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1Center for Biomedical Engineering, University of Kentucky, Lexington, Kentucky 40506; and 2Department of Surgery, University of Wisconsin Medical School, Madison, Wisconsin 53706
Submitted 4 June 2003 ; accepted in final form 29 August 2003
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ABSTRACT |
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 TOP ABSTRACT MATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGMENTSREFERENCES |
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lung fluid balance; interstitium; epithelium; transport; reflection coefficient; isolated lung
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In isolated rabbit lungs inflated with a 3 g/dl albumin solution to a constant airway inflation pressure, interstitial cuffs reached a maximum size by 1-5 h and remained constant in size thereafter (22, 23). The growth of interstitial cuffs was modeled by fluid flow through resistive and compliant elements, analogous to the flow of an electric current through ohmic resistances with shunt capacitors by using electrical analog models. In this analysis, the epithelial resistance was lumped with the interstitial resistance, and cuff growth was assumed to be due entirely to bulk flow driven by the hydrostatic pressure difference between the alveolar space and interstitium. The maximum cuff size was achieved when the interstitial pressure measured by micropuncture at the lung hilum equilibrated to the airway pressure (22, 23).
The growth of interstitial cuffs measured by the interstitial pressure response at the lung hilum was found to be faster with albumin and positively charged solutions and slower with Ringer and negatively charged solutions (23). These responses due to albumin concentration and charged solutions were attributed to the properties of the interstitium because they were consistent with the results from previous measurements of steady flow through lung interstitial segments (32).
Because interstitial albumin concentration was not measured in the foregoing studies, the albumin colloid osmotic (oncotic) pressure acting across the epithelium was not considered in the analysis. A permeable epithelial barrier to protein was implied in isolated lung studies that showed an interstitial tracer protein concentration that was 90% of the instilled airway liquid (17). However, a recent study in rat lung indicated a significant barrier to protein with a relatively high reflection coefficient to albumin of 0.83 (13). This high reflection coefficient of the epithelium implied a relatively low interstitial protein concentration during cuff growth and a significant airway-to-interstitial osmotic pressure gradient that would oppose the hydrostatic pressure gradient. Thus we wondered how interstitial cuffs would form against a relatively large transepithelial osmotic pressure gradient between the alveolar and interstitial compartments.
Accordingly, we studied the change in interstitial cuff albumin concentration and cuff size as a function of inflation time at low and high inflation pressures in liquid inflated rabbit lungs. Our results showed that the growth of interstitial cuffs depended primarily on the airway inflation pressure and was largely independent of the albumin concentration in the airway solution. During cuff growth to maximum size, the cuff-to-airway albumin concentration ratio increased at high airway pressure, which indicated an increased epithelial permeability. At low inflation pressure, we found that the cuffs reached a maximum size early on and then decreased in size thereafter, although cuff albumin concentration continued to rise. This behavior was consistent with reabsorption of cuff liquid by osmotic flow into the vascular and alveolar spaces over time. At high inflation pressure, the increase in cuff albumin concentration with a nearly constant cuff size was consistent with diffusion through restrictive epithelial pores.
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MATERIALS AND METHODS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGMENTSREFERENCES |
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In separate experiments, to determine the effect of an increased Paw on the size and albumin concentration of interstitial cuffs, we used an inflation pressure of 15 cmH2O, with inflation times of 0.1, 0.25, 0.5, 1, 2, and 5 h.
In other experiments, we determined the effect of an absence of a vascular osmotic pressure by inflating the vessels with lactated Ringer solution instead of a 3 g/dl albumin solution. Here we used inflation times of 1, 3, and 7 h at an inflation pressure of 5 cmH2O.
To determine the effect of an increased airway osmotic pressure, we increased the albumin concentration in the airway and vessel solutions to 5 g/dl. We used an inflation time of 1 h at airway inflation pressures of 5 and 15 cmH2O.
Size and Albumin Concentration of Perivascular Interstitial Cuffs
In the cryostat (-20°C), the frozen lungs were cut into slabs (
1 cm thick) transverse to the cranial-dorsal direction. The surfaces of blocks (1 x 1 x 1 cm) cut from the slabs were planed smooth with a microtome. Lung samples and the calibration plate (see below) were kept frozen in a covered glass petri dish containing dry ice. The dish was placed on a micromanipulator attached to the stage of a compound microscope that allowed both fluorescent [Evans blue labeled albumin (EBA)] and white light (color) imaging of blood vessels and their surrounding interstitial cuffs. The fluorescence videomicroscope used in previous studies (45) was modified to measure a color image.
Color images of vessels with interstitial cuffs were examined on a video monitor (model no. PVM 1390, Sony) via a digital camera (Nikon COOLPIX 990) mounted to an eyepiece port of the microscope. Lung samples were illuminated with an external fiber-optic source. Directing a flow of air on the cover eliminated water condensation on the glass cover of the dish. Images were stored on a videocassette recorder (SVHS, Panasonic) coupled to a time-code generator. Image size was adjusted by using various objective lenses (x2.5, x8, x25, or x50, American Optical and Zeiss). A calibration scale (minimum division, 20 µm) was simultaneously imaged. Digital color images were transferred to a computer and analyzed for vessel diameter, vessel area (Av), and cuff area (Ac) by using Adobe Photo-Shop, Scion Image (National Institutes of Health), and ImageTool (UTHSCSA). The actual Ac observed on the color image was verified by comparison with the fluorescent image (see below).
Albumin concentration of perivascular interstitial cuffs was measured by using fluorescence videomicroscopy with a video camera (C2400, Hamamatsu, SIT) that allowed both bright and ultra-low-level light imaging. For EBA fluorescent imaging, light from a high-pressure mercury lamp (Zeiss illuminator 100 with HBO 50) was filtered through the following lens system (Zeiss): an infrared absorbing filter (300-750 nm band pass), a bypass filter (BP 510-560 nm), and a dichromatic beam splitter (FT 580). The fluorescent light image was recorded by the video camera through a barrier filter (LP 590) and an adjustable (x2) interface lens (Zeiss), observed on a video monitor (Panasonic WV 5490), and stored in a videocassette recorder (Panasonic NV-8950). A time-code generator superimposed a time signal on the recordings.
After obtaining the color image of a vessel with interstitial cuff, its entire fluorescent image was examined on the video monitor. Figure 1 shows a color image of an artery (dyed red) surrounded by an interstitial cuff and surrounding alveolar space (dyed blue). Figure 2 shows the corresponding black and white image of EBA fluorescence. Note that the cuff observed in both images was not uniform in thickness. The fluorescent image showed a definite demarcation in light intensity that separated the vessel, cuff, and surrounding alveolar region. Note that the artery had the least brightness (least EBA), the interstitial cuff an intermediate brightness, and the surrounding alveolar space the most brightness, an indication of EBA concentration. To obtain the fluorescent image shown in Fig. 2, the entire field (within the outer circle) was subjected to incident light. Light intensity from this image could not be used to determine relative albumin concentration, because light from the brightest regions greatly affected regions with lower intensity. Some fluorescence was observed in vessels because the endothelium was partially permeable to albumin, so that, with absorption of interstitial liquid, some EBA entered the vessels.
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To determine albumin concentration in the interstitial cuff, only a small region of interest within the interstitial cuff was illuminated (small circle, Fig. 2). We used the minimum illuminated region (3.5-cm diameter on the video monitor) set by the adjustable field diaphragm (minimum diameter, 0.7 mm) of the light source. We chose a location where the cuff was relatively thick. The image of the cuff on the video monitor was magnified with an appropriate objective lens to expand its size relative to the illuminated region. The illuminated region was located within the boundaries of the cuff near the vessel wall and distal from the alveolar region, where light intensity was maximal. Fluorescent light intensity was measured from a square cursor (2.2 x 2.2 cm on the monitor) superimposed within the circular illuminated region (Fig. 2) by using a video photo analyzer (model 204A, IPM). After each measurement of cuff light intensity, the identical procedure was followed to measure light intensity from the five diluted samples in the calibration plate (see below).
The minimum illuminated region and the maximum magnification of the microscope (x50 objective lens) limited the cuff size that could be imaged accurately for albumin concentration. Cuff albumin concentration (Cc) was limited to vessels larger than 200 µm in diameter, with a mean Ac-to-Av ratio (Ac/Av) of 0.2. The mean cuff thickness of these vessels was 10 µm. Maximum image magnifi-cation on the video screen with the x50 objective lens was approximately x550.
The calibration plate consisted of five frozen diluted samples of the stock EBA solution located in five parallel channels (3 mm wide and 5 cm long). The plate surface was painted black to eliminate surface reflection of the fluorescent light. The depth of each channel varied linearly from 0 to 3.3 mm along its length. The plate was placed in dry ice before the channels were filled with the diluted samples. This procedure produced a uniform ice crystal formation within samples and a uniform light intensity that was independent of position within the channel. A uniform light intensity was produced by a spacing between the ice crystals that was small relative to the cursor area over which light intensity was measured. Channel depth, i.e., thickness of the diluted sample, had no effect on light intensity. This indicated that fluorescence from frozen solutions was limited to light emitted only from the ice crystal layers just below the surface, unlike that from unfrozen FITC-labeled dextran solutions that scaled with thickness up to 60 µm (45). Thus changes in cuff light intensity due to changes in interstitial depth caused by vessel eccentricity were not observed.
Statistics
The data are reported as mean values ± SD in Table 1 and as mean values ± SE in Figs. 4 and 5. Paired and unmatched Student's t-tests were used where appropriate to test for significant differences between two groups. Linear and multilinear regression analyses were used to test for correlation between two variables and among three variables, respectively. A P value of <0.05 indicated significance.
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RESULTS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGMENTSREFERENCES |
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Figure 3 is a representative calibration curve from a frozen diluted sample of the stock EBA solution used to fill the airways. Table 1 is a summary of the Cc-to-airway albumin concentration (Ca) ratio (Cc/Ca) and Ac/Av measured in lungs inflated with 3 g/dl albumin solution at different inflation times and at airway inflation pressures (Paw) of 5 and 15 cmH2O. Figure 4, A and B, shows plots of Ac/Av and Cc/Ca, respectively, vs. inflation time at 5- and 15-cmH2O Paw. These data included only the cuffs in which Cc was measured. Thus Ac/Av at Paw of 5 cmH2O appeared to reach a minimum value of 0.2 between 2 and 10 h, only because smaller cuffs with no measurement of Cc were excluded. The number of vessels with no measurable cuffs increased with inflation time, which indicated a monotonic decrease in interstitial cuff volume. Vessel diameters ranged from 200 to 3,800 µm. Some cuffs occurred around arteries that adjoined an airway. Airway cuffs were too small for a measure of albumin concentration. Not all vessels observed had cuffs. Vessel of diameter <100 µm produced no observable cuffs, in keeping with previous studies (7, 10, 11, 22, 23). Vessels <200 µm in diameter produced cuffs that were too small for a measurement of albumin concentration (see MATERIALS AND METHODS). The fraction of vessels with cuffs did not vary significantly with inflation time or inflation pressure.
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At Paw of 5 cmH2O, the minimum value of Cc/Ca of 0.1 occurred at inflation times of 0.5 and 1 h, which corresponded to the rapid phase of cuff growth during which Ac/Av rose to a value of 0.8 (Fig. 4). By contrast, at Paw of 15 cmH2O, the minimum value of Cc/Ca of 0.3 occurred at an inflation time of 0.25 h, which corresponded to a time when the peak value of Ac/Av was measured. Both Cc/Ca and Ac/Av were immeasurable at the inflation time of 0.11 h. We associated these minimum values of Cc/Ca during cuff growth with bulk flow of liquid across the epithelium at a high Péclet number so that the epithelial reflection coefficient, 
e = 1 - Cc/Ca, was 0.9 and 0.7 at Paw of 5 and 15 cmH2O, respectively (see Eq. A13, APPENDIX).
At Paw of 5 cmH2O, Cc/Ca increased monotonically from 0.1 at 0.5-1 h to 0.72 at 10 h. The increase in Cc/Ca between 1 and 2 h was accompanied by a rapid fall (75%) in Ac/Av to a value of 0.2. This was attributed to the absorption of cuff liquid with a reduced albumin concentration into the vascular and alveolar spaces. Between 2 and 10 h, Ac/Av remained constant at 0.2, whereas Cc/Ca increased. The replacement of the 3 g/dl albumin solution in the vessels with Ringer solution (Table 1, groups F-H, and Fig. 5) eliminated the absorption of cuff liquid into the vessels. These experiments showed a relatively small but significant increase in Cc/Ca from 0.11 at 1 h to 0.22 at 3 h and a relatively small (not significant) reduction in Ac/Av (25% at 3-7 h). This behavior was attributed to reabsorption of cuff liquid into the alveolar space (see below). However, the 75% reduction in cuff size measured by both vascular and alveolar absorption, compared with the smaller reduction measured by alveolar absorption alone, implied that vascular absorption was the major route of clearance of cuff liquid.
In contrast to the behavior at 5-cmH2O Paw, Cc/Ca at 15-cmH2O Paw increased more rapidly from 0.3 at 0.25 h to 0.74 at 5 h. No measurement of Cc/Ca was obtained at 0.11 h because Ac/Av was too small (<0.2). The increase in Cc/Ca after 0.25 h occurred in conjunction with a nearly constant Ac/Av. This implied that liquid absorption into the vessels was negligible, consistent with an increased endothelial permeability at high inflation pressure (31). Accordingly, the increase in Cc/Ca that occurred after 0.25 h at 15-cmH2O Paw was modeled as passive restricted diffusion through epithelial pores (see below).
Airway and vessel inflation to 5-cmH2O Paw at 1 h with 5 g/dl albumin solution produced values for Cc/Ca and Ac/Av that were not significantly different from those measured with 3 g/dl albumin solution (Table 1, groups B and N). Thus the rate of cuff growth was largely independent of the Ca and depended only on the Paw-to-interstitial hydrostatic pressure difference. This was attributed to a much larger hydraulic conductivity of the epithelial barrier than that of the interstitial cuffs, as discussed below. However, at 15-cmH2O Paw, Cc/Ca decreased significantly from 0.48 at 1 h after airway and vessel inflation, with a 3 g/dl albumin solution in the airway, to 0.34 with a 5 g/dl albumin solution, whereas Ac/Av was unchanged (Table 1, groups K and O). This behavior might have been caused by a slower rate of cuff growth with the higher albumin concentration.
Data Analysis
Effect of interstitial resistance on cuff formation and reabsorption. We developed an analysis to show the reasons why the growth of interstitial cuffs to maximum size depends primarily on the hydrostatic pressure difference. The important results are presented here with details in the APPENDIX. Consider transport across a two-membrane system, namely the epithelium in series with the interstitial cuff. The epithelial-interstitial reflection coefficient (ec) is related to the epithelial (Ke)to-interstitial conductance (Kc) ratio (Ke/Kc) and the e-to-c ratio (e/c)
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ec vs. Ke/Kc for the values of e of 0.9 and c of 0.1. For an interstitial resistance (reciprocal of conductance) that was much greater than epithelial resistance during the initial phase of cuff growth, both c and ec were near zero, so that the bulk flow was determined primarily by the hydrostatic pressure difference and was largely independent of the osmotic pressure difference (Table 1, groups B and K and groups N and O). As the cuffs grew, interstitial resistance was reduced, and ec increased above c. When ec became large enough so that the effective osmotic pressure difference exceeded the hydrostatic pressure difference, alveolar reabsorption of cuff liquid occurred (Fig. 4A).
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The reduced interstitial cuff size, together with an increased interstitial protein concentration between 2 and 10 h at 5 cmH2O Paw (Figs. 4 and 5), was attributed, in part, to vascular absorption and, in part, to alveolar reabsorption of the interstitium liquid. After the cuffs had grown to maximum size, interstitial resistance was reduced. This reduced resistance, coupled with a relatively high endothelial resistance due to the zone 1 conditions, produced an close to that of the endothelium. A relatively high , together with the low interstitial albumin concentration, produced an interstitial-to-vascular osmotic pressure gradient that was greater than the hydrostatic pressure gradient, which resulted in an osmotic absorption of interstitial liquid into the vascular space.
Transport properties of the epithelium. We determined the transport properties of the epithelium by considering flow and diffusion through a homoporous system of cylindrical pores. We present a summary of the results with details in the APPENDIX. First, the increase in interstitial albumin concentration with a constant cuff size at 15-cmH2O Paw was modeled as a passive diffusion process. The diffusion model produced a time constant for diffusion (to) at 15-cmH2O Paw of 4.7 h (Fig. 4B). The to was related to the apparent diffusion coefficient (De), ratio of total diffusion area (Ae) to diffusion length (Le) (Ae/Le), and maximum cuff volume (Vc). Vc was estimated from our present estimate of maximum cuff size (Fig. 4A) and the maximum cuff size and Vc measured previously in sheep lung (10). Second, the pore radius (Rp) was determined from the reflection coefficient (e) obtained from the initial values of albumin concentration during the initial phase of cuff growth, where interstitial albumin concentration was flow independent (high Péclet number). Values for e were 0.9 and 0.7 at 5 and 15 cmH2O, respectively, and associated Rp values were 4.5 and 6.1 nm. Third, the De was calculated by considering restricted diffusion through cylindrical pores of constant radius. Based on the estimated pore size, to was 174 h at 5-cmH2O Paw, supporting our explanation that the increase in Cc/Ca and reduction in Ac/Av with time at 5-cmH2O Paw (Fig. 4) were due to osmotic absorption of interstitial cuff liquid by the vascular and alveolar spaces. Fourth, the Ae was calculated from to with the estimates of De, Vc, and Le based on epithelial thickness. Finally, the Ae, together with Rp, alveolar radius, and alveolar number, was used to estimate pore number per alveolus and pore spacing. The transport parameters are summarized in Table 2.
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DISCUSSION |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGMENTSREFERENCES |
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e was 0.9 and 0.7 at 5 and 15 cmH2O inflation pressure, respectively. The initial cuff growth to maximum size was determined by the airway-tointerstitial hydrostatic pressure difference and was largely independent of osmotic pressure gradients. We attributed this behavior to a relatively high interstitial resistance that reduced the effective 
c to that of the interstitium. At 5-cmH2O inflation pressure, after the initial cuff growth, the decrease in cuff size in conjunction with an increase in Cc was attributed to an osmotic flow of cuff liquid of reduced albumin concentration into the vascular and alveolar spaces. At 15-cmH2O inflation pressure, interstitial cuff concentration increased with time with little change in cuff size, consistent with a diffusion process. Method
We modified the method used previously to study interstitial cuff growth in liquid-filled rabbit (22, 23), dog (7, 11), and sheep lungs (10). There are several advantages in using liquid-filled rather than air-filled lungs. First, filling the lung with liquid eliminated the effect of alveolar surface tension so that the pressure acting on the epithelial surface was the inflation pressure. Second, submerging the lung in saline eliminated the effect of gravity on vascular pressure (46). Third, we subjected the vessels and airways to the same hydrostatic pressure and albumin concentration solution to eliminate any airway-to-vessel hydrostatic and osmotic pressure gradients. Using similar vascular and Paw values (zone 1) reduced the surface area for vascular-to-interstitial flow (12, 19, 46). Accordingly, the growth of interstitial cuffs occurred predominantly by flow from the alveolar space. Thus the albumin concentration measured in the interstitium reflected predominantly the sieving properties of the alveolar epithelium.
Because of the presence of lung parenchymal tissue, light intensity measured from the alveolar space was 70% of that measured from the stock solution. Thus the light measured in interstitial cuffs might have underestimated actual Cc. However, we believe this effect was small because the tissue in the interstitial cuff was diluted at least fivefold based on cuff size (22, 23).
Comparison with Previous Studies
In our laboratory's previous experiments in isolated rabbit lungs inflated with albumin solution (22, 23), the Ac/Av increased monotonically to a plateau that depended on the size of the vessels and the airway inflation pressure. In our present study, in addition to measuring cuff size, we also measured the increase in albumin concentration of the interstitial cuffs as a function of inflation time.
In the present study, the number of vessels examined was 100, which was considerably less than that measured in the previous studies (1,000; Refs. 22, 23). The number of cuffs examined was relatively small, mainly because of the time required to measure Cc. The small number of cuffs examined might account, in part, for the following differences between the present and previous studies. First, because of the small number of cuffs examined, no effect of vessel size on Ac/Av or Cc/Ca was observed. Second, the time required to reach a plateau in cuff size was shorter in the present study (0.5 vs. 1-5 h). No reduction of cuff size was observed in the previous study (22), which required 3-5 h to reach its maximum size. The reduction of cuff size also implied an interstitial cuff pressure that was below the airway inflation pressure (7).
Relation to Other Studies of Alveolar Clearance
Our results at the low inflation pressure confirmed our laboratory's previous observation (22) that cuff growth in rabbit lungs was slower than in dog (7) or sheep lungs (10) inflated to a higher inflation pressure (14 cmH2O). However, at the high inflation pressure, cuff growth rate was comparable to that measured in dog and sheep lungs. We attributed the growth of interstitial cuffs in our previous measurements to passive transport properties of the interstitium and ignored the effects of the epithelium. The slower cuff growth in the isolated rabbit lung contrasts to in vivo studies showing that clearance of liquid instilled into lobular regions was fastest in the rabbit and human and slowest in the dog (27). In these studies, clearance of alveolar liquid was accompanied by an increase in protein concentration in the remaining alveolar liquid. Active transport of liquid was postulated as the primary mechanism of clearance of airway liquid.
Whatever the role of active mechanisms in the absorption of alveolar liquid into the circulation, the results of the present study indicated that the clearance of alveolar liquid can occur via the interstitium into the vasculature by passive mechanisms. Interstitial clearance of alveolar liquid has been demonstrated in unanesthetized sheep that showed significant interstitial cuffs 4 h after the instillation of 100 ml of Evans blue dyed serum into the airways (26). The observed interstitial cuffs contained little albumin, which was evident from the lack of Evans blue color, and was consistent with the small Cc measured in the present study. The increasing protein concentration in the liquid instilled in sheep lungs, as the instilled liquid volume was reduced (26), might be brought about by the formation of interstitial cuffs of low-protein concentration followed by osmotic absorption of interstitial liquid by the circulation and by an active lymphatic pump. However, the magnitude of alveolar clearance by osmotic absorption of interstitial liquid relative to that by active epithelial pumps remains to be evaluated.
In the present study, the growth of interstitial cuffs at an inflation pressure of 5 cmH2O reached a maximum value in 1 h and was reduced by 75% in 2 h. In the adult rat, edema produced during 2 min of ventilation with an increased peak inspiratory pressure was reabsorbed by 45 min (14). The absorption of interstitial liquid mimics the behavior observed in the newborn lung at birth. In rabbits, perivascular cuffs that formed after birth decreased to the prenatal size by 6 h (1, 5). A more rapid clearance has been reported in newborn lambs (24). After birth, alveolar liquid is partially cleared by transepithelial active sodium ionic pumps (39), similar to the effect observed for the clearance of a solution instilled into lobular regions of adult sheep lungs (26).
Transport Properties of the Epithelium
The equivalent Rp of the epithelium of 4.5 nm estimated at 5-cmH2O inflation pressure is comparable to the value (5.6 nm) estimated from the transport of dextran molecules across rat alveolar epithelial type II cell monolayers (25). A similar value (5 nm) was estimated from the transport of hetastarch from the alveolar to vascular space in isolated perfused rat lungs (13). The number of equivalent pores estimated in the present study for the rabbit lung was 4.2 x 106/cm2 alveolar surface area, somewhat greater than the value of 2.5 x 106/cm2 estimated in the cell monolayers (25) and the value of 1 x 106/cm2 estimated in the rat lung (13).
In the present study, the e of 0.9 at 5-cmH2O inflation pressure decreased to 0.7 at the higher inflation pressure of 15 cmH2O. These values are consistent with the estimate (0.83) obtained in the isolated rat lung (13). The reduced reflection coefficient with lung inflation was attributed to an increase in the equivalent Rp due to pore stretching by the increased inflation pressure. This behavior was consistent with the results in adult sheep in which the equivalent epithelial pores increased their size in response to lung inflation (15). A similar behavior was indicated in rats in which 2 min of ventilation with an increased inspiratory pressure produced edema that was cleared by 45 min (14). Other studies have reported a transient increase in epithelial Rp from 1 to 4 nm in the newborn lung during birth (16). The Cc/Ca values of 0.34-0.37 measured in adult dog lungs (8, 9) are comparable to those measured in the present study.
Relationship to Alveolar Flooding
In the present study, alveolar reabsorption only occurred after the cuffs had reached maximum size when Kc was increased, which resulted in an ec greater than that of the interstitium. A similar mechanism might be at work in the alveolar flooding stage of high-pressure-type pulmonary edema, when interstitial and alveolar liquid have low but equal protein concentrations, or in high-permeability-type pulmonary edema, when interstitial and alveolar liquid have relatively high but equal protein concentrations (43, 44). Both situations demand a low ec. This behavior is obtainable with an increased Kc that produces an Ke/Kc of 1:3 with an ec of 0.3 (Fig. 6). Alveolar flooding in vivo occurs after the cuffs are formed (36) when the interstitial-to-airway hydrostatic pressure gradient just offsets the interstitial-to-airway osmotic pressure gradient. Under these conditions, Péclet numbers are relatively small, and the airway-to-interstitial protein concentration ratio approaches 1 (Eq. A11, APPENDIX).
Differences Between the Isolated Lung and the In Vivo Lung
There are major differences between the isolated lung as used in the present experiments and the in vivo lung. First, the isolated lung experiment was designed to study the growth of interstitial cuffs by transport of alveolar liquid across the epithelium. In vivo, the normal capillary pressure results in filtration into the interstitium, whereas a relatively high plasma protein concentration results in osmotic absorption of alveolar liquid into the circulation. Microvascular filtration in volume-loaded lambs (33) produced interstitial-to-plasma albumin concentration ratios of 0.3-0.7 that were similar to values measured after vascular and alveolar reabsorption in the present study. Second, in the isolated lung, clearance by interstitial lymphatics was absent so that any absorption of interstitial liquid by a restrictive endothelial and epithelial barrier resulted in an increase in interstitial albumin concentration. In vivo, the clearance of interstitial liquid and protein can occur by interstitial lymphatics that do not restrict the passage of protein. Third, in liquid-filled lungs, the maximum cuff size is achieved when the interstitial pressure reaches the Paw. In vivo, alveolar surface tension reduces the pressure acting on the epithelial surface, and the maximum cuff size is lower than that achieved in liquid-filled lungs (21). Fourth, in the air-filled lung at total lung capacity where alveolar surface tension is maximal, most of the inflation pressure is resisted by alveolar surface tension, and the effective pressure acting on the epithelial surface is reduced (3). Thus, in the liquid-filled lung, the 15-cmH2O inflation pressure required to produce an increased pore size is equivalent to a much higher inflation pressure in the air-filled lung (14-16).
Mechanisms Producing Cuff Growth and Reabsorption
We considered passive forces rather than active transport to be the predominant mechanism for the growth of interstitial cuffs. Vesicular transport, although a possibility, was considered unlikely in view of studies showing that the vesicular inhibitor nocodazole had no effect on alveolar protein clearance in the in vivo rabbit lung (18). Moreover, vesicular inhibitors increased tissue permeability in many isolated organ systems (6, 28, 29, 34). However, the role of active transport mechanisms in attenuating the growth and resolution of interstitial fluid cuffs needs to be specifically addressed in further studies.
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APPENDIX |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGMENTSREFERENCES |
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ec as a Function of Interstitial Resistance
The following analysis illustrates the reasons why the growth of interstitial cuffs to maximum size depends primarily on the hydrostatic pressure difference. The Starling equation relates bulk flow (
b) across a membrane to the differences in hydrostatic pressure (
P) and protein colloid osmotic (oncotic) pressure (
) acting across the membrane (36, 40)
 | (A1) |
= 0, as follows
 | (A2) |
ec is related to the e and c, obtained from Eq. A1, with P = 0
 | (A3) |
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| (A4) |
ec in terms of the Ke/Kc. Figure 6 is a linear-log plot of ec vs. Ke/Kc for the values of e of 0.9 and c of 0.1. For an interstitial resistance (reciprocal of conductance) that is much greater than epithelial resistance (Ke/Kc >> 1), ec 
c. This case was applicable to the initial phase of cuff growth when both c and ec were near 0, so that the b was determined primarily by P and was largely independent of (Eq. A1). As the cuff grows, interstitial resistance was reduced and Ke/Kc decreased, so that ec increased above c. When ec became big enough so that ec > P, alveolar reabsorption of cuff liquid occurred. In the limit, as Ke/Kc << 1, ec e. The condition during cuff growth, Ke/Kc >> 1, ec c, implied that Ke was much greater than Kc, as the following estimates during cuff growth showed.
First, we estimated the Vc relative to the value of 5% of air space volume measured in sheep lungs, where maximum Ac/Av was 2.4 (10). Based on the maximum Ac/Av of 0.7 measured in our present study (Fig. 4A), Vc was 1.5% of air space volume. Because rabbit air space volume was 100 ml (35 ml/kg; Ref. 47), Vc was, therefore, 1.5 ml.
We obtained an estimate of Kec from the results of electrical analog models of cuff growth measured in previous studies (22, 23). Fluid resistance (R) of the Kec in those studies was defined by using Darcy's law for a porous material
 | (A5) |
P per unit flow () normalized by dividing by vessel volume (Vv). Here Kp is a permeability constant and 
is the fluid viscosity; and Lv is the lumped vessel length. Note that, with cuff growth, R decreases as Ac/Av increases. R at the start of cuff growth was 35 cmH2O/h (23). From the maximum Vc value of 1.5 ml, and maximum Ac/Av of 0.8, Vv was 2 ml. Kec, equal to Vv/R, was, therefore, 6 x 10-2 ml·h-1·cmH2O-1.
Epithelial conductivity in the rat lung (13) was estimated to be 2 x 10-5 ml·h-1·cm-2·mmHg-1. For an alveolar surface area in rabbit lung of 7.5 x 104 cm2 (see below), Ke was 1 ml·h-1·cmH2O-1. For Kec of 6 x 10-2 ml·h-1·cmH2O-1 (above), Ke/Kc was 16 (Eq. A2). With the use of typical values of e of 0.9, c of 0.1 (42), and Ke/Kc of 16 in Eq. A4, ec was 0.11; that is, c was a good approximation of ec during cuff growth.
Interstitial Cuff Liquid Reabsorption by Osmotic Flow
We used the Starling equation to estimate the absorptive pressure from interstitial cuffs into vessels after the cuffs had grown to maximum size
 | (A6) |
cn is the bulk flow of liquid across the interstitial-endothelial barrier; Kcn is interstitial-endothelial barrier conductance; Pc is interstitial hydrostatic pressure; Pv is vascular hydrostatic pressure; cn is interstitial-endothelial barrier reflection coefficient; c is interstitial protein colloid osmotic pressure; and v is vascular protein colloid osmotic pressure. We used an equation analogous to Eq. A4 to evaluate the cn
 | (A7) |
n is the endothelial reflection coefficient, and Kn is endothelial conductance. Because the vascular pressure was equal to or slightly below the Paw (zone 1), the entire capillary bed was collapsed so that osmotic reabsorption occurred across precapillary corner vessels (12, 19). Under these conditions, Kc was much greater than Kn (Kn/Kc << 1), so that cn was associated with the endothelium. In other words, cn = n.
At 5-cmH2O Paw, after the cuffs have grown to maximum size so that Pc = Paw = Pv, the absorptive pressure from the cuffs into the vessels was proportional to the difference in the effective osmotic pressure between the cuff and vessel, n(c - v). We used Landis and Pappenheimer's equation (20) relating albumin osmotic pressure (cmH2O) to albumin concentration (C; g/dl): = 1.36 (2.8C + 0.18C2). With Cc/Ca of 0.1, Ca (and Cv) of 3 g/dl, and, assuming n for the endothelium to be 0.7 (40), n(c - v) was 8.2 cmH2O. This absorptive osmotic pressure was reduced to 6.4 and 2.7 cmH2O as Cc/Ca was increased to 0.3 and to 0.7, respectively. The reduction of the Ac from the maximum value of Ac/Av of 0.8 to 0.2 as cuff liquid was absorbed into the vessel resulted in a reduction of Pc from 5 to 1.3 cmH2O, based on an initial value of 0 cmH2O for Pc at the start of cuff growth (4) and a constant interstitial compliance. Accordingly, the net absorptive pressure into the vessels was reduced from its maximum value of 8.2 cmH2O (with a P of 0 cmH2O) at 1 h to -1 cmH2O (with a P of 3.7 cmH2O) at 10 h. Thus net absorption at 1 h diminished with inflation time, becoming a small net filtration at 10 h. The increase in Cc/Ca between 1 and 10 h was caused by an osmotic flow of cuff liquid with a reduced C into the vascular and alveolar spaces that was maximal at 1 h and became smaller as the increasing Cc/Ca reduced the effective osmotic pressure difference.
Our results with Ringer solution in the vessels (Table 1, groups F-H, Fig. 5) indicated that reabsorption of cuff liquid also occurred into the alveolar space between 1 and 3 h, because Cc/Ca increased from 0.1 at 1 h to 0.22 at 3 h. This was associated with a small (insignificant) decrease in Ac/Av. Reabsorption of cuff liquid into the alveolar space required that ec increase above c during cuff growth, as interstitial resistance decreased with cuff growth (Eq. A5). After cuff growth to maximal size, an ec value of 0.3 would be sufficient to produce alveolar reabsorption. This could be obtained with a reduction in Ke/Kc to 1:3 (Eq. A4, Fig. 6); that is, with an interstitial resistance that was threefold smaller than the epithelial resistance. For ec of 0.3, the effective osmotic pressure difference for alveolar reabsorption [ec(c - a)] was 2.5 cmH2O at 1 h and was reduced to 1.8 cmH2O at 7 h. Accordingly, net absorption into the airways occurred at 1 h, with a maximal absorptive pressure of 2.5 cmH2O (P of 0 cmH2O), and changed to net filtration with an absorptive pressure of -1.9 cmH2O (P of 3.7 cmH2O) at 7 h. In the foregoing analysis, we neglected the effects of diffusion. We showed later that diffusion was negligible at 5-cmH2O Paw based on the estimated Rp.
At Paw of 15 cmH2O, an effective osmotic pressure difference of 3 cmH2O would reduce Ac/Av by 20% and would be offset by a reduction of Pc by 3 cmH2O. The small decrease in Ac/Av was not detected in our measurements and was consistent with previous measurements of perivenular interstitial pressure by micropuncture at the lung hilum that equilibrated to the inflation pressure of 15 cmH2O (23). Thus any opposing osmotic force due to reabsorption might have been too small to be detected or might be masked by the much larger number of cuffs with a slower growth rate that was measured in the previous study (see DISCUSSION; Refs. 22, 23). However, studies in dog lungs showed that hilar interstitial pressure equilibrated to 11.5 cmH2O with a lung inflation pressure of 14 cmH2O and suggested a small absorptive pressure of 2.5 cmH2O (7).
Modeling Diffusion Across the Epithelium
At 15-cmH2O Paw, because Ac/Av remained constant after cuff growth, the increase in Cc/Ca with inflation time was modeled as a diffusion process to determine the to for diffusion across epithelial pores. Diffusion from the cuffs into the vessels was neglected because of the small endothelial surface area associated with the zone 1 conditions (Paw = Pv; Refs. 12, 19, 46). We used the differential form of Fick's law to describe the time (t) rate of transfer of a solute mass (Mc) into the interstitial cuff volume (solute concentration Cc, volume Vc, Cc = Mc/Vc) across the epithelial membrane from the alveolar space (solute concentration Ca)
 | (A8) |
 | (A9) |
 | (A10) |
b. A linear regression fit to the values of ln(1 - Cc/Ca) vs. t data produced a slope of -1/to and intercept ln(1 - Co/Ca), from which the values of to of 4.7 h and Co/Ca of 0.33 were obtained (P < 1 x 10-5).
Modeling Transport During Cuff Growth: Relationship Among Cc/Ca, , and Solute-to-Rp Ratio
We modeled the epithelium as a membrane to determine its e from measured values of Cc/Ca. The equilibrium solution for Cc/Ca for solute flow across a membrane with uniform cylindrical pores is as follows (40)
 | (A11) |
e is due to solute drag for the epithelium. The parameter x is the Péclet number, defined as the ratio of the solute flux due to b to that due to diffusion (DeAe/Le)
 | (A12) |
b relative to diffusion (Péclet number > 4), exp(-x) 0, and Eq. A12 becomes
 | (A13) |
 | (A14) |
is the solute distribution function, the core-to-pore area ratio. The core area is the area within one solute radius of the pore wall. We assumed that the initial cuff growth to maximal size occurred by b with high Péclet number so that e = 1 - Cc/Ca (Eq. A13). This was justified below. From the minimum values of Cc/Ca of 0.1 and 0.33, e was 0.9 and 0.67 for Paw of 5 and 15 cmH2O, respectively. The a/Rp values were 0.77 and 0.57 for Paw of 5 and 15 cmH2O, respectively (Eq. A14). With an albumin molecular radius (a) of 3.5 nm, Rp was 4.5 and 6.1 nm for Paw of 5 and 15 cmH2O, respectively (Table 2). Transport Properties of the Epithelium
The to at 15-cmH2O Paw allowed the determination of Ae/Le for the epithelial membrane by specifying values for Vc and De. We modeled the diffusion through cylindrical pores of uniform diameter. The diffusion of a solute through a cylindrical pore is as follows (35)
 | (A15) |
was 0.19, and De = 0.02Df was 0.12 x 10-7 cm2/s. We assumed an interstitial Vc of 1.5 ml. From to = VcLe/(DeAe), Ae/Le was then 7,400 cm. At Paw of 5 cmH2O, k was 53, was 0.053, and De was 0.001Df. Ae/Le was 4,000 (proportional to 
). We assumed that Vc was similar at both 5- and 15-cmH2O Paw, based on the maximum lung volume at Paw of 6 cmH2O measured in saline-filled lungs (3). We verified that the Péclet number was in the range for which Eq. A14 was valid, as follows. With flows of 1.5 and 6 ml/h (maximum Vc of 1.5 ml divided by time of 1 and 0.25 h) at 5- and 15-cmH2O Paw, respectively, the Péclet numbers were 17 and 6, respectively, justifying the assumption used to determine Eq. A13. The to at 5-cmH2O Paw, with an Ae/Le of 4,000, Vc of 1.5 ml, and De of 6 x 10-10 cm2/s, was 174 h. Thus the diffusive flux at 5-cmH2O Paw was too small to explain the increase in Cc/Ca observed over the 10 h (Fig. 4B). This supported our explanation that the increase in Cc/Ca was due to absorption by an osmotic flow into the vascular and alveolar spaces.
For an epithelial thickness (Le) of 0.5 µm and Ae/Le of 4,000 cm at 5-cmH2O Paw, the total pore area was 0.20 cm2. Total alveolar surface area was 7.4 x 104 cm2, based on an alveolar diameter of 80 µm and total alveolar volume of 100 ml (47). The pores numbered 3.1 x 1011, based on a Rp of 4.5 nm. The number of pores was 4.2 x 106/cm2 alveolar surface area. The number of pores per alveolus was 840, based on the number of alveoli of 3.7 x 108, equal to the total alveolar volume divided by the volume of an alveolus. The interpore spacing for a square lattice distribution was 5 µm. A summary of the transport parameters is given in Table 1.
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ACKNOWLEDGMENTS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGMENTSREFERENCES |
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This research was supported by National Heart, Lung, and Blood Institute Grants HL-40362 and HL-36597.
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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REFERENCES |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGMENTSREFERENCES |
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). 
, Measurement from the interstitial cuff.