Hydraulic Conductivity, Albumin Reflection and Diffusion Coefficients of Pig Mediastinal Pleura

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Microvascular Research 58, 114–127 (1999)Article ID mvre.1999.2168, available online at http://www.idealibrary.com on

Hydraulic Conductivity, Albumin Reflection andDiffusion Coefficients of Pig Mediastinal Pleura

Sandhya Parameswaran,* Laura V. Brown,* Geoffrey S. Ibbott,†and Stephen J. Lai-Fook*,1

*Center for Biomedical Engineering and †Department of Radiation Medicine, University of Kentucky,exington, Kentucky 40506-0070

eceived February 26, 1999

Hydraulic conductivity (L), albumin reflection coefficient(s), and albumin diffusion coefficient (D) were measuredacross pig mediastinal pleura. The tissue (7 mm diame-ter) was bonded between two chambers. Flow (Q) of lac-tated Ringer solution between the chambers was mea-sured in turn at driving pressures (DP) of 2, 4, and 6 cmH2O. Value of L was proportional to the slope of the Q–DPcurve. Then Q was measured in turn at three albuminosmotic pressure differences (Dp equivalent to 21, 22,nd 23 g/dl albumin concentration difference, DC) withP constant at either 2, 3, 4, or 6 cm H2O. From Starling’squation, magnitude of s was the slope of the Q–Dp

curve divided by the slope of the Q–DP curve. We mea-sured the diffusion of 0, 2, 5, and 10 g/dl albumin withtracer 125I-albumin. Tracer mass (M) that diffused acrossthe pleura was measured for 10 h using a well-typeNaI(T1) detector. D was calculated from the slope of the

–time curve. Values of L averaged 2.0 3 1028 cm3 z s21 z

dyne21 (n 5 23). Values of s were small (0.02–0.05) ands increased as flow increased 20-fold. D (n 5 24) in-creased 3-fold from 2.7 3 1028 cm2/s as DC increasedfrom 0 to 10 g/dl. The small values of s indicated that

1 To whom correspondence and reprint requests should be ad-ressed at Center for Biomedical Engineering, Wenner-Gren Re-
earch Laboratory, University of Kentucky, Lexington, KY 40506-070. Fax: (606) 257-1856. E-mail: [email protected].
114

mediastinal pleura provided little restriction to the pas-sage of protein. © 1999 Academic Press

Key Words: fluid exchange; pleura; interstitium; diffu-sion coefficient; hydraulic conductivity; reflection coeffi-cient; albumin; hyaluronan; hyaluronidase.

INTRODUCTION

The parietal pleura is a major barrier to the flow ofmicrovascular filtrate from the pleural capillaries tothe pleural space. Thus its transport properties forliquid and protein are important to understanding thelubrication properties of the pleural space. Microvas-cular sieving of protein is usually associated with theendothelial barrier of capillaries, whereas the extracel-lular matrix is considered completely permeable toprotein (Bert and Pearce, 1984). However, recent stud-ies have suggested that parietal pleura restricts thepassage of albumin with a relatively high reflectioncoefficient: 0.30 in the dog and 0.44 in the rabbit (Ne-grini et al., 1994). These results are at odds with pre-vious studies indicating that the albumin reflectioncoefficient was close to zero (Payne et al., 1988; Negriniet al., 1990, 1991, 1994).

Accordingly we measured the transport propertiesof pig mediastinal pleura. The mediastinal pleura sep-

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115Transport Properties of Mediastinal Pleura

arates the other thoracic viscera from the lung andforms part of the parietal pleura that lines the thoraciccavity. The mediastinal pleura is continuous with thecostal pleura lining the surface of the ribs and inter-costal muscles, the diaphragmatic pleura covering theconvex surface of the diaphragm, and the cervicalpleura at the lower neck adjacent to the apex of thelung (Crouch, 1965). The advantage of studying themediastinal part of the parietal pleura is that it is freestanding so that the trauma associated with strippingoff other parts of the parietal pleura for tissue bathstudies (Payne et al., 1988) is avoided.

In the present studies, a segment of mediastinalpleura was fixed between two chambers filled witheither Ringer or albumin solution. Changes in flowacross the pleura were measured in response tochanges in hydrostatic and protein osmotic pressuredifferences. Hydraulic conductivity and albumin re-flection coefficient as defined by the Starling equationwere determined from these changes in flow. Albumindiffusion coefficient was calculated using Fick’s lawfrom the measurements of the diffusion of radioactivetracer 125I-albumin with a well-type NaI(T1) scintilla-tion detector.

METHODS

Farm pigs (18–27 kg body weight) were sedatedwith ketamine (20 mg/kg), acepromazine (1 mg/kg),and atropine (0.04 mg/kg), administered intramuscu-larly. Each animal was anesthetized with sodium pen-tobarbital (30 mg/kg) and then killed with an over-dose of the anesthetic. Postmortem, the chest wasopened by a sternotomy, the rib cage separated byspreaders, and the thoracic cavity filled with saline.Part of the mediastinal pleural membrane that waseasily accessible was removed by dissection and im-mersed in a dish containing lactated Ringer solution.A segment of the dissected mediastinal pleura wasmounted in vitro between two chambers. The cham-bers were constructed as previously described(Parameswaran et al., 1998). In brief, the membrane in
the relaxed state was bonded using cyanoacrylate ad-hesive to one chamber. The other chamber was then
bonded to the other side of the membrane. Both cham-bers were filled with lactated Ringer solution. Themembrane surface exposed to the liquid in the cham-bers was 7 mm in diameter. The two chambers werethen bolted together to stabilize the assembly. Themembrane was kept moist by applying lactatedRinger solution during the setting-up procedure.Chamber 2 was connected to a length of PE200 tubingand the entire chamber and part of the tubing werefilled with liquid. Flow between the two chamberswas determined by measuring the movement of themeniscus in the tubing through a macroscope with acalibrated scale at timed intervals. The meniscus waseasily observed with Evans blue in the liquid. Eachmillimeter of PE200 tubing contained 0.00145 ml.Chamber 1 contained a nipple attached to a syringe sothat the liquid in the chamber could be exchanged.Each chamber was connected to an adjustable air pres-sure source and its pressure measured by a watermanometer. In the experiments with albumin solution,the albumin solution in chamber 1 was stirred with asmall magnetic bar (6 mm long, 1 mm diameter) ro-tated by an external electromagnetic source.

Theory. We designed experiments to determinethe hydraulic conductance (L) per unit surface area( A) and reflection coefficient (s) of the mediastinalpleura as defined by the Starling equation:

Q 5 LA@~P2 2 P1! 2 s~p2 2 p1!#. (1)

Here Q is the bulk flow across the membrane. P 1 andP 2 are hydrostatic pressures and p1 and p2 are proteinosmotic pressures in chambers 1 and 2 adjacent to themembrane, respectively. For a constant Dp 5 p2 2 p1,L is given by

L 51A

QDP . (2)

Here DP 5 P 2 2 P 1, and Q/DP is the slope of theQ–DP curve at constant Dp. For a constant DP, s isgiven by

s 5 21

LAQ

Dp. (3)

Here Q/Dp is the slope of the Q–Dp curve at
constant DP. Substituting for L of Eq. (2) into Eq. (3)gives s as
Copyright © 1999 by Academic PressAll rights of reproduction in any form reserved.

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116 Parameswaran et al.

s 5 2Q/Dp

Q/DP . (4)

To compare values of L with published values of otherissues, we define hydraulic conductivity (K) from

Darcy’s law for one-dimensional flow through a po-rous medium:

Q 5 KADP/DX. (5)

ith the assumption that either s or p2 2 p1 is zero inEq. (1), K is equal to LDX, where DX is the thicknessof the membrane.

Measurement of L and s. In each membrane spec-imen, we measured Q at three DP (P 2 . P 1) values of2, 4, and 6 cm H2O with Ringer solution in bothchambers (p1 5 p2 5 0). Mean pressure [P m 5 (P 1 1P 2)/ 2] in the membrane was maintained constant at 2cm H2O. Then Q was measured with p1 correspond-ing to three different concentrations of albumin (1, 2,and 3 g/dl; bovine, Batch No. A9647, Sigma Chemical)and p2 5 0 (lactated Ringer solution) at a constant DPof 2, 3, 4, or 6 cm H2O. Note that the bulk flow due toDP and the osmotic flow due to Dp were in the samedirection from chamber 2 to chamber 1. Except fordiffusion, solute movement between the chamberswas eliminated and solute dilution in chamber 1 couldbe precisely calculated. Based on the volume of cham-ber 1 (3 ml) and the flow of lactated Ringer solutionfrom chamber 2 to chamber 1 during the 40 min offlow, the dilution of albumin in chamber 1 was negli-gible. Here diffusion of albumin across the membranewas neglected in view of independent measurementsof the diffusion coefficient (see Discussion).

In separate experiments, we measured the effect ofhyaluronidase on L. Flow was measured at DP (P 1 .P 2) of 22, 24, and 26 cm H2O with Ringer solution inboth chambers and was remeasured with hyaluroni-dase solution (0.02 g/dl Ringer solution; bovine testes,Batch No. H3506, Sigma Chemical) in chamber 1 at thesame DP values.

All solutions were filtered (0.45 mm pore diameter)and adjusted to a pH of 7.4. Five to seven sections ofmediastinal pleura were obtained from each pig. Flowwas measured every 5 min for 40 min. A constant flow
was usually attained in the first 5 min and the flowwas measured for 40 min to ensure that the flow

remained steady. The average flow over the 40 minwas obtained by a linear regression analysis of thevolume–time curve. Flows that were not steady wererejected. At the end of each experiment, the membranewas dissected from the retaining plates and weighedto estimate thickness. Membrane thickness was calcu-lated from membrane weight, surface area (0.39 cm2),and density (1 g/cm3).

Measurement of albumin diffusion. We measuredthe effect of albumin concentration on the diffusion ofalbumin using the radioactive tracer 125I-albumin. Theprocedure was similar to that used for the mesenterymembrane (Parameswaran et al., 1999). In brief, a seg-ment of mediastinal pleura was mounted between twoidentical chambers. The membrane surface exposed tothe solutions in the chambers was similar in size tothat used for the hydraulic conductivity experiments(7 mm diameter). The chamber (1.8-ml volume) con-structed from a plastic tube (4.5 cm long, 7 mm diam-eter) was designed so that a 4 cm length of the tubewould fit in a well-type scintillation counter (ModelNo. TB-2L, Oxford Instruments Inc., Oak Ridge, TN)through a hole in the lead cap that covered the open-ing of the counter.

Stock solutions (18 ml) were made with albumin ofdifferent test concentrations (0, 2, 5, and 10 g/dl bo-vine serum albumin, Batch No. A9647, Sigma Chemi-cal) and 125I-albumin (;0.5 mC/ml; Batch No. NEX-076, New England Nuclear, Boston, MA) in lactatedRinger solution. Different pairs of albumin concentra-tions were studied (0 and 2, 0 and 5, and 0 and 10g/dl). One chamber (outer) was filled with the stocksolution of 0 g/dl albumin concentration while theother (inner) chamber was filled with lactated Ringersolution. Both chambers were capped and sealed withvacuum grease to eliminate flow due to osmosis. Thechamber with lactated Ringer solution was placedwithin the counter and the gamma radiation from thediffused tracer was measured for intervals of 10 minover a period of 10 h. At the end of this period thesolution in the outer chamber was replaced with a(second) stock solution of a different albumin concen-tration (2, 5, or 10 g/dl), and the solution in the innerchamber was replaced with fresh lactated Ringer so-
lution. Radiation from the inner chamber was countedfor a further 10 h. Then the solution in the outer

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chamber was replaced with the second stock solutioncontaining hyaluronidase (0.02 g/dl; bovine tested,440 U/mg solid, Batch No. H3506, Sigma Chemical)and the solution in the inner chamber was replacedwith fresh lactated Ringer solution. Radiation from theinner chamber was counted for a further 10 h. Duringall diffusion measurements, the solutions in bothchambers were stirred with magnetic bars.

In separate experiments, we studied the question oftissue deterioration over the period of 30 h of thediffusion experiments. In these experiments (n 5 4)

e measured the diffusion of 125I-albumin in lactatedRinger solution across mediastinal pleura continu-ously for 30 h. The 10-h period chosen for albumindiffusion at each albumin concentration was the min-imum time deemed necessary to establish a represen-tative steady state (see Results).

In separate experiments we measured the amount ofunbound 125I present in the stock solution containing125I-albumin by dialysis using a membrane (Wescor,S-030, Logan, UT). Unbound 125I accounted for ,2%

of the radioactivity from the stock solution, verifyingthe manufacturer’s specification (Parameswaran et al.,1999).

All solutions were filtered (0.45 mm pore diameter)and adjusted to a pH of 7.4. Four sections of pleurawere studied simultaneously from each pig. At leastthree sections produced acceptable results. Causes offailure included leaks from one or both of the cham-bers due to incomplete bonding of the membrane tothe chambers. These results were not reported. At theend of each experiment, the membrane was dissectedfrom the chambers and weighed to obtain thickness(DX) from the equation: DX 5 m/(rA). Here m ismass, r is density (1 g z cm23), and A is area.

The scintillation detector (counter). We used asystem consisting of four NaI(T1) scintillators, eachconnected to a photomultiplier tube (to detect the lightemitted from the scintillator when subjected togamma radiation), preamplifier, and amplifier, with asingle high-voltage power supply (Model 5040, Ox-ford Instruments Inc.). The output of the amplifier wasinterfaced to a computer (PC-AT&T 386) via a pulseheight selector and a count-rate meter for automatic
data collection. To minimize the radiation from theouter chamber from reaching the detector, the outside
surface of the detector and the bottom of the detectorwell were covered with 2-mm-thick lead sheeting. Thedetector was oriented with its cylindrical axis horizon-tal. A guide attached to the inner surface of the capthat covered the well of the detector maintained thechamber axis horizontal and at a fixed and reproduc-ible orientation relative to the detector. Calibration ofthe detector has been described elsewhere (Qiu et al.,1998; Parameswaran et al., 1999).

Calculation of albumin diffusion coefficient. Weused Fick’s law for steady-state diffusion of a solutethrough a membrane of surface area ( A) and uniformthickness (DX):

dM2/dt 5 DA~C1 2 C2!/DX. (6)

ere dM 2/dt is the steady-state diffusive flow of sol-ute mass, D is the solute diffusion coefficient, andC 1 2 C 2 is the difference between the solute concen-trations in the outer and inner chambers on the oppo-site sides of the membrane.

The mass flow of albumin (dM 2/dt) was calculatedusing the mass of albumin in the outer chamber (M 1),the mean slope of radioactivity–time (R 2–t) curvemeasured in the inner chamber (dR 2/dt), and theadioactivity measured in the outer chamber (R 1) in

the following equation:

dM2/dt 5 M1~dR2/dt!/R1. (7)

Here we assumed that the radiation measured by thecounter scaled directly with the dilution of 125I-albu-min in the range between R 2 and R 1, as verifiedpreviously (Qiu et al., 1998; Parameswaran et al., 1999).Since M 1 5 C 1V 1, where V 1 is the volume of the outerchamber and C 2 is assumed zero, Eq. (6) becomes

D 5 V1DX~dR2/dt!/~R1A!. (8)

ote from Eq. (8), C 1 does not enter in the calculationof D. Thus D can be calculated even if C 1 is not knownexactly, as is the case with the diffusion of only thetracer 125I-albumin. The assumption that C 2 was al-ways zero in the experiment produced a small under-estimate in the calculated value of D (see Discussion
and Appendix, Section B).
To compare values of D with published values from


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other species, note that D is equal to PeDX, where Peis the permeability coefficient in the equation:

dM2/dt 5 PeA~C1 2 C2!.

Statistical analysis. Data are reported as meanalues 6 SD (n). We used an unmatched t test or aaired t test, where appropriate, to assess any signif-

cant difference between two experimental groups.inear regression analysis was used to evaluate corre-

ation between two variables and the slope of theurve of a dependent variable versus an independentariable. Significance was set at the P , 0.05 level.

RESULTS

Hydraulic conductivity and reflection coefficient.Figure 1A shows an example of the flow (Q, ml/h) oflactated Ringer solution measured across a segment ofmediastinal pleura at DP (P 2 2 P 1) values of 2, 4, and6 cm H2O. The mean flow at each DP value wascalculated from the slope of the volume–time curve.The slope (Q/DP) of the Q–DP curve for p1 5 p2 50 was obtained from the linear regression equation:Q 5 20.12 1 0.065DP, r 2 5 0.99. From Q/DP of0.065 ml z h21 z cm H2O

21 and an A value of 0.385 cm2,L from Eq. (2) was 4.8 3 1028 cm3 z s21 z dyne21. Thefinite DP value at zero flow was caused by a smallhydrostatic head between the two chambers (;0.5 cmH2O) and the surface tension across the meniscus (;1m H2O). These errors in DP were constant with

changes in DP and thus did not contribute to the slopeof the Q–DP curve or the value of L.

Figure 1B shows the flow measured at constant DPof 4 cm H2O and with albumin concentrations of 1, 2,nd 3 g/dl in chamber 1 and lactated Ringer solutionn chamber 2, for the same pleural segment of Fig. 1A.

from chamber 2 to chamber 1 is plotted versusalbumin osmotic pressure difference (2Dp 5 p1 2 p2,m H2O). We used the following equation to convert

albumin concentration (C, g/dl) to p (Landis andPappenheimer, 1963):

p 5 1.36~2.8C 1 0.18C 2!. (9)


The slope (Q/Dp 5 20.0027 ml z h21 z cm H2O21)

of the Q–Dp curve was obtained from the linear re-gression equation: Q 5 0.12 2 0.0027Dp, r 2 5 0.99.A s value 0.042 was obtained by dividing the negativeof the slope of the Q–p curve by the slope of the Q–DPcurve [Eq. (4)]. Hydraulic conductivity (K) defined by

arcy’s law [Eq. (5)], the product of L and DX (0.016cm), was 7.7 3 10210 cm4 z s21 z dyne21.

Table 1 summarizes the mean values (6SD) of L, K,and s for the four groups in which DP was set at 2, 3,4, and 6 cm H2O while DC was varied. Also shown inTable 1 are the flow values (Q 0) corresponding to

FIG. 1. (A) An example of flow (Q) of lactated Ringer solutionversus driving pressure (P 2 2 P 1) across pig mediastinal pleura. (B)

smotic flow of lactated Ringer solution versus osmotic pressureifference (2Dp 5 p1 2 p2) across same membrane shown in A.

Points correspond to albumin concentration differences of 1, 2, and3 g/dl. Constant DP was 4 cm H2O.

these DP values. Neither L nor K values varied sig-nificantly among the four groups; that is, flow had no

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effect on L or K. The pooled values of L averaged.0 3 1028 6 1.5 3 1028 cm3 z s21 z dyne21 (n 5 23). The

pooled values of K using the measured values of DX(130 6 97 mm, n 5 23) averaged 2.1 3 10210 6 1.8 310210 cm4 z s21 z dyne21.

The values of s significantly increased with Q 0 (Fig.2). A linear regression analysis showed that s in-creased from 0.02 to 0.05 as Q increased 20-fold from.4 3 1025 to 8 3 1025 cm z s21: s 5 0.016 1 4.2 3 10 2

TABLE 1

Hydraulic Conductance (L), Hydraulic Conductivity (K), and AlbuConvective Flows (Q 0) in Mediastinal Pleura

DP(cm H2O)

Q 0 3 10 5

(cm/s)L 3 10 8

(cm3 z s21 z dyne21)

2 0.31 6 0.05 (4)a 1.0 6 1.2 (5)3 0.80 6 0.50 (4) 2.2 6 1.9 (6)4 7.1 6 3.8 (6) 3.3 6 1.2 (6)6 6.2 6 2.2 (4) 1.5 6 0.74 (6)

Mean 4.0 6 3.9 (18) 2.0 6 1.5 (23)

Note. L, flow (cm3 z s21) per unit DP (dynes z cm22) per unit surfaurface area at constant DP and p 5 0 in experiment to obtain Q–

a mean 6 SD (N). N is number of samples.

FIG. 2. Albumin reflection coefficient (s) versus convective flowper unit surface area (Q 0, cm/s) due to the constant DP in medi-astinal pleura. Linear regression line: s 5 0.016 1 4.2 3 10 2 Q 0,

2 5 0.31, n 5 18, P 5 0.016. Values of Q 0 corresponding to the
ae
our groups (DP of 2, 3, 4, and 6 cm H2O) are represented bysymbols (F, {, Œ, and E), respectively.

Q 0, r 2 5 0.31, n 5 18, P 5 0.016. The small valuesof s indicated that for flows near the physiologicalrange, pig mediastinal pleura did not restrict the pas-sage of albumin.

The effect of hyaluronidase (0.02 g/dl) on hydraulicconductivity was measured in response to DP of 2, 4,and 6 cm H2O before and after hyaluronidase wasadded to the lactated Ringer solution in chamber 1.The linear response of the volume–time curve withhyaluronidase occurred within 5 min of adding hyal-uronidase, indicating that hyaluronidase caused animmediate increase in flow. The ratio of the flow afterhyaluronidase to the flow before hyaluronidase aver-aged 2.2 6 0.39 (n 5 4, range 1.8–2.8) and wassignificantly greater than 1 (P , 0.001). Thus, hyal-uronidase had the effect of increasing the hydraulicconductivity of mediastinal pleura on average by120%.

Albumin diffusion coefficient. Figure 3 shows anexample of radioactivity (R) measured during 30 h fordiffusion of 125I-albumin (1 mC) in lactated Ringersolution across mediastinal pleura. Note that the dif-fusion rate was constant over the 30 h with a smallcyclic variation, indicating that the tissue maintained aconstant diffusion rate for 30 h. The reasons for thesmall cyclic variation in diffusion are speculative. Asimilar behavior was measured in the mesentery(Parameswaran et al., 1999). A linear regression anal-

sis of the data indicated that the slope of the R–timeurve was constant over the time scales of 0–10, 0–20,

eflection Coefficient (s) at Different Driving Pressures (DP) and

DX(mm)

K 3 10 10

(cm4 z s21 z dyne21) s

6 0.11 (5) 2.3 6 2.5 (5) 0.0043 6 0.03 (4)6 0.079 (6) 2.4 6 2.4 (6) 0.022 6 0.03 (4)

2 6 0.054 (6) 2.4 6 1.2 (6) 0.052 6 0.02 (6)2 6 0.037 (6) 1.4 6 1.1 (6) 0.044 6 0.02 (4)

6 0.097 (23) 2.1 6 1.8 (23) 0.033 6 0.03 (18)

(cm2); K 5 L 3 DX (membrane thickness); and Q 0, flow per unitve.

min R

0.260.110.080.090.13

ce area

nd 0–30 h. We used the time scale of 10 h for thexperiments to maintain the albumin concentration in


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the inner chamber to ,6% of the concentration of theouter chamber and to minimize tissue deterioration. A,6% diffusion of albumin produced an underestimateof ,8% in the calculation of D (Appendix, Section B).

Figure 4 shows an example of radioactivity (R,ounts/10 min) measured versus time (t, h) for anlbumin concentration difference (DC) of ;0 g/dltracer 125I-albumin), 5 g/dl, and 5 g/dl with hyaluron-

idase (0.02%). The measurement at each concentrationwas carried out for 10 h. The data from the initial 2.5 hwere disregarded because of transient effects associ-ated with the diffusion of unbound 125I (see Discussionnd Appendix, Section A) and with the establishmentf the albumin concentration gradient within theembrane (Appendix, Section C). The linear regres-

ion equations between 2.5 and 10 h were as follows:or ;0 g/dl DC, R 5 0.49 3 10 5 1 0.15 3 10 5 t, r 2 5

.98; for 5 g/dl DC, R 5 24.79 3 10 5 1 0.66 3 10 5

t, r 2 5 0.99; for 5 g/dl DC with hyaluronidase, R 5

9.37 3 10 5 1 0.57 3 10 5 t, r 2 5 0.99. The diffusioncoefficient was calculated for each R–t curve by sub-stituting the slope of the curve, measured A and DX(0.0091 cm) in Eq. (8). Albumin diffusion coefficientwas 2.3 3 1028 cm2/s for ;0 g/dl DC, 5.3 3 1028

FIG. 3. An example of radioactivity (R, counts/10 min) measuredover 30 h across mediastinal pleura. Note the small cyclic variationfrom linearity over the 30 h. Linear regression equation: R 5

.910 3 10 5 1 4.80 3 10 3 t, R 2 5 0.993.

cm2/s for 5 g/dl DC, and 4.8 3 1028 cm2/s for 5 g/dlC with hyaluronidase. Membrane thickness in all


iffusion experiments averaged 0.023 6 0.012 cm (SD,5 12).Figure 5 shows albumin diffusion coefficient (D a)

lotted versus DC (0, 2, 5, and 10 g/dl). D a increased;3-fold from a mean value of 2.7 3 1028 cm2/s at ;0

/dl DC to a mean value of 8.3 3 1028 cm2/s at 10g/dl DC. A linear regression analysis showed a sig-nificant increase in D a with DC: D a 5 0.55 3 1028

DC 1 2.9 3 1028, r 2 5 0.53, n 5 24, P , 0.0001. Inach experimental group in which two albumin con-entrations were used in turn, the diffusion coefficientas always significantly (paired t test, P , 0.05)

reater at the higher albumin concentration.Table 2 summarizes values of albumin diffusion

oefficient with (D h) and without hyaluronidase (D a),and ratios D h/D a. There was no significant change inD h/D a with DC by a linear regression analysis: D h/D a

5 20.034 DC 1 1.5, r 2 5 0.06, n 5 12, P 5 0.43.The pooled values of D h/D a averaged 1.3 6 0.47 (SD),

FIG. 4. An example of radioactivity (counts/10 min) measuredacross mediastinal membrane for albumin concentration differences(DC) of ;0 g/dl (tracer 125I-albumin alone), 5 g/dl albumin, and 5g/dl with 0.02% hyaluronidase (HSE). Linear regression lines ne-glected the first 2.5 h of data partly attributed to the faster diffusionof unbound 125I, as observed in the two curves on the right. Note thatradioactivity (counts/10 min) increased linearly with time for eachDC but the slope was greater for the higher DC, indicating an
increased diffusion coefficient with DC. Hyaluronidase had no sig-nificant effect on diffusion of albumin. See text for details.

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but were not significantly greater than 1 (P , 0.07),indicating no significant effect of hyaluronidase onalbumin diffusion coefficient. Also, D h did not changewith albumin concentration: D h 5 2.7 3 1029 DC 16.0 3 1028, r 2 5 0.09, n 5 12, P 5 0.34.

DISCUSSION

The major results of this study are as follows. Thereflection coefficient of the pig mediastinal pleura tothe flow of albumin was close to zero with values thatincreased from 0.02 to 0.05 as flow per unit surfacearea increased 20-fold from 3 3 1026 to 6 3 1025 cm z

s21. These values are within the range measured pre-viously in rabbit mesentery (Parameswaran et al., inpress). Hydraulic conductivity of pig mediastinalpleura (Parameswaran et al., in press). Hydraulic con-ductivity of pig mediastinal pleura averaged 2.1 30210 cm4 z s21 z dyne21, similar to values of the rabbit

mesentery (Parameswaran et al., 1998). Hyaluronidase

FIG. 5. Albumin diffusion coefficient (D, mean 6 SE) versus al-umin concentration difference (DC 5 ;0, 2, 5, and 10 g/dl).inear regression equation of pooled data was as follows: D 5

.9 3 1028 1 0.55 3 1028 DC, r 2 5 0.53, n 5 24.

increased hydraulic conductivity of the mediastinalpleura by 120%. The diffusion coefficient of albumin

through the mediastinal pleura increased ;3-foldfrom 2.7 3 1028 to 8.3 3 1028 cm2/s as albumin con-centration difference increased from ;0 to 10 g/dl.

yaluronidase had no significant effect on the diffu-ion of albumin across mediastinal pleura.Method. The design of the experiments used to

alculate L and s of the Starling equation [Eq. (1)] andD entailed several assumptions, as discussed previ-ously (Parameswaran et al., 1998; 1999). First, for thesmall range of DP and Dp used in the experiment, Land s were assumed constant and flow independent.However, the experimental results showed that s foralbumin increased with flow. A previous analysisshowed that a small change in s is a second-ordereffect and has a negligible effect on the calculation ofL or s (Parameswaran et al., 1998).

Second, we assumed that L and s were independentof the direction of flow across the membrane. Thus theflow due to the constant DP was from the chamberwith zero p in the same direction as the osmotic flow,opposite to in vivo conditions existing in capillaries.

his ensured no transfer of albumin across the mem-rane and caused a dilution in the chamber containinghe albumin which could be calculated from the mea-ured change in volume. The alternative approachith the flow due to DP directed from the chamber

containing the albumin would result in an albuminflux across the membrane and changes in albuminconcentration within the two chambers that could notbe estimated without the a priori knowledge of s, theoefficient to be estimated from the experiment.Third, we assumed that in the measurements of L

TABLE 2

Effect of Albumin Concentration Difference (DC) andyaluronidase on Albumin Diffusion Coefficienteasured in Pig Mediastinal Pleura

DC(g/dl)

D a

1028 cm2 z s21D h

1028 cm2 z s21 D h/D a

0a 2.7 6 1.5 (12)b — —2 5.0 6 1.9 (4) 6.9 6 1.9 (4) 1.5 6 0.42 (4)5 5.6 6 0.94 (4) 6.9 6 3.3 (4) 1.2 6 0.49 (4)10 8.3 6 3.9 (4) 8.9 6 4.1 (4) 1.2 6 0.56 (4)

Note. D h and D a are albumin diffusion coefficients with andithout hyaluronidase.

a Tracer 125I-albumin in Ringer solution.b Mean 6 SD (n). (n) is number of samples.


Dm(

dt

a(d

tdemoi

lm(um

i


and s, diffusive flow of albumin across the mesenterywas negligible and did not change the albumin con-centration difference between the chambers. This isshown to be the case as follows. The diffusive massflow (dm/dt) of albumin across rabbit mesenterybased on Fick’s law (dm/dt 5 DADC/DX) with D of4.6 3 1028 cm2/s, A of 0.39 cm2, DC of 0.03 g/cm3, andDX of 0.013 cm was 4.1 3 1028 g/s. The mass ofalbumin that diffused across during the experimentaltime period of 40 min was 9.8 3 1025 g. This mass ina chamber volume of 2 ml represented an albuminconcentration of 4.9 3 1025 g/cm3, that is, 0.2% of DC.

Fourth, the effects of an unstirred layer adjacent tothe membrane were minimized by stirring the solu-tions containing albumin during the course of theexperiment (Pedley, 1983).

Fifth, damage to the membrane might result fromexposure to air (Zocchi et al., 1998). This effect wasminimized by ensuring during dissection that the tis-sue was always immersed in saline and by minimizingthe time of the bonding procedure to a few seconds.Tissue damage due to stretching during the bondingprocedure was avoided by maintaining the tissue in arelaxed state. Accordingly, tissue tension during thestudy was most likely less than that existing in vivo,the effect of which would be to reduce L and D and toincrease s.

Sixth, the experiments were done at room tempera-ture (22–24°C). Thus the parameters measured mightbe different from values appropriate to in vivo condi-tions. Previous studies have shown ;20% increase in

measured in solution (Keller et al., 1971) and in theesentery as temperature increased from 25 to 37°C

Rasio, 1970).Seventh, the measured unbound 125I determined by

ialysis was only a small fraction (,2%) of the radioac-ive tracer 125I-albumin and its effect on the diffusion

measurements was virtually eliminated from the steady-state response of the diffused tracer by carrying out theexperiment over a relatively long time scale (10 h) and bydisregarding the initial 2.5 h of data. The initial 2.5 h alsoincluded the time (;1 h) required to establish a constantlbumin concentration gradient within the membraneAppendix, Section C). Over the time scale of 10 h, the
iffusion of unbound 125I across the mediastinal pleura
occurred as an initial transient with a time constant of 1 h


(Appendix, Section A). The much faster diffusion of 125Icompared to albumin (D } M21/2) was consistent withthe molecular weights (M) of iodine (125) and albumin(66,000). Thus the diffusion of unbound 125I offset thedelay needed to establish the albumin concentration gra-dient. The 10-h time scale also ensured that the unbound125I that diffused across the membrane (,1%) was asmall fraction of the total diffused tracer (,6%). The 10-hime scale for albumin diffusion that produced a totaliffused tracer of ,6% of the upstream tracer had theffect of reducing the concentration difference across theembrane with time and resulted in an underestimate

f the diffusion coefficient. An analysis showed this errorn D to be ,8% (Appendix, Section B).

Eighth, the constant bulk flow of hyaluronidase so-ution over 40 min and the constant diffusion of albu-

in measured over 10 h after adding hyaluronidaseFig. 4) provided evidence that the amount of hyal-ronidase used in each experiment (0.02 g/dl 3 1.8l 5 3.6 3 1024 g) was sufficient to degrade the

hyaluronan present in mediastinal pleura.Finally, we determined whether the measurements

of L, s, and D were affected by a protease contami-nation of the albumin solution during the course of theexperiment. We measured albumin concentration(Lowry method) of 2 and 5 g/dl albumin solutionsand 2 and 5 g/dl albumin solutions containing 0.02%hyaluronidase before and after 30 h of exposure toroom air. Albumin concentration was unchanged after30 h. There is the question of tissue deterioration overthe 30 h used for the diffusion experiments. Indepen-dent experiments showed that D did not change dur-ing the course of 30 h (Fig. 3). Similar behavior wasobserved for D measured in mesentery (Parameswa-ran et al., 1999) over 24 h and L measured in lungnterstitium over 2 days (Qiu et al., 1998).

Hydraulic conductance and conductivity. Hydrau-lic conductance (L) of the parietal pleura, defined asflow per unit area per unit driving pressure [Eq. (2)],varies considerably among species because interspe-cies variation of pleural thickness (DX) is not takeninto account. Thus we use hydraulic conductivity(K 5 LDX), defined as flow per unit area per unitdriving pressure gradient, as a more appropriate com-
parison among species because it takes into accountpleural thickness. Table 3 compares values of L and K

tehIl1r2F

N


measured in previous studies on dog and rabbit pari-etal pleura with the present values in the pig. Weassumed a value of parietal pleural thickness of 0.015mm for the dog (Payne et al., 1988) and 0.013 mm forthe rabbit (Lai-Fook and Kaplowitz, 1985). Note that Kvalues for pig mediastinal parietal pleura were similarto those measured in the dog using stripped parietalpleura (Payne et al., 1988), but substantially greater(2–3 orders of magnitude) than values measured insitu in the dog (Negrini et al., 1990, 1991, 1994) and inthe rabbit (Negrini et al., 1994). Hydraulic conductivitymeasured in pig mediastinal pleura was similar tothat measured previously in rabbit mesentery(Parameswaran et al., 1998).

Degradation of tissue hyaluronan (and other glycos-aminoglycans that are degraded by hyaluronidase) byhyaluronidase has been found to increase hydraulicconductivity in skin fascia (Day, 1952), pulmonaryinterstitium (Lai-Fook et al., 1989; Tajadinni et al.,1994), synovial lining (Scott et al., 1997), mesentery(Parameswaran et al., 1998), and other tissues (Hed-bys, 1963; Knepper et al., 1984). In pulmonary intersti-ium (Tajadinni et al., 1994) and synovial lining (Scottt al., 1997), the hyaluronidase response increased withydration caused by elevation of interstitial pressure.n the present study, hyaluronidase increased hydrau-ic conductivity of pig mediastinal pleura on average20%, comparable to the 70% increase measured inabbit mesentery, but much smaller than that (5- to

TABLE 3

Hydraulic Conductance (L), Hydraulic Conductivity (K), AlbuminParietal Pleura in Pigs, Dogs, and Rabbits

Study SpeciesL

(cm3 z s21 z dyne21)

Present study Pig 2 3 1028

Payne et al. (1988) Dog 1.9 3 1027

Negrini et al. (1990) Dog 3 3 10210

Negrini et al. (1991) Dog 2.6 3 1029

Negrini et al. (1994) Dog 3 3 10210

egrini et al. (1994) Rabbit 6 3 10210

Note. L, flow (cm3 z s21) per unit DP (dynes z cm22) per unit sucoefficient; Pe (permeability coefficient) 5 D/DX.

a From Payne et al. (1988).b From Lai-Fook and Kaplowitz (1985).

5-fold) measured in other tissues (Day, 1952; Lai-ook et al., 1989; Scott et al., 1997). In view of the

hydration-induced hyaluronidase response observedin pulmonary interstitium (Tajadinni et al., 1994) andsynovial lining (Scott et al., 1997), the relatively smallhyaluronidase response measured in mediastinalpleura and mesentery might be due to the absence ofhydration.

Reflection coefficient. The values of s (0.02–0.05)for albumin measured in mediastinal pleura werecomparable to values close to zero measured instripped pleura of dogs (Payne et al., 1988; Negrini etal., 1991), in situ studies of parietal pleura of anesthe-tized dogs (Negrini et al., 1990), and extrapolated fromexcluded volume measurements in rat mesentery(Parameswaran et al., 1995). The present results indi-cate that s for albumin increased with flow, consistentwith the behavior measured across rabbit mesentery(Parameswaran et al., 1998). The latter study showedthat s increased from 0.02 to 0.14 as flow (per unitsurface area) increased 8-fold from 5 3 1025 to 4 3 1024

cm/s. The present results showed that s increasedfrom 0.02 to 0.05 as flow increased 20-fold from 4 31026 to 8 3 1025 cm/s. Thus the low values of s

measured in the mediastinal pleura were consistentwith the values measured at the lower range of flowsacross the rabbit mesentery. Also both studies showedcomparable changes in s with flow; by linear regres-sion analysis, Ds/DQ 0 was 4.2 3 102 s z cm21 formediastinal pleura and 6.5 3 102 s z cm21 for mesen-tery (Parameswaran et al., 1998).

ability Coefficient (Pe), and Albumin Diffusion Coefficient (D) of

)K

(cm4 z s21 z dyne21)Pe

(cm/s)D

(cm2/s)

2.1 3 10210 1.2 3 1026 3 3 1028

a 2.9 3 10210 1.3 3 1024 2 3 1027

a 4.5 3 10213 8 3 1027 1.2 3 1029

a 3.8 3 10212 1 3 1025 1.5 3 1028

a 4.5 3 10213 — —b 7.8 3 10213 1.5 3 1027 2.0 3 10210

area (cm2); DX, membrane thickness; K 5 L 3 DX; D, diffusion

Perme

DX(mm

0.130.0150.0150.0150.0150.013

rface

In contrast to the low values of s measured in me-diastinal pleura and mesentery, some studies of pari-


1

c

meOga

d

smsaorliwmmf

pat(wwm(1eosbp


etal pleura of spontaneously breathing dogs and rab-bits have produced much larger values of s foralbumin: 0.3 for dogs and 0.44 for rabbits (Negrini etal., 1994). In the latter studies, the pleura was subjectedto driving pressures up to 30 cm H2O, resulting inflows that were most likely much greater than thoseproduced during normal breathing. Accordingly, inview of the much smaller driving pressure used tomeasure the flow-induced increases in s in the presentstudy and in the mesentery (Parameswaran et al.,998), the wide variation in s values measured in the

foregoing studies might be partly attributed to theexperimental conditions. However, anatomic andphysiologic differences among different regions of theparietal pleura and among different species might becontributing factors. Values of s of 0.23–0.28 for se-rum albumin have been measured in the inner liningof perforated capsules implanted in subcutaneous in-terstitium of dogs (Granger and Taylor, 1975) and inthe umbilical cord (Granger and Shepherd, 1979).

The range of flows used in the present experimentswas produced by small perturbations in DP (0–6 cmH2O) that are in the physiologic range expected forinterstitial tissue in general (Bert and Pearce, 1984).The flows measured across mediastinal pleura in thepresent study (3 3 1026–6 3 1025 cm z s21) werecomparable to values (4 3 1026–1024 cm z s21) forparietal pleura estimated from a pleural liquid turn-over rate (0.09 ml z hr21 z kg21) of a 3-kg rabbit with a15-cm2 pleural surface area that increased 30-fold be-fore the formation of pleural effusions (Miserocchi,1991).

Diffusion coefficient for albumin. The diffusionoefficient (2.7 3 1028–8.3 3 1028 cm2 z s21) for albumin

measured in pig mediastinal pleura in this study was;10-fold smaller than the free diffusion coefficient ofalbumin (6 3 1027 cm2/s; Keller et al., 1971; VanDamme et al., 1982). Our values of albumin diffusioncoefficient in mediastinal pleura were near to those(1.6 3 1028 cm2/s) measured in rabbit mesentery(Parameswaran et al., 1999), in the intact perfused rat

esentery (Fox and Wayland, 1979) and in the rabbitar chamber preparation (Nugent and Jain, 1984).ther studies in isolated subcutaneous tissue (Gran-
er and Taylor, 1975), human umbilical cord (Grangernd Shepherd, 1979), rat diaphragm interstitium
ct


(Schultz, 1976), and rat mesentery (Rasio, 1970) haveindicated albumin diffusion coefficients that wereclose (30–100%) to the free diffusion coefficient. In thestudy by Rasio (1970), the diffusion coefficient of al-bumin increased with temperature.

The comparison of the albumin diffusion coefficientof parietal pleura among species requires the conver-sion of permeability coefficient (Pe 5 D/DX) to D(Table 3). Values for D measured in pig mediastinalpleura were similar to values measured in isolatedchest wall segments of dogs (Negrini et al., 1991),6-fold smaller than values measured for stripped pa-rietal pleura in dogs (Payne et al., 1988), but 1–2 ordersof magnitude greater than values measured in situ in

ogs and rabbits (Negrini et al., 1990, 1994).The notion (Negrini et al., 1990, 1991, 1994) that

tripping caused the increased hydraulic conductivityeasured in the study of Payne et al. (1988) was not

upported by the present results showing values for Knd D similar (within an order of magnitude) to thosef Payne et al., since the isolation of mediastinal pleuraequired no stripping for tissue bath studies. Moreikely, the studies by Negrini et al. (1990, 1991, 1994)ncluded both parietal pleura and endothoracic fascia

hich were isolated by the removal of intercostaluscle, and the smaller L and Pe values measuredight be caused by the presence of endothoracic

ascia.The diffusion of albumin across the pig mediastinal

leura measured in the present study increased withlbumin concentration difference (Fig. 5), similaro the behavior measured in rabbit mesenteryParameswaran et al., 1999). This behavior is consistent

ith an albumin-excluded volume that was reducedith albumin concentration, opposite to the effectseasured in albumin and hyaluronan solutions

Ogston and Sherman, 1961; Laurent and Ogston,963), and albumin and collagen solutions (Wied-rhielm and Black, 1976). Accordingly, steric exclusionf albumin by hyaluronan or collagen measured inolution cannot explain the increased diffusion of al-umin with concentration measured in mediastinalleura.In the present study, hyaluronidase had no signifi-

ant effect on the diffusion of albumin across medias-inal pleura, different from that observed in mesentery

dwsehh

ddrpscd(tPcrT(

Hir


where hyaluronidase decreased the diffusion of albu-min (Parameswaran et al., 1999). The reasons for these

ifferences require further study. The mechanism byhich albumin interacts with mediastinal pleural con-

tituents to increase diffusion of albumin needs to belucidated. An interaction between albumin and tissueyaluronan might be excluded since hyaluronidasead no effect on albumin diffusion.Relationship between diffusion coefficient and hy-

raulic conductivity. The increased hydraulic con-uctivity measured across the mediastinal pleura inesponse to hyaluronidase might appear to be incom-atible with the constant diffusion coefficient in re-ponse to hyaluronidase. The reason for this apparentontradiction lies in the essential differences betweeniffusion and bulk flow. In a previous analysis

Parameswaran et al., 1999) that modeled the intersti-ium as a number of parallel tubes, we consideredoiseuille’s flow through the tubes in response to aonstant driving pressure and steady-state diffusion inesponse to a constant solute concentration difference.he ratios of tube (pore) number (N) and tube radiusR) required to explain the flow and diffusion of two

different solutes were as follows:

Nh/Na 5 b 2/a, Rh/Ra 5 @a/~b!# 1/2. (10)

ere subscript (h) represents albumin with hyaluron-dase and subscript (a) represents albumin. The pa-ameter b is cross-sectional area ratio ( A h/A a) and a is

flow ratio. As a specific example, consider the casewhere b 5 1; that is, the cross-sectional area remainsconstant with hyaluronidase causing no change indiffusion while a 5 2, that is, hydraulic conductivitydoubled with hyaluronidase. We assume that hyal-uronidase in low concentrations (0.02%) has no effecton viscosity (Lai-Fook et al., 1989). Then from Eq. (10),N h/N a 5 1/4, R h/R a 5 1.4. Thus, hyaluronidase hasthe effect of reducing the number of pores 4-fold whileincreasing the pore radius by 40%. Previous results forthe mesentery showed that a 2-fold reduction in dif-fusion by hyaluronidase in conjunction with a 2-foldincrease in hydraulic conductivity was consistent witha 8-fold reduction in pore number and 2-fold increasein pore radius (Parameswaran et al., 1999). These ide-
alized examples of parallel tubes illustrate that hy-draulic conductivity can increase with a constant or
decreasing diffusion coefficient depending on thechange in the number of pores and pore radius. Theultrastructural correlates to these changes are pres-ently unknown.

In summary, reflection coefficients for albumin mea-sured in pig mediastinal pleura increased from a valueof 0.02 to 0.05 as bulk flow increased 20-fold. Thisbehavior is in keeping with the notion that the restric-tion to flow of albumin through membrane pores isreduced at low flows as diffusion reduces the concen-tration differences set up by restriction in the pores(Curry, 1984). The range in flows was near to thatestimated for physiological flows across parietalpleura in vivo. The relatively low values of s wereassociated with the sieving properties of the extracel-lular matrix and indicated that the mediastinal pleuraoffered little restriction to the passage of albumin.Hydraulic conductivity of mediastinal pleura in-creased 120% after enzymatic degradation by hyal-uronidase, indicating that tissue hyaluronan provideda fluid resistance to bulk flow, similar to results fromother interstitial tissues. By contrast, hyaluronidasehad no significant effect on albumin diffusion. Albu-min diffusion across mediastinal pleura increasedwith albumin concentration difference, a behavior thatmight enhance interstitial clearance of albumin underconditions of increased microvascular permeability.

APPENDIX

A. Time Constant for Diffusion of Unbound 125I

We used Fick’s law for steady-state diffusion [Eq.(6)] across a membrane to calculate albumin diffusioncoefficient. However, the experimental data oftenshowed an initial transient faster diffusion rate thatwe attributed in part to the diffusion of the smallermolecule unbound 125I. Here we develop the solutionto the dynamical equation associated with this tran-sient effect. This analysis ignores the time required toinitially establish the solute concentration gradientwithin the membrane; this effect is treated separately
below. Consider the differential form of Fick’s law thatdescribes at arbitrary time (t) the rate of transfer

Hsb

E

Tt

H

a

T

s

H

u

W

u


across the membrane of solute mass (dM 2/dt) fromchamber 1 (solute concentration C 1 5 M 1/V, volumeV) into chamber 2 (solute concentration C 2 5 M 2/V,volume V):

dM2/dt 5 @M1 2 M2#DA/~VDX!. (A1)

ere D, A, and DX are solute diffusion coefficient,urface area, and thickness, respectively, of the mem-rane separating the two chambers. Let M 1 1 M 2 5

M 0, the initial amount of solute (unbound 125I) inchamber 1 at the start (t 5 0) of the experiment. Thus

q. (A1) becomes

dM2/dt 5 @M0 2 2M2#DA/~VDX!. (A2)

he solution of this first-order linear differential equa-ion is as follows:

M2 5 ~M0/2!@1 2 e 2t/t0#. (A3)

ere t 0 5 VDX(2DA), the time constant for the trans-fer of solute by diffusion from chamber 1 into chamber2. The maximum solute transferred is M 0/ 2, that is,half of the initial value in chamber 1. Based on a valuefor iodine D of 1.4 3 1025 cm2/s (free diffusion coef-ficient of iodine), DX of 0.023 cm (mediastinal pleura),V of 1.8 cm3, and A of 0.39 cm2 (experimental set-up),t 0 has the value of ;1 h. Equation (A3) indicates thatt 1 h 63% of M 0/ 2 is transferred and by 2.5 h 92% of

M 0/ 2 is transferred, a behavior consistent with thetransient effects observed in the R-time data (Fig. 4).

he value t 0 will be somewhat longer if the mediasti-nal pleura were to restrict the diffusion of iodine or tohave a significant volume that is excluded from io-dine.

In a previous study of albumin diffusion acrossrabbit mesentery (Parameswaran et al., 1999), the tran-ient response (;20 min) attributed to unbound 125I

was shorter than that observed in the present studyprimarily because DX was 8-fold smaller (30 mm)resulting in a t 0 value of 8 min.

B. Error in the Calculation of Albumin D

Equation (A3) in theory is also applicable to the
diffusion of 125I-albumin. Because albumin D (3 31028–8 3 1028 cm2/s) measured in the present study

was much smaller than iodine D, t 0 for albumin dif-fusion (80–500 h) was much longer than that for io-dine. From the exponential series expansion for t ! t 0,a close approximation to e2t/t0 correct to second orderin t/t 0 is 1 2 (t/t 0). Thus Eq. (A3) reduces to

dM2/dt 5 ~DA/DX!C1@1 2 ~t/t0!#. (A4)

ere M 0/V is replaced by the initial concentration(C 1) of 125I-albumin in chamber 1. Equation (A4) re-duces to Fick’s law for steady-state diffusion [Eq. (6)]with C 2 5 0 at t 5 0. With t between 2.5 and 10 h andt 0 of .80 h, D calculated from Eq. (6) with C 2 5 0

nderestimates D calculated from Eq. (A4) by ,8%.

C. Time Required to Establish Initial ConcentrationGradient across a Membrane

The time (T) required to establish steady-state uni-directional diffusion of a solute across a membraneafter a constant solute concentration (C 1) is applied attime 0 to one side of the membrane with solute con-centration (C 2) maintained at zero on the other side isas follows (Crank, 1967; Qiu et al., 1998):

T 5 ~DX! 2/~2D!. (A5)

ith DX of 0.023 cm and albumin D of 6 3 1028 cm2/sfor the mediastinal pleura, T for albumin is 1.2 h. T for

nbound 125I with iodine D of 1.4 3 1025 cm2/s is 20 s.The corresponding T values for albumin and iodinefor the mesentery membrane (Parameswaran et al.,1999) with DX of 30 mm are 10 min and 3 s, respec-tively.

ACKNOWLEDGMENTS

This research was funded by NIH Research Grants HL 40362 andHL 36597.

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Hydraulic Conductivity, Albumin Reflection and Diffusion Coefficients of Pig Mediastinal Pleura

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