## Abstract

In ischemic organs, the protein reflection coefficient (ς) can be estimated by measuring blood hematocrit (Hct) and protein after increasing static vascular pressure (P_{v}). Our original equation for ς (*J Appl Physiol* 73: 2616–2622, 1992) assumed a constant vascular volume during convective fluid flux (*J˙*). In this study, we*1*) quantified the rate of vascular volume change (dV/d*t*) still present in ischemic single ferret lungs after 20 min of P_{v} = 30 Torr and *2*) developed an equation for ς that allowed a finite dV/d*t*. In 25 lungs, we estimated the dV/d*t* after 20 min at P_{v} = 30 Torr by subtracting *J˙* from the rate of lung weight gain (W˙_{L}). The relationship between *J˙* (0.15 ± 0.02 ml/min) andW˙_{L} (0.24 ± 0.02 g/min) was significant (*R* = 0.66, *P *< 0.001), but the slope was <1 (0.41 ± 0.10, *P *< 0.05). dV/d*t*(0.10 ± 0.02 ml/min) was similar in magnitude to*J˙* at 20 min. The modified equation for ς revealed that a finite dV/d*t* caused the original ς measurement to underestimate true ς. A low ς, high*J˙*, high baseline Hct, and long filtration time enhanced the error. The error was small, however, and could be minimized by adjusting experimental parameters.

- pulmonary circulation
- vascular permeability
- lung injury
- filtration coefficient

the permeability of the pulmonary vasculature to plasma proteins is an important determinate of transvascular fluid flux (*J˙*). This is described by the Starling equation (15)
Equation 1where *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 Π_{v} and Π_{i} are the osmotic pressures in the plasma and interstitial fluids, respectively, of an osmotically-active substance. ς is a dimensionless index that modifies the effect of the osmotic pressure gradient based on the vascular permeability of the osmotic agent. ς 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 ς 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 ς for albumin (ς_{alb}) from changes in hematocrit (Hct) and albumin concentration (C) assuming that diffusive protein flux was negligible (2)
Equation 2where Hct_{0} and C_{0} represent the initial values before fluid filtration. With the use of these relationships, ς_{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 ς_{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 ς_{alb} in ischemic ferret lungs and *2*) determine the theoretical effect of a changing vascular volume on the measurement of ς derived for the no-flow condition. To assess the rate of vascular volume increase in ischemic lungs, we measured*J˙* 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 (W˙_{L}) at the end of the 20-min period.

## METHODS

#### 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% O_{2}-5% CO_{2} 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.

After the lungs were flushed of residual blood, P_{v} was controlled by connecting the vascular cannulas to a pressurized reservoir containing the same flush solution. The temperature was maintained at 37°C by enclosing the lungs in plastic and submerging them in a water bath. The lungs (*n* = 25) were then subjected to either 45 or 180 min of ischemia. The 180-min ischemic lungs were further subdivided into groups of low (1–2 Torr) or high (7–8 Torr) P_{v}. Some of the low-P_{v}lungs were treated with either a nitric oxide donor or a cell-permeable analog of cGMP (10). After the desired ischemic time, the right lung was removed, and the left lung was weighed and suspended from a force transducer. The pulmonary artery cannula was connected to a pressurized stirred reservoir containing a mixture of PSS and autologous washed erythrocytes (hematocrit 20%). After the vasculature of the left lung was flushed with 10 ml of this solution, the left atrial cannula was connected to the same reservoir, and intravascular pressure was increased from 15 to 30 Torr by 5-Torr increments in 5-min intervals to allow assessment of vascular leaks. Vascular compliance was estimated by dividing the weight gain observed 5 min after the first increase in P_{v} by the change in P_{v}. P_{v} was then maintained at 30 Torr for 20–30 min to allow convective fluid filtration. After the increase in P_{v}, the intravascular PSS-erythrocyte mixture was pumped at 17 ml/min from the left atrial cannula to a fraction collector adjusted to obtain 1-ml samples. The C and Hct were measured in each sample, and ς_{alb} was calculated using *Eq. 2.J˙* was measured by separate analysis of the Hct values using *Eq. 12
* (derived below) and compared withW˙_{L} present over the final 5 min of increased P_{v.} The measurement of *J˙* by this method is unaffected by changes in vascular volume outside the fluid-conducting regions or loss of edema fluid from the surface of the lung (10). The W˙_{L} at 20 min was considered to be the sum of any continued increase in vascular volume (dV/d*t*) and *J˙*. Therefore, dV/d*t* was considered to be the difference betweenW˙_{L} and *J˙* estimated from the Hct curve.

A complete Hct curve was present in 13 of 25 experiments. In the remainder, the downslope of the curve failed to intersect the*x*-axis. Under these circumstances, the curve was extrapolated on a semilog plot. The average extrapolated sample number necessary to complete these curves was 4.3 ± 0.8. The filtration time used in the calculation of *J˙* was chosen as the time spent at a P_{v} of 30 Torr because the contribution to filtration made by the short times (≤5 min) at the lower levels of P_{v} was trivial based on our previous measurements of the filtration coefficient (*K*
_{f}) in this preparation (1).

#### Theoretical derivation of equations for J˙ and ς in nonflowing condition with changing vascular volume.

During the measurement of ς, 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 (Q˙_{i}) because of an increasing vascular volume (V) and the onset of*J˙*. The change in the intravascular plasma water volume (V_{w}) per unit period of time (*t*) is
Equation 3Because Q˙_{i} =*J˙* + dV/d*t*
Equation 4The change in the volume of red blood cells (V_{rbc}) per unit time is
Equation 5Because Hct = V_{rbc}/V
Equation 6By substituting *Eq. 5
* into *Eq. 6
*, we get
Equation 7If we assume that dV/d*t* and*J˙* are constant, *Eq. 8
* can be integrated to yield
Equation 8By solving *Eq. 8
* for *J˙*and simplifying, we get
Equation 9If we assume that hemorrhage, edema clearance, and evaporation are negligible, then dV/d*t* = W˙_{L}− *J˙*. By substituting into *Eq.9
* and simplifying, we get
Equation 10The excess V_{rbc} due to*J˙* 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
Equation 11where V_{s} is the sample volume, Hct_{n} is the Hct in the *n*th sample, and *x* is the last sample with a Hct value above Hct_{0}. By solving *Eq. 11
* for Hct, substituting into *Eq. 10
*, and simplifying, we get
Equation 12Note that dV/d*t*, Hct (the actual average Hct in the fluid exchanging region before collecting the serial blood samples), and W˙_{L} have dropped out of the equation, indicating that this measurement of *J˙* is independent of these factors.

If we assume that diffusive transvascular protein flux was small relative to convective flux, the change in the amount of intravascular protein (Prot) per unit time would be
Equation 13Because Prot = V_{w}C
Equation 14By combining *Eqs. 13
* and *
14 *and rearranging, we get
Equation 15By substituting *Eq. 4
* into *Eq. 15
* and replacing V_{w} with an equivalent expression, we get
Equation 16By rearranging *Eq. 8
*, it can be shown that
Equation 17
By substituting *Eq. 17
* into *Eq. 16
*, integrating, and solving for C/C_{0}, we get

#### Statistics.

The relationship between *J˙* andW˙_{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

#### Relationship between J˙ and W˙_{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 *J˙* and W˙_{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. W˙_{L} (0.24 ± 0.02 g/min) was 1.5-fold greater than*J˙*, which averaged 0.15 ± 0.02 ml/min. dV/d*t* averaged 0.10 ± 0.02 ml/min. ς_{alb} averaged 0.38 ± 0.05 and ranged from 0.09 to 0.89. Although W˙_{L} and*J˙* (10) were significantly different between subgroups of lungs (data not shown), there were no differences in dV/d*t* or vascular compliance, which averaged 0.27 ± 0.01 ml/Torr.

#### Theoretical effect of dV/dt on measured ς.

To determine the effects of an increasing vascular volume on the measurement of ς, 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 ς were entered into *Eq. 18* to allow calculation of C/C_{0}. We used this ratio to calculate a measured ς by iteration from *Eq. 2
*, which assumes that dV/d*t* is 0 during the increased P_{v}.

Figure 2 shows the effect of an increasing dV/d*t* on the ratio of the measured to the true ς at three different levels of true ς and*J˙*. We selected a Hct_{0}of 0.20, a measurement time of 20 min, and a V_{0} of 4 ml (based on weight gain over first 5 min) to mimic the conditions in the single ferret lungs shown in Fig. 1. The measured ς from *Eq.2
* correctly predicted the true ς when dV/d*t* was 0 but underestimated the true ς when dV/d*t* exceeded 0. The amount of underestimation increased at lower levels of true ς and higher levels of *J˙* but plateaued at a dV/d*t* of 0.2 ml/min in all cases. As dV/d*t* was increased further, the ratio of measured to true ς increased in all cases and approached 1 (data not shown). Over this range of*J˙*, the magnitude of the error was small. For example, the measured ς in a lung with a true ς of 0.1, a dV/d*t* > 0.2 ml/min, and a*J˙* of 0.15 ml/min would underestimate the true ς by only 0.005.

As shown in Figs. 3 and4, an increase in either Hct_{0} or filtration time associated with a constant but finite dV/d*t* (0.3 ml/min) also caused a discrepancy between the measured and true ς, but the error was small over the range of values for Hct_{0} and filtration time typically used in isolated lung preparations.

## DISCUSSION

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 W˙_{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 *J˙* as assessed byW˙_{L}. We were also interested in the potential effect of a changing vascular volume on our calculation of ς_{alb}(2).

To demonstrate the presence of a continued vascular volume change in the absence of pulmonary blood flow, we compared W˙_{L}after 20 min of increased static P_{v} with a measurement of*J˙* 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/d*t* was present after 20 min of increased P_{v}, approximating the magnitude of *J˙*. These data are similar to the relationship between dV/d*t* and*J˙* 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/d*t* between 3 and 40 min of ∼0.36 ml · min^{−1} · 100 g wet wt^{−1} in perfused lungs compared with 0.95 ± 0.20 ml · min^{−1} · 100 g wet wt^{−1} in ischemic ferret lungs in the present study.

Our results suggest that a slow vascular volume change significantly contributes to W˙_{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/d*t* could have overestimated the true dV/d*t* if either the gravimetric assessment of *J˙* + dV/d*t*was an overestimate or the Hct-derived*J˙* 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 *J˙* by*Eq. 12. *Alternatively, the estimate of dV/d*t*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 ς_{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 ς_{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 ς given that ς was present in multiple places in the equation, including the exponential term. We therefore selected baseline conditions, including a true ς, and time to allow calculation of the resulting Hct by *Eq. 8
*. These values determined C/C_{0} by *Eq. 18 *and the measured ς by *Eq. 2.*

To avoid undue complexity, we made dV/d*t* and*J˙* constant over the time frame of the measurements. A constant dV/d*t* is not out of keeping with direct measurements of the slow change in vascular volume in perfused lungs (7). Although*J˙* probably does increase as V increases, the use of an average *J˙*in *Eq. 18* does not affect the calculation of the measured ς from *Eq. 2
* at any time *t*. The same is true for dV/d*t*; 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/d*t*. We tested this by comparing the measured ς obtained after 20 min with a constant dV/d*t*and *J˙* to the ς resulting from a ramp increase in *J˙* designed to maintain proportionality between *J˙*and V. The time was divided into equal segments allowing incremental increases in V_{0}, Hct_{0}, Hct, and C/C_{0} for each segment of time based on the increasing*J˙*. The same final Hct and C/C_{0} (and therefore ς) values resulted if the average*J˙* 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 ς to underestimate the true ς. Moreover, this effect was magnified when the true ς was low, the*J˙* was high, the filtration time was long, and the Hct_{0} 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 ς is based on the change in C relative to the change in Hct, the mixing effect would therefore produce an artifactual decrease in ς that would be enhanced under conditions that generated greater final Hct values, such as a decreased true ς, an increased*J˙*, a long filtration time, and an increased Hct_{0}.

The quantitative analysis of the effect of a changing V on ς indicated that the effect on even the extreme combination of a true ς of 0.1, dV/d*t* of 3 ml/min,*J˙* of 0.3 ml/min (a twofold greater *J˙* than the average observed in the ferret lungs), Hct_{0} of 0.40, and a time of 60 min produced a measured ς that was 83% of the true value. Assuming that our estimate of dV/d*t* was correct for the ferret lungs shown in Fig. 1, the average error present in the measured ς_{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/d*t* of the ferret lung experiments. Given that the average *J˙*, Hct_{0}, and measured ς_{alb} were 0.15 ml/min, 0.21, and 0.40, respectively, the measured ς_{alb}underestimated the true ς_{alb} by <3%. On the basis of these results and the inherent difficulties in accurately measuring V_{0}, dV/d*t*, and*J˙* under the usual experimental conditions, we feel it is reasonable to continue to use *Eq.2
* to measure ς_{alb} in the ischemic pulmonary vasculature. When possible, however, conditions should be set to minimize the error between the measured and true ς. These include a Hct_{0} 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 ς_{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 ς_{alb} when performed by our previously described (2) modification of the filtered volumes technique. Failure to consider the increasing vascular volume caused the measured ς to underestimate the true ς. 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.

## Acknowledgments

The authors thank Wendy Buchanan and Teresa Privett for expert technical assistance and Wanda Moran for excellent secretarial support.

## Footnotes

This work was supported by National Heart, Lung, and Blood Institute Grants HL-50504 (to D. B. Pearse) and HL-02933 (to P. M. Becker) and by a grant-in-aid (to D. B. Pearse) and an Established Investigator Award (to D. B. Pearse) from the American Heart Association, with funds contributed in part by the American Heart Association, Maryland Affiliate.

Address for reprint requests and other correspondence: D. B. Pearse, Div. of Pulmonary and Critical Care Medicine, Hopkins Bayview Medical Center, 5501 Hopkins Bayview Circ., Baltimore, MD 21224 (E-mail: dpearse{at}welch.jhu.edu).

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- Copyright © 2001 the American Physiological Society