J Appl Physiol
89: 163–168, 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 2Mayo Clinic and Foundation, Rochester, Minnesota 55905
Received 10 December 1999; accepted in final form 10 March 2000
elastic properties; lung mechanics; interdependence
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 pressurevolume (P-V) test. To describe nonuniform lung behavior requires the knowledge of another constant such as
the shear modulus (␮), 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).
PROBLEMS OF NONUNIFORM LUNG
Address for reprint requests and other correspondence: S. J. LaiFook, Center for Biomedical Engineering, Wenner-Gren Research
Laboratory, Univ. of Kentucky, Lexington, KY 40506–0070 (E-mail:
[email protected]).
http://www.jap.org
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 ␮ to
age have been carried out in pig lungs with ages from
5 to 95 days (18). K decreased whereas ␮ 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 ␮ 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.
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 costs of publication of this article were defrayed in part by the
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8750-7587/00 $5.00 Copyright © 2000 the American Physiological Society
163
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Lai-Fook, Stephen J., and Robert E. Hyatt. Effects of
age on elastic moduli of human lungs. J Appl Physiol 89:
163–168, 2000.— 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.
164
ELASTIC MODULI OF HUMAN LUNGS
The following procedure was used to determine K and ␮
(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 ␮,
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.
RESULTS
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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
Table 1. Data on human lungs
Subject
Number
Age,
yr
Sex
Lung Mass, g
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
20
36
61
22
37
23
42
17
18
55
35
19
20
19
35
41
39
40
10
78
M
F
M
M
F
M
F
M
M
F
F
M
M
M
M
F
M
F
F
M
192
302
484
291
223
291
271
377
260
412
315
461
296
570
474
325
645
420
108
M, male; F, female; TLC, total lung capacity.
TLC,
ml
2,170
1,600
3,980
3,300
3,140
3,730
2,650
3,315
2,270
2,200
3,100
4,490
2,560
3,720
3,840
2,630
3,000
1,560
775
3,100
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.
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.
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
ELASTIC MODULI OF HUMAN LUNGS
165
(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 ⫻
10⫺6 age, r2 ⫽ 0.015, P ⫽ 0.6. The latter result is
consistent with that reported previously (20).
K, ␮, and Poisson ratio. We determined from the
experiments the values of K and ␮ 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
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.
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.
The slope of the L-w curve of the indentation tests
was used to calculate ␮/(1⫺␴) from the elasticity solution for the indentation of an elastic half-space with a
rigid cylindrical rod (15)
␮/(1 ⫺ ␴) ⫽ (L/w)/(2␲d)
(1)
Here ␮ is the shear modulus of the lung parenchyma, ␴
is the Poisson ratio, and d is the rod diameter. From
elasticity theory, ␮ is related to K and ␴ as follows
␮ ⫽ 3K(1 ⫺ 2␴)/[2(1 ⫹ ␴)]
Fig. 3. Values of ␣1 (log scale) vs. age (yr) computed from best fit of
equation Ptp ⫽ ␣1e␣2V 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.
(2)
Thus with the values of K from the incremental P-V
test (Fig. 4), values of ␮ and ␴ were computed from
Eqs. 1 and 2. Figure 5 shows values of ␮ vs. age at
constant test Ptp values of 4, 8, 12, and 16 cmH2O.
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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.
166
ELASTIC MODULI OF HUMAN LUNGS
DISCUSSION
Fig. 5. Shear modulus (␮, cmH2O) 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 4
cmH2O.
Linear regression analyses of the data showed that ␮
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.
Figure 7 shows values of K, ␮, 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 ␮ increased with
age at each Ptp measured. However, the fractional
increase in K was greater than that in ␮ 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.
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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The major finding of this study is that both K and ␮
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 ␮/(1⫺␴), from which both ␮ and ␴ can be
calculated from Eqs. 1 and 2 if K is known. The elas-
ELASTIC MODULI OF HUMAN LUNGS
ticity 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 ␮
values were 0.7– 0.9 Ptp in the Ptp range between 4
and 25 cmH2O (9, 15, 25). The values of K and ␮
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 ␮ values in the newborn compared with
the 3- to 5-day-old lung and a constant ␮ 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 ␮ (11, 25, 26). Both tissue
and surface forces contribute to tension in alveolar
walls. Surface forces that arise from the alveolar airliquid 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 ␮ (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 ␮ 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 ␮ with age. The increased tissue
elastin content with age (22) might contribute to the
intrinsic tissue force and the increase in K and ␮ 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 ␮ 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 ␣1antitrypsin deficiency (17). The increased K and ␮ 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
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Fig. 7. Values of K, ␮, and ␴ vs. Ptp at 20, 40, and 60 yr. Values were
computed from linear regression equations shown in Figs. 4–6.
167
168
ELASTIC MODULI OF HUMAN LUNGS
(12). The physiological effects of aging arising from
these interactions need to be evaluated.
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.
This research was supported by National Heart, Lung, and Blood
Institute Research Grants HL-21584, HL-18354, and HL-40362.
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