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Surface tension at low lung volumes: Dependence on time and alveolar size
339
Respiration Physiology (1982) 48, 339-355 Elsevier Biomedical Press
SURFACE TENSION AT LOW LUNG VOLUMES: DEPENDENCE ON TIME AND ALVEOLAR SIZE
SAMUEL S C H U R C H Department of'Biophysics, Health Sciences Center, University oj Western Ontario, London, Canada N6A 5C1
Abstract. We measured surface tension in individual alveoli by observing the spreading properties of fluid droplets placed by micropipette on the alveolar surfaces. The test fluids were calibrated on monolayers of dipalmitoyl phosphatidylcholine spread at the air-saline interface of a captive bubble. The air bubble was floated by buoyancy against a ceiling of 0.5% agar. The bubble surface tension could be altered by inflating or deflating the bubble, and the value of the surface tension was determined by shape analysis for a sessile drop. Test fluid droplets were placed by micropipette onto the upper, flat bubble surface and the diameters of these droplets were measured with a microscope. In cat lungs held at 40% total lung capacity and 37 °C the surface tension remained below 1 mN• m for about 10 min, and then increased slowly in a linear fashion to 9 mN. m - t in 70 min. During stepwise deflation from 70% to 40% total lung capacity the surface tension changed from approximately 10 m N - m -I to less than 1 m N . m 1. At each step during deflation we compared surface tension in alveoli of differing size and location. At any given lung volume in the range between 70% and 40% total lung capacity we found equal values for the alveolar surface tension regardless of alveolar size and location. Alveolus Cat Lung
Surface tension Surfactant Volume
In 1955 Pattie reported the extraordinary lifetime or stability of bubbles from lung surfactant extracts and concluded that this is a function of near zero surface tension produced by surface active material at the air-liquid interface. He assumed that the film lining the bubbles was the same as the alveolar surface film and thus that the surface tension in the lung was below 1 r a N . m -1 Clements introduced in 1957 the application of the surface balance to studies of lung extracts. He compressed and expanded films of surfactant periodically and Accepted for publication 4 March 1982 0034-5687/82/0000-0000/$02.75 © Elsevier Biomedical Press
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demonstrated that the surface tension varied from 40 to 10 m N . m ~. Based on these observations he formulated a theory of alveolar stability (Clements et al., 1961) which states that as area decreases during deflation of the lung, surface tension falls toward zero so that at small volumes the surface force, which tends to promote alveolar collapse, is negligible. Other authors have used pressure-volume measurements on excised lungs to calculate alveolar surface tension (e.g. Bachofen et al., 1970). In studies of alveolar extracts in the surface balance as well as in pressure-volume studies of lungs, indirect methods were used to determine pulmonary surface tension (see Notter and Morrow, 1975 for a review). Investigators who used lung extracts for study in the surface balance assumed that the behavior of the film in vitro represented the behavior of the alveolar film in situ. Investigators who worked with pressure-volume data made assumptions about alveolar geometry and maximum surface tension (e.g. Hoppin and Hildebrandt, 1977). The latter was estimated from in vitro surface balance studies (Clements, 1957) and was usually taken as 50 m N • m ~. It is not surprising that these indirect methods gave conflicting results. Lempert and Macklem (1971) pointed out that the behavior of surface films in the balance is not necessarily reflected in the mechanical behavior of intact lungs. Recently a method to measure surface tension directly in individual alveoli has been reported (Schfirch et al., 1976, 1978). The method is based on the observation that drops of fluorocarbon and other test fluids spread to a thin lens on top of a monolayer if the surface tension of that monolayer is raised past a characteristic value. The surface tension in rat lung at 37°C and at 4 0 ~ total lung capacity (TLC) was less than 9 mN • m ~. The relationship between lung volume and surface tension during deflation from about 85 to 6 0 ~ TLC was linear, with surface tensions ranging from 20 to 9 r a N . m -l. At TLC, the surface tension was approximately 30 m N . m-~. In lungs held at 4 0 ~ TLC the surface tension changed slowly, rising to 9 m N - m -~ in 30 min with a subsequent approximately linear rise to 16 raN. m l at 115 min. These results are in good agreement with a study by Valberg and Brain (1977) who calculated the variation of surface tension in the lung as a function of volume from multiple pressure-volume curves without assuming a specific surface area vs volume function or a maximum surface tension. Recently Wilson (1981) determined the surface tension in rabbit lungs with an analysis of the relations among lung recoil, surface area and surface tension. Unlike previous methods of calculating surface tension from recoil pressure, he took into account the energy of distortion of the lung caused by surface tension. He obtained surface tensions in close agreement with those obtained by alveolar micropuncture in rat lungs (Schfirch et al., 1976). Furthermore, the direct approach to measuring alveolar surface tension by using test fluid droplets confirmed directly what pressure-volume data (e.g. Horie and Hildebrandt, 1971) had suggested. The lining substance is more stable in situ when it is spread on the alveolar subphase than in vitro in the film balance. This led to the conclusion that the alveolar film especially at 40~°~,~TLC is probably greatly enriched in dipalmitoyl phosphatidylcholine (DPPC) (Clements,
L U N G S U R F A C E T E N S I O N : STABILITY A N D A L V E O L A R SIZE
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1977). Recently Hildebran et al. (1979) studied the physical characteristics of model lipid monolayers in a surface balance. They found that only monolayers rich in D P P C have characteristics which match those directly measured or calculated for the alveolar monolayer in situ. Furthermore, they suggested a differential loss of surface components during early expiration when the surface tension is falling. The major purpose of the present work was to extend the direct measurements o f ~ v e o l a r surface tension to values below 9 m N . m -~. A set of new test fluids allowed us to determine surface tensions from 10 m N . m -~ to approximately 0.5 m N - m -~, for the volume range from 70~o T L C to 40~o TLC. A second objective of our study was to investigate whether there are local or regional differences in alveolar surface tension and whether there is a variation of surface tension between alveoli of differing sizes for a given lung volume at and near 40°(, TLC. Alveolar size determines the mean surface curvature in the alveolus, and forces generated at the air-liquid interface are related to the curvature of this interface (Weibel and Gil, 1977).
Materials and methods CONTROL EXPERIMENTS AND CALIBRATION
The method is based on the observation that drops of a variety of nonpolar test fluids placed on top of monolayers at the air-water interface begin to spread as the surface tension of the monolayer rises beyond a value characteristic of the test fluid. We found previously (Schfirch et al., 1976, 1978) that fluorocarbon test liquids and silicone oil were suitable for surface tensions ranging from 9 to 20 m N . m while mixtures of slightly less hydrophobic fluids such as dimethylphthalate and normal octanol were suitable for the range between 25 and 35 m N • m -~ . For the present study we chose two fluorocarbon liquids FC 40 and FC 70 (Fluorinert ®, 3M Co.). Each of the two liquids was doped with 1 mg/ml of a blue fluorocarbon dye to aid visualization. The fluorocarbon dye L-1802 was a gift from Dr. D. Danielson, 3M Co., Saint Paul, MN. We discovered that this substance did not only improve visualization of the test fluid droplets inside alveoli but the combination of the dye with FC 70 or FC 40 made the two liquids also suitable test fluids to measure monolayer surface tensions from approximately 0.5 to 10 m N . m A droplet of the pure FC 40 fluorocarbon liquid sitting on a monolayer of D P P C supported by a 0.5~o agar block changes its shape from approximately hemispherical to a thin lens as the monolayer tension rises past 16 m N - m -~ (Schiirch et al., 1978). However, for the combination of FC 40/L-1802 (1 mg/ml) a similar change of shape occurs at a much lower monolayer surface tension, between 0.5 and 5 m N . m ~. The reason for this shift to lower values is the reduced interfacial tension
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between the test fluid droplet and the D P P C monolayer for the combination of FC 40/L-1802. The fluorocarbon dye is surface active at the fluorocarbon hydrocarbon interface. For example we found that the interfacial tension between FC 40 and an uncompressed D P P C monolayer on a 0 . 9 ~ NaC1 solution was approximately 5 m N . m -~ (Boyce et al., 1980), while the minimum interracial tension between FC 40/L-1802 and an uncompressed D P P C monolayer was only about 1 mN • m -~ . This reduction of the interfacial tension is likely because of a similarity between the hydrocarbon moiety of L-1802 and the hydrocarbon chains of DPPC. In our earlier studies (e.g. Schtirch et al., 1976) we used a Teflon ® (polytetrafluoroethylene) surface balance and monolayers of DPPC, DSPC (distearoyl phosphatidylcholine) and films from purified lung surface active material (SAM) to calibrate the spreading of the test fluid droplets. All of these films gave equivalent results. For the present work, however, we attempted to mimic the alveolar situation more closely by designing a 'model alveolus' in form of a captive air bubble (fig. 1). We formed an air bubble from a 30 gauge needle connected to a 5 ml graduated syringe below a layer of 0.5']~ agar gel that was molded into the lucite cover of a chamber with optically flat glass walls. The chamber was filled with 0.9~i NaC1.
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Microscope ]': :;.|~Mi""r_ro..... .r--//.-.0.9C~O.. .~.:..] Fig. 1. Calibration of mouolayer surface tension vs test fluid droplet diameter (see text). Test fluid droplets are placed (C) onto a monolayer of dipalmitoyl phosphatidylcholine (DPPC) or pulmonary surfactant spread by means of needle A on the surface of an air bubble. A microscope is adjusted vertically to photograph the air babble for the determination of the interracial tension (upper position). In the lower position, the test fluid droplets are photographed by means of a mirror, before and after placing them onto the monolayer, at the upper, interior surface of the bubble. By removal of air (B) from the bubble the surface tension of the monolayer decreases because the interracial area is reduced and the monolayer is compressed in a similar way to compressing monolayers in a Langmuir tray.
LUNG SURFACE TENSION: STABILITY AND ALVEOLAR SIZE
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A h e a t i n g coil inside the b a t h a n d 2 t h e r m i s t o r p r o b e s were used to a d j u s t the t e m p e r a t u r e to 37 _+ 0.5 °C. H o l e s in the lucite c o v e r filled with a g a r gel a l l o w e d us to a d v a n c e m i c r o p i p e t t e s t h r o u g h the a g a r gel into the air b u b b l e . F r o m one o f the p i p e t t e s d r o p l e t s o f a s o l u t i o n o f D P P C or D S P C (2 m g / m l in e t h a n o l ) c o u l d be s p r e a d at the a i r - l i q u i d interface o f the b u b b l e to f o r m a m o n o l a y e r . Because the m o n o l a y e r s r e d u c e d the a i ~ s a l i n e interfacial tension, the b u b b l e flattened i m m e d i a t e l y a n d c o n t i n u e d to d o so, as m o r e s p r e a d i n g s o l u t i o n was a d d e d , until the interfacial tension r e a c h e d a value o f a p p r o x i m a t e l y 25 m N • m J, the m i n i m u m for an u n c o m p r e s s e d m o n o l a y e r o f D P P C , D S P C o r S A M (Tierney, 1965 ; W a t k i n s , 1968). By r e m o v i n g air f r o m the b u b b l e we were able to r e d u c e the interfacial a r e a a n d to c o m p r e s s the m o n o l a y e r in a similar w a y to c o m p r e s s i n g m o n o l a y e r s in a L a n g m u i r surface tray. W i t h c o m p r e s s i o n the interfacial tension d e c r e a s e d to a m i n i m u m value o f 0.5 m N - m -~ o r less. Figs. 2 A - C d e m o n s t r a t e the air b u b b l e
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Fig. 2. Shape of the air bubble at different monolayer surface tensions : (A) 25 mN • m l, (B) 5 mN • m - I and (C) 1 mN. m-I.
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s. SCHURCH
in various stages of its monolayer. In each case the bubble profile was photographed by means of a Nikon S M Z microscope and the interfacial tension was determined from projected slides by shape analysis using the tables of Hartland and Hartley (1976) or the computer program by Maze and Burnet (1969). For bubbles of a diameter of about 0.5 cm and interfacial tensions of 5 m N - m J or less the bubble was always flat with negligible apex curvature. This enabled us to determine the interfacial tension with a very simple formula (Adamson, 1976, pp. 32-33), 7 = A pgh2/2
where the interfacial tension 7 can be computed from h, the height between the m a x i m u m diameter and the apex of the bubble, and from Ap, the density difference between air and saline. This 'bubble surface balance' was leak-proof. A D P P C monolayer compressed to a surface tension of 0.5 m N . m 1 at 37°C, did not demonstrate any measurable change in surface tension for more than 12 hours. The experimentor can also control the a m o u n t of material adsorbed at the bubble interface by adding tiny droplets of a spreading solution with a precision microsyringe and a micropipette. Using the microscope in the upper position we were able to p h o t o g r a p h the bubble profile, while in the lower position we could observe and photograph the upper, interior surface of the bubble. In order to place test fluid droplets onto the monolayer on the upper, interior bubble surface, we advanced a second micropipette that was mounted onto a micromanipulator through the agar gel until the tip of the pipette (2 10 /~m) was in the bubble interior. With a graduated microsyringe we then squeezed out a test fluid droplet of a diameter between 10 and 30 #m, and measured the diameter of the spherical droplet while it was still hanging on the tip of the pipette before placing the droplet onto the upper monolayer surface by moving back the micropipette gently. Taking the diameter of the spherical droplet on the pipette as 1.0, we noticed that for the minimum monolayer surface tension of 0.5 m N • m ~, the diameter of the droplet increased to 1.2-1.3 after placing it onto the monolayer.
Fig. 3. Drop of the fluorocarbon fluid FC 40/L-1802, (A) prior to deposition, approximately 15 #m in diameter, (B) after deposition on the DPPC monolayer at the surface tension of 0.5 m N . m -t, and (C) at 1.5 mN • m I. Temperature 37 °(7.
L U N G S U R F A C E T E N S I O N : STABILITY A N D A L V E O L A R SIZE
345
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Fig. 4. Relative diameter of droplets of two different test fluids v s the surface tension of a D P P C monolayer of the air bubble agar interface. O, test fluid FC 40/L-1802, [3, test fluid F C 70/L-1802 (see text for details). Error bars indicate _+ 1 SE.
This corresponds to a sphere-to-hemisphere transition with a contact angle of 90 ° +_ 5 ° (Schtirch et al., 1978). Above the minimum surface tension, the drop diameter increased, at 1 m N . m -~ to 1.7, at 2 r a N . m -~ to about 2.5, and above 5 m N . m -~ to more than 2.5 (figs. 3 and 4). We either placed a new droplet for each given surface tension onto the monolayer or observed the same droplet at various monolayer surface tensions. The diameter of the test fluid droplets changed in a reversible fashion according to the change of the monolayer surface tension of the bubble. Test fluid droplets of FC 70 with 1 mg/ml of blue fluorocarbon dye L-1802 denoted FC 70/L-1802, showed a similar behavior to FC 40/L-1802 when placed onto DPPC, or DSPC monolayers. However, the change in diameter with film surface tension was more gradual below 5 m N . m -~ but greater between 5 and 14 m N . m -I (fig. 4). In a series of additional calibration experiments we used the surface balance as described previously (Schiirch et al., 1978), and obtained equivalent results for test fluid droplets of less than 100/xm in diameter.
346
S. SCn(~RCn
ALVEOLAR MICROPUNCTURE The data were obtained from 10 excised cat lungs. The animals were anesthetised with pentobarbital sodium (60 mg/kg body wt., i.p.), exsanguinated, and the lungs excised and cannulated. After degassing, the lungs were put onto a lucite tray partially filled with saline, inside a temperature controlled lucite chamber and allowed to warm up to 37°C for 10-15 rain. The lungs were then inflated slowly with air to a peak pressure of 25 cm H20, where total lung capacity (TLC) was recorded. Functional residual capacity (FRC) was taken as 40% TLC. During deflation 30 ml of air was withdrawn and an equilibration time of 2 min was allowed at each step. At F R C the pressure recorded was usually between 2.0 and 3.0 cm H~O. The lungs were then reinflated to T L C with humidified air and kept there for 2 min before they were deflated stepwise by withdrawing 30 ml of air down to 6 cm H20 transpulmonary pressure, where we started the surface tension measurements. About one hour elapsed between removal of the lung from each experimental animal and the first measurements of surface tension as a function of lung volume on expiration. For the surface tension vs time relationship, the lungs were deflated stepwise down to F R C , where the diameter of test fluid droplets vs time as well as the transpulmonary pressure vs time were recorded. Alveolar micropuncture and deposition of test fluid droplets onto alveolar surfaces was performed as reported previously (Schtirch e t al., 1976). Again, we took special care to measure the drop diameter while the spherical drop was still hanging on the tip of the pipette inside an alveolus. By moving the micromanipulator gently, we could move the spherical drop on the pipette back and forth in the a!veolar space. The micropipette was then gently withdrawn until the drop was deposited onto an alveolar surface adjacent to the pleural surface, where its new diameter was determined. Occasionally a droplet moved to an alveolar surface almost vertically oriented which allowed us to estimate the contact angle the droplet made with the alveolar surface. Cat lungs are especially suitable for alveolar micropuncture because they have two relatively long and thin lobes which facilitates transillumination. Furthermore their average alveolar diameter is twice as great as that of rats (Valberg and Brain, 1977) making cat lungs especially suitable to study with our technique.
Results
MINIMUM SURFACE TENSION AND SURFACE TENSION wsTIME AT FRC We deflated the lungs stepwise from T L C to F R C for 3 4 min. After equilibration for approximately 4 min at F R C the pressure was between 2.0 and 3.0 cm H20, and timing was started. During the first 10 rain we placed about 10 droplets of FC 40/L-1802 at random into alveoli at the very edge of a lung lobe and another
347
L U N G S U R F A C E T E N S I O N : STABILITY A N D A L V E O L A R SIZE
series of 10 droplets into alveoli up to 0.5 cm from the edge of the lobe. We noticed that alveoli at the edge of a lobe may have diameters of up to 500 p m at F R C while most alveoli belonging to other lung regions have usually diameters of about 100-150 p m at F R C . Test fluid droplets increased in relative diameter from 1.2 to 1.3 when they were placed onto alveolar surfaces at FRC. This indicated a surface tension of 0.5 m N . m ~ regardless of alveolar size. Occasionally by pulling back the pipettes, the pleural surface and the adjacent alveolar wall were pulled out slightly causing the alveolar surface area to increase. In such alveoli the droplets increased their relative diameter to 2.5 or more, corresponding to an alveolar surface tension of 5-10 m N - m -l. However within a few seconds after removal of the pipette, the droplets usually shrank to their original diameter of less than 1.3 indicating that alveolar surface tension of approximately 0.5 m N . m -~ had been restored. We checked the diameters of the test fluid droplets at 10-rain intervals. After the first 10 min there was no measurable change in diameter, however, after 20 min the average relative diameter of the test fluid droplets had increased to approximately 1.8, corresponding to an alveolar surface tension of 1.5 r a N . m - ' . Figure 5 shows a linear increase of surface tension with time, reaching approximately 9.5 r a N . m ' after 70 min. The transpulmonary pressure recorded simultaneously with surface tension at constant volume (FRC) had risen from an average of 2.8 cm H~O at F R C to approximately 3.8 cm H20 in 110 rain. The data were obtained from a series of 6 cat lungs with a total of 30 60 obser-
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Fig. 5. 0 , surface tension time relationship for cat lung at 37 °C; D, transpulmonary pressure time relationship recorded simultaneously. Error bars indicate _+ 1 SE.
348
s. SCHURCH
vations for a given time. Between time intervals, whenever there was enough time, we placed additional test fluid droplets into alveoli close to the two original regions, and averaged their relative diameters together with the ones from the original drops. S U R F A C E TENSION
vs
L U N G VOLUME, A N D S U R F A C E TENSION
vs
A L V E O L A R SIZE
F O R A GIVEN V O L U M E
For these experiments we deflated the lungs slowly over a period of 2 3 min from TLC to 70% TLC. After 3-4 min equilibration at this volume we started to puncture alveoli and placed test fluid droplets of FC 70/L-1802 into alveoli of various sizes with the following characteristics: (1) alveoli belonging to the same terminal air sac, (2) adjacent alveoli but belonging to different air sacs, (3) large alveoli at the edge of a lobe with diameters of up to 500/~m, and (4) alveoli at least 0.5 cm apart but belonging to the same lung lobe. From 70~o TLC to FRC we deflated the lungs stepwise by withdrawing about 20 ml of air at each step. After 2 min of equilibration we placed between 4 and 10 droplets within 10 min after equilibration at a particular volume into alveoli at each of the locations mentioned above. Below 5 0 ~ TLC we PRESSURE (crn HzO) 0,,, #,
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T E N S I O N ( m N - m ~)
Fig. 6. Surface t e n s i o n - v o l u m e relationship (O), and p r e s s u r ~ v o l u m e relationship ( A ) on deflation for cat lung at 37 °C. Error bars indicate _+ 1 SE.
L U N G SURFACE TENSION: STABILITY A N D ALVEOLAR SIZE
349
used F C 40/L-1802 as test fluid because of its better spreading properties at low surface tensions (fig. 4). Figure 6 shows the volume vs surface tension relationship on deflation, found from 4 lungs at 37 °C. Each point represents the average of a total o f 30-40 measurements. At 70~o TLC, the surface tension was approximately 10 m N - m -j, falling first gradually and then more steeply toward zero as the volume approached FRC. Figure 7 demonstrates test fluid droplets sitting in alveoli that belong to the same alveolar duct or alveolar sac (a) and droplets in alveoli of various sizes situated around structure (a). Figure 7A shows the lung at the volume of 62~o TLC, the droplets spread to a relative diameter of 2.4 immediately after deposition onto the alveolar surfaces, indicating a surface tension of approximately 7 m N . m -j . Figure 7B shows the lung at F R C with the test fluid droplets at their minimum diameter corresponding to a surface tension of approximately 1 m N . m -j . The test fluid was FC 70/L-1802. The white arrow points to a test fluid droplet that had been placed onto an alveolar surface almost vertically oriented with respect to the photographic plane. In fig. 7A the drop cannot be seen clearly, however, in fig. 7B the droplet appears like a sessile lens of hemispherical shape. We have carefully c o m p a r e d relative diameters of the test fluid droplets at various locations pointed out above: for a given volume we were unable to find a relation between alveolar size and drop diameter, even when we compared droplets in an alveolus of 300-500/~m at the edge of a lobe with droplets in average sized alveoli of 100-150 #m. This follows from an analysis of variance at the 5 ~ level for 2 0 ~ 0 observations at each lung location.
Discussion M I N I M U M SURFACE TENSION A N D SURFACE TENSION
vs
TIME AT CONSTANT
VOLUME (FRC)
The new test fluids with their excellent spreading behavior from a hemisphere to a thin lens for monolayer surface tensions between 0.5 and 10 m N . m -j, enabled us to demonstrate that alveolar surface tension reaches a value below 1 m N . m -~ at F R C and 37 °C. The surface tension not only falls toward zero but it remains at approximately 0.5 m N • m - I for a b o u t 10 min if the lung is kept at constant volume at F R C (fig. 5). The transpulmonary pressure recorded simultaneously with surface tension was constant for approximately 15 min with a subsequent slow rise and finally a linear rise after about 40 min. Surface crumpling at F R C (Bachofen et al., 1979) could be responsible for the time lag between the surface tension rise and the pressure rise. The low minimum surface tension of approximately 0.5 m N . m ~ at 37°C obtained ~in the present work and the extraordinary stability of surface tension with time at F R C are in good agreement with film behavior calculated from
Fig. 7. Test fluid droplets of FC 70/L-1802 sitting in alveoli that belong to the same alveolar duct or alveolar sac (a) and droplets in alveoli of various sizes situated around structure (a). A: The lung at a volume of 62% TLC, the droplet diameter indicated a surface tension of approximately 7 mN • m r. B: The lung at 40% total lung capacity with the test fluid droplets at their minimum diameter indicating a surface tension of less than 1 m N . m -l. The white arrow points to a droplet that had been placed onto an alveolar surface almost vertically oriented with respect to the photographic plane. In B, this droplet appears as a sessile lens of hemispherical shape, in A the same drop at a larger diameter, cannot be seen clearly.
L U N G S U R F A C E T E N S I O N : STABILITY A N D A L V E O L A R SIZE
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pressure volume plots of intact lungs. Bachofen e t al. (1970) determined a minimum surface tension of less than 5 m M . m f in excised cat lungs at 4 0 ~ T L C and 22 °C. Horie and Hildebrandt (1971) calculated from pressure-volume diagrams of excised rat lungs held at 40~¢o T L C and 22 °C that surface tension increased by only 1 2 m N . m ~ in 20 rain. Recently Wilson and Bachofen (1981) used physiologic and morphometric data from rabbit lungs to estimate the surface tension by an energy analysis which takes into account the interaction between forces and structure. They obtained values of 2, 6 and 16 m N - m t at 40~,~, 60'~/o and 8n°',,/o TLC, respectively, in very good agreement with our values. Monolayers of purified pulmonary surfactant have been shown to develop a low surface tension of 5 m N • m -~ at 37 °C at a compression of the surface to 2070 of its m a x i m u m (King and Clements, 1972a). At 20 or 25j°;i m a x i m u m film area, the area was held constant and surface tension increased as film collapse or desorption occurred. At r o o m temperature, surface tension increased from 5 to 20 m N . m -~ in 40 min. At 37°C the increase was faster, going from 5 to 20 m N . m ~ in 20 rain. (Clements, 1962). In similar experiments at 35-38 °C (Tierney e t al., 1965), surface tension increased from 10 to 20 m N • m ~ in 5.3 min. These films, however, seem to have far less stability than the alveolar film itself as shown in the present study and calculated from lung compliance change in experimental animals (Mead and Collier, 1959; Horie and Hildebrandt, 1971). Monolayers of pure D P P C on the other hand are far more stable (Goerke, 1974). Watkins (1968) found that D P P C monolayers, compressed to a surface tension of 1 m N - m J at 25 °C collapsed at approximately 0.1 m N . m ~ - hr 1. More recently, Hildebran e t al. studied monolayers of three well-defined highly purified lipids typical of those found in greatest abundance in surface active material (SAM). These authors defined a fractional monolayer collapse rate at constant surface area, defined as k.1 (dT)~ ' 7e,i - 70 ~ is taken as 26 m N • m-~, the equilibrium value of surface tension toward which films of D P P C and other lecithins collapse after long periods of time (King, 1974), and Y0 is the m i n i m u m surface tension, 0.5-1 m N • m l . We determined k; for the linear part of the graph 7 vs time (fig. 4) for 7o = 0.5 m N • m -~, and Ycq = 2 6 r a N . m -~, and obtained k. = 0.42 h ~. Comparing our value with results obtained by Hildebran e t al. (1979), we see that only pure D P P C monolayers have a lower collapse rate, 0.07-0.20. h -~. Two of their mixed monolayers had collapse rates relatively close to our value" D P P C + monoenoic PC (9 • 1 molar ratio) 1 2 h -t, and D P P C + monoenoic PC + cholesterol (9 : 0.5 : 0.5 molar ratio) 4-7 h 1, while monolayers of purified dog SAM had a much greater collapse rate of 121 h -~ Hildebran e t al. (1979) suggested that only monolayers containing more than 90~o molto D P P C satisfy the criterion of k~. estimated from intact lungs. These authors w h e r e Yeq
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s. SCHURCH
suggested further that in the lung, SAM containing about 4 0 ~ m o l ~ DPPC adsorbs rapidly at alveolar air-water interface when surface tension is high during inflation, but subsequently is converted to a monolayer of greater than 90 molto DPPC on compression during deflation. Clements (1977) concluded that DPPC closely imitates the alveolar film at 4 0 ~ TLC and he suggested a self-purification process for the alveolar film upon expiration by squeezing out of less stable components. Bangham et al. (1979) suggested, based on their search for an effective synthetic lung surfactant, that the alveoli are kept open at full expiration by a residue of nearly pure DPPC in the condensed state. Our measurements of the collapse rate of the alveolar film in situ support these conclusions.
SURFACE TENSION
vs
L U N G VOLUME, A N D S U R F A C E T E N S I O N
vs
A L V E O L A R SIZE
FOR A GIVEN VOLUME
Weibel and his co-workers demonstrated clearly, crumpling of the alveolar surface at low lung volumes (Gil et al., 1979). They suggested that the deflation of the lung to lower volumes is accompanied by crumpling of septa and alveolar surfaces, or accordion-like distortions of the peripheral air spaces. Thus lung alveoli can be reduced in volume while surface area remains nearly constant near 40~o TLC. This would tend to decrease the change in surface tension because the tension decreases in response to surface compression. Assuming for static conditions that the gas pressure throughout an alveolar duct is the same, one might apply Laplace's relation to alveoli of the same duct and conclude that a small alveolus with a large mean curvature (small radius) should have a smaller surface tension than a larger alveolus with a smaller mean curvature. However, our results show that alveolar surface tension is the same, not only in alveoli of the same alveolar duct or sac but also in alveoli of differing size accessible to measurement by micropuncture. Equal surface tension throughout an alveolar duct or sac is not surprising; near zero surface tension means relatively high surface pressure. High surface pressure in an alveolus would promote spreading of film material along a surface pressure gradient into an alveolus with a lower surface pressure or a higher surface tension until the surface tension is equal throughout the structure. We may conclude that on stepwise deflation, between each step the area change in each alveolus is approximately the same throughout a lung lobe. Therefore, starting at a given surface tension, the reduction of the surface tension during deflation would be the same regardless of alveolar size, because surface tension decreases in response to surface compression as the area decreases. The early theory of alveolar stability (Clements et al., 1961) held that as area decreases during deflation, surface tension falls toward zero. This has been confirmed
L U N G S U R F A C E T E N S I O N : STABILITY A N D A L V E O L A R SIZE
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by pressure volume studies and by in situ alveolar micropuncture. Mead et al. (1970) and r u n g (1975) drew attention to the fact that alveoli are interdependent units connected by septa septa junctions. If a group of lung units becomes out of phase with its neighbors during ventilation, stresses are set up within the elastic elements of the parenchyma surrounding the elements that are out of phase. Therefore, interdependence has a stabilizing effect by diminishing asynchronous volume change (Comroe, 1975, p. 114). Our present observations demonstrate directly what the pioneering work of Pattie (1955) and Clements (1957) suggested. Alveolar surface tension reaches extremely low values, approximately 0.5 m N - m -l at 40% TLC. This near zero surface tension at 40% TLC explains why very small radii of curvature ( < 0.5 #m) are tolerated at sites of surface crumpling (Bachofen et al., 1979). These authors also pointed out that low surface tension and interdependence are required to stabilize the lung. Near zero surface tension is required to minimize pressure differences created at the alveolar surface, especially at sites of extremely low radii of curvature. Interdependence provided by the fibrous continuum of the lung and low surface tension appear to be necessary for maintaining a large alveolar surface area.
Summary (1) Alveolar surface tension in excised cat lungs at 37 °C reaches a minimum surface tension of approximately 0.5 m N . m ~at 40% TLC. (2) For lungs held at 40~o TLC the surface tension started to rise slowly after approximately 10 rain, reaching 1.5 m N . m - ~after 20 min. (3) This extraordinary stability of surface tension in situ at and near 40% TLC suggests strongly that the alveolar film at end expiration is almost pure DPPC. (4) During stepwise deflation from 70% TLC the surface tension decreased from approximately 10 m N - m -1 to less than 1 m N • m -~ at 40% TLC. For a given volume in the interval from 70% TLC to 40% TLC no difference in surface tension according to alveolar size could be detected.
Acknowledgements The author gratefully acknowledges the helpful discussions with Drs. D. J. L. McIver, F. Possmayer, S.H. Song and E.R. Weibel. This study was supported by the Medical Research Council of Canada and the Ontario Thoracic Society.
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References A d a m s o n , A. W. (1976). Physical Chemistry of Surfaces. New York, John Wiley, pp. 1 698. Bachofen, H., T. Hildebrandt and M. Bachofen (1970). Pressure volume curves of air- and liquid-filled excised lungs surface tension in situ. J. Appl. Physiol. 29:422 431. Bachofen, H., P. Gehr and E. R. Weibel (1979). Alterations of mechanical properties and morphology in excised rabbit lungs rinsed with a detergent. J. Appl. Physiol. 47 : 1002 1010. Bangham, A . D . , C.J. Morley and M . C . Phillips (1979). The physical properties of an effective lung surfactant. Biochim. Biophys. Acta 573:552 556. Boyce, J. F., S. Schfirch and D . J . L . Mclver (1980). lnterfacial tensions in healthy and atherosclerotic rabbit aortae: higher values on lesion surt;aces. A therosclerosis 37 : 361 370. Clements, J. A. (1957). Surface tension of lung extracts. Prec. Exp. Biol. Med. 95:170 172. Clements, J.A., R.F. Hustead, R.P. Johnson and I. Gribetz (1961). Pulmonary surface tension and alveolar stability. J. Appl. Pl~vsiol. 16: 444-450. Clements, J. A. (1962). Surface p h e n o m e n a in relation to p u l m o n a r y function. The Physiologist 5:1 I--28. Clements, J. A. (1977). Functions of the alveolar lining. Am. Rev. Resp. Dis. 115 (Suppl.): 67 71. Comroe, J. H. (1975). Physiology of Respiration. Second edition. Chicago, Year Book Medical Publishers, pp. 1 316. Fung, Y.-C. (1975). Does surface tension make the lung inherently unstable? Circ. Res. 3 7 : 4 9 7 502. Gil, J., H. Bachofen and E. R. Weibel (1979). Alveolar v o l u m e surface area relation in air- and salinefilled lungs fixed by vascular perfusion. J. Appl. Phy,siol. 47 : 990-1001. Goerke, J. (1974). Lung surfactant. Biochim. Bioph.vs. Acta. 344:241 26 I. Hartland, S. and R . W . Hartley (1976). Axisymmetric Fluid Liquid Interfaces. New York, Elsevier, pp. 552 629. Hildebran, J. N., J. Goerke and J. A. Clements (1979). Pulmonary surface film stability and composition. J. Appl. Physiol. 47:604-611. Hoppin, F. G. and J. Hildebrandt (1977). Mechanical properties of the lung. In : Bioengineering Aspects of the Lung, edited by J. B. West. New York, Dekker, pp. 83 162. Horie, T. and J. Hildebrandt (1971). Dynamic compliance, limit cycles, and static equilibria of excised cat lung. J. Appl. Physiol. 31 : 423 430. King, R.J. and J.A. Clements (1972a). Surface active materials from dog lung. II. Composition and physiological correlations. Ant. J. Physiol. 223 : 715 726. King, R.J. and J.A. Clements (1972b). Surface active materials from dog lung. Ill. Thermal analysis. Am. J. Physiol. 223:727 733. King, R. J. (1974). The surfactant system of the lung. Fed. Prec. 33 : 2238 2247. Lempert, J. and P.T. Macklem (1971). Effect of temperature on rabbit lung surfactant and pressur~ volume hysteresis. J. Appl. Ph.vsiol. 31 : 380-385. Maze, C. and G. Burnet (1969). A non-linear regression method for calculating surface tension and contact angle from the shape e r a sessile drop. Stoj~lce Sci. 13 : 451 470. Mead, J. and C. Collier (1959). Relation of volume history of lungs to respiratory mechanics in anesthetized dogs. J. Appl. Ph),siol. 14:669 678. Mead, J., T. Takashima and D. Leith (1970). Stress distribution in lungs: a model of pulmonary elasticity. J. Appl. Physiol. 28 : 596 608. Notter, R . H . and P.E. Morrow (1975). Pulmonary surfactant: a surface chemistry viewpoint. Ann. Biomed. Eng. 3 : 119 159. Pattle, R. E. (1955). Properties, function and origin of the alveolar lining layer. Nalur¢' JLamhm) 175: 1125 1126. Schfirch, S., J. Goerke and J.A. Clements (1976). Direct determination of surface tension in the lung. Prec. Natl. Acad. Sci. U.S.A. 73:4698 4702. Schfirch, S., J. Goerke and J. A. Clements (1978). Direct determination of volume- and time-dependence of alveolar surl:ace tension in excised lungs. Prec. Vatl..4cad. ,S'ci. U.~S'..4.75:3417 3421.
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Tierney, D. F. (1965). P u l m o n a r y surfactant in health and disease. Dis. Chest 47 : 247 253. Valberg, P.A. and J.D. Brain (1977). Lung surface tension and airspace dimensions from multiple pressure-volume curves. J. Appl. Physiol. 43 : 730-738. Watkins, J. C. (1968). The surface properties of pure phospholipids in relation to those of lung extracts. Biochim. Biophys. Acta 152 : 293 306. Weibel, E. R. and J. Gil. (1977). Structure-function relationship at the alveolar level. In: Bioengineering Aspects of the Lung, edited by J. B. West. New York, Dekker, pp. 1 81. Wilson, T. A. (1981). The relations a m o n g recoil pressure, surface area and surface tension in the lung. J. Appl. Physiol. 50:921 926. Wilson, T . A . and H. Bachofen (1981). A model for the mechanical structure of the alveolar duct. J. Appl. Physiol. (in press).
Respiration Physiology (1982) 48, 339-355 Elsevier Biomedical Press
SURFACE TENSION AT LOW LUNG VOLUMES: DEPENDENCE ON TIME AND ALVEOLAR SIZE
SAMUEL S C H U R C H Department of'Biophysics, Health Sciences Center, University oj Western Ontario, London, Canada N6A 5C1
Abstract. We measured surface tension in individual alveoli by observing the spreading properties of fluid droplets placed by micropipette on the alveolar surfaces. The test fluids were calibrated on monolayers of dipalmitoyl phosphatidylcholine spread at the air-saline interface of a captive bubble. The air bubble was floated by buoyancy against a ceiling of 0.5% agar. The bubble surface tension could be altered by inflating or deflating the bubble, and the value of the surface tension was determined by shape analysis for a sessile drop. Test fluid droplets were placed by micropipette onto the upper, flat bubble surface and the diameters of these droplets were measured with a microscope. In cat lungs held at 40% total lung capacity and 37 °C the surface tension remained below 1 mN• m for about 10 min, and then increased slowly in a linear fashion to 9 mN. m - t in 70 min. During stepwise deflation from 70% to 40% total lung capacity the surface tension changed from approximately 10 m N - m -I to less than 1 m N . m 1. At each step during deflation we compared surface tension in alveoli of differing size and location. At any given lung volume in the range between 70% and 40% total lung capacity we found equal values for the alveolar surface tension regardless of alveolar size and location. Alveolus Cat Lung
Surface tension Surfactant Volume
In 1955 Pattie reported the extraordinary lifetime or stability of bubbles from lung surfactant extracts and concluded that this is a function of near zero surface tension produced by surface active material at the air-liquid interface. He assumed that the film lining the bubbles was the same as the alveolar surface film and thus that the surface tension in the lung was below 1 r a N . m -1 Clements introduced in 1957 the application of the surface balance to studies of lung extracts. He compressed and expanded films of surfactant periodically and Accepted for publication 4 March 1982 0034-5687/82/0000-0000/$02.75 © Elsevier Biomedical Press
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s. SCHORCH
demonstrated that the surface tension varied from 40 to 10 m N . m ~. Based on these observations he formulated a theory of alveolar stability (Clements et al., 1961) which states that as area decreases during deflation of the lung, surface tension falls toward zero so that at small volumes the surface force, which tends to promote alveolar collapse, is negligible. Other authors have used pressure-volume measurements on excised lungs to calculate alveolar surface tension (e.g. Bachofen et al., 1970). In studies of alveolar extracts in the surface balance as well as in pressure-volume studies of lungs, indirect methods were used to determine pulmonary surface tension (see Notter and Morrow, 1975 for a review). Investigators who used lung extracts for study in the surface balance assumed that the behavior of the film in vitro represented the behavior of the alveolar film in situ. Investigators who worked with pressure-volume data made assumptions about alveolar geometry and maximum surface tension (e.g. Hoppin and Hildebrandt, 1977). The latter was estimated from in vitro surface balance studies (Clements, 1957) and was usually taken as 50 m N • m ~. It is not surprising that these indirect methods gave conflicting results. Lempert and Macklem (1971) pointed out that the behavior of surface films in the balance is not necessarily reflected in the mechanical behavior of intact lungs. Recently a method to measure surface tension directly in individual alveoli has been reported (Schfirch et al., 1976, 1978). The method is based on the observation that drops of fluorocarbon and other test fluids spread to a thin lens on top of a monolayer if the surface tension of that monolayer is raised past a characteristic value. The surface tension in rat lung at 37°C and at 4 0 ~ total lung capacity (TLC) was less than 9 mN • m ~. The relationship between lung volume and surface tension during deflation from about 85 to 6 0 ~ TLC was linear, with surface tensions ranging from 20 to 9 r a N . m -l. At TLC, the surface tension was approximately 30 m N . m-~. In lungs held at 4 0 ~ TLC the surface tension changed slowly, rising to 9 m N - m -~ in 30 min with a subsequent approximately linear rise to 16 raN. m l at 115 min. These results are in good agreement with a study by Valberg and Brain (1977) who calculated the variation of surface tension in the lung as a function of volume from multiple pressure-volume curves without assuming a specific surface area vs volume function or a maximum surface tension. Recently Wilson (1981) determined the surface tension in rabbit lungs with an analysis of the relations among lung recoil, surface area and surface tension. Unlike previous methods of calculating surface tension from recoil pressure, he took into account the energy of distortion of the lung caused by surface tension. He obtained surface tensions in close agreement with those obtained by alveolar micropuncture in rat lungs (Schfirch et al., 1976). Furthermore, the direct approach to measuring alveolar surface tension by using test fluid droplets confirmed directly what pressure-volume data (e.g. Horie and Hildebrandt, 1971) had suggested. The lining substance is more stable in situ when it is spread on the alveolar subphase than in vitro in the film balance. This led to the conclusion that the alveolar film especially at 40~°~,~TLC is probably greatly enriched in dipalmitoyl phosphatidylcholine (DPPC) (Clements,
L U N G S U R F A C E T E N S I O N : STABILITY A N D A L V E O L A R SIZE
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1977). Recently Hildebran et al. (1979) studied the physical characteristics of model lipid monolayers in a surface balance. They found that only monolayers rich in D P P C have characteristics which match those directly measured or calculated for the alveolar monolayer in situ. Furthermore, they suggested a differential loss of surface components during early expiration when the surface tension is falling. The major purpose of the present work was to extend the direct measurements o f ~ v e o l a r surface tension to values below 9 m N . m -~. A set of new test fluids allowed us to determine surface tensions from 10 m N . m -~ to approximately 0.5 m N - m -~, for the volume range from 70~o T L C to 40~o TLC. A second objective of our study was to investigate whether there are local or regional differences in alveolar surface tension and whether there is a variation of surface tension between alveoli of differing sizes for a given lung volume at and near 40°(, TLC. Alveolar size determines the mean surface curvature in the alveolus, and forces generated at the air-liquid interface are related to the curvature of this interface (Weibel and Gil, 1977).
Materials and methods CONTROL EXPERIMENTS AND CALIBRATION
The method is based on the observation that drops of a variety of nonpolar test fluids placed on top of monolayers at the air-water interface begin to spread as the surface tension of the monolayer rises beyond a value characteristic of the test fluid. We found previously (Schfirch et al., 1976, 1978) that fluorocarbon test liquids and silicone oil were suitable for surface tensions ranging from 9 to 20 m N . m while mixtures of slightly less hydrophobic fluids such as dimethylphthalate and normal octanol were suitable for the range between 25 and 35 m N • m -~ . For the present study we chose two fluorocarbon liquids FC 40 and FC 70 (Fluorinert ®, 3M Co.). Each of the two liquids was doped with 1 mg/ml of a blue fluorocarbon dye to aid visualization. The fluorocarbon dye L-1802 was a gift from Dr. D. Danielson, 3M Co., Saint Paul, MN. We discovered that this substance did not only improve visualization of the test fluid droplets inside alveoli but the combination of the dye with FC 70 or FC 40 made the two liquids also suitable test fluids to measure monolayer surface tensions from approximately 0.5 to 10 m N . m A droplet of the pure FC 40 fluorocarbon liquid sitting on a monolayer of D P P C supported by a 0.5~o agar block changes its shape from approximately hemispherical to a thin lens as the monolayer tension rises past 16 m N - m -~ (Schiirch et al., 1978). However, for the combination of FC 40/L-1802 (1 mg/ml) a similar change of shape occurs at a much lower monolayer surface tension, between 0.5 and 5 m N . m ~. The reason for this shift to lower values is the reduced interfacial tension
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between the test fluid droplet and the D P P C monolayer for the combination of FC 40/L-1802. The fluorocarbon dye is surface active at the fluorocarbon hydrocarbon interface. For example we found that the interfacial tension between FC 40 and an uncompressed D P P C monolayer on a 0 . 9 ~ NaC1 solution was approximately 5 m N . m -~ (Boyce et al., 1980), while the minimum interracial tension between FC 40/L-1802 and an uncompressed D P P C monolayer was only about 1 mN • m -~ . This reduction of the interfacial tension is likely because of a similarity between the hydrocarbon moiety of L-1802 and the hydrocarbon chains of DPPC. In our earlier studies (e.g. Schtirch et al., 1976) we used a Teflon ® (polytetrafluoroethylene) surface balance and monolayers of DPPC, DSPC (distearoyl phosphatidylcholine) and films from purified lung surface active material (SAM) to calibrate the spreading of the test fluid droplets. All of these films gave equivalent results. For the present work, however, we attempted to mimic the alveolar situation more closely by designing a 'model alveolus' in form of a captive air bubble (fig. 1). We formed an air bubble from a 30 gauge needle connected to a 5 ml graduated syringe below a layer of 0.5']~ agar gel that was molded into the lucite cover of a chamber with optically flat glass walls. The chamber was filled with 0.9~i NaC1.
Air Surfactant ~ B
Testfluid
c//
Lucite
~---"-- l 0"3-0"5%A g o r ~
~.. ~!~
iMonotayer _J
Glass -..']]'. droplet.'.'.' .'.'.'.',:., --"-chamber
Microscope ]': :;.|~Mi""r_ro..... .r--//.-.0.9C~O.. .~.:..] Fig. 1. Calibration of mouolayer surface tension vs test fluid droplet diameter (see text). Test fluid droplets are placed (C) onto a monolayer of dipalmitoyl phosphatidylcholine (DPPC) or pulmonary surfactant spread by means of needle A on the surface of an air bubble. A microscope is adjusted vertically to photograph the air babble for the determination of the interracial tension (upper position). In the lower position, the test fluid droplets are photographed by means of a mirror, before and after placing them onto the monolayer, at the upper, interior surface of the bubble. By removal of air (B) from the bubble the surface tension of the monolayer decreases because the interracial area is reduced and the monolayer is compressed in a similar way to compressing monolayers in a Langmuir tray.
LUNG SURFACE TENSION: STABILITY AND ALVEOLAR SIZE
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A h e a t i n g coil inside the b a t h a n d 2 t h e r m i s t o r p r o b e s were used to a d j u s t the t e m p e r a t u r e to 37 _+ 0.5 °C. H o l e s in the lucite c o v e r filled with a g a r gel a l l o w e d us to a d v a n c e m i c r o p i p e t t e s t h r o u g h the a g a r gel into the air b u b b l e . F r o m one o f the p i p e t t e s d r o p l e t s o f a s o l u t i o n o f D P P C or D S P C (2 m g / m l in e t h a n o l ) c o u l d be s p r e a d at the a i r - l i q u i d interface o f the b u b b l e to f o r m a m o n o l a y e r . Because the m o n o l a y e r s r e d u c e d the a i ~ s a l i n e interfacial tension, the b u b b l e flattened i m m e d i a t e l y a n d c o n t i n u e d to d o so, as m o r e s p r e a d i n g s o l u t i o n was a d d e d , until the interfacial tension r e a c h e d a value o f a p p r o x i m a t e l y 25 m N • m J, the m i n i m u m for an u n c o m p r e s s e d m o n o l a y e r o f D P P C , D S P C o r S A M (Tierney, 1965 ; W a t k i n s , 1968). By r e m o v i n g air f r o m the b u b b l e we were able to r e d u c e the interfacial a r e a a n d to c o m p r e s s the m o n o l a y e r in a similar w a y to c o m p r e s s i n g m o n o l a y e r s in a L a n g m u i r surface tray. W i t h c o m p r e s s i o n the interfacial tension d e c r e a s e d to a m i n i m u m value o f 0.5 m N - m -~ o r less. Figs. 2 A - C d e m o n s t r a t e the air b u b b l e
~!~~U~~ii
Fig. 2. Shape of the air bubble at different monolayer surface tensions : (A) 25 mN • m l, (B) 5 mN • m - I and (C) 1 mN. m-I.
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in various stages of its monolayer. In each case the bubble profile was photographed by means of a Nikon S M Z microscope and the interfacial tension was determined from projected slides by shape analysis using the tables of Hartland and Hartley (1976) or the computer program by Maze and Burnet (1969). For bubbles of a diameter of about 0.5 cm and interfacial tensions of 5 m N - m J or less the bubble was always flat with negligible apex curvature. This enabled us to determine the interfacial tension with a very simple formula (Adamson, 1976, pp. 32-33), 7 = A pgh2/2
where the interfacial tension 7 can be computed from h, the height between the m a x i m u m diameter and the apex of the bubble, and from Ap, the density difference between air and saline. This 'bubble surface balance' was leak-proof. A D P P C monolayer compressed to a surface tension of 0.5 m N . m 1 at 37°C, did not demonstrate any measurable change in surface tension for more than 12 hours. The experimentor can also control the a m o u n t of material adsorbed at the bubble interface by adding tiny droplets of a spreading solution with a precision microsyringe and a micropipette. Using the microscope in the upper position we were able to p h o t o g r a p h the bubble profile, while in the lower position we could observe and photograph the upper, interior surface of the bubble. In order to place test fluid droplets onto the monolayer on the upper, interior bubble surface, we advanced a second micropipette that was mounted onto a micromanipulator through the agar gel until the tip of the pipette (2 10 /~m) was in the bubble interior. With a graduated microsyringe we then squeezed out a test fluid droplet of a diameter between 10 and 30 #m, and measured the diameter of the spherical droplet while it was still hanging on the tip of the pipette before placing the droplet onto the upper monolayer surface by moving back the micropipette gently. Taking the diameter of the spherical droplet on the pipette as 1.0, we noticed that for the minimum monolayer surface tension of 0.5 m N • m ~, the diameter of the droplet increased to 1.2-1.3 after placing it onto the monolayer.
Fig. 3. Drop of the fluorocarbon fluid FC 40/L-1802, (A) prior to deposition, approximately 15 #m in diameter, (B) after deposition on the DPPC monolayer at the surface tension of 0.5 m N . m -t, and (C) at 1.5 mN • m I. Temperature 37 °(7.
L U N G S U R F A C E T E N S I O N : STABILITY A N D A L V E O L A R SIZE
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3.0 -
2..5
f9
E
(p _J
"I
2.0
n."
1.5
0
5 I0 Surfoce Tension (mN.m-I)
15
Fig. 4. Relative diameter of droplets of two different test fluids v s the surface tension of a D P P C monolayer of the air bubble agar interface. O, test fluid FC 40/L-1802, [3, test fluid F C 70/L-1802 (see text for details). Error bars indicate _+ 1 SE.
This corresponds to a sphere-to-hemisphere transition with a contact angle of 90 ° +_ 5 ° (Schtirch et al., 1978). Above the minimum surface tension, the drop diameter increased, at 1 m N . m -~ to 1.7, at 2 r a N . m -~ to about 2.5, and above 5 m N . m -~ to more than 2.5 (figs. 3 and 4). We either placed a new droplet for each given surface tension onto the monolayer or observed the same droplet at various monolayer surface tensions. The diameter of the test fluid droplets changed in a reversible fashion according to the change of the monolayer surface tension of the bubble. Test fluid droplets of FC 70 with 1 mg/ml of blue fluorocarbon dye L-1802 denoted FC 70/L-1802, showed a similar behavior to FC 40/L-1802 when placed onto DPPC, or DSPC monolayers. However, the change in diameter with film surface tension was more gradual below 5 m N . m -~ but greater between 5 and 14 m N . m -I (fig. 4). In a series of additional calibration experiments we used the surface balance as described previously (Schiirch et al., 1978), and obtained equivalent results for test fluid droplets of less than 100/xm in diameter.
346
S. SCn(~RCn
ALVEOLAR MICROPUNCTURE The data were obtained from 10 excised cat lungs. The animals were anesthetised with pentobarbital sodium (60 mg/kg body wt., i.p.), exsanguinated, and the lungs excised and cannulated. After degassing, the lungs were put onto a lucite tray partially filled with saline, inside a temperature controlled lucite chamber and allowed to warm up to 37°C for 10-15 rain. The lungs were then inflated slowly with air to a peak pressure of 25 cm H20, where total lung capacity (TLC) was recorded. Functional residual capacity (FRC) was taken as 40% TLC. During deflation 30 ml of air was withdrawn and an equilibration time of 2 min was allowed at each step. At F R C the pressure recorded was usually between 2.0 and 3.0 cm H~O. The lungs were then reinflated to T L C with humidified air and kept there for 2 min before they were deflated stepwise by withdrawing 30 ml of air down to 6 cm H20 transpulmonary pressure, where we started the surface tension measurements. About one hour elapsed between removal of the lung from each experimental animal and the first measurements of surface tension as a function of lung volume on expiration. For the surface tension vs time relationship, the lungs were deflated stepwise down to F R C , where the diameter of test fluid droplets vs time as well as the transpulmonary pressure vs time were recorded. Alveolar micropuncture and deposition of test fluid droplets onto alveolar surfaces was performed as reported previously (Schtirch e t al., 1976). Again, we took special care to measure the drop diameter while the spherical drop was still hanging on the tip of the pipette inside an alveolus. By moving the micromanipulator gently, we could move the spherical drop on the pipette back and forth in the a!veolar space. The micropipette was then gently withdrawn until the drop was deposited onto an alveolar surface adjacent to the pleural surface, where its new diameter was determined. Occasionally a droplet moved to an alveolar surface almost vertically oriented which allowed us to estimate the contact angle the droplet made with the alveolar surface. Cat lungs are especially suitable for alveolar micropuncture because they have two relatively long and thin lobes which facilitates transillumination. Furthermore their average alveolar diameter is twice as great as that of rats (Valberg and Brain, 1977) making cat lungs especially suitable to study with our technique.
Results
MINIMUM SURFACE TENSION AND SURFACE TENSION wsTIME AT FRC We deflated the lungs stepwise from T L C to F R C for 3 4 min. After equilibration for approximately 4 min at F R C the pressure was between 2.0 and 3.0 cm H20, and timing was started. During the first 10 rain we placed about 10 droplets of FC 40/L-1802 at random into alveoli at the very edge of a lung lobe and another
347
L U N G S U R F A C E T E N S I O N : STABILITY A N D A L V E O L A R SIZE
series of 10 droplets into alveoli up to 0.5 cm from the edge of the lobe. We noticed that alveoli at the edge of a lobe may have diameters of up to 500 p m at F R C while most alveoli belonging to other lung regions have usually diameters of about 100-150 p m at F R C . Test fluid droplets increased in relative diameter from 1.2 to 1.3 when they were placed onto alveolar surfaces at FRC. This indicated a surface tension of 0.5 m N . m ~ regardless of alveolar size. Occasionally by pulling back the pipettes, the pleural surface and the adjacent alveolar wall were pulled out slightly causing the alveolar surface area to increase. In such alveoli the droplets increased their relative diameter to 2.5 or more, corresponding to an alveolar surface tension of 5-10 m N - m -l. However within a few seconds after removal of the pipette, the droplets usually shrank to their original diameter of less than 1.3 indicating that alveolar surface tension of approximately 0.5 m N . m -~ had been restored. We checked the diameters of the test fluid droplets at 10-rain intervals. After the first 10 min there was no measurable change in diameter, however, after 20 min the average relative diameter of the test fluid droplets had increased to approximately 1.8, corresponding to an alveolar surface tension of 1.5 r a N . m - ' . Figure 5 shows a linear increase of surface tension with time, reaching approximately 9.5 r a N . m ' after 70 min. The transpulmonary pressure recorded simultaneously with surface tension at constant volume (FRC) had risen from an average of 2.8 cm H~O at F R C to approximately 3.8 cm H20 in 110 rain. The data were obtained from a series of 6 cat lungs with a total of 30 60 obser-
IO
C~- 38
/
~f
9 8
36 ~
/
Z E
6
I
0
20
40
T/I
I
GO
I
I
80
"
i
-34
I
.
I00
Time (rain)
Fig. 5. 0 , surface tension time relationship for cat lung at 37 °C; D, transpulmonary pressure time relationship recorded simultaneously. Error bars indicate _+ 1 SE.
348
s. SCHURCH
vations for a given time. Between time intervals, whenever there was enough time, we placed additional test fluid droplets into alveoli close to the two original regions, and averaged their relative diameters together with the ones from the original drops. S U R F A C E TENSION
vs
L U N G VOLUME, A N D S U R F A C E TENSION
vs
A L V E O L A R SIZE
F O R A GIVEN V O L U M E
For these experiments we deflated the lungs slowly over a period of 2 3 min from TLC to 70% TLC. After 3-4 min equilibration at this volume we started to puncture alveoli and placed test fluid droplets of FC 70/L-1802 into alveoli of various sizes with the following characteristics: (1) alveoli belonging to the same terminal air sac, (2) adjacent alveoli but belonging to different air sacs, (3) large alveoli at the edge of a lobe with diameters of up to 500/~m, and (4) alveoli at least 0.5 cm apart but belonging to the same lung lobe. From 70~o TLC to FRC we deflated the lungs stepwise by withdrawing about 20 ml of air at each step. After 2 min of equilibration we placed between 4 and 10 droplets within 10 min after equilibration at a particular volume into alveoli at each of the locations mentioned above. Below 5 0 ~ TLC we PRESSURE (crn HzO) 0,,, #,
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SURFACE
T E N S I O N ( m N - m ~)
Fig. 6. Surface t e n s i o n - v o l u m e relationship (O), and p r e s s u r ~ v o l u m e relationship ( A ) on deflation for cat lung at 37 °C. Error bars indicate _+ 1 SE.
L U N G SURFACE TENSION: STABILITY A N D ALVEOLAR SIZE
349
used F C 40/L-1802 as test fluid because of its better spreading properties at low surface tensions (fig. 4). Figure 6 shows the volume vs surface tension relationship on deflation, found from 4 lungs at 37 °C. Each point represents the average of a total o f 30-40 measurements. At 70~o TLC, the surface tension was approximately 10 m N - m -j, falling first gradually and then more steeply toward zero as the volume approached FRC. Figure 7 demonstrates test fluid droplets sitting in alveoli that belong to the same alveolar duct or alveolar sac (a) and droplets in alveoli of various sizes situated around structure (a). Figure 7A shows the lung at the volume of 62~o TLC, the droplets spread to a relative diameter of 2.4 immediately after deposition onto the alveolar surfaces, indicating a surface tension of approximately 7 m N . m -j . Figure 7B shows the lung at F R C with the test fluid droplets at their minimum diameter corresponding to a surface tension of approximately 1 m N . m -j . The test fluid was FC 70/L-1802. The white arrow points to a test fluid droplet that had been placed onto an alveolar surface almost vertically oriented with respect to the photographic plane. In fig. 7A the drop cannot be seen clearly, however, in fig. 7B the droplet appears like a sessile lens of hemispherical shape. We have carefully c o m p a r e d relative diameters of the test fluid droplets at various locations pointed out above: for a given volume we were unable to find a relation between alveolar size and drop diameter, even when we compared droplets in an alveolus of 300-500/~m at the edge of a lobe with droplets in average sized alveoli of 100-150 #m. This follows from an analysis of variance at the 5 ~ level for 2 0 ~ 0 observations at each lung location.
Discussion M I N I M U M SURFACE TENSION A N D SURFACE TENSION
vs
TIME AT CONSTANT
VOLUME (FRC)
The new test fluids with their excellent spreading behavior from a hemisphere to a thin lens for monolayer surface tensions between 0.5 and 10 m N . m -j, enabled us to demonstrate that alveolar surface tension reaches a value below 1 m N . m -~ at F R C and 37 °C. The surface tension not only falls toward zero but it remains at approximately 0.5 m N • m - I for a b o u t 10 min if the lung is kept at constant volume at F R C (fig. 5). The transpulmonary pressure recorded simultaneously with surface tension was constant for approximately 15 min with a subsequent slow rise and finally a linear rise after about 40 min. Surface crumpling at F R C (Bachofen et al., 1979) could be responsible for the time lag between the surface tension rise and the pressure rise. The low minimum surface tension of approximately 0.5 m N . m ~ at 37°C obtained ~in the present work and the extraordinary stability of surface tension with time at F R C are in good agreement with film behavior calculated from
Fig. 7. Test fluid droplets of FC 70/L-1802 sitting in alveoli that belong to the same alveolar duct or alveolar sac (a) and droplets in alveoli of various sizes situated around structure (a). A: The lung at a volume of 62% TLC, the droplet diameter indicated a surface tension of approximately 7 mN • m r. B: The lung at 40% total lung capacity with the test fluid droplets at their minimum diameter indicating a surface tension of less than 1 m N . m -l. The white arrow points to a droplet that had been placed onto an alveolar surface almost vertically oriented with respect to the photographic plane. In B, this droplet appears as a sessile lens of hemispherical shape, in A the same drop at a larger diameter, cannot be seen clearly.
L U N G S U R F A C E T E N S I O N : STABILITY A N D A L V E O L A R SIZE
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pressure volume plots of intact lungs. Bachofen e t al. (1970) determined a minimum surface tension of less than 5 m M . m f in excised cat lungs at 4 0 ~ T L C and 22 °C. Horie and Hildebrandt (1971) calculated from pressure-volume diagrams of excised rat lungs held at 40~¢o T L C and 22 °C that surface tension increased by only 1 2 m N . m ~ in 20 rain. Recently Wilson and Bachofen (1981) used physiologic and morphometric data from rabbit lungs to estimate the surface tension by an energy analysis which takes into account the interaction between forces and structure. They obtained values of 2, 6 and 16 m N - m t at 40~,~, 60'~/o and 8n°',,/o TLC, respectively, in very good agreement with our values. Monolayers of purified pulmonary surfactant have been shown to develop a low surface tension of 5 m N • m -~ at 37 °C at a compression of the surface to 2070 of its m a x i m u m (King and Clements, 1972a). At 20 or 25j°;i m a x i m u m film area, the area was held constant and surface tension increased as film collapse or desorption occurred. At r o o m temperature, surface tension increased from 5 to 20 m N . m -~ in 40 min. At 37°C the increase was faster, going from 5 to 20 m N . m ~ in 20 rain. (Clements, 1962). In similar experiments at 35-38 °C (Tierney e t al., 1965), surface tension increased from 10 to 20 m N • m ~ in 5.3 min. These films, however, seem to have far less stability than the alveolar film itself as shown in the present study and calculated from lung compliance change in experimental animals (Mead and Collier, 1959; Horie and Hildebrandt, 1971). Monolayers of pure D P P C on the other hand are far more stable (Goerke, 1974). Watkins (1968) found that D P P C monolayers, compressed to a surface tension of 1 m N - m J at 25 °C collapsed at approximately 0.1 m N . m ~ - hr 1. More recently, Hildebran e t al. studied monolayers of three well-defined highly purified lipids typical of those found in greatest abundance in surface active material (SAM). These authors defined a fractional monolayer collapse rate at constant surface area, defined as k.1 (dT)~ ' 7e,i - 70 ~ is taken as 26 m N • m-~, the equilibrium value of surface tension toward which films of D P P C and other lecithins collapse after long periods of time (King, 1974), and Y0 is the m i n i m u m surface tension, 0.5-1 m N • m l . We determined k; for the linear part of the graph 7 vs time (fig. 4) for 7o = 0.5 m N • m -~, and Ycq = 2 6 r a N . m -~, and obtained k. = 0.42 h ~. Comparing our value with results obtained by Hildebran e t al. (1979), we see that only pure D P P C monolayers have a lower collapse rate, 0.07-0.20. h -~. Two of their mixed monolayers had collapse rates relatively close to our value" D P P C + monoenoic PC (9 • 1 molar ratio) 1 2 h -t, and D P P C + monoenoic PC + cholesterol (9 : 0.5 : 0.5 molar ratio) 4-7 h 1, while monolayers of purified dog SAM had a much greater collapse rate of 121 h -~ Hildebran e t al. (1979) suggested that only monolayers containing more than 90~o molto D P P C satisfy the criterion of k~. estimated from intact lungs. These authors w h e r e Yeq
352
s. SCHURCH
suggested further that in the lung, SAM containing about 4 0 ~ m o l ~ DPPC adsorbs rapidly at alveolar air-water interface when surface tension is high during inflation, but subsequently is converted to a monolayer of greater than 90 molto DPPC on compression during deflation. Clements (1977) concluded that DPPC closely imitates the alveolar film at 4 0 ~ TLC and he suggested a self-purification process for the alveolar film upon expiration by squeezing out of less stable components. Bangham et al. (1979) suggested, based on their search for an effective synthetic lung surfactant, that the alveoli are kept open at full expiration by a residue of nearly pure DPPC in the condensed state. Our measurements of the collapse rate of the alveolar film in situ support these conclusions.
SURFACE TENSION
vs
L U N G VOLUME, A N D S U R F A C E T E N S I O N
vs
A L V E O L A R SIZE
FOR A GIVEN VOLUME
Weibel and his co-workers demonstrated clearly, crumpling of the alveolar surface at low lung volumes (Gil et al., 1979). They suggested that the deflation of the lung to lower volumes is accompanied by crumpling of septa and alveolar surfaces, or accordion-like distortions of the peripheral air spaces. Thus lung alveoli can be reduced in volume while surface area remains nearly constant near 40~o TLC. This would tend to decrease the change in surface tension because the tension decreases in response to surface compression. Assuming for static conditions that the gas pressure throughout an alveolar duct is the same, one might apply Laplace's relation to alveoli of the same duct and conclude that a small alveolus with a large mean curvature (small radius) should have a smaller surface tension than a larger alveolus with a smaller mean curvature. However, our results show that alveolar surface tension is the same, not only in alveoli of the same alveolar duct or sac but also in alveoli of differing size accessible to measurement by micropuncture. Equal surface tension throughout an alveolar duct or sac is not surprising; near zero surface tension means relatively high surface pressure. High surface pressure in an alveolus would promote spreading of film material along a surface pressure gradient into an alveolus with a lower surface pressure or a higher surface tension until the surface tension is equal throughout the structure. We may conclude that on stepwise deflation, between each step the area change in each alveolus is approximately the same throughout a lung lobe. Therefore, starting at a given surface tension, the reduction of the surface tension during deflation would be the same regardless of alveolar size, because surface tension decreases in response to surface compression as the area decreases. The early theory of alveolar stability (Clements et al., 1961) held that as area decreases during deflation, surface tension falls toward zero. This has been confirmed
L U N G S U R F A C E T E N S I O N : STABILITY A N D A L V E O L A R SIZE
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by pressure volume studies and by in situ alveolar micropuncture. Mead et al. (1970) and r u n g (1975) drew attention to the fact that alveoli are interdependent units connected by septa septa junctions. If a group of lung units becomes out of phase with its neighbors during ventilation, stresses are set up within the elastic elements of the parenchyma surrounding the elements that are out of phase. Therefore, interdependence has a stabilizing effect by diminishing asynchronous volume change (Comroe, 1975, p. 114). Our present observations demonstrate directly what the pioneering work of Pattie (1955) and Clements (1957) suggested. Alveolar surface tension reaches extremely low values, approximately 0.5 m N - m -l at 40% TLC. This near zero surface tension at 40% TLC explains why very small radii of curvature ( < 0.5 #m) are tolerated at sites of surface crumpling (Bachofen et al., 1979). These authors also pointed out that low surface tension and interdependence are required to stabilize the lung. Near zero surface tension is required to minimize pressure differences created at the alveolar surface, especially at sites of extremely low radii of curvature. Interdependence provided by the fibrous continuum of the lung and low surface tension appear to be necessary for maintaining a large alveolar surface area.
Summary (1) Alveolar surface tension in excised cat lungs at 37 °C reaches a minimum surface tension of approximately 0.5 m N . m ~at 40% TLC. (2) For lungs held at 40~o TLC the surface tension started to rise slowly after approximately 10 rain, reaching 1.5 m N . m - ~after 20 min. (3) This extraordinary stability of surface tension in situ at and near 40% TLC suggests strongly that the alveolar film at end expiration is almost pure DPPC. (4) During stepwise deflation from 70% TLC the surface tension decreased from approximately 10 m N - m -1 to less than 1 m N • m -~ at 40% TLC. For a given volume in the interval from 70% TLC to 40% TLC no difference in surface tension according to alveolar size could be detected.
Acknowledgements The author gratefully acknowledges the helpful discussions with Drs. D. J. L. McIver, F. Possmayer, S.H. Song and E.R. Weibel. This study was supported by the Medical Research Council of Canada and the Ontario Thoracic Society.
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References A d a m s o n , A. W. (1976). Physical Chemistry of Surfaces. New York, John Wiley, pp. 1 698. Bachofen, H., T. Hildebrandt and M. Bachofen (1970). Pressure volume curves of air- and liquid-filled excised lungs surface tension in situ. J. Appl. Physiol. 29:422 431. Bachofen, H., P. Gehr and E. R. Weibel (1979). Alterations of mechanical properties and morphology in excised rabbit lungs rinsed with a detergent. J. Appl. Physiol. 47 : 1002 1010. Bangham, A . D . , C.J. Morley and M . C . Phillips (1979). The physical properties of an effective lung surfactant. Biochim. Biophys. Acta 573:552 556. Boyce, J. F., S. Schfirch and D . J . L . Mclver (1980). lnterfacial tensions in healthy and atherosclerotic rabbit aortae: higher values on lesion surt;aces. A therosclerosis 37 : 361 370. Clements, J. A. (1957). Surface tension of lung extracts. Prec. Exp. Biol. Med. 95:170 172. Clements, J.A., R.F. Hustead, R.P. Johnson and I. Gribetz (1961). Pulmonary surface tension and alveolar stability. J. Appl. Pl~vsiol. 16: 444-450. Clements, J. A. (1962). Surface p h e n o m e n a in relation to p u l m o n a r y function. The Physiologist 5:1 I--28. Clements, J. A. (1977). Functions of the alveolar lining. Am. Rev. Resp. Dis. 115 (Suppl.): 67 71. Comroe, J. H. (1975). Physiology of Respiration. Second edition. Chicago, Year Book Medical Publishers, pp. 1 316. Fung, Y.-C. (1975). Does surface tension make the lung inherently unstable? Circ. Res. 3 7 : 4 9 7 502. Gil, J., H. Bachofen and E. R. Weibel (1979). Alveolar v o l u m e surface area relation in air- and salinefilled lungs fixed by vascular perfusion. J. Appl. Phy,siol. 47 : 990-1001. Goerke, J. (1974). Lung surfactant. Biochim. Bioph.vs. Acta. 344:241 26 I. Hartland, S. and R . W . Hartley (1976). Axisymmetric Fluid Liquid Interfaces. New York, Elsevier, pp. 552 629. Hildebran, J. N., J. Goerke and J. A. Clements (1979). Pulmonary surface film stability and composition. J. Appl. Physiol. 47:604-611. Hoppin, F. G. and J. Hildebrandt (1977). Mechanical properties of the lung. In : Bioengineering Aspects of the Lung, edited by J. B. West. New York, Dekker, pp. 83 162. Horie, T. and J. Hildebrandt (1971). Dynamic compliance, limit cycles, and static equilibria of excised cat lung. J. Appl. Physiol. 31 : 423 430. King, R.J. and J.A. Clements (1972a). Surface active materials from dog lung. II. Composition and physiological correlations. Ant. J. Physiol. 223 : 715 726. King, R.J. and J.A. Clements (1972b). Surface active materials from dog lung. Ill. Thermal analysis. Am. J. Physiol. 223:727 733. King, R. J. (1974). The surfactant system of the lung. Fed. Prec. 33 : 2238 2247. Lempert, J. and P.T. Macklem (1971). Effect of temperature on rabbit lung surfactant and pressur~ volume hysteresis. J. Appl. Ph.vsiol. 31 : 380-385. Maze, C. and G. Burnet (1969). A non-linear regression method for calculating surface tension and contact angle from the shape e r a sessile drop. Stoj~lce Sci. 13 : 451 470. Mead, J. and C. Collier (1959). Relation of volume history of lungs to respiratory mechanics in anesthetized dogs. J. Appl. Ph),siol. 14:669 678. Mead, J., T. Takashima and D. Leith (1970). Stress distribution in lungs: a model of pulmonary elasticity. J. Appl. Physiol. 28 : 596 608. Notter, R . H . and P.E. Morrow (1975). Pulmonary surfactant: a surface chemistry viewpoint. Ann. Biomed. Eng. 3 : 119 159. Pattle, R. E. (1955). Properties, function and origin of the alveolar lining layer. Nalur¢' JLamhm) 175: 1125 1126. Schfirch, S., J. Goerke and J.A. Clements (1976). Direct determination of surface tension in the lung. Prec. Natl. Acad. Sci. U.S.A. 73:4698 4702. Schfirch, S., J. Goerke and J. A. Clements (1978). Direct determination of volume- and time-dependence of alveolar surl:ace tension in excised lungs. Prec. Vatl..4cad. ,S'ci. U.~S'..4.75:3417 3421.
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Tierney, D. F. (1965). P u l m o n a r y surfactant in health and disease. Dis. Chest 47 : 247 253. Valberg, P.A. and J.D. Brain (1977). Lung surface tension and airspace dimensions from multiple pressure-volume curves. J. Appl. Physiol. 43 : 730-738. Watkins, J. C. (1968). The surface properties of pure phospholipids in relation to those of lung extracts. Biochim. Biophys. Acta 152 : 293 306. Weibel, E. R. and J. Gil. (1977). Structure-function relationship at the alveolar level. In: Bioengineering Aspects of the Lung, edited by J. B. West. New York, Dekker, pp. 1 81. Wilson, T. A. (1981). The relations a m o n g recoil pressure, surface area and surface tension in the lung. J. Appl. Physiol. 50:921 926. Wilson, T . A . and H. Bachofen (1981). A model for the mechanical structure of the alveolar duct. J. Appl. Physiol. (in press).