC
did not change with age, whereas those responsible for the intermediate lung volumes did.
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Fig. 1.
Lung volume (V) measured as percent total lung capacity
(%TLC) vs. age (yr) at constant transpulmonary pressure (Ptp) values
of 0, 2, 4, 6, 8, 12, and 16 cmH2O. Linear regression
equations are shown.
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Fig. 2.
Lung volume (%TLC) vs. Ptp at 20, 40, and 60 yr. Values
were computed from linear regression equations shown in Fig. 1.
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Each P-V curve was fitted to the relationship (20):
Ptp = 
1e
2V,
which in linear form is ln Ptp = ln 1 + 2V. Figure 3
shows the values of 1 plotted vs. age. Note that ln
1, a measure of the elasticity of the lung, decreased
significantly (P < 0.05) with increasing age: ln
1 = 0.22 0.037 age,
r2 = 0.59 (solid line, Fig. 3). This
equation is comparable to that found previously (20): ln
1 = 0.35 0.044 age (dotted line, Fig. 3). By contrast, 2, a measure of the maximal lung
volume, was uncorrelated with age: 2 = 2.23 × 10
3 9.2 × 106 age,
r2 = 0.015, P = 0.6. The
latter result is consistent with that reported previously
(20).
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Fig. 3.
Values of 1 (log scale) vs. age (yr)
computed from best fit of equation Ptp = 1e2V
to each pressure-volume (P-V) curve. Solid line represents the linear
regression equation. Dashed line represents results from Niewoehner and
Kleinerman (20). See text for details.
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K, µ, and Poisson ratio.
We determined from the experiments the values of K and µ that are
required to describe the lung parenchyma as a linear elastic continuum.
Each constant was evaluated at Ptp values of 4, 8, 12, and 16 cmH2O. K, a measure of the resistance of the lung in response to a uniform expansion, was calculated from the formula K = V(P/V), where P/V was the slope of the small P-V loop and
V was the lung volume at the test Ptp. Figure
4 shows the values of K plotted vs. age
at the constant test Ptp values of 4, 8, 12, and 16 cmH2O.
Linear regression analyses of the data showed that, at each test Ptp, K
increased significantly (P < 0.05) with age. The rate
of the increase in K with age increased with the increase in Ptp, with
values of 0.25, 0.65, 1.28, and 1.71 cmH2O/yr at the test
Ptp values of 4, 8, 12, and 16 cmH2O, respectively.
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Fig. 4.
Bulk modulus (K, cmH2O) vs. age (yr) at
constant Ptp values of 4, 8, 12, and 16 cmH2O. Note the
significant increase in K with age as shown by linear regression
equations at all Ptp values.
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The slope of the L-w curve of the indentation
tests was used to calculate µ/(1
) from the elasticity
solution for the indentation of an elastic half-space with a rigid
cylindrical rod (15)
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(1)
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Here µ is the shear modulus of the lung parenchyma, is the
Poisson ratio, and d is the rod diameter. From elasticity
theory, µ is related to K and as follows
![&mgr;=3K(<IT>1−2&sfgr;</IT>)<IT>/</IT>[<IT>2</IT>(<IT>1+&sfgr;</IT>)]](/content/vol89/issue1/fulltext/163/img002.gif)
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(2)
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Thus with the values of K from the incremental P-V test
(Fig. 4), values of µ and were computed from Eqs. 1 and 2. Figure 5 shows values
of µ vs. age at constant test Ptp values of 4, 8, 12, and 16 cmH2O. Linear regression analyses of the data showed that µ increased significantly (P < 0.05) with age at all
test Ptp values except 4 cmH2O. The corresponding values of
are shown in Fig. 6. Note that increased significantly (P < 0.05) with age at all Ptp
values except 16 cmH2O.
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Fig. 5.
Shear modulus (µ, cmH2O) vs. age (yr) at
constant Ptp values of 4, 8, 12, and 16 cmH2O. Note the
significant increase in µ with age as shown by linear regression
equations at all Ptp values except 4 cmH2O.
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Fig. 6.
Poisson ratio () vs. age (yr) at constant Ptp values
of 4, 8, 12, and 16 cmH2O. Note the significant increase in
with age as shown by linear regression equations at all Ptp values
except 16 cmH2O.
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Figure 7 shows values of K, µ, and plotted vs. Ptp at ages of 20, 40, and 60 yr as determined from the
linear regression equations shown in Figs. 4-6. Like the P-V
behavior (Fig. 2), both K and µ increased with age at each Ptp
measured. However, the fractional increase in K was greater than that
in µ at each Ptp, resulting in an increase in with age at each
Ptp value. Thus there was a tendency of the lung parenchyma to become
more like an incompressible material ( = 0.5) with
increasing age; that is, the lung became more resistant to uniform
expansion in relation to its resistance to shear.
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Fig. 7.
Values of K, µ, and vs. Ptp at 20, 40, and 60 yr.
Values were computed from linear regression equations shown in Figs.
4-6.
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DISCUSSION |
The major finding of this study is that both K and µ of human
lungs increase with age at constant Ptp. This indicates that the lung
parenchyma becomes more resistant to both uniform expansion and shear
deformation with increasing age.
Method.
We used the local loops of the P-V curve rather than the slope of the
deflation P-V curve to determine K. This resulted in values of
K (reciprocal of the specific compliance) that were larger than those
based on the slope of the deflation P-V curve (Fig. 2). One reason for
using the small P-V loops was the absence of any measurable hysteresis,
a behavior expected of an ideal elastic material. Also, the small
perturbation in P-V behavior satisfied the assumption of elasticity
theory that stresses and strains imposed on an initial isotropic state
were linearly related.
We used the indentation test on the lung surface to determine
µ/(1), from which both µ and can be calculated from
Eqs. 1 and 2 if K is known. The elasticity
solution of the indentation test (Eq. 1) assumed that the
lung surface was flat with boundaries that were an infinite distance
from the site of indentation. This assumption was closely approached
because the rod diameter was small compared with the distance between
the rod and the lung boundary. We assumed that the lung was a
homogeneous elastic material and neglected the effect of the pleural
membrane in resisting the force of indentation into the lung. This
effect was minimized by using a large enough rod diameter
(9, 15, 18).
Comparison with previous results.
Elastic moduli measured in a variety of mammals (dog, pig, horse, and
rabbit) showed that K values equaled 4-6 Ptp and µ values were
0.7-0.9 Ptp in the Ptp range between 4 and 25 cmH2O
(9, 15, 25). The values of K and µ measured in human lungs in the present study were consistent with
this behavior for an age of ~20 yr (Fig. 7). As age increased above
20 yr, there was a trend toward greater values for K. These changes
with age were associated with a greater lung volume at each Ptp value
as age increased (Fig. 2), in agreement with previous studies using
isolated human lungs at autopsy (4, 7,
12) and with in vivo measurements in humans
(28). The increased lung volume at each Ptp with age is
consistent with an increase in lung tissue elastin and a constant collagen content with age (22). The latter result explains
why TLC did not increase with age (1).
Except for one subject (subject 19, Table 1) of age 10 yr,
all the lungs studied were in the adult age group (>17 yr). Thus the
age-related increases in elastic moduli measured in this study were
associated with the aging process that included both intrinsic and
extrinsic factors rather than with changes due to lung development. Thus extrinsic factors such as smoking and unknown disease on the
age-related change in the elastic moduli cannot be ruled out. The
effect of lung development on elastic moduli measured in the pig lung
between the ages of 12 h and 85 days showed higher K and µ values in the newborn compared with the 3- to 5-day-old lung and a
constant µ and a decreasing K as age increased from 5 to 85 days
(18). These changes with age due to lung development are
opposite to those observed in the present study.
Models relating the microstructural properties of lung parenchyma to
the macrostructural properties have shown that tension in the alveolar
walls is the major determinant of K and µ (11, 25, 26). Both tissue and surface forces
contribute to tension in alveolar walls. Surface forces that arise from
the alveolar air-liquid interface are modified by pulmonary surfactant
(23, 24). The contribution of tissue forces
to the elastic constants can be measured by studying the lung filled
with saline (8). Studies in rabbit lungs showed that an
increase in alveolar surface tension imposed by washing isolated lungs
with liquids of constant surface tensions caused a decrease in K and an
increase in µ (26).
Morphometric studies have shown that, at a constant Ptp, alveolar mean
linear intercept and mean alveolar diameter increase with age whereas
alveolar surface area decreases (8, 27). Thus
in the absence of any change in surface active properties of pulmonary
surfactant with age, the increase in K and µ with age might be
related to changes in alveolar configuration that result in changes in
surface forces. An increase in intrinsic tissue forces might also
contribute to the increase in K and µ with age. The increased tissue
elastin content with age (22) might contribute to the
intrinsic tissue force and the increase in K and µ with age. These
effects need to be evaluated in saline-filled lungs.
Summary.
The greater stiffness of lung parenchyma with increasing age as
measured by K and µ is consistent with the behavior found in many
body organs, such as systemic arteries (2). An increased K
has also been found in lungs with chronic obstructive pulmonary disease
and in emphysematous lungs with 1-antitrypsin deficiency (17). The increased K and µ of the lung with age implies
that deformation characteristics of structures embedded within the lung
parenchyma depend on age. Specific examples include the force interaction among lung parenchyma, blood vessels, and airways, and its
effects on perivascular interstitial pressure (14), blood
flow, and flow in airways (12). The physiological
effects of aging arising from these interactions need to be evaluated.
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ACKNOWLEDGEMENTS |
The experiments described in this communication were done between
1974 and 1981 at the Thoracic Disease Research Unit of the Mayo Clinic.
We thank the pathology department of the Mayo Clinic for providing the
lungs at autopsy.
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FOOTNOTES |
This research was supported by National Heart, Lung, and Blood
Institute Research Grants HL-21584, HL-18354, and HL-40362.
Address for reprint requests and other correspondence: S. J. Lai-Fook, Center for Biomedical Engineering, Wenner-Gren Research Laboratory, Univ. of Kentucky, Lexington, KY 40506-0070
(E-mail: laifook{at}pop.uky.edu).
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. §1734 solely to indicate this fact.
Received 10 December 1999; accepted in final form 10 March 2000.
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ABSTRACT
INTRODUCTION
