INTRODUCTION

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THE PERMEABILITY of the pulmonary vasculature to plasma proteins is an important determinate of transvascular fluid flux (). This is described by the Starling equation (15)

(1)

where K_f is the filtration coefficient (a term describing the transvascular hydraulic conductance); P_v and P_i are intravascular and interstitial pressures, respectively; and _v and _i are the osmotic pressures in the plasma and interstitial fluids, respectively, of an osmotically-active substance.  is a dimensionless index that modifies the effect of the osmotic pressure gradient based on the vascular permeability of the osmotic agent.  varies between 0 and 1 such that a value of 0 indicates free permeability and a value of 1 indicates complete impermeability of the osmotic agent across the vascular barrier.

We (2) previously described a modification of the filtered volumes technique (14) for measuring  in an isolated lung under conditions of no pulmonary blood flow. Static pulmonary vascular pressure was increased to cause convective fluid filtration. After a defined period of time, reservoir blood was pumped rapidly through the pulmonary vasculature without recirculation to allow collection of the pulmonary vascular blood volume in serial samples by a fraction collector. To assess protein permeability, we derived an analytical solution for the  for albumin (_alb) from changes in hematocrit (Hct) and albumin concentration (C) assuming that diffusive protein flux was negligible (2)

(2)

where Hct₀ and C₀ represent the initial values before fluid filtration. With the use of these relationships, _alb values could be calculated from individual vascular volume samples. The advantages of this method over approaches to assess vascular permeability in perfused lungs included 1) direct measurement and precise control over the P_v driving filtration, 2) generation of larger changes in Hct for any degree of filtration because the vascular volume was not continuously mixed with recirculating blood, and 3) the ability to measure changes in vascular permeability secondary to pulmonary ischemia independent from reperfusion (2, 3, 11, 12). We (2) previously showed that this measurement of _alb was not affected by either hemorrhage or vascular leak from the fluid-filtering regions of the lung.

The derivation of Eq. 2 assumed that vascular volume remained constant during the time that filtration occurred (2). This assumption may not be correct for filtration times 30 min, however, because pulmonary vascular volume continued to increase 20-30 min after a step increase in vascular pressure in isolated perfused dog lungs (5, 7, 9).

The purpose of the present study was to 1) estimate the magnitude of the change in vascular volume during the measurement of _alb in ischemic ferret lungs and 2) determine the theoretical effect of a changing vascular volume on the measurement of  derived for the no-flow condition. To assess the rate of vascular volume increase in ischemic lungs, we measured in isolated ferret lungs subjected to 20 min of increased static P_v and compared the result with the steady-state rate of lung weight gain (_L) at the end of the 20-min period.

	METHODS

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Preparation. The isolated ferret lungs analyzed in this study were from a recently completed study, which examined the role of P_v and cyclic nucleotides on the increased pulmonary vascular permeability caused by ischemia (10). As previously described (10), adult male ferrets were anesthetized with pentobarbital sodium (50 mg/kg ip). After tracheostomy, mechanical ventilation began with room air at a tidal volume of 12 ml/kg body wt and a respiratory rate of 20 breaths/min. The animals were exsanguinated via an abdominal aortic catheter, and ventilation was adjusted to 10 breaths/min with 95% O₂-5% CO₂ and a positive end-expiratory pressure of 3 Torr. These settings were constant for the remainder of the experiment. The pulmonary artery and left atrium were cannulated, and the lungs were excised. The pulmonary vasculature was flushed with 50 ml of physiological salt solution (PSS) containing 3 g/dl albumin, 2 g/dl Ficoll, and no glucose.

Eq. 2.

Theoretical derivation of equations for and  in nonflowing condition with changing vascular volume. During the measurement of , P_v was increased to a constant level by increasing pressure in a common reservoir connected to the pulmonary artery and left atrium. As a result, fluid flowed into the lung from the reservoir (_i) because of an increasing vascular volume (V) and the onset of . The change in the intravascular plasma water volume (V_w) per unit period of time (t) is

(3)

Because _i =  + dV/dt

(4)

The change in the volume of red blood cells (V_rbc) per unit time is

(5)

Because Hct = V_rbc/V

(6)

By substituting Eq. 5 into Eq. 6, we get

(7)

If we assume that dV/dt and are constant, Eq. 8 can be integrated to yield

(8)

By solving Eq. 8 for and simplifying, we get

(9)

If we assume that hemorrhage, edema clearance, and evaporation are negligible, then dV/dt = _L  . By substituting into Eq. 9 and simplifying, we get

(10)

The excess V_rbc due to in the vasculature at the end of the filtration period is equal to the sum of the excess V_rbc (above baseline) in the serial vascular volume samples obtained by a fraction collector at the end of the experiment. Thus

(11)

where V_s is the sample volume, Hct_n is the Hct in the nth sample, and x is the last sample with a Hct value above Hct₀. By solving Eq. 11 for Hct, substituting into Eq. 10, and simplifying, we get

(12)

Note that dV/dt, Hct (the actual average Hct in the fluid exchanging region before collecting the serial blood samples), and _L have dropped out of the equation, indicating that this measurement of is independent of these factors.

(13)

(14)

(15)

(16)

(17)

(18)

Statistics. The relationship between and _L was determined by least-squares linear regression. The values presented in the text are means ± SE. Differences were considered significant when P  0.05.

	RESULTS

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Relationship between and _L in ischemic ferret lungs. The average wet weight of the ferret lungs was 10.2 ± 0.2 g. As shown in Fig. 1, the relationship between and _L was significant (R = 0.66, P < 0.001), with a slope that was significantly <1 (0.41 ± 0.10, P < 0.05). An attempt to fit a second-degree polynomial resulted in nonsignificant coefficients, suggesting that a nonlinear relationship was unlikely. _L (0.24 ± 0.02 g/min) was 1.5-fold greater than , which averaged 0.15 ± 0.02 ml/min. dV/dt averaged 0.10 ± 0.02 ml/min. _alb averaged 0.38 ± 0.05 and ranged from 0.09 to 0.89. Although _L and (10) were significantly different between subgroups of lungs (data not shown), there were no differences in dV/dt or vascular compliance, which averaged 0.27 ± 0.01 ml/Torr.

View larger version (12K): [in this window] [in a new window]   Fig. 1.   Relationship between the rate of lung weight gain (L) measured after 20 min of static vascular pressure (Pv) = 30 Torr to rate of fluid flux () determined from the vascular hematocrit (Hct) profile in single ischemic ferret lungs (n = 25).

Theoretical effect of dV/dt on measured . To determine the effects of an increasing vascular volume on the measurement of , we chose values for the baseline conditions in Eqs. 8 and 18. Equation 8 was used to determine the Hct resulting from these starting values. This Hct and a true  were entered into Eq. 18 to allow calculation of C/C₀. We used this ratio to calculate a measured  by iteration from Eq. 2, which assumes that dV/dt is 0 during the increased P_v.

View larger version (17K): [in this window] [in a new window]   Fig. 2.   Effect of increasing rate of vascular volume increase (dV/dt) on the ratio of measured to true reflection coefficient () under conditions of three different true  and rates of . Filtration time and baseline hematocrit values for all curves were 20 min and 0.20, respectively.

View larger version (17K): [in this window] [in a new window]   Fig. 3.   Effect of increasing baseline hematocrit (Hct0) on the ratio of measured to true  under conditions of three different true  and rates of . Filtration time and rate of vascular volume increase for all curves were 20 min and 0.3 ml/min, respectively.

View larger version (18K): [in this window] [in a new window]   Fig. 4.   Effect of increasing filtration time on the ratio of measured to true  under conditions of three different true  and rates of . The rate of vascular volume increase and baseline hematocrit for all curves were 0.3 ml/min and 0.20, respectively.

	DISCUSSION

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In perfused lungs, several investigators (4-9) have shown that step increases in pulmonary vascular pressure can result in prolonged slow increases in pulmonary vascular blood volume. These measurements have been made by indicator dilution (7), by the accumulation of labeled erythrocytes (5), and by comparing _L with the concentration of an intravascular marker (4-6, 8, 9). For example, Maron and Lane (7) increased P_v in isolated dog lung lobes and found that vascular volume, measured by indicator dilution, continued to increase after 40 min of pressure elevation. Interestingly, this effect was exacerbated by increasing P_v within 30 min of initiating perfusion compared with waiting 70 min after the start of perfusion (7). Given the apparent inhibitory effect of perfusion on this phenomenon (7), we wondered whether static increases of P_v in the ischemic lung would also be associated with a prolonged increase in vascular volume. Similar to the situation in perfused lungs (5), this effect would impact the gravimetric measurement of K_f by causing an overestimation of as assessed by _L. We were also interested in the potential effect of a changing vascular volume on our calculation of _alb (2).

To demonstrate the presence of a continued vascular volume change in the absence of pulmonary blood flow, we compared _L after 20 min of increased static P_v with a measurement of that was not affected by vascular volume change and did not require continuous perfusion during the increase in P_v. This analysis suggested that a significant dV/dt was present after 20 min of increased P_v, approximating the magnitude of . These data are similar to the relationship between dV/dt and in perfused dog lung lobes after increasing P_v by 18 Torr for 20 min in Ref. 7. Assuming that the wet weight of an average dog lung lobe is 40 g (9), Maron and Lane (7) demonstrated a constant dV/dt between 3 and 40 min of ~0.36 ml · min¹ · 100 g wet wt¹ in perfused lungs compared with 0.95 ± 0.20 ml · min¹ · 100 g wet wt¹ in ischemic ferret lungs in the present study.

Our results suggest that a slow vascular volume change significantly contributes to _L after a step increase in P_v in ischemic ferret lungs. Before accepting this conclusion, however, it is important to consider possible limitations of our measurements. Our assessment of dV/dt could have overestimated the true dV/dt if either the gravimetric assessment of  + dV/dt was an overestimate or the Hct-derived was an underestimate of the true values. The inadvertent collection of leaked perfusate on the lung surface or lung hemorrhage would cause the weight to be an overestimate, whereas hemolysis, hemorrhage, or the inability to remove red blood cells from fluid-filtering regions of the vasculature would cause an underestimation of by Eq. 12. Alternatively, the estimate of dV/dt could have underestimated the true value if significant edema was cleared across the pleural surface (13).

We previously showed (2) that hemolysis did not occur in this preparation, and we were careful not to allow any extravascular fluid to accumulate on the preparation to avoid the potential problem of weighing leaked perfusate. We did not directly assess for the presence of lung hemorrhage and thus cannot exclude the possibility that a component of the decreased slope in Fig. 1 resulted from hemorrhage. We do not think this was the major explanation, however, because the relationship in Fig. 1 appeared to be reasonably linear over a wide range of vascular permeability; if hemorrhage was the predominant factor, one might expect a greater discrepancy in the more injured lungs.

The mechanism of the slow increase in pulmonary vascular volume has been attributed to both stress relaxation (6) and recruitment of previously closed vessels (7). In isolated perfused lungs, pretreatment with the vasodilator papaverine had no effect on the slow increase in vascular volume after a step change in P_v, suggesting that recruitment of closed vessels rather than stress relaxation may have been the predominant explanation (7). Although the mechanism may differ in the ischemic pulmonary vasculature, the large magnitude of the change in vascular volume observed in the present study was also more compatible with vessel recruitment than stress relaxation.

Given the likely presence of a prolonged increase in vascular volume in our preparation, we next attempted to determine whether this would have any theoretical influence on the calculation of _alb by our (2) modification of the filtered volumes technique (14) . The anatomic location of the changing vascular volume within the pulmonary circulation is an important consideration in this regard. An increase in vascular volume in nonfluid-filtering conduit vessels would have no effect on our measurement, whereas the influx of reservoir blood into fluid-filtering regions from an expanding vascular volume would clearly alter the effect of fluid filtration on Hct and C. Although we did not determine the anatomical location of the change in vascular volume in the ferret lung experiments, we assumed for the sake of our analysis that it occurred in the fluid-filtering regions to allow a "worst case" assessment of the effect on our measurement of _alb. To accomplish this, we modified our original analysis to allow a changing vascular volume during the increase in P_v. Similar to the original equation (Eq. 2), the new relationship (Eq. 18) was too complex to solve directly for  given that  was present in multiple places in the equation, including the exponential term. We therefore selected baseline conditions, including a true , and time to allow calculation of the resulting Hct by Eq. 8. These values determined C/C₀ by Eq. 18 and the measured  by Eq. 2.

To avoid undue complexity, we made dV/dt and constant over the time frame of the measurements. A constant dV/dt is not out of keeping with direct measurements of the slow change in vascular volume in perfused lungs (7). Although probably does increase as V increases, the use of an average in Eq. 18 does not affect the calculation of the measured  from Eq. 2 at any time t. The same is true for dV/dt; the rate may change over time, but the resulting values of Hct and C at time t can be predicted by using an average value of dV/dt. We tested this by comparing the measured  obtained after 20 min with a constant dV/dt and to the  resulting from a ramp increase in designed to maintain proportionality between and V. The time was divided into equal segments allowing incremental increases in V₀, Hct₀, Hct, and C/C₀ for each segment of time based on the increasing . The same final Hct and C/C₀ (and therefore ) values resulted if the average was used over the total time starting from the same original baseline values (data not shown).

As shown in Figs. 2-4, we found that an increasing V caused the measured  to underestimate the true . Moreover, this effect was magnified when the true  was low, the was high, the filtration time was long, and the Hct₀ was increased. These results are conceptually compatible with the predicted effect of mixing a given volume of reservoir blood with vascular blood from the fluid-filtering region on the final values of Hct and C. Mixing equal volumes of these solutions will generate a final Hct that is the arithmetic mean of the original Hct values, whereas the final C will be less than the mean C value because the protein is dissolved only in the plasma volume of the blood. Moreover, the deviation of the final C from the arithmetic mean C would be increased at greater final Hct values. Given that the calculation of  is based on the change in C relative to the change in Hct, the mixing effect would therefore produce an artifactual decrease in  that would be enhanced under conditions that generated greater final Hct values, such as a decreased true , an increased , a long filtration time, and an increased Hct₀.

The quantitative analysis of the effect of a changing V on  indicated that the effect on even the extreme combination of a true  of 0.1, dV/dt of 3 ml/min, of 0.3 ml/min (a twofold greater than the average observed in the ferret lungs), Hct₀ of 0.40, and a time of 60 min produced a measured  that was 83% of the true value. Assuming that our estimate of dV/dt was correct for the ferret lungs shown in Fig. 1, the average error present in the measured _alb by Eq. 2 in these lungs can be determined from Fig. 3 because all of these measurements employed the filtration time and average dV/dt of the ferret lung experiments. Given that the average , Hct₀, and measured _alb were 0.15 ml/min, 0.21, and 0.40, respectively, the measured _alb underestimated the true _alb by <3%. On the basis of these results and the inherent difficulties in accurately measuring V₀, dV/dt, and under the usual experimental conditions, we feel it is reasonable to continue to use Eq. 2 to measure _alb in the ischemic pulmonary vasculature. When possible, however, conditions should be set to minimize the error between the measured and true . These include a Hct₀ of 0.20 and the minimal P_v and filtration time necessary to produce an accurate increase in Hct.

In summary, increasing static pulmonary vascular pressure to 30 Torr in ischemic ferret lungs for 20 min to allow measurement of _alb appeared to be associated with a prolonged increase in vascular volume. This persistent changing vascular volume confounded the gravimetric assessment of fluid filtration and introduced an error in the measurement of _alb when performed by our previously described (2) modification of the filtered volumes technique. Failure to consider the increasing vascular volume caused the measured  to underestimate the true . Over a wide range of experimental conditions, however, the error was small (<10%) and could be further minimized by the appropriate adjustment of baseline parameters.