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Center for Biomedical Engineering, University of Kentucky, Lexington, Kentucky
Submitted 21 June 2005 ; accepted in final form 5 August 2005
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ABSTRACT |
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3 h after injection with both IP injection volumes. This behavior indicated transport of tracer through the diaphragm into the pleural space. A dynamic analysis of the tracer uptake with 5-ml IP injections showed that at least 50% of the total pleural flow was via the diaphragm. A similar estimate was derived from an analysis of total protein concentrations. Both estimates were based on restricted pleural capillary filtration and unrestricted transdiaphragmatic transport. The 5-ml IP injections did not change plasma protein concentration but increased pleural and peritoneal protein concentrations from control values by 22 and 30%, respectively. These changes were consistent with a small (8%) increase in capillary filtration and a small (20%) reduction in transdiaphragmatic flow from control values, consistent with the small (3%) decrease in hydration measured in diaphragm muscle. Thus the pleural uptake of tracer via the diaphragm with the IP injections occurred by the near-normal transport of liquid and protein. fluid transport; conscious rat; pleural liquid and protein transport; reflection coefficient; microvascular exchange
Accordingly, in conscious Wistar-Kyoto rats, we studied the transport of radioactive tracer 125I-albumin from the peritoneal cavity into the pleural space and circulation. We injected the rats intraperitoneally (IP) with 1 or 5 ml of Ringer solution containing 3 g/dl albumin and tracer. At selected times (2–48 h) after injection, we collected postmortem samples of pleural liquid, peritoneal liquid, and blood plasma and measured their radioactivity and total protein concentration. An analysis of tracer uptake and protein concentrations indicated that 50–80% of the total flow into the pleural space (
p) was contributed by a transdiaphragmatic flow.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIXGRANTSREFERENCES |
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5% of the total radioactivity) and molecular weight components below 5,000 Da (PD-10 desalting column; Amersham Biosciences, Piscataway, NJ). All solutions were filtered (0.45 µm) before injection into the animals.
After a selected time (2, 4, 6, 12, 24, and 48 h for the 5-ml IP injections or 3 and 6 h for the 1-ml IP injections), the animal was anesthetized with an intramuscular injection of ketamine (50 mg/kg) and xylazine (4 mg/kg), a blood sample was withdrawn from a jugular vein, and the animal was euthanized with an intravenous injection of pentobarbital sodium solution (100 mg/kg) and exsanguination. Postmortem, we dissected the overlying tissue of the abdomen and sampled peritoneal liquid by suction with a syringe via a length of PE-10 tubing. Then, with the supine animal tilted to allow pleural liquid to drain into the costophrenic region, we punctured the ventral region of the diaphragm to produce a pneumothorax. Through two holes pierced in the diaphragm, we collected pleural liquid from the costophrenic region of both sides of the thorax by suction with a syringe via a length of PE-10 tubing. To avoid contamination by blood, no attempt was made to collect all of the peritoneal and pleural liquid. Plasma samples were separated from the whole blood by centrifugation. The lung, diaphragm, and a sample of left thigh muscle were removed by dissection. The diaphragm was separated into its muscular part and central tendon. Samples of diaphragm muscle (0.4 g), central tendon (0.02 g), lung (0.8 g), and thigh muscle (0.3 g) were weighed, and their radioactivity counted. Then the samples were dried in an oven at 70°C to a constant weight to determine their wet-to-dry weight ratios (W/D). In some experiments, we also dissected samples of intercostal muscles of the first and seventh intercostal space.
Specific radioactivity (counts per second per gram) of the collected peritoneal liquid, pleural liquid, and plasma was measured before and after separation of their albumin fraction by desalting columns. In initial experiments, we used IP injection volumes with unpurified tracer and measured the total specific radioactivity of peritoneal liquid, pleural liquid, plasma, diaphragm muscle, diaphragm central tendon, thigh muscle, and lung. In the latter experiments, we measured (total) protein concentration of pleural liquid, peritoneal liquid, and plasma using a protein assay (Coomassie Plus, Pierce Biotechnology, Rockford, IL).
In some studies, we measured pleural liquid volume (Vp) by the following procedure. Postmortem, after the pleural liquid was sampled, a 2-ml Ringer solution containing 1 g/dl albumin was injected into the chest cavity to lavage the visceral and parietal pleural surfaces. The lavage liquid was collected by suction and weighed, and its specific radioactivity measured. The weight and the radioactivity of the initial pleural liquid collected and of the lavage liquid were used to calculate the Vp using a mass balance analysis.
To determine whether the 5-ml IP injection volumes per se affected the normal transport of liquid and protein, we repeated the entire experiment in seven rats without IP injections.
In separate studies, we repeated the foregoing studies, but, instead of injecting tracer into the peritoneal cavity, we injected tracer into the circulation. In these studies, the rat was anesthetized, and purified tracer (2 x 105 count/s in 0.3 ml of Ringer solution with 1 g/dl albumin) was injected into the tail artery. After 1 min, a sample of blood was withdrawn and its plasma radioactivity measured. The animal was allowed to recover from the anesthetic. After a selected time (0.5 and 1 h) following tracer injection, the animal was studied postmortem following the procedures identical to those used for the IP injection studies.
Statistics
Data are reported as means ± SD in Tables 1–4 and means ± SE in Figs. 2 and 3. We used a paired t-test or an unmatched t-test, where appropriate, to test for a significant difference between two groups. We accepted P < 0.05 to be significant.
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIXGRANTSREFERENCES |
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Tracer measurements in pleural liquid, peritoneal liquid, and plasma.
Figure 1 shows an example of the relative fraction of bound 125I-albumin in collected samples of peritoneal liquid (92%), pleural liquid (77%), and plasma (61%) separated by desalting columns. The IP injection volume consisted of 5 ml of 3 g/dl albumin in Ringer solution containing tracer with unbound 125I removed. The time after injection was 2 h. The fraction of bound 125I-albumin was the radioactivity of the first 6-ml eluent (3 min) relative to the total radioactivity eluted. In general, with the 5-ml IP injections, the fraction of bound 125I-albumin in the three liquids was 70–90% after 2–24 h and fell to 50% after 48 h. Tracer breakdown was faster with 1-ml IP injections: after 3 h, the bound tracer was 60%, and after 6 h it decreased to 40%. Accordingly, we reported no data of 1-ml IP experiments longer than 6 h. Specific activity (count per second per gram) was corrected by multiplying total tracer radioactivity by the fraction of bound tracer.
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Table 1 summarizes pleural tracer concentration (Cp)-to-Ca (Cp/Ca), plasma tracer concentration (Cc)-to-Ca (Cc/Ca), and Cp-to-Cc (Cp/Cc) ratios at different times after 1- and 5-ml IP injections. We used subscripts p for pleural, a for peritoneal (abdominal), and c for plasma (capillary). Ratios were corrected for unbound tracer. Figure 3 is a plot of tracer ratios Cp/Ca and Cc/Ca (A), and Cp/Cc (B) vs. time (t in h) for 5-ml IP injections. Note that tracer concentration was always higher in pleural liquid (Cp/Ca) than in plasma (Cc/Ca) up to 12 h, consistent with a transdiaphragmatic transport of tracer into the pleural space from the peritoneal cavity, in addition to transport from the circulation. At 2 and 4 h, Cp/Ca values (0.14 and 0.54) were significantly greater than the Cc/Ca values (0.026 and 0.057). Smaller Cp/Ca than Cc/Ca values would be expected if the tracer were to enter the circulation from the peritoneal cavity before it entered the pleural space. Consistent with the greater Cp than Cc, Cp/Cc was considerably >1 and varied between 10 and 3 between 2 and 12 h. This also indicated a transdiaphragmatic source of tracer other than from the circulation, since restricted microvascular filtration alone was expected to produce values for Cp/Cc < 1 (18).
The greater Cp/Ca than Cc/Ca values observed with 5-ml IP injections between 2 and 12 h was only observed at 3 h with 1-ml IP injections (Table 1). At 6 h with 1-ml IP injections, Cp/Ca and Cc/Ca values were not statistically different. The values for Cp/Ca, Cc/Ca, and Cp/Cc measured with 1-ml IP injections were much smaller than the values with 5-ml IP injections. The reason for the smaller values with 1-ml IP injections is speculative (see DISCUSSION).
For 5-ml IP injections, tracer Cp/Ca and Cp/Cc tended to values of 0.67 and 0.55 at 48 h, respectively, slightly lower than the equilibrium values (0.77 and 0.59) measured for protein concentration (see below, Table 3). This might indicate that a steady state was not reached, not unexpected with the continual washout of the tracer (Fig. 2). However, tracer Cc/Ca tended to a value of 1.3 at 48 h, consistent with the measured protein Ca/Cc of 0.76 (see Table 3).
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0.5) for Cdm/Ca than for Cdt/Ca (1) at 96 h. This behavior occurred in parallel with an increase in the Cp/Ca (Fig. 3). This indicated that pleural tracer was derived in part from the peritoneal liquid via the diaphragm. In contrast to the latter behavior, the response in lung [(Cl)/Cc] and thigh muscle [(Cm)/Cc] tracer concentrations relative to Cc values (Table 2) were, in general, invariant with time (3–96 h), a reflection of rapid equilibration of the tracer in these tissues with plasma because of microvascular filtration. We note that Cl was overestimated because of trapped blood (see below).
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Restricted tracer transport across the microvasculature was demonstrated by the ratios Cl/Cc and Cm/Cc for the lung and thigh muscle that attained steady-state values of 0.3 and 0.1, respectively, by 3 h with 5-ml IP injections (Table 2). The Cl/Cc values were overestimated by 30% because of the trapped blood in the isolated lung, estimated to be 25% of the lung wet weight in sheep (11). No correction was necessary for the Cm/Cc values because residual blood in muscle has been estimated to be <1% (29). Thigh muscle Cm/Cc values of 0.1 were near the expected value for a reflection coefficient (0.9) for the vascular endothelial barrier (18) and somewhat lower than interstitial protein concentration of skeletal muscle (3). Intercostal muscle Cm/Cc values were similar to those of thigh muscle.
Total protein measurements. Table 3 summarizes data of (total) protein concentrations in pleural liquid (Cp), peritoneal liquid (Ca), and plasma (Cc), and of Cp/Cc, Ca/Cc, and Cp/Ca. These measurements were done on samples collected from the experiments of Table 2 for 5-ml IP injections and the similar experiments for 1-ml IP injections. The data from the 3- to 96-h IP injections were pooled because there was no significant trend with time. In the control animals without IP injections, protein concentration averaged 5.0 g/dl for plasma, 2.4 g/dl for pleural liquid, and 2.9 g/dl for peritoneal liquid. Compared with control, the 5-ml IP injections increased peritoneal and pleural liquid protein concentration by 30 and 22%, respectively, with no change in the plasma protein concentration. A similar behavior was observed for the 1-ml IP injections, except for the absence of any change in the pleural protein concentration compared with control.
The changes in pleural and peritoneal liquid protein concentrations with the IP injections provided further evidence in support of transport across the diaphragm. First, plasma protein concentration did not change with 5-ml IP injections compared with control. Thus microvascular filtration across pleural capillaries cannot alone be responsible for the 22% increase in pleural liquid protein concentration measured with the 5-ml IP injections. The increased protein concentration in pleural and peritoneal liquid was consistent with a small increase in pleural flow across pleural capillaries coupled with a small decrease in pleural flow across the diaphragm (see DISCUSSION). Accordingly, the change in pleural protein concentration was attributed to the increase in protein concentration of peritoneal liquid that occurred with the 5-ml IP injections compared with control. Second, protein concentration was always less in Cp than in Ca. Cp/Ca averaged 0.82, 0.71, and 0.77 for control, 1-ml IP, and 5-ml IP injections, respectively. These values were consistent with transdiaphragmatic transport with a relatively small restriction to protein, with reflection coefficients (
d) of 0–0.3 based on a predominantly bulk flow (b) (see below and Eq. A2 of APPENDIX).
Previous measurements showed normal Cp/Cc values of 0.73 and 0.55 for albumin and protein, respectively, that were somewhat higher than values measured for tracer albumin (0.55) and protein (0.48) in the present study (17). These differences might reflect the different assays used to measure protein (Bromcresol Green) and albumin (Biuret) concentration in the previous study (17).
W/D. Table 4 summarizes the data of W/D values for the diaphragm tendon, diaphragm muscle, lung, and thigh muscle. W/D values did not vary with time (3–96 h) and were pooled. In general, there were only minor differences in W/D (<6%) among the control values and 1-ml IP and 5-ml IP injections. The diaphragm tendon had the lowest W/D values, followed by the diaphragm muscle, thigh muscle, and lung. The 1- and 5-ml IP injections produced a significantly small (2–4%) reduction in W/D values for diaphragm muscle compared with control. The reduced hydration might have resulted from a reduced flow and greater osmotic absorption of water from muscle tissue into the fluid that crossed the diaphragm with an increased protein concentration (20).
Pleural liquid volume. Pleural liquid volume (Vp) measured in the experiments after 3–48 h averaged 0.15 ± 0.082 ml with 5-ml IP injections (n = 48), 0.12 ± 0.053 ml with 1-ml IP injections (n = 43), and 0.14 ± 0.068 ml with intra-arterial tracer injections (n = 18). These values were not significantly different among the groups. The pooled values averaged 0.13 ± 0.070 ml (n = 115). Vp normalized by dividing by body weight averaged 0.62 ± 0.33 ml/kg, comparable to published values of 0.6 ml/kg (19). The similar pleural volume measured with 1- and 5-ml IP injections and with control supported the estimated small changes in pleural flow due to the IP injections (see Transport Analysis and DISCUSSION).
Transport Analysis
Model of albumin and liquid transport into the pleural space.
We developed a mathematical model of liquid and albumin transport from the circulation and peritoneal cavity into the pleural space. A brief outline is presented with details in the APPENDIX. Consider the pleural space as an input-output system (Fig. 4) with two input sources and one output source. One input source is the circulation, and the other is the peritoneal cavity via the diaphragm. The output is lymphatic outflow. Cp/Ca is given by the following first-order linear ordinary differential equation:
 | (1) |
c and d, respectively:
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c and a are the steady-state flows across the pleural microvascular barrier and diaphragm, respectively, and are related to p:
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p/Vp of 0.46 h–1. With only these values, it was not possible to determine a unique set of values for the remaining four constants (a, c, c, and d) using the three equations (Eqs. 2–4). Accordingly, values for a/p were obtained within the expected range for c (0.75–0.91) and d (0.03–0.39) that were consistent with restricted microvascular filtration (18) and a relatively unrestrictive diaphragm (20), respectively. Table 5 summarizes the calculated values. Here p was 0.06 ml/h based on the measured Vp (0.13 ml) and the computed p/Vp value (0.46 h–1). Note that a/p was in the range 0.52–0.83, that is, 52–83% of the total flow into the pleural space was across the diaphragm. These estimates agreed with those based on a steady-state analysis of protein data (see below).
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a/p.
The value of p of 0.06 ml/h, equivalent to 0.24 ml·h–1·kg–1, with 5-ml IP injections, was 12 times the value of 0.02 ml·h–1·kg–1 measured in sheep (28), dogs (22), and rabbits (9). Part of the greater pleural flow in the rat might be attributed to transdiaphragmatic flow that was reduced in the larger animals (see DISCUSSION).
Estimates of c, d, and a/p based on total protein concentrations.
The steady-state values of protein concentrations Cp, Ca, and Cc (Table 3) are related to a/p, c, and d by the equilibrium solution of Eq. 1 at infinite time when d(Cp/Ca)/dt = dCa/dt = 0:
 | (5) |
c, d, and a/p based on the average values for Cp/Cc and Ca/Cc measured in the control, 1-ml IP, and 5-ml IP experiments (Table 3). Note that, for c of 0.90–0.65 and d of 0–0.19, a/p ranged from 0.5 to 0.8. Thus both the tracer uptake and equilibrium protein analyses showed that flow into the pleural space via the diaphragm was 50–80% of the total flow.
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p, the protein concentration data allowed the estimate of the fractional changes in p and a with the IP injections from control values by the application of the Starling and solute flux equations (see DISCUSSION). |
DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIXGRANTSREFERENCES |
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p occurred across the diaphragm. Methods
To study albumin transport using tracer 125I-albumin, we needed to correct for the unbound 125I in the collected samples of the peritoneal liquid, pleural liquid, and plasma. This procedure for correcting for tracer breakdown was not applied to the radioactivity measured in tissue (lung, diaphragm, thigh skeletal muscle). Thus the tracer concentration ratios measured in the tissues involved the transport of both bound 125I-albumin and unbound 125I. Accordingly, only qualitative estimates were possible with regard to the transport of albumin through these tissues.
Tracer breakdown also limited the time that could be studied after the IP injection. The fraction of unbound 125I in the collected pleural liquid, peritoneal liquid, and plasma increased to 50% of the total tracer radioactivity after 48 h with 5-ml IP injections and after 6 h with the 1-ml IP injections. Thus our studies with 1-ml IP injections were limited to the initial stages of tracer uptake up to 6 h.
In general, tracer breakdown increased with the resident time in the body, tending to nearly the same fraction (50%) of total radioactivity in the peritoneal liquid, pleural liquid, and plasma at 48 h. This behavior might reflect recirculation that produced near steady-state values of bound and unbound tracer in the three compartments. The constant breakdown in the three compartments at 48 h also indicated that tracer concentration ratios based on the uncorrected total tracer radioactivity were subjected to little error. This was supported by the experimental data. In an in vitro experiment, the unbound 125I-albumin measured in a 3 g/dl albumin solution with tracer at 37°C was 20% after 48 h, much less than the 50% measured in vivo. One reason for tracer breakdown in vivo might be an immunological reaction to the bovine serum albumin used in the experiments, a substance that was foreign to the rats studied. These effects warrant further study.
The continuous breakdown of tracer also put into question the interpretation of the tracer albumin concentration ratios measured at each time point. However, the correction for unbound 125I did not substantially change the relative magnitudes of the tracer ratios measured in the pleural, peritoneal, and plasma liquids. Thus the data with no correction for unbound 125I produced the same conclusion that pleural tracer uptake occurred across the diaphragm. That the bound albumin tracer reflected to a large degree the actual transport of endogenous albumin was supported by the values of tracer concentration ratios at 48 h that approached the equilibrium values of protein concentration ratios.
The control Cp/Cc for protein (0.48) were close to previous values (0.55) measured in Wistar-Kyoto rats (17). However, in the latter study (17), the Cp/Cc was greater for albumin (0.73) than for protein (0.55), a reflection of the higher molecular weights of some proteins. These differences between albumin and protein were not observed in the present study with tracer albumin and protein. This might be due in part to the separation of the lower molecular weight fraction (<5,000 Da) from the tracer before use and in part to the insensitivity of the assay used in the present study.
Comparison with Previous Studies
In addition to the present tracer studies, transdiaphragmatic transport of peritoneal liquid into the pleural space would be supported by the following studies. Zakaria and Rippe (31) reported a small pleural effusion with an increased IP pressure of 8 mmHg induced by abdominal cuff compression in anesthetized rats with a large dialysate. The present study showed this effect under conditions closer to normal in conscious rats with much smaller IP volumes. In vitro studies in the isolated rat diaphragm muscle (20) showed a relatively high hydraulic conductivity and low reflection coefficient, similar to those of the pleural membrane (16). The greater thickness of the diaphragm would be partly offset by the much lower hydraulic conductivity and high reflection coefficient associated with the capillary endothelium, the predominant resistance to microvascular filtration (18).
The present studies did not allow us to separate the relative contribution of the central tendon and muscle to total flow across the diaphragm. The faster tracer uptake into the diaphragm central tendon than into the diaphragm muscle (Table 2) might seem to indicate a predominant role for the central tendon. However, the actual predicted transdiaphragmatic flow in conjunction with measured hydraulic conductivity of the isolated diaphragm muscle would suggest that most of the flow was across the diaphragm muscle. The flow across the diaphragm with 5-ml IP injections was estimated from the analysis to be 50–80% of the total pleural flow (0.06 ml/h), that is, 0.03–0.05 ml/h. Using a diaphragm muscle mass of 0.35 g and thickness of 0.07 cm (20), surface area was 5 cm2. Hydraulic conductivity of the rat diaphragm measured in previous studies was 1.4 x 10–3 ml·cm–2·h–1·cmH2O–1 (20). This value is consistent with a flow of 0.05 ml/h for a diaphragm surface area of 5 cm2 and transdiaphragmatic pressure of 7 cmH2O (2, 20). For a transit time (t) of 1 h and flow () of 0.05 ml/h, the tissue volume for flow ( x t) was 0.05 ml. With the total diaphragm volume of 0.35 ml, the flow would occur through 14% of the total volume, close to the measured extracellular tissue volume (8, 15). Thus the estimated flow across the diaphragm was consistent with the estimated transit time for the tracer to cross the diaphragm via its extracellular volume. The flow of tracer albumin via 14% of the diaphragm volume would predict a Cdm/Ca of 0.14 that was smaller than the values of 0.3–0.5 measured with the IP injections. However, the measured values included the effects of microvascular filtration, lymphatic clearance (32), and unbound 125I, which would increase tracer concentration in the muscle.
In the analysis, we assumed that transport across the diaphragm and pleural capillaries was due to b with a relatively high Peclet number, so that tracer concentration of the flow into the pleural space was flow independent and related only to the upstream tracer concentration and reflection coefficient of the membrane (Ref. 25; Eq. A2 of APPENDIX). Accordingly, the primary force for transdiaphragmatic transport was the difference between the IP pressure and pleural pressure. The effect of protein osmotic pressure differences was neglected because both the measured transdiaphragmatic protein concentration difference (0.5–1 g/dl, Table 3) and reflection coefficient (d of 0.1, Ref. 20) was small (see Eq. 6 below). Transdiaphragmatic pressure has a mean value of 8 cmH2O based on pleural pressure (–9 to –22 cmH2O) measured in conscious rats by telemetry (21) and IP pressure (–2 cmH2O) measured in anesthetized rats (33). In vitro studies in the diaphragm showed that this pressure difference was sufficient to produce flow-independent sieving coefficients of albumin and reliable estimates of reflection coefficient (20).
The Cc/Ca corrected for unbound 125I at 6 h after IP injections was threefold greater for 5-ml than 1-ml IP injections (Table 1). By contrast, the experiments with unpurified tracer and no correction for unbound 125I showed no significant difference in Cc/Ca between 1- and 5-ml IP injections. Thus the correction for unbound 125I was crucial to the determination of the true tracer uptake into the circulation from the peritoneal cavity.
We used a 3 g/dl albumin solution for the IP injections to approximate the normal peritoneal liquid protein concentration (23). Clearance of albumin from the peritoneal cavity has been reported to be independent of the albumin concentration in the dialysate (4). However, in the present study, the use of bovine serum albumin produced short-term and long-term (3–96 h) changes in both peritoneal and pleural protein concentrations, even for relatively small IP injections in the rat.
Differences Between the Rat and Other Species
There are major differences between the rat and other species with regard to pleural and peritoneal transport. Abdominal counterpressure resulted in improved fluid recovery with isotonic dialysis in rats but had no effect on recovery of fluid in humans (13). A reason for this interspecies difference might be that the rat has a significant transdiaphragmatic flow that is reduced in the larger human with a thicker diaphragm.
Pleural liquid protein concentration has been shown to be greater in smaller animals (19). In particular, the Cp/Cc of 0.5 measured in rats (17, 19) was greater than values reported for bigger species such as sheep (0.15; Ref. 28).
One explanation for this difference is an increased capillary-to-pleural pressure gradient in the larger animals (19). This was supported by studies in hypertensive rats compared with normotensive controls (17) and in sheep as vascular pressure increased during development from the fetus to adulthood (10). Another explanation is that pleural liquid protein concentration is increased in smaller animals because of absorption of protein-free pleural liquid by the visceral pleural capillaries with a relatively low pulmonary capillary pressure (16). In the present study, we propose the following explanation: a relatively unrestrictive transport across the diaphragm.
Pleural liquid protein concentration relative to that in plasma measured in the larger animals, such as in sheep (0.15; Ref. 28), was near to that expected for a microvascular filtrate (0.10; Ref. 18) because transport across the diaphragm was relatively small. Microvascular filtration would produce a pleural liquid-to-plasma protein concentration ratio that was independent of body mass because the thickness of the microvascular barrier attributed to the endothelium is largely independent of species size (18). By contrast, transport across the diaphragm would decrease with body size because hydraulic conductance of the diaphragm is inversely proportional to its thickness, which increases with body size (thickness 
mass1/3).
Effect of the IP Injections on Normal Pleural Liquid Flow
To demonstrate a transdiaphragmatic tracer transport from the peritoneal liquid to the pleural space, the use of a 5-ml IP injection rather than 1-ml IP injection was more definitive, because the difference between the Cp and the Cc, easily detected with 5-ml IP injections, was considerably reduced with 1-ml IP injections. This was most likely caused by nonuniform mixing of the 1-ml IP injection with the resident peritoneal liquid and longer transit times required for the smaller injected volumes to reach the diaphragm from the caudal injection site (32). Moreover, the analysis of tracer transport from the peritoneal liquid to the pleural liquid and plasma assumed uniformly mixed compartments, more likely to occur with the larger IP injection volumes. However, the use of 5-ml IP injections could conceivably result in a departure from the normal physiological state. Indeed, injections of 1–5 ml of liquid into the pleural space were shown to increase the clearance rate of pleural liquid by 10-fold (16), and a similar behavior might occur with peritoneal effusions, particularly in relation to lymphatic clearance (5, 13, 14).
Transdiaphragmatic transport of tracer albumin from the peritoneal liquid to the pleural liquid with the IP injections most likely occurred along with the normal liquid and protein transport for the following reasons. First, pleural liquid and plasma protein concentrations did not change significantly from control values with 1-ml IP injections, although peritoneal protein concentration increased by 25%. Thus the pleural flow was identical with 1-ml IP injections and control. Part of this flow must have been through the diaphragm to explain why tracer concentration measured 3 h after 1-ml IP injections was greater in pleural liquid than in plasma.
Second, the measured protein concentrations showed no change in plasma and small increases in pleural liquid (22%) and in peritoneal liquid (30%) with 5-ml IP injections. The following analysis using the Starling and solute flux equations showed these results to be consistent with relatively small changes in flow across the pleural microcirculation and diaphragm. According to the Starling equation, b is related to the microvascular-to-pleural hydrostatic pressure difference (
P), the plasma-to-pleural protein osmotic pressure difference (
), and c:
 | (6) |
P was assumed constant with the IP injections, because previous results in anesthetized rats showed little change in vascular pressures, even with large amounts of dialysate fluid (26). Studies in the rat showed a P value of 37 cmH2O (7) and c of 10 cmH2O (17) with c of 0.9 (18). With 5-ml IP injections, Cp increased by 22%, resulting in a 22% decrease in c. Thus, from Eq. 6 with P constant, b increased by 8% with the 5-ml IP injections. The protein flux (s) associated with this increase in b is given by the solute flux equation (25):
 | (7) |
is the solvent drag reflection coefficient, D is the apparent diffusion coefficient, A is the surface area, L is the thickness, and C is the concentration difference. The first term on the righthand side of Eq. 7 is the s due to b, and the second term is the s due to diffusion. Neglecting diffusion, which was estimated to be small (see below), the fractional change in s (ds/s) is related to the fractional changes in b, Cm, and by the following equation obtained by implicit differentiation of Eq. 7:
 | (8) |
(20) in Eq. 8, the 8% increase in b across the capillary membrane plus the 7% increase in Cm (Table 3) produced a 15% increase in s. However, the 22% increase in pleural protein concentration with the 5-ml IP injections was produced by an identical increase in s. Thus, of the total increase in s, 7% was associated with transport across the diaphragm. For transport across the diaphragm, with dCm/Cm of 0.26 (Table 3) and ds/s of 0.07 in Eq. 8, db/b was –0.19. That is, the flow across the diaphragm was reduced by 19%. For 1-ml IP injections with no change in Cp and ds/s of 0, db/b was equal to –dCm/Cm or –0.17 (Table 3), slightly smaller than the reduced flow across the diaphragm for 5-ml IP injections. The small reduction in flow across the diaphragm with the IP injections was consistent with the small (2–4%) reduction in tissue hydration (W/D) measured for the diaphragm muscle (Table 4).
In the present study, differences in protein concentration across the diaphragm averaged 0.5 g/dl under control conditions and increased by 70% after 5-ml IP injections. Thus the increase in s due to concentration-induced changes in diffusion per se could not explain why Cp relative to that of peritoneal liquid was ninefold greater with 5-ml IP than with 1-ml IP injections at 6 h after injection (Table 1). In in vitro studies of the rat diaphragm, albumin diffusion coefficient averaged 1 x 10–7 cm2/s (19). Thus the albumin diffusive flux was 2.5 x 10–4 g/h, based on C of 1 g/dl, A of 5 cm2, and L of 0.7 mm. The s due to b was 9 x 10–4 g/h, based on b of 0.04 ml/h and d of 0.2 estimated in the analysis, and Cm of 3 g/dl (Table 3). Thus 80% of the albumin flux was attributed to b, which supported the assumption of high Peclet number used to model transport across the diaphragm (Eq. A2 of APPENDIX).
Several other factors might contribute to an increased b and diffusive s across the diaphragm with the IP injections compared with control. One factor is a tissue hydration-induced increase in hydraulic conductivity and diffusion that would result in an increased liquid and protein transport (12, 14). This effect was not consistent with the measured reduction (2–4%) in diaphragm muscle hydration (W/D) or the estimated reduction in transdiaphragmatic flow, with the IP injections. Another factor is an increased diaphragm surface area available for flow and diffusion that might increase with the size of the IP injections (14). This effect would not be supported by the tracer concentration measured in the diaphragm relative to that in the peritoneal liquid that was similar for both 1- and 5-ml IP injections. A third factor is an increase in IP hydrostatic pressure with the size of the IP injections. However, IP pressure measured in anesthetized rats was slightly subatmospheric (–2 cmH2O) and increased minimally by 0.5 cmH2O with 5-ml IP injections (33). Accordingly, the 1- and 5-ml IP injections had only minor effects on the transport characteristics of the diaphragm and the forces driving flow into the pleural space.
In summary, tracer Cp/Ca were greater than Cc/Ca at 3 h after both 1- and 5-ml IP injections. This behavior indicated a transdiaphragmatic tracer and liquid transport. The 5-ml IP injections produced no change in plasma protein concentration, with 22 and 30% increases in pleural and peritoneal protein concentrations, respectively, above control values. These increases in protein concentration were consistent with a small decrease in b across the diaphragm that produced a small (2–4%) reduction in diaphragm muscle hydration (W/D) with no change in Vp. We conclude that flow across the diaphragm changed only minimally with the IP injections and that the tracer transport into the pleural space with 1- and 5-ml IP injections occurred simultaneously with the near normal transport of albumin and liquid across the diaphragm.
In the analysis of tracer transport, we assumed that the transport processes were entirely passive (24), although active transport by the mesothelium has been proposed for both peritoneal and pleural liquid transport (6). The results of this study would support passive mechanisms to be dominant in the determination of pleural liquid transport.
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APPENDIX |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIXGRANTSREFERENCES |
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The following analysis extends the single-source analysis (1) to two sources. Other more complex analyses of peritoneal transport related predominantly to peritoneal dialysis have appeared (13).
Consider the pleural space as an input-output system (Fig. 4). The mass flux of tracer (125I-albumin) entering the pleural space across the capillary endothelial-interstitial membrane from the circulation (dMc/dt) plus the mass flux entering from the peritoneal (abdominal) cavity across the diaphragm (dMa/dt) minus the mass flux exiting the pleural space via lymphatics (dMl/dt) equal the rate of change of the total mass in the pleural space with respect to time t (dMp/dt):
 | (A1) |
cCpc, where c is the flow from the circulation into the pleural space and Cpc is the tracer concentration in c. dMa/dt = aCpa, where a is the flow from the peritoneal cavity across the diaphragm into the pleural space and Cpa is the tracer concentration in a. dMl/dt = pCp, where p is the flow out of the pleural space equal to c + a and Cp is the tracer concentration in p. We assume that the outflow occurs via the lymphatic vessels that do not restrict the passage of albumin (5). We consider only convective transport across the membranes so that, for a flow of relatively high Peclet number through cylindrical pores (25):
 | (A2) |
c is the reflection coefficient of the capillary membrane, and d is the reflection coefficient of the diaphragm. With a constant Vp = Mp/Cp, Eq. A1 reduces to:
 | (A3) |
IP injection experiments.
To study the transport of tracer after injection into the peritoneal cavity, we use the following equation that results from Eq. A3 after normalizing by dividing each term by Ca and Vp:
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| (A4) |
 | (A5) |
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| (A6) |
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| (A7) |
c, a, Vp, c, and d are constants. Ca(t) is the measured input function of the tracer from the peritoneal cavity (Fig. 2), and Cc/Ca(t) is the measured input function from the circulation (Fig. 3). Thus Eq. A4 is a first-order linear differential equation in the variable Cp/Ca.
The input function representing the washout of tracer from the peritoneal cavity for 5-ml IP injections was obtained by a curve fit to the Ca/Cao(t) data (Fig. 2):
 | (A8) |
The input functions from the peritoneal cavity into the circulation for 5-ml IP injections were obtained by a polynomial curve fit to the Cc/Ca(t) data (Fig. 3):
 | (A9) |
Vascular injection experiments.
An equation appropriate for intravascular (IV) tracer injection that is analogous to Eq. A4 for peritoneal injection results from Eq. A3 after normalizing by dividing each term by Cc and Vp:
 | (A10) |
We used MATLAB (ode45) to solve numerically Eq. A4 for Cp/Ca(t). A Kc value of 0.02 ml/h was specified from the slope of the Cp/Cc(t) curve near t = 0 for IV tracer injection. Eq. A10 for IV injection shows that d(Cp/Cc)/dt = Kc at t = 0. The IV injection studies produced Cp/Cc values of 0.011 ± 0.004 (SD; n = 3) and 0.018 ± 0.003 (n = 3) at times of 0.5 and 1 h after injection, respectively. A linear regression fit to the data was Cp/Cc = 0.019t, P = 10–5. The slope (0.019 h–1) was near the value (0.02 h–1) for Kc used in the computations. It was not possible to determine Ka from the Cp/Ca(t) curve using the IP injection data, because experiments at time periods of 0.5 and 1 h after injection showed an initial delay of 1 h for the tracer to cross the diaphragm (see below). With Kc specified and Vp measured, there are four unknown parameters (c, d, c, and a) in the three equations (A5–A7) that describe transport of tracer into the pleural space.
By a trial-and-error procedure, with Kc specified, Ka and p/Vp were perturbated to fit the measured Cp/Ca(t) curve (Fig. 3). Simultaneously, values of c, d, a, and c that were consistent with p/Vp, Kc, and Ka were calculated using the following procedure. p was computed by the product of p/Vp and measured Vp. c values corresponding to a range of c values were calculated using the computed Kc value (Eq. A5). Then a values equaled the difference between p value and c values (Eq. A7). Next, values of d were calculated by using the computed Ka value and values of a (Eq. A6). We chose computed values of p/Vp and Ka that fit the measured Cp/Ca(t) curve with values of c and d in the range 0.75–0.91 and 0.03–0.39, respectively (Table 5). The associated range for a/p was 0.52–0.83. To determine values of c, d, and a/p for 1-ml IP injections and control conditions, we used the equilibrium solution to Eq. A4 for infinite time given by Eq. 5 with total protein concentrations measured in pleural liquid, peritoneal liquid, and plasma (Table 3). The solutions are tabulated in Table 6.
The effect of the two time constants for the tracer decay in the peritoneal liquid (Eq. A8) was to produce a biphasic Cp/Ca(t) behavior, with Cp/Ca increasing to a peak value of 1.1 at 12 h and then decaying to a value of 0.6 after 24–48 h (Fig. 3). Note also that the initial part of the Cp/Ca(t) curve occurred earlier in time by 1–2 h than the measured data, a reflection of the delay time for the tracer to cross the diaphragm, a behavior that was ignored in the modeling. This biphasic behavior in Cp/Ca(t) was in contrast to the monotonic increase calculated if transport of tracer was entirely from the circulation (see below).
The long decay time constant (Eq. A8) determined the near equilibrium value for Cp/Ca at long time at t = 48 h, when d(Cp/Ca)/dt = 0 in Eq. A4:
 | (A11) |
(Eq. A8), and with Ka = 0.23 h–1, Kc = 0.02 h–1, Cc/Ca = 1.3, and p/Vp = 0.46 h–1, Cp/Ca = 0.66. A lower equilibrium value (Cp/Ca = 0.55) is obtained if microvascular filtration is neglected (Kc = 0).
Single-source analysis.
We considered the case of no transdiaphragmatic transport with only microvascular filtration so that Ka = a = 0 and c = p in Eq. A4:
 | (A12) |
p/Vp of 0.46 h–1 obtained from the two-source solution produced a monotonic increase in Cp/Ca to a value of 0.17 at 48 h. By contrast, with only transdiaphragmatic transport and no microvascular filtration so that Kc = c = 0 and a = p in Eq. A4:
 | (A13) |
p/Vp of 0.46 h–1 obtained from the two-source solution produced a biphasic Cp/Ca(t) behavior with an equilibrium value of Cp/Ca of 0.55 at 48 h that closely approximated the solution of the two-source problem. Thus transport across the diaphragm was essential for modeling tracer uptake into the pleural space and was the predominant contributor to the measured behavior in tracer uptake. |
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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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TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIXGRANTSREFERENCES |
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