Effect of temperature on the biaxial mechanics of excised lung parenchyma of the dog JACK

C. DEBES

Department

AND

Y. C. FUNG

of AMES-Bioengineering,

University

DEBES, JACK C., AND Y. C. FUNG. Effect of temperature on the biaxial mechanics of excised lungparenchyma of the dog. J. Appl. Physiol. 73(3): 1171-1180, 1992.-The influence of temperature on the mechanical properties of excised saline-filled lung parenchyma of the dog was studied at low lung volume. The motivation of this study was to determine whether lung tissue material without the influence of surface tension undergoes a phase transition in the ZO-40°C range, as does synthetic elastin studied by Urry in 1984-1986. Dynamic biaxial and uniaxial tensile tests were done, and strain vs. Lagrangian stress curves were recorded during slow cooling and heating between 40 and 10°C. To emphasize the effects of elastin, strains (defined as stretch ratio minus one) were kept below 30%. A slight decrease in compliance occurred with cooling over the entire temperature range. This effect may be attributed to collagen. It was accompanied by a gradual increase in length as the tissue cooled, an effect that may be attributed to elastin. This process was partially reversible with reheating. However, this effect is in contrast with the sudden drastic change in mechanical properties of synthetic elastin described by Urry. Hysteresis, creep, and stress relaxation were small at these low strains. Possible causes of these effects are discussed.

lung; temperature;

elastin;

collagen;

compliance;

elasticity

ACCORDINGTO Otis (20)) studies on the elastic properties of the lung were first reported by Carson in 1820 (2), and hysteresis was first reported by Heynsius in 1882 (6). Since then, extensive studies have been done by many investigators on lung mechanics, and the roles played by the lung tissue and the surface tension at the gas-liquid interface have become more clear (3). The full structural mechanics, which should include a detailed account of how collagen and elastin fibers in the lung contribute to the mechanical properties of the lung tissue, still have not been worked out. Orsos (19) published striking photomicrographs of the structural fibers in the lung. The three-dimensional geometry of the lung microstructure has been quantified by Mercer and Crapo (17) and Oldmixon and Hoppin (18). The statistical distributions of the fiber width and curvature of collagen and elastin in alveolar walls and alveolar mouths have been measured (16,22), but the elastic moduli of these fibers in the lung are still unknown. Surveys of literature on the Young’s modulus of collagen fibers in various organs leave a margin of uncertainty amounting to two orders of magnitude. Similar uncertainty exists about elastin, which is important to the structural integrity of the lung. According to Reed et al. (2l), destruction of lung elastin causes failure of the alveolar walls, as in emphysema. By differential 0161-7567/92

of California,

San Diego, La Jolla, California

92093-0412

application of collagenase and elastase in hamster lung, Karlinsky et al. (13) showed that when the lung volume is small, elastin bears the major load of recoil in the pressure-volume relationship of excised lung. At larger lung volume, collagen takes on more load. In 1984-1986, Urry et al. (25-27) presented evidence that the mechanical properties of elastin change drastically around 25°C and that elastin is soluble in water below 20°C. According to Urry (25) On raising temperature aggregation occurs; and on standing, the aggregates settle to form a dense viscoelastic phase that is roughly 60% water by volume. The dense viscoelastic phase is called a coacervate and the process of coacervation is reversible. . . . Coacervation is considered to be the process of fiber formation, involving an inverse temperature transition wherein there is an increase in order, both intermolecularly and intramolecularly (with increasing temperature from below 20°C to body temperature).

When the temperature of Urry’s elastin is lowered from 40 to 2O”C, a sudden decrease in elastomeric force and turbidity, which is a measure of the extent of coacervation, occurs at ~25’C, as shown in Fig. 1. This is a remarkable observation. Our objective is to determine whether the elastin of the lung has a critical temperature in the IO-40°C range for mechanical property changes as in Urry’s elastin. Most investigations on the mechanical properties of the lungs in the past have been carried out at body temperature or room temperature. If the elastin in the lung is similar to the synthetic elastin used by Urry, then the existing data need to be reinterpreted. Karlinsky et al. (12) reported on the quasi-static properties of uniaxially deformed lung strips at various temperatures and saw no drastic change in the stress-strain relationship from 20 to 40°C for strains between 60 and 110% (strains corresponding to high lung volumes where forces due to collagen are dominant). Inoue et al. (11) investigated the temperature effects on rabbit lung mechanics by studying quasi-static pressure-volume relationships and reported no transition temperature for sudden mechanical property changes. We have made a detailed study of the mechanical properties of lung tissue at low lung volume to emphasize the role of elastin. We have eliminated surface tension to study the mechanics of the structural proteins alone. We have used excised specimens to remove the effects of large blood vessels, bronchi, and pleura. We have tested lung parenchyma in a biaxial stress state in our TRIAX testing machine (14, 30), because it is the

$2.00 Copyright 0 1992 the American Physiological

Society

1171

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1172

EFFECT

OF TEMPERATURE

ON LUNG

MECHANICS

0 0

80

c3

-6.0

-6.5 !

10

-

&

20

1

30

-

1

40

-

1

50

Temperature

-

I

60

-

1

=

70

! 0

8

80

(“C)

FIG. 2. Targeting method. A square target (1 X 1 cm2) was made in central region of each specimen. A target was defined by 4 wire markers made from 225pm-diam tinned copper wire. Wires, each -0.5 cm long, were bent in the middle at a right angle to an L shape. Four target markers were then pressed into surface of each specimen in a pattern that defined sides of a square.

-4-r IO

20

30

40

Temperature

50

60

I 70

.

fo 80

(“C)

1. Urry’s thermoelasticity data of a synthetic elastin. A: 20mrad y-irradiation cross-linked polypentapeptide coacervate (lefthand ordinate) and temperature profile for aggregation (right-b& o&inate) for the same polypentapeptide preparation before cross linking. B: fibrous elastin purified from bovine ligamenturn nuchae and temperature profile for aggregation of cu-elastin (right-hand ordinate) derived from the same bovine ligamenturn nuchae preparation. Note very large increase in natural logarithm of force (f) normalized with respect to temperature (T, OK), measured on a specimen held at constant length (X = 1.60) as temperature is raised from 20 to 40°C. This is the temperature range over which coacervation occurs and that has been shown to involve an increase in order, intramolecularly and intermolecularly, of polypeptide part of the system. Turbidity is measure of extent of coacervation. Low slope above 50°C has been taken to reflect large entropic component of elastomeric force. [Replotted from data by Urry (27).] FIG.

that strain range, then the biaxial testing would indeed yield the full three-dimensional stress-strain law (in this relatively small range of strain). METHOD

Specimen preparation. Atelectatic lungs were obtained from three mongrel dogs [25 t 5 (SD) kg body wt]. The animals were anesthetized with pentobarbital sodium, heparinized, and then killed by asphyxiation after 3 h of respiration on pure oxygen to obtain fully collapsed lungs. The chest was then opened along the mediasti1.3

only mode of testing in which we know how to assess stress and strain accurately with large deformations and “edge effects” on the specimen. The TRIAX testing machine allows large movement of the edges of the specimen and measures the strain in the central part of the specimen optically without touching, thus minimizing the edge effect. This method allows for a direct quantita1.o tive measure of stress and strain in the tissue. In the following, the experimental results on the LAMBDA vda stress-strain relationship of dog lung parenchyma de(dimsnslonlerr) rived from biaxial loading in the temperature range of FIG. 3. Validation of targeting method. Stretch ratio measured by IO-40°C are reported. For strains between 0 and 30%, video dimensional analyzer was compared with that measured in phothe stress-strain relationship is linear. Hence, if we can tomicrographs. The 2 methods yielded virtually identical values, with a assume that the stress-strain relationshin is isotrobic in correlation coefficient of R2 = 0.992. Error bars. SD: n = 3. Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (129.081.226.078) on January 17, 2019.

EFFECT

OF TEMPERATURE

ON LUNG

1173

MECHANICS

1. Summary of experimental protocol

TABLE

Temperature Run No.

Uniaxial

Paused Triangle

Biaxial

X

2 3 4 5 6 7

Unpaused Triangle

X X X

X X X

X

X X

X

g

600

1.1

I: 3it 400

a c 0 5!

1.05fi

100

200

300

Time

v

(8)

400500

Stretch

p--El-WE++--fil---/’ Strmr8

600

700

saw. The frozen sections were cut randomly into squares measuring -5.0 X 5.0 cm by use of a razor blade. After thawing, the specimens used in all the experiments had mean dimensions of 4.2 t 0.04 X 4.2 t 0.04 (SD) cm2 and a mean thickness of 0.36 t 0.08 (SD) cm. These dimensions were measured with the specimen resting on a glass plate by use of a tissue micrometer, without applied load but with the influence of gravity and the possibility of some shear between the specimen and the glass. This will be referred to as the “no-load” condition. To estimate the magnitude of distortion due to gravity and frictional shear between the specimen and the glass, the thickness of a specimen was measured in air (under the full influence of gravity) and then with the specimen submerged in saline (with a reduced normal force due to buoyancy). Because the specimen is already saline filled, submersion in saline should not cause further inflation of the tissue.

A I.152

200

300

Time

400500

(8)

600

P+-El-w

-El--

’

,o

l l

i a

h.1 .

= 0 '; f)

a

6001 :

. a

]

2 400 3i * . 200,

700

1.05 1

a

0

FIG. 4. Data from biaxial creep test performed at 20°C. A: x-axis data; B: y-axis data. Protocol described in text.

-100

0

100

200

300 flmm

num, and the lungs were excised and filled with isotonic saline to functional residual capacity (-20 ml/kg body wt) (28). This method of lung degassing leads to almost total collapse of the lungs. We chose this method over others, such as vacuum degassing through the airway, because it results in much less trapped gas in the peripheral tissue. The individual lobes of the lungs were then ligated with umbilical tape and slowly frozen to -2OOC to render the lung parenchyma stiff enough to be cut into specimens of desired dimensions. Yager (32) found, from the results of pressure-volume tests performed on salinefilled rabbit lungs, that a single freezing and thawing resulted in a 20-50% decrease in compliance. Repeated freezing and thawing cause further decrease in compliance. To minimize this, we were careful to freeze and thaw our lung specimens only once. The frozen lobes were then sectioned into slabs ~0.5 cm thick on a band

1.15

a

?

E100

. .

800,

-

1.2

Strm88

IOOO-

1

0

1200-'"--~1.25 a .

G a c 0 z

1.05z

0

X

a/24 8/24 918 918 9/22 9/22

Ratio

1.1

-100

Dois No.

X

1.15;

0

Creep Relaxation

X X X X

X

800

100

Constant

X

1.25

“;-

Variable

Ia

’ Strmtch ---a--B--e---~-

IOOOA "E

s z i

8001 600-

400500 (8)

a a

600

700

R8tlO

f St f.88

. a

l

. a 400 a a 200a -100

a

L 1.1

c 0 s

1.05i

0

10020

9 300 Imm

(8)

400500600

700

FIG. 5. Data from biaxial relaxation test performed at 20°C. A: xaxis data: B: v-axis data. Protocol described in text.

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1174

EFFECT

OF TEMPERATURE

A

100l

o-7

v

-0.05

,

-0.00

r

,

1,

0.05

,

0.10

STRAIN,

6

,

v

,

0.15

0.20

1

,

0.25

.j

0.30

hy - 1

1

00 -0.05

-0.00

0.05

0.10

STRAIN,

0.15

0.20

0.25

0.30

5 - 1

FIG. 6. Data from uniaxial test with a constant preload & = 120 N/m2 applied in the x-direction. A: cooling specimen; B: heating specimen. Temperature variation and protocol described in text.

The thickness of the specimen was measured at nine points. Measurements made in air yielded an average thickness of 4.105 t 0.325 (SD) mm, and those made in saline had an average thickness of 4.346 t 0.599 mm. Hence there was no statistically significant difference in thickness. Therefore it may be concluded that distortion due to gravity and frictional shear between the specimen and the glass is insignificant. This justifies considering B 1000

ON LUNG

MECHANICS

this to be the no-load condition. The axes of orientation of the lung and the lower and middle lobes were not differentiated. Vawter (28) showed that directional effects and variation of response between lobes are small. Each animal yielded one or more specimens. Strain measurement. A square target (- 1 X 1 cm2) was made on the center of each specimen by means of four wire markers made from 2%pm-diameter tinned copper wire. The wires, each -0.5 cm long, were bent in the middle at a right angle so that they formed an L shape. One leg of the L was pressed into the specimen perpendicular to the surface, leaving the other leg resting on the surface. Four markers defined the sides of a square (Fig. 2). The specimen was then mounted on the TRIAX testing machine. The distance between parallel target wires on each axis was measured by a video dimensional analyzer. The current distance divided by the initial distance at the zero-stress state is the stretch ratio (X). If the edges of the square are defined as the x- and y-axes and the square deforms into a rectangle without change of edge directions, then X is defined in the x- and y-directions. The strain e, is defined as X, - 1, and e, is defined as x - 1. To validate this method, the strains measured by the video dimensional analyzer were compared with the strains measured in photomicrographs. The two methods yielded virtually identical values for X with a correlation coefficient of R 2 = 0.992 (Fig. 3). Testing machine. The TRIAX testing machine that we used is an improved version of that used by Yager (32) and Zeng et al. (33). Briefly, the specimen is bathed in a basin of physiological saline that is circulated through a thermal regulator. Each edge of the specimen is stapled to five threads, which are attached to a force transducer, which is controlled to move horizontally at controlled rates. The deformation of the central region of the specimen marked by four target wires is monitored by a pair of TV cameras, one for the x-direction and one for the y-

1000 900

T

Oi -0.05-0.00

0.05 0.10 STRAIN,,,

0.15 -1

0.20

0.25

00 -0.05-0.00

0.30

D

1000

0.05 0.10 STRAIN,

0.15 &.-I

0.20

0.25

0.30

1000 900 800

000 4OOC 30°C

700

20°C

600

FIG. 7. Data from biaxial test. A: x-axis data (cooling specimen); B: x-axis data (heating specimen); C: y-axis data (cooling specimen); D: y-axis data (heating specimen). Temperature variation and protocol described in text.

700 10°C

$z

500

600

g 2 500 5; z 400

400 300

300

200 _i100

00

-0.05-0.000.05

c

0.10 STRAIN.

0.15 0.20 b,- 1

0.25

0.30

.OO 0.05

0.10 STRAIN.

0.20 0.15 h- 1

0.25

0.30

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EFFECT

OF

TEMPERATURE

ON

LUNG

1175

MECHANICS

4 A

HUN

n

RUN6

5

0 W

0

10

8. Incremental elastic 13, vs. temperature for biaxial n = 39. FIG.

0

0

20

30

Temperature

0

40

(“C)

50

500

modulus [E/( 1 - v)], as defined in Eq. tests. Data are from both axes of 3 tests;

0 0

direction. Each edge can be operated in the force mode, controlling the force acting on that edge, or the deformation mode, controlling the strain rate. The operation is computer controlled; data are collected, analyzed, and plotted on-line or later via a computer. Preconditioning the specimens and experimental approximation of zero-stress state. It is well known that the zero-stress state of lung tissue is unique and stable but difficult to control, because lung tissue is very soft at zero stress. We can measure the specimen thickness and cross-sectional area at a no-load state mentioned earlier, but the unloaded specimen, resting on a glass plate, may be subjected to a set of self-equilibrating frictional forces between the plate and the specimen. Complete assurance of the absence of this frictional force is virtually impossible. Yet, for the description of the constitutive equation, we want to refer the stress and strain to the zero-stress state. Because the no-load state is the closest approximation to zero stress available, we use it as our reference state for calculating strain. Furthermore the process of specimen preparation disturbs the tissue from its homeostatic condition. To obtain a repeatable stress-strain relationship, the tissue must be preconditioned by imposing a cyclic loading-unloading process on it until a new homeostasis is established. According to Fung (5), preconditioning occurs because the internal structure of the tissue changes with repeated cycling until eventually a steady state is reached at which no further change will occur unless the cycling routine is changed. A repeatable stress-strain relationship is necessary to establish a well-defined constitutive equation. For the biaxial tests on lung specimens, we preconditioned them by cycling them between an isotropic biaxial stress of oXX= a,, = 122 +- 5 and 543 t 65 (SD) N/m2 (the same stress range at which they were tested) in a 20°C bath for 256 cycles in 30 min while the specimen reached thermal equilibrium with its environ3 0.20

G G 2

Slope Gives Thermal Expansion Coe lfficient

0

a a=

1

2.21 x lo3

FIG.

10.

temperature

10

Incremental for uniaxial

20

(“0

40

50

Young’s modulus (E), as defined in Eq. 16, vs. tests. Data are from 1 test; n = 7.

ment. All experimental stress-strain data presented below refer to the no-load state of the tissue at 20°C. Dynamic testing. In biaxial dynamic testing, the loads were applied according to four protocols: 1) from time 0.0 to 9.5 s, a.n increase in oXX= Q (where CTis stress) at a uniform rate from a preload of 122 t 5 to 534 t 65 (SD) N/m’, a decrease at the same rate back to the preload stress from 9.5 to 19 s, and then cycling at the same rate continuously thereafter; 2) introduction of a 13-s pause into protocol 1 at the preload stress level in every cycle; 3) a step change in oXX= a,, from the preload to 894 t 102 (SD) N/ m2 at time 0; and 4) a step change in A, = A, from 1.032 t 0.001 to 1.184 t 0.052 (SD) at time 0. If the protocols above were changed so that u,, = a constant = the prestress, then the test is said to be uniaxial. Both biaxial and uniaxial tests were performed according to protocols 1 and 2; only biaxial tests were performed according to protocols 3 and 4 (Table 1). Protocols 1 and 2 yield information on the viscoelastic properties of the tissue. Comparison of hysteresis data from protocols 1 and 2 is an indication of the magnitude of the viscous effect. Furthermore, protocol 3 is a measure of viscoelastic creep, and protocol 4 is a measure of viscoelastic relaxation. Lung tissue was tested in a temperature-controlled bath of isotonic saline. In a constant-temperature experiment, the specimen was held at 22.5 t 0.5”C. In vari-

80 g CT v, E Ego cn-

0 40

:

_’ 20 0

RUN4

ox{

0

0.1

STRAIN,k -20

-10

0

Temperature

10

- 20 PC)

20

30

9. Strain at zero stress, as defined in Eq. 14, vs. temperature for biaxial tests. Slope equals coefficient of thermal expansion. Data are from both axes of 3 tests: n = 39. FIG.

30

Temperature

0.2

0.3

0.4

- 1

FIG. 11. Stress-strain curve of elastin. Material is canine ligamenturn nuchae, which contains a small amount of collagen that was denatured by heating at 100°C for 4 h. Such heating does not change mechanical properties of elastin. Loading was uniaxial. Curves show that compliance of elastin is unchanged by freezing to -20°C and thawing. Tests were performed at 20°C.

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1176

EFFECT

OF

TEMPERATT

JRE

ON

LU NG

20-

z E Va

1 exx = - ( Oxx- zwyy) + CY(T- T,) E

15II URRY’S ELASTIN OUR LUNG TISSUE DATA: x 2 cm2 LUNG TISSUE

IO-

E E

MECHANICS

50 0

I

I

20

40 TEMPERATURE

-

A

3 cm2LUNG

TISSUE

0

4 cm2LUNG

TISSUE

1

60

(

a,, = E 1 _ u2 (eYY+ ye,n) - g

(“C)

exx =X,-l, eyy=X,-l The faces of the tissue slab are stress free 0zz = (72x= (7 Z 0 ZY

The load is applied in the X- and y-directions the stress is uniform in the central region a,, = constant,

(exx+ ueyy) -c

1

80

able-temperature experiments, specimens were loaded onto the testing machine at 20°C and then heated to 4O”C, at which point data acquisition commenced and continued while the specimens were gradually cooled to 10°C and then reheated to 40°C. The temperature was changed slowly (SO min between each 10°C increment). The mean total time for the variable-temperature experiments, from the beginning of cycling to the end of the experiment, was 4.5 t 0.4 (SD) h. Incremental thermoelasticity laws. To describe the experimental results mathematically, we make use of features shown in Figs. 4-7: at any given temperature the stress-strain relationship is approximately linear, the hysteresis loop is small, and creep and stress relaxation are negligible in the range of strains chosen for this investigation. This implies that the viscoelastic effects may be ignored, and the quasi-steady constitutive equation given in Refs. 7 and 8 is applicable in the linearized form. The nonlinear constitutive equation used by Vawter et al. (Z&30), Fung et al. (8), Yager (32), and Zeng et al. (33) for the lung tissue is greatly simplified when linearized. At constant temperature the constitutive equation in Refs. 7 and 8 is expressed in terms of the strain-energy function. Generalization to variable temperature can be done by replacing the strain energy with Helmholtz free energy (Ref. 4, p. 387). On linearizing the nonlinear law for small strain, we note that no distinction needs to be made between Green’s and Cauchy’s strains or among and Cauchy’s stresses. The Lagrange’s, Kirchhoff’s, stress-strain relationship is linearized into the DuhamelNeumann law (Ref. 4, p. 354, 385). Let X, y, and z be a rectangular Cartesian frame of reference with the z-axis perpendicular to the plane of the tissue. Let aii be the stresses, eGbe the strains, and Xi be the stretch ratio. Then

u

(

where E is the incremental Young’s modulus, u is the Poisson’s ratio, a is the coefficient of thermal expansion, T is the temperature, and T, is a reference temperature. An isotropic form is assumed in Eqs. 4 and 5 because the lung tissue structure has no apparent preferred direction. A detailed discussion of the isotropy question based on experimental data is given by Vawter et al. (29). In the particular case of a “uniaxial” experiment in which 0

(6)

-uexx + a( 1 + u)(T - T,)

(7)

XX

a,,

Eqs. 4 and 5 are simplified to e

= YY

and

xx = E exx - cxE (T - T,)

(8)

CJ

In uniaxial experiments with a constant tare a,, = giy, then from Eqs. 4 and 5

~ ---_

I

1

I

increases

temperature

decreases

1

Fx=Fy Rate

temperature

I

1

1

1

1

=0

of temperature

changes

35”C/min

(I) (2) only, and

oxy = 0

(3) If Ey. 2 is assumed to be true throughout the specimen, the Duhamel-Neumann law is reduced to the planestress case (Ref. 4, p. 233, 354) XX

or

CJ xx= +

FIG. 12. Force exerted by a strip of uniaxially extended synthetic elastin (X = 1.60) vs. temperature, as reported by Urry (27), compared with force exerted by uniaxially extended lung specimen (X = 1.20) vs. temperature.

o- = constant,

(4)

1 eY Y = - ( a,, - ucrxx)+ CY(T- T,) E

Q800 0.75 0 4

8

12

I6

20

Tempsroture

24

28

32

36

40

(*Cl

FIG. 13. Variation of equilibrium dimensions I, and ZY in x- and ydirections under two cycles of rapidly changing temperature in rabbit skin when forces F, and FY were zero. [From Lanir and Fung (14).]

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EFFECT

OF

TEMPERATURE

1 - v2 + CT&+ a(1 + v)(T - T,)

e, = -ve,

E

(10)

to Eqs. 1, 5, 8, and 10, then, at constant

Kkx

= E

(uniaxial

tem-

loading)

n

(10

E

6a &I:=iz

(isotropic

biaxial

loading)

CT, + cu(T - 20) (12) E where (T - 20) is the change in temperature from 20°C. The material constants E/(1 - v) and a! are identified first for each isothermal curve by fitting the experimental data with regression lines by the method of least squares. Then the values of E/(1 - v) from all the biaxial tests are plotted against temperature, as shown in Fig. 8. A least-squares fit yields E = a, T + a,

Biaxial and unianial tests. Typical data on creep at constant stress are shown in Fig. 4. Typical data on stress relaxation at constant stretch are shown in Fig. 5. Typical results of uniaxial and biaxial experiments are shown in Figs. 6 and 7, respectively. At constant temperature, our results show. that the mechanical behavior of the lung tissue does not change significantly as a function of time during biaxial cycling over the course of 2.7 h. Thus it may be assumed that the changes in mechanical behavior observed in the variabletemperature experiments are due to the effects of temperature and not of time. The results of biaxial creep and relaxation tests performed at 20°C shown in Figs. 4 and 5 indicate that creep and relaxation are negligible in the range of strain in our experiments. The stress-strain loops are plotted in Figs. 6 and 7 for various temperatures between 40 and 10°C in 10°C decre-

; hy = 1.257

1177

MECHANICS

l-v 0 x- I) = -

RESULTS

xx = 1.810

LUNG

ments during cooling and 10°C increments during reheating. These plots show a gradual shift of the u vs. e curves to the right with cooling from 40 to 10°C and a gradual return to the left from 10 to 40°C with reheating. This represents a reversible thermally induced increase in length that occurs with cooling of the tissue. When the results of the unpaused triangle forcing function are compared with that of the paused triangle forcing function, we find no significant difference. In the biaxial experiments with a= = a,, Eq. 4 becomes

(9)

%x = E e, + z$,, - E ar(T - T,) According perature

ON

l-v

a, = -4.371 t 14.45 (SE) N/m2

(13)

a, = 3,446 t 417.1 (SE) N/m2 The stretch ratio at zero stress is, from Eq. 12 (14) x0 = a(T - 20) + 1 A least-squares fit of the data on X, as a function of T (Fig. 9) yields the dimensionless coefficient of thermal expansion

-s-s10 --

I ? * III ----v----*----w1. -- ----w-----------j

11

,.

T, ., ----==a

.,

:

1L

:

II

1,

,*

,,

,

----------_--------

I,

I,

r

f-------+-----

4 -h, = 1.649 ; hy = 1.276

I,

,1

6 --

FIG. 14. Variation of relaxed stresses under rapidly changing temperature for different values of stretch ratios in rabbit skin. A, and AY, principal stretch ratios; F, and F,,, forces in x- and y-directions, respectively. [ Replotted from data by Lanir and Fung (14).]

-Z,

---2 --

2.0 -h, = 1.258 ; ky = 1.13610 A

1

12 1

&

14

1*,,

16

1.0 -18

I

20 L

-,

TEMPERATURE

-

10 A (“C)

I

12 IL

14 II

16 11’

18

14

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1178

EFFECT

OF

TEMPERATURE

= -2.213 x 1O-3t 7.790 x 1O-4 (SE)

(15) Equation I3 shows that, on average, there is a 4.0% increase in the elastic modulus from 40 to 10°C. A onetailed t test shows that a, in Eq. 13 is not significantly less than zero. If, however, data from a given axis of an individual biaxial test are treated separately, the slope of the E/(1 - Y) vs. T curve is significantly less than zero at P = a

0.025. Equation

14 shows that, on average, there is a 6.9% increase in X, from 40 to 10°C. A one-tailed t test shows that cy in Eq. 15 is significantly less than zero at P = 0.005.

In a uniaxial experiment, axr was fixed at the preload value 0: = 120 N/m2 and Eq. 10 is reduced to (AY-

- 1 1) -E%Y

+ cr(T - 20) E 0%

(16)

The experimental values of E are plotted against temperature in Fig. 10. A least-squares fit yields E = b,T -t- b,

k 1.127 (SE) N/m2 b0 = 1,724 t 32.73 (SE)N/m2

b 1 = -3.246

(17)

17 shows a 6.1% increase in E from 40 to t test shows that b, in Eq. 17is significantly less than zero at P = 0.025. Comparison of Eqs. 13 and 17yields Y = 0.51 within the strain and temperature ranges we tested. If the standard errors in Eqs. I3 and 17 are considered in this calculation of V, it is seen not to be statistically significantly >0.50. This indicates that the lung tissue behaved nearly incompressibly in these low-strain tests. By Eq. 17, the uniaxial test gives a value of a = -1.503 X 10w3.A two-tailed t test shows that this value is not significantly different from the value for a! in Eq. 15, which was determined from the three biaxial tests. Substitution of v = 0.50 and Eq. 17 into Eq. 16 shows a 5.2% increase in X0 in the y-axis of the uniaxial test from Equation

10°C. A one-tailed

40to

1o*c*

DISCUSSION

Advantages of biaxial testing over pressure-volume measurements. The merit of the two experiments can be com-

pared relative to the objective of this study, which is to assess the thermoelastic properties of lung tissue in terms of the principal stress and strain components. From the pressure-volume data, one may obtain the volume expansion ratio, which is the third invariant of the deformation tensor, but it does not give information on the individual components of the strain tensor. To correlate strains with stresses, we need data on stress distribution. The evaluation of stresses from pressure-volume data presents further complications. The tissue stress in the lung is not equal to the pulmonary gas pressure. For a given inflation pressure, the stress in lung parenchyma is nonuniform in the lung and depends on lung geometry. Furthermore the contribution of the pleura must be accounted for. Studies by Hajji et al. (9), which have compared the tension-area curve of the pleural membrane with the pressure-volume curve of an

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intact lobe, indicate that the pleural membrane contributes ~20% of the work done by the lung during deflation. Hence extraction of information on stress in the lung from pressure-volume data is not simple. Effect of freezing on elastin. If freezing and thawing of elastin do not change its mechanical properties, then freezing and thawing of lung tissue should not affect the interpretations of our data, because the objective of our research is to study the mechanics of lung elastin. Although the overall compliance of the lung tissue appears to be changed by freezing (32), the mechanical properties of elastin itself do not. To verify this, we prepared a specimen of elastin from canine ligamenturn nuchae by heating at lOO”C, according to the method described by Fung (5, p. 192). Using one axis of the TRIAX testing machine, we tested the elastin specimen uniaxially at 2O*C. Then we removed the specimen from the testing environment and froze it slowly to -2OOC. The specimen was then removed from the freezer, thawed to 2O”C, and retested. As shown in Fig. 11, we found no significant change in the compliance of the ligamenturn nuchae caused by freezing and thawing. Isotropy. The assumption of isotropy was used in the analysis of experimental data. However, in Fig. 7 the data from the y-axis of the testing machine display a slightly more compliant behavior with less hysteresis than the data from the x-axis. This same anisotropy is present in all the biaxial experimental results; i.e., the y-axis data consistently appear slightly more compliant with less hysteresis than the x-axis data. Because the specimens were randomly cut and randomly oriented on the testing machine and because lung tissue has been shown by Vawter (28) to behave with in-plane isotropy, it may be deduced that this slight apparent anisotropy is due to the testing apparatus and not to the actual test specimens. The stress and strain levels studied in these experiments are at the lower limit of the mechanical and optical capabilities of the testing machine. Thus it is plausible that the testing apparatus does not behave equally in the xand y-directions at very low levels of stress and strain. Agreement and disagreement with Urry’s data. We found that the coefficient of thermal expansion of the lung tissue is negative. This may be attributed to the decoacervation of the elastin fibers at lower temperature, as described by Urry (25-27). On the other hand, we found that the lung displays a gradual change in mechanical behavior over the entire 40 to 10°C temperature range. This result is in contrast with Urry’s data on the synthetic polypentapeptide of elastin (L-Vail-L-ProlGly3-L-Va14-Gly5), and of ac-elastin, both of which show a sudden and drastic phase transition at 20-25*C. Furthermore the lung tissue stiffens (Young’s modulus increases) with lowering of temperature, whereas the two elastins named above soften with the phase transition at lower temperature. Thus the lung tissue does not show the same phase transition described by Urry. Of course, we cannot directly equate the properties of the lung parenchyma with those of elastin. The elastic property of the lung tissue depends partly on the structure of the alveoli and alveolar ducts and partly on the elasticity of the structural materials, especially collagen and elastin.

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EFFECT

OF

TEMPERATURE

Stamenovic and Wilson (23) presented a strain energy function for lung tissue in terms of structural and material factors on the basis of an alveolar model proposed by Wilson and Bachofen (31). Fung (6) presented another model of the alveoli and alveolar ducts and used it to derive the elastic moduli of lung tissue (7) on the basis of the morphometric data of collagen and elastin presented in Refs. 16 and 22. However, in both Refs. 23 and 18, the thermoelastic law of elastin and collagen were hypothetical and the temperature effect was not considered. Hence we do not have a validated theory to separate the structural and material properties and cannot infer directly that the lung parenchyma elasticity is that of pulmonary elastin. However, the elasticity of the lung tissue and that of elastin are closely related. If the pulmonary elastin does have a phase change around 25°C with a large drop in turbidity below the critical temperature, that feature should be detectable in the thermoelastic behavior of the lung parenchyma. The difference between the thermoelastic characteristics of the elastin investigated by Urry and those of our lung tissue studies is illustrated in Fig. 12. Urry (25) performed a uniaxial test on a strip of polypentapeptide of elastin, which was held at a constant length (X = 1.60). He plotted the force exerted by the strip against temperature between 70 and 20°C but did not report the crosssectional area of the specimen; thus it is not possible to compute stress. To compare our uniaxial test of lung with Urry’s test, we have plotted in Fig. 12 the force exerted by lung specimens with various cross sections at a range of temperatures between 40 and 10°C by use of Eq. 16, arbitrarily choosing X, = 1.20, because our lung data do not include strains as high as Urry’s X = 1.60. The qualitative difference is evident. However, Urry also notes that some other forms of elastin, such as tropoelastin, undergo a more gradual phase transition (e.g., 2050°C). The differences between the thermoelastic behavior of our lung and that of Urry’s synthetic polypentapeptide elastin may be due to a difference in the lung’s elastin. However, the exact molecular structure of lung elastin has yet to be determined. It is also possible that the role of elastin in the lung differs from that of Urry’s simple uniaxially tested specimens because of the complex microstructure of the lung, and therefore elastin’s thermoelastic contribution to the overall behavior of lung parenchyma appears attenuated. Although verification of these hypotheses may be difficult, this is an area that deserves further study. Comparison with collagen properties. Apter’s (1) data on uniaxial extension of pure collagen show an increase in elastic modulus of ~5% with cooling from 40 to 10°C. By comparison, we found a 6.1% increase in elastic modulus of lung tissue with cooling from 40 to 10°C in our uniaxial tests. Thus it appears possible that the change of elastic modulus of the lung may be attributed to collagen. Negative thermal expansion coefficient of skin. Skin, like lung, is largely composed of collagen and elastin. Experiments done by Lanir and Fung (14, 15) on rabbit skin also indicate a negative thermal expansion coefficient (Fig. 13), which, however, is not a constant during ranid thermal cvcline. Another wav to observe this same

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MECHANICS

effect is to plot the force exerted by a specimen held at a constant length at various temperatures. Figure 14 shows the data of Lanir and Fung (15) on skin held at various fixed values of X. In the case of skin, df/dT > 0 for small values of X, whereas df/dT < 0 for large values of X, where f is force. This may be compared with our data shown in Fig. 11, which show Urry’s data at X = 1.60 and our data at X = 1.20. According to Treolar (24), this behavior is similar to that of rubber. Conclusions. The results of these experiments lead us to speculate that both elastin and collagen may play a role in the mechanical properties of the lung at low lung volumes. The collagen and elastin fibers of the alveolar wall are comparable in diameter, curvature, and number (22). The stress-strain relationship of collagen is highly nonlinear; that of elastin is linear. For the evaluation of the mechanical properties of the lung, the information missing is the zero-stress state of these fibers relative to the zero-stress state of the lung parenchyma and the material constants of these fibers in the lung. Future experiments should address these questions. The practical knowledge gained from these experiments that is of interest to investigators of biomechanics is that the lung does not have a critical temperature in the IO-40°C range for mechanical property changes similar to those of Urry’s elastin. Instead there is a gradual change according to Eqs. 13 and 14, where, with cooling from body temperature to room temperature (25”C), there is only a 1.6% increase in elastic modulus and only 2.8% thermal expansion in biaxially loaded saline-filled lung parenchyma at strains ~30%. This implies that biomechanical studies performed on lung tissue at room temperature may be considered to be very close approximations to those performed at physiological temperature. The technical assistance of Eugene Mead and Eric Nakakura is gratefully acknowledged. This study was supported by National Science Foundation Grant BCS 89-17576 and National Heart, Lung, and Blood Institute Research Grant HL-26647 and Training Grant HL-07089. Address reprint requests to J. C. Debes. Received

6 March

1991; accepted

in final

form

21 April

1992.

REFERENCES 1. APTER, J. T. Influence of composition on thermal properties of tissues. In: Biomechunics: Its Foundations and Objectives, edited by Y. C. Fung. Englewood Cliffs, NJ: Prentice-Hall, 1972, p. 217-235. 2. CARSON, J. On the elasticity of the lungs. Philos. Trans. R. Sot. Ser. v 110: 29-44, 1820. 3. CLEMENTS, J. A. Functions of the alveolar lining. Am. Rev. Respir. Dis. 115: 67-71, 1977. 4. FUNG, Y. C. Foundations of Solid Mechanics. Englewood Cliffs, NJ: Prentice-Hall, 1965. 5. FUNG, Y. C. Biomechanics: Mechanical Properties of Living Tissue. New York: Springer-Verlag, 1981. 6. FUNG, Y. C. A model of the lung structure and its validation. J. Appl. Physiol. 64: 2132-2141, 1988. 7. FUNG, Y. C. Biomechanics: Motion, Flow, Stress, and Growth. New York: Springer-Verlag, 1990. 8. FUNG, Y. C., P. TONG, AND P. PATTITUCCI. Stress and strain in the lung. ASCE J. Eng. Mech. Div. 104(EMI): 201-223, 1978. 9. HAJJI, M. A., T. A. WILSON, AND S. J. LAI-FOOK. Improved measurements on shear modulus and pleural membrane tension of the lung. J. Appl. Physiol. 47: 175-181, 1979. A. Ueber die Grosse des negativen Drucks in Thorax 10. HEYNSIUM, beim ruhigen Athmen. Arch. Ges. Physiol. 29: 265-310, 1882.

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H., C. INOUE, AND J. HILDEBRANDT. on lung mechanics in air- and liquid-filled

11. INOUE,

Physiol. 53: 567-575, 12. KARLINSKY, J. B.,

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Temperature effects rabbit lungs. J. Appl.

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J. T. BOWERS III, J. V. FREDE?TE, AND J. EVANS. Thermoelastic properties of uniaxially deformed lung strips. J. Appl. Physiol. 58: 459-467, 1985. 13. KARLINSKY, J. B., S. L. SNIDER, C. FRANZBLAU, P. J. STONE, AND F. G. HOPPIN. In vitro effects of elastase and collagenase on mechanical properties of hamster lungs. Am. Reu. Respir. Dis. 113: 769-777,1976. 14.

LANIR, Y., AND Y. C. FUNG. Two-dimensional mechanical properties of rabbit skin. I. Experimental system. J. Biomech. 7: 29-34,

15.

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T., Y. C. FUNG, AND S. S. SOBIN. Collagen and elastin fibers in human pulmonary alveolar mouths and ducts. J. Appl.

Physiol. 63: 1185-l 194, 1987. 17. MERCER, R. R., AND J. D. C&PO. Spatial distribution of collagen and elastin fibers in the lungs. J. Appl. Physiol. 69: 756-765, 1990. 18. OLDMIXON, E. H., AND F. G. HOPPIN, JR. Distribution of elastin and collagen in canine lung alveolar parenchyma. J. Appl. Physiol. 67: 1941-1949,1989. 19. ORSOS, F. The frameworks of the lung and their physiological and pathological significance. Beitr. Klin. Tuberk. Spezif. Tuberk. Forsch. 87: 568-609, 1936. 20. OTIS, A. B. History of respiratory mechanics. In: Handbook of Physiology. The Respiratory System. Mechanics of Breathing. Bethesda, MD: Am. Physiol. Sot., 1986, sect. 3, vol. III, pt. 1, p. 1-12. 21. REED, W. B., R. E. HOROWITZ, AND P. BEIGHTON. Acquired cutis laxa: primary generalized elastolysis. Arch. Dermatol. 103: 661-669, 1971.

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S. S., Y. C. FUNG, AND H. M. TREMER. Collagen and elastin fibers in human pulmonary alveolar walls. J. Appl. Physiol. 64:

22. SOBIN,

1659-1675,1988. 23. STAMENOVIC,

D., AND T. A. WILSON. A strain energy function for lung parenchyma. J. Biomech. Eng. 107: 81-86, 1985. 24. TREOLAR, L. R. G. Elasticity of network of long chain molecules. I. Trans. 25. URRY,

Farad.

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D. W. Protein elasticity based on conformations of sequential polypeptides: the biological elastic fiber. J. Protein Chem. 3:

403-436,1985. 26. URRY, D. W.

Elasticity of the polypentapeptide of elastin due to a regular, nonrandom dynamic conformation: review of temperature studies. Biomol. Stereodyn. III Proc. 4th Conf. Biomol. Stereodyn. 1986, p. 173-196. 27. URRY, D. W., R. HENZE, R. HARRIE, AND K. PRASAD. Polypentapeptide of elastin: temperature dependence correlation of elastomeric force and dielectric permittivity. Biochem. Biophys. Res. Commun. 28. VAWTER,

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125: 1082-1088,1984.

D. L. Mechanics of Excised Lung Parenchyma (Ph.D. dissertation). La Jolla: University of California, San Diego, 1975. VAWTER, D. L., Y. C. FUNG, AND J. B. WEST. Elasticity of excised dog lung parenchyma. J. Appl. Physiol. 45: 261-269, 1978. VAWTER, D. L., Y. C. FUNG, AND J. B. WEST. Constitutive equation of lung tissue elasticity. J. Biomech. Eng. 101: 38-45, 1979. WILSON, T. A., AND H. BACHOFEN. A model for mechanical structure of alveolar duct. J. Appl. Physiol. 52: 1064-1070, 1982. YAGER, D. C. Mechanical Aspects of the Lung: Microstructure to Macrostructure (Ph.D. dissertation). La Jolla: University of California, San Diego, 1985. ZENG, Y. J., D. YAGER, AND Y. C. FUNG. Measurement of the mechanical properties of the human lung tissue. J. Biomech. Eng. 109: 169-174,

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