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J Appl Physiol 89: 163-168, 2000;
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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


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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 (Delta V/Delta 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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  		Table 1.   Data on human lungs



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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.

Each P-V curve was fitted to the relationship (20): Ptp = alpha 1ealpha 2V, which in linear form is ln Ptp = ln alpha 1 + alpha 2V. Figure 3 shows the values of alpha 1 plotted vs. age. Note that ln alpha 1, a measure of the elasticity of the lung, decreased significantly (P < 0.05) with increasing age: ln alpha 1 = -0.22 - 0.037 age, r2 = 0.59 (solid line, Fig. 3). This equation is comparable to that found previously (20): ln alpha 1 = -0.35 - 0.044 age (dotted line, Fig. 3). By contrast, alpha 2, a measure of the maximal lung volume, was uncorrelated with age: alpha 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).


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  		Fig. 3.   Values of alpha 1 (log scale) vs. age (yr) computed from best fit of equation Ptp = alpha 1ealpha 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.

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(Delta P/Delta V), where Delta P/Delta 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.

The slope of the L-w curve of the indentation tests was used to calculate µ/(1-sigma ) from the elasticity solution for the indentation of an elastic half-space with a rigid cylindrical rod (15)
&mgr;/(1−&sfgr;)=(<IT>L</IT><IT>/</IT><IT>w</IT>)<IT>/</IT>(<IT>2&pgr;</IT><IT>d</IT>) (1)
Here µ is the shear modulus of the lung parenchyma, sigma  is the Poisson ratio, and d is the rod diameter. From elasticity theory, µ is related to K and sigma  as follows
&mgr;=3K(<IT>1−2&sfgr;</IT>)<IT>/</IT>[<IT>2</IT>(<IT>1+&sfgr;</IT>)] (2)
Thus with the values of K from the incremental P-V test (Fig. 4), values of µ and sigma  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 sigma  are shown in Fig. 6. Note that sigma  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 (sigma ) vs. age (yr) at constant Ptp values of 4, 8, 12, and 16 cmH2O. Note the significant increase in sigma  with age as shown by linear regression equations at all Ptp values except 16 cmH2O.

Figure 7 shows values of K, µ, and sigma  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 sigma  with age at each Ptp value. Thus there was a tendency of the lung parenchyma to become more like an incompressible material (sigma  = 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 sigma  vs. Ptp at 20, 40, and 60 yr. Values were computed from linear regression equations shown in Figs. 4-6.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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-sigma ), from which both µ and sigma  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 alpha 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.


    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.


    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.


    REFERENCES
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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4.   Berend, N, Skoog C, and Thurlbeck WM. Pressure-volume characteristics of excised human lungs: effects of sex, age, and emphysema. J Appl Physiol 49: 558-565, 1980[Abstract/Free Full Text].

5.   Cotes, JE. Physiology of the aging lung. In: The Lung: Scientific Foundations (2nd ed), edited by Crystal RG, West JB, Barnes PJ, Cherniak NS, and Weibel ER.. New York: Raven, 1996, vol. 2, chapt. 168, p. 2193-2203.

6.   Ganesan, S, Rouch KE, and Lai-Fook SJ. A finite element analysis of the effects of the abdomen on regional lung expansion. Respir Physiol 99: 341-353, 1995[Web of Science][Medline].

7.   Gibson, GJ, Pride NB, O'Cain C, and Quagliato R. Sex and age differences in pulmonary mechanics in normal nonsmoking subjects. J Appl Physiol 41: 20-25, 1976[Abstract/Free Full Text].

8.   Haber, PS, Colebatch HJH, Ng CKY, and Greaves IA. Alveolar size as a determinant of pulmonary distensibility in mammalian lungs. J Appl Physiol 54: 837-845, 1983[Abstract/Free Full Text].

9.   Hajji, MA, Wilson TA, and Lai-Fook SJ. Improved measurements of shear modulus and pleural membrane tension of the lung. J Appl Physiol 47: 175-181, 1979[Abstract/Free Full Text].

10.   Hyde, DM, Robinson NE, Gillespie JR, and Tyler WS. Morphometry of the distal airspaces in lungs of aging dogs. J Appl Physiol 43: 86-91, 1977[Abstract/Free Full Text].

11.   Kimmel, E, and Budiansky B. Surface tension and the dodecahedral model for lung elasticity. J Biomech Eng 112: 160-167, 1990[Web of Science][Medline].

12.   Knudson, RJ, Clark DF, Kennedy TC, and Knudson DE. Effect of aging alone on mechanical properties of the normal adult human lung. J Appl Physiol 43: 1054-1062, 1977[Abstract/Free Full Text].

13.   Kuhn, C, III. Morphology of the aging lung. In: The Lung: Scientific Foundations (2nd ed), edited by Crystal RG, West JB, Barnes PJ, Cherniak NS, and Weibel ER.. New York: Raven, 1996, vol. 2, chapt. 167, p. 2187-2192.

14.   Lai-Fook, SJ. A continuum mechanics analysis of pulmonary vascular interdependence in isolated dog lobes. J Appl Physiol 46: 419-429, 1979[Abstract/Free Full Text].

15.   Lai-Fook, SJ, Wilson TA, Hyatt RE, and Rodarte JR. Elastic constants of inflated lobes of dog lungs. J Appl Physiol 40: 508-513, 1976[Abstract/Free Full Text].

16.   Liu, S, Margulies SS, and Wilson TA. Deformation of the dog lung in the chest wall. J Appl Physiol 68: 1979-1987, 1990[Abstract/Free Full Text].

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18.   Mansell, AL, Moalli RR, Calista CL, and Pipkin AC. Elastic moduli of lungs during postnatal development in the piglet. J Appl Physiol 67: 1422-1427, 1989[Abstract/Free Full Text].

19.   Mead, J, Takishima T, and Leith D. Stress distribution in lungs: a model of pulmonary elasticity. J Appl Physiol 28: 596-608, 1970[Free Full Text].

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21.   Pierce, JA, and Ebert RV. The elastic properties of the lung in the aged. J Lab Clin Med 51: 63-71, 1958[Web of Science][Medline].

22.   Pierce, JA, and Hocott JB. Studies on the collagen and elastin content of the human lung. J Clin Invest 39: 8-14, 1960.

23.   Schurch, S, Goerke J, and Clements JA. Direct determination of surface tension in the lung. Proc Natl Acad Sci USA 73: 4698-4702, 1976[Abstract/Free Full Text].

24.   Smith, JC, and Stamenovic D. Surface forces in lungs. I. Alveolar surface tension-lung volume relationships. J Appl Physiol 60: 1341-1350, 1986[Abstract/Free Full Text].

25.   Stamenovic, D. Micromechanical foundations of pulmonary elasticity. Physiol Rev 70: 1117-1134, 1990[Free Full Text].

26.   Stamenovic, D, and Smith JC. Surface forces in lungs. III. Alveolar surface tension and elastic properties of lung parenchyma. J Appl Physiol 60: 1358-1362, 1986[Abstract/Free Full Text].

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J APPL PHYSIOL 89(1):163-168
8570-7587/00 $5.00 Copyright © 2000 the American Physiological Society


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