Effect of Concentration and Hyaluronidaseon Albumin Diffusion Across

Rabbit MesenterySANDHYA PARAMESWARAN,* LAURA V. BROWN,*

GEOFFREY S. IBBOTT,† AND STEPHEN J. LAI-FOOK**Center for Biomedical Engineering and †Department of Radiation Medicine,

University of Kentucky, Lexington, KY, USA

ABSTRACT

Objective: To measure the diffusion coefficient of albumin through rabbit mes-entery using the steady-state flux of radioactive tracer 125I-albumin. The effectof albumin concentration and testicular hyaluronidase were also studied.Methods: Mesenteric tissue was bonded between two plates, exposing a 7 mmdiameter surface, with two chambers on either side. One chamber was filled witha test solution of albumin containing the radioactive tracer and the other withlactated Ringer solution. The solutions in both chambers were stirred with smallmagnetic cylinders. The chamber filled with lactated Ringer solution was placedin a well-type NaI(Tl) detector, and the radiation emitted from the tracer thatdiffused across the mesentery was monitored continuously for 9 hours. Thediffusion coefficient (D) was calculated using Fick’s law of diffusion. The dif-fusion coefficient was measured at albumin concentration differences (DC) be-tween ∼0 and 10 g/dL. The diffusion coefficient was also measured with tes-ticular hyaluronidase at three different albumin-concentration differences.Results: The diffusion coefficient increased significantly (P < 0.0001) ∼ three-fold from a mean value of 2.2 × 10−8 ± 1.2 × 10−8 (SD) cm2/s at 0–0.5 g/dL DCto 5.9 × 10−8 ± 1.1 × 10−8 (SD) cm2/s at 10 g/dL DC. The values are much lessthan the free diffusion coefficient of albumin (6 × 10−7 cm2/s). Testicularhyaluronidase added to the albumin solution decreased D by ∼ 60%, but did noteliminate the increase in D with DC.Conclusions: The increase in D with DC and the reduced D with hyaluronidasewere attributed to a reduced albumin-excluded volume caused by an interactionbetween albumin and hyaluronan. Further studies are required to define thisinteraction.

KEY WORDS: diffusion coefficient, albumin, interstitium, hyaluronidase, hyaluro-nan

INTRODUCTION

The movement of macromolecules between capillar-ies and lymphatics via the interstitium surroundingthe blood vessels depends partly on bulk flow causedby hydrostatic pressure differences and partly ondiffusion caused by protein concentrations differ-ences. Several studies have established that tissue

hyaluronan contributed a major hydraulic resistanceto bulk flow. For example, hyaluronidase increasedbulk flow through skin fascia (3), hydrated pulmo-nary interstitium (12,16,29), synovial lining (28),rabbit eye (11), and bovine corneal stroma (8) in-dicating that tissue hyaluronan provided the majorresistance to bulk flow. More recent studies showedthat hyaluronidase increased bulk flow through mes-entery tissue by 70% (23). The bulk flow of albuminsolution might also be influenced by the steric ex-clusion of albumin by tissue hyaluronan (2,20).

Hyaluronan, through its ability to retain water andexclude protein, might affect the diffusion of albu-min through interstitial tissue. For example, studies

Supported by National Heart, Lung, and Blood Institute GrantsHL 40362 and HL 36597.For reprints of this article, contact S. J. Lai-Fook, Center forBiomedical Engineering, Wenner-Gren Research Laboratory,University of Kentucky, Lexington, KY 40506-0070, USA.Received 5 December 1997; accepted 4 November 1998

Microcirculation (1999) 6, 117–126© 1999 Stockton Press All rights reserved 1073-9688/99 $12.00http://www.stockton-press.co.uk

on the diffusion of a 5% FITC-labeled serum albu-min across rat mesentery showed an apparent diffu-sion coefficient 14-fold smaller than the free diffu-sion coefficient (4). Studies in mesentery indicatedthat temperature increased the apparent diffusioncoefficient to the passage of lipid-insoluble mol-ecules, and suggested that diffusion across the mes-entery occurred partly by an active-transport pro-cess (26). In vitro studies on binary systems indi-cated that the diffusion coefficient increased withpolymer concentration (14). However, the effects ofprotein concentration and hyaluronan on diffusionin the interstitium have not been extensively studied.

In this study, we measured the effect of albuminconcentration and hyaluronidase on the diffusion co-efficient of albumin through rabbit mesentery usinga radioactive tracer (125I-albumin) technique. Dif-fusion of albumin increased with concentration andwas reduced with hyaluronidase. The degradation oftissue hyaluronan by hyaluronidase reduced, but didnot eliminate the albumin concentration-dependentincrease in diffusion.

MATERIALS AND METHODS

New Zealand White rabbits (body weight 3–4 kg, n4 18) were sedated with ketamine (130 mg) andxylazine (4 mg) administered intramuscularly andanesthetized with sodium pentobarbital (30 mg/kg)injected through an ear vein. A 4 cm midline incisionwas made in the abdominal surface, and a loop ofthe mesentery was exteriorized. A segment of themesentery was isolated and excised from the animaland mounted in vitro between two chambers filledinitially with lactated Ringer solution (100-mL lac-tated Ringer solution contains 600 mg sodium chlo-ride, 310 mg sodium lactate, 30 mg potassium chlo-ride, 20 mg calcium chloride). Figure 1 shows a dia-gram of the experimental assembly used to measurethe diffusion of 125I-albumin across a piece of rabbitmesentery. The membrane exposed to the solutionsin the chambers had a circular area of 0.7 cm indiameter. Each chamber was constructed of a thin-walled plastic tube (0.22-mm wall thickness, 0.73-cm outer diameter, 4.5 cm in length) bonded to oneside of a plastic plate (6.5 cm × 8.5 cm × 0.3 cm) tofit a 0.7 cm diameter hole in the plate. The other sideof each plate contained a collar (0.7 cm internaldiameter and 1.3 cm outer diameter) that projectedout 0.7 cm from the plate. The mesentery membranewas bonded in turn to the flat outer surface of eachcollar using cyanoacrylate adhesive. This particulardesign allowed the bonding of the flat outer surfaceof the collar to the membrane situated in a natural

configuration and ensured that tension in the mem-brane was close to that existing in situ. The assemblywas further stabilized by bolting the two plates to-gether at the four corners. The membrane was pre-vented from drying by applying lactated Ringer to itssurfaces during the setting up procedure.

Each chamber (1.8-mL volume) was of identical ge-ometry and was designed so that 4.5 cm length of thecylinder would fit into a well-type NaI(Tl) scintilla-tion counter (Model no. TB-2L, Oxford InstrumentInc., Oak Ridge, TN) through a 0.9-cm-diameter en-try hole made in the lead cap that covered the open-ing of the counter. The chamber outside the counterwas filled with the albumin solution containing ∼ 1mC 125I-albumin. The chamber volume is consistentwith a > 95% overall efficiency for a well-type de-tector (1). The amount of 125I-albumin (< 1 mC) waschosen to avoid counting loss due to dead time in awell counter (1). The other (inner) chamber that waspartially located in the counter was filled with lac-tated Ringer solution. To prevent radiation from theoutside chamber from falling on the outer surface ofthe counter, the outside surface of the detector wascovered with a 2-mm-thick lead sheet. In addition,the bottom surface of the counter was lined with leadto prevent the radiation emanating from the outerchamber in the axial direction from falling on thebottom surface of the counter. The counter was ori-ented with its cylindrical axis horizontal. A guideconstructed of a thin-walled plastic tube (1-cm-inner diameter, 3-cm long) was bonded to the innersurface of the cap to locate and maintain the cham-ber axis horizontal and at a fixed orientation relativeto the counter. The plastic material used to construct

Figure 1. Cross-sectional view of experimental set-upused to measure diffusion coefficient of albumin throughmesentery membrane. See text for details.

Diffusion across rabbit mesenteryS Parameswaran et al.

118

the two chambers and supporting plate and collarwere tested initially to ensure that it did not absorbthe radioactive tracer. During diffusion of albumin,the solution in each chamber was stirred continu-ously by slowly rotating a magnetic stirrer placedwithin each chamber using an external electromag-netic source (Thermix stirrer, Model 120S, FisherScientific, PA).

Calibration of the Scintillation Detector (Counter)

We used a gamma-ray spectrometry system consist-ing of four NaI(Tl) scintillators, each connected to aphotomultiplier tube (to detect the light emittedfrom the scintillator when subjected to radiation),preamplifier and amplifier, with a single high-voltage power supply (Model 5040, Oxford Instru-ments, Inc., Oak Ridge, TN). The output of eachamplifier was interfaced to a computer (PC-AT 386,AT&T) via a single-channel-pulse height selectorand a count-rate meter for automatic data collection.The four single-channel analyzers were calibrated bymeasuring the spectrum of X-rays and gamma raysfrom a 1 mC sample of 125I-albumin. The high volt-age supplied to the photomultiplier tubes, and theamplifier gain settings were adjusted so that thresh-old voltage settings of 0.2 volts to 10 volts corre-sponded approximately to gamma-ray energies of 2to 100 keV. Three of the detectors showed roughlyidentical sensitivities, while the fourth detector re-quired an adjustment to the gain settings. Figure 2

shows a representative energy spectrum obtained bymoving a 0.04 volts window incrementally throughthe range from 0 to 10 volts. The principle gamma-ray peak at 35 keV is seen as well as a coincidencepeak at 70 keV. Measurements of 125I-albumin con-centrations were made with the lower discriminatorset to 0.2 volts to eliminate detector noise and low-energy background radiation, and the upper dis-criminator at 10.2 volts to accept pulses in the 35keV photopeak and the 70 keV coincidence peak. Atthe low concentrations used for the experiment, thenumber of coincidence events was expected to beinsignificant.

Experimental Protocols

We measured the diffusion of albumin across rabbitmesentery at different albumin concentrations.Stock solutions (18 mL) were made with albumin(bovine serum albumin, batch no. A9647, SigmaChemical) of the test concentrations and 125I-albumin (∼ 0.5 mC/mL; batch no. NEX-076, NewEngland Nuclear Research Products, Boston, MA).The outside chamber was filled with a stock solution(0, 0.1, 0.5, 1.5, 5, or 10 g/dL albumin solution),and the downstream chamber filled with lactatedRinger solution. Both chambers were capped andsealed with vacuum grease to eliminate flow of so-lution between the chambers due to osmosis. Thechamber with lactated Ringer solution was placed inthe well counter and the radiation emitted by theradioactive sample that accumulated by diffusionfrom the outer chamber was measured during 10-minute intervals for 9–10 hours. At the end of thisperiod, the solution in the outer chamber was re-placed with a stock solution of a different albuminconcentration with 125I-albumin tracer. The radia-tion emanating from each stock solution was mea-sured before filling the outer chamber and remea-sured at the end of the experiment, using a calibra-tion chamber of identical geometry to the outerchamber. Different pairs of albumin concentrationswere studied (0.5 g/dL and 1.5 g/dL, 0.1 g/dL and5 g/dL, 5 g/dL and 10 g/dL) to determine whethertissue deterioration or the order in which differentpaired concentrations was done had an effect on theresults.

In separate experiments, the effect of hyaluronidaseon albumin diffusion through rabbit mesentery wasstudied. After the diffusion of albumin (0.5, 5 or 10g/dL in outer chamber) was measured for 9–10hours using the foregoing procedure, hyaluronidase(0.02 g/dL Ringer solution; bovine testes, 440 U/mgsolid, batch no. H3506, Sigma Chemical) was added

Figure 2. Representative energy spectrum, count rate(counts/s) versus energy (volts), of a 1 mC sample 125I-albumin measured in a well-type NaI(Tl) detector. Lowercurve represents spectrum without the 1 mC sample.

Diffusion across rabbit mesenteryS Parameswaran et al.

119

to the outer chamber, and the radioactivity appear-ing in the inner chamber counted for a further 9–10hours.

All solutions were filtered (0.45 mm pore diameter),and adjusted to a pH of 7.4. Four sections of mes-entery were studied simultaneously from each rab-bit. Failure was sometimes caused by leaks in thepreparation as indicated by an abnormally high ra-diation count-rate in the inner chamber, or loss ofliquid from one or both chambers. These resultswere not reported. Usually at least three sectionsproduced acceptable results. At the end of each ex-periment, the membranes were dissected from theretaining plates and weighed to estimate membranethickness. The experiments were carried out at roomtemperature (22–24 °C).

In separate experiments, we measured the amount ofunbound 125I present in the 125I-albumin stock so-lution. We dialyzed a small amount of 125I-albuminstock solution using a pre-mounted wet-packedmembrane, made for Model 4000 series colloid os-mometers (Wescor, SS-030, Logan, UT) for 2 hours.The radioactivity from unbound 125I that passedthrough the membrane was measured and comparedwith that from the stock solution. Unbound 125I ac-counted for less than 2% of the stock solution, veri-fying the manufacturer’s specification.

Calculation of Albumin Diffusion Coefficient

We used Fick’s law for steady-state diffusion of asolute through a membrane of surface area (A) anduniform thickness (L):

dM2/dt = DA~C1 − C2!/L (1)

Here, dM2/dt is flow of the solute mass (M2) thatoccurred by diffusion, D is the solute diffusion coef-ficient and C1 − C2 is the difference (DC) in soluteconcentration between the outer and inner chamberson the opposing sides of the membrane. Applicationof this equation to determine the diffusion coefficientof albumin entailed several assumptions as discussedbelow (see Discussion).

The mass flow of albumin (dM2/dt) was calculatedusing the mass of albumin present in the outerchamber (M1) times the ratio of the slope (dR2/dt,tracer flux) of the measured radioactivity (R2,counts/s) − time curve to the radioactivity measuredin the outer chamber (R1):

dM2/dt = M1~dR2/dt!/R1 (2)

Here we assumed that the radiation measured by thecounter scaled directly with the dilution of 125I-

albumin in the range between R2 and R1 (see Re-sults, Fig. 3). Because M1 4 C1V1, where V1 is thevolume of the outer chamber and C2 is assumed to be0, then Eq. (1) becomes:

D = LV1 ~dR2/dt!/~R1A! (3)

Note that Eq. (3) shows that C1 does not enter intothe calculation of D. Thus, D can be calculated evenif C1 is not exactly known, as is the case with thediffusion of only the tracer 125I-albumin.

RESULTS

The small amount of radioactive tracer used for thediffusion across the mesentery membrane produceda linear calibration curve. The radioactive label of∼1mC 125I-albumin/1.8 mL Ringer solution wasmeasured in the calibration chamber and remea-sured at dilutions of 10, 102, and 103 Ringer solu-tion. Figure 3 (log–log plot) shows the resulting plotof count rate (R) versus relative concentration (C). Aregression analysis showed that log R versus log Cwas linear: log R 4 −0.978 logC + 4.45, r2 4 0.999.

Figure 4 shows an example of radioactivity mea-sured during 24 hours for diffusion of 0.5 g/dL al-bumin with 1 mC tracer across mesentery mem-brane. Note the cyclic variation from linearity over24 hours. The reasons for this variation are specu-lative (see Discussion). The 9–10 hour period chosenfor the length of subsequent experiments was basedon the shortest time required for the data to repre-sent the curve over 24 hours. We used the shortestperiod because we wished to maintain the concen-tration of albumin in the inner chamber to less than10% of concentration in the outer chamber and to

Figure 3. Calibration curve of radioactivity (counts/s)versus relative concentration of 1 mC 125I-albumin.

Diffusion across rabbit mesenteryS Parameswaran et al.

120

minimize the effects of tissue deterioration. This pro-duced an error of less than 20% in the calculation ofdiffusion coefficient using a fixed albumin concen-tration difference in Fick’s law of diffusion [Eq. (1)].

Figure 5 shows an example of radioactivity (R,counts/10 min) measured versus time (t, 10 min) foran albumin concentration difference (DC) of 0.1g/dL for 9 hours followed by an albumin concentra-

tion difference of 5 g/dL for a further 9 hours. Thelinear regression equation for DC of 0.1 g/dL was: R4 8503 t + 127274, r2 4 0.999. The linear regres-sion equation for DC of 5 g/dL was: R 4 22019 t +760433, r2 4 0.995. The diffusion coefficient wascalculated by substituting the slope of the R–t curve,measured A and L in Eq. (3). We used an A value of0.39 cm2 based on a membrane diameter of 7 mm.Membrane thickness (∼30 mm) was determined fromthe weight of the membrane, A, and a membranedensity of 1 g/cm3. Albumin diffusion coefficientwas 1.9 × 10−8 cm2/s at DC of 0.1 g/dL and 5.0 ×10−8 cm2/s at DC of 5 g/dL. Membrane thicknesswith and without hyaluronidase averaged 32 ± 13mm (SD, n 4 12) and 29 ± 19 mm (SD, n 4 11)respectively, and was not significantly different (P4 0.66).

Figure 6 shows the albumin diffusion coefficientplotted versus albumin concentration difference (0,0.1, 0.5, 1.5, 5, and 10 g/dL) across mesenterymembrane. Albumin diffusion coefficient was notsignificantly different for DC values between 0 and0.5 g/dL, and averaged 2.2 × 10−8 ± 1.2 × 10−8 (SD,n 4 29) cm2/s. Albumin diffusion coefficient in-creased threefold from the value at DC of 0–0.5 g/dLto a value of 5.9 × 10−8 ± 1.1 × 10−8 (SD, n 4 5)cm2/s at 10g/dL. A linear regression analysis of thepooled data showed a significant increase in diffu-sion coefficient with albumin concentration differ-ence: D 4 0.41 × 10−8 DC + 2.2 × 10−8, r2 4 0.88,n 4 61, P < 0.0001. In each experimental group inwhich two albumin concentrations were used inturn, the diffusion coefficient was always signifi-cantly (paired t-test, P < 0.05) greater at the higher

Figure 4. An example of radioactivity (R, counts perhour) measured over 24 hours across mesentery mem-brane. Note the cyclic variation from linearity over the 24hours. Linear regression analyses of the data over the timescales 0–8 hours, 0–16 hours, and 0–24 hours indicatedthat the slope of the R-time curves was constant over thethree scales. Thus, we used the time scale 0–8 hours forthe experiment.

Figure 5. An example of radioactivity (counts/10 min)measured across mesentery membrane at two albuminconcentration differences (DC of 0.1 g/dL and 5 g/dL) inturn. Note that radioactivity (counts/10 min) increasedlinearly with time for each DC but the slope was greaterfor the greater DC, indicating an increasing diffusion co-efficient with DC.

Figure 6. Albumin diffusion coefficient (D, mean ± SD)versus albumin concentration difference (DC 4 ∼0, 0.1,0.5, 1.5, 5, and 10 g/dl). Linear regression equation ofpooled data was as follows: D 4 2.2 × 10−8 + 0.41 × 10−8

DC, r2 4 0.88, n 4 61, P < 0.0001.

Diffusion across rabbit mesenteryS Parameswaran et al.

121

albumin concentration. This was also the case whenthe diffusion with the higher albumin concentrationwas measured first, indicating that tissue deteriora-tion was not the reason for the increased diffusioncoefficient with albumin concentration.

Figure 7 shows an example of radioactivity (R,counts/10 minutes) measured for the diffusion of 5g/dL albumin across mesentery membrane for 9.5hours followed by measurements for a further 9.5hours after the addition of hyaluronidase to the al-bumin solution. The small increase in radioactivityat 9.5 hours was an artifact of removing the chamberfor the addition of hyaluronidase. The linear regres-sion equation (t, 10 min) without hyaluronidase was: R 4 15069 t + 319906, r2 4 0.999. The linearregression equation with hyaluronidase was : R 47914 t + 1294125, r2 4 0.987. Note that the slopeof the R–t curve, which is proportional to the diffu-sion coefficient, decreased by 48% with the additionof hyaluronidase. Also, the change in the linear re-sponse of the R–t curve with hyaluronidase occurredwithin 1 hour of adding hyaluronidase, and this ef-fect of glycosaminoglycan degradation by hyaluron-idase was constant thereafter. Table 1 summarizesthe data of diffusion coefficient at different DC val-ues with and without hyaluronidase. The effect ofhyaluronidase was to decrease significantly (P <0.01) the albumin diffusion coefficient on averageby 55% ± 5.6% (n 4 18) from control values with-out hyaluronidase (Table 1). At each albumin con-centration (0.5, 5, or 10 g/dL), the diffusion coeffi-cient was significantly (paired t-test, P < 0.05) lower

with hyaluronidase (Fig. 8). Linear regressionanalysis indicated a significant increase in D withalbumin concentration difference (DC) without hy-aluronidase (D 4 0.41 × 10−8 DC + 2.2 × 10−8, r2 40.88, n 4 18, P < 0.0001) and with hyaluronidase(Dh 4 0.18 × 10−8 DC + 1.0 × 10−8, r2 4 0.75, n 418, P < 0.01). However, the fractional change indiffusion coefficient [DD/D 4 (Dh − D)/D] causedby hyaluronidase did not vary significantly with al-bumin concentration. The regression equation was:DD/D 4 −0.005DC − 0.46, r2 4 0.002, n 4 18, P4 0.86. The smaller slope of the D-DC behaviorwith hyaluronidase indicated that hyaluronidase re-duced but did not eliminate the increase in D withDC.

DISCUSSION

This study showed that the diffusion coefficient ofalbumin through rabbit mesentery increased ap-

Figure 7. An example of radioactivity (counts/10 min)measured across the mesentery membrane at an albuminconcentration difference of 5 g/dL before and after hyal-uronidase (0.02%) was added to the albumin solution.Note that hyaluronidase decreased the rate of diffusionand that the change occurred within the first hour. Seetext for details.

Figure 8. Albumin diffusion coefficient versus albuminconcentration difference (DC of 0.5, 5 and 10 g/dL) be-fore and after hyaluronidase was added to the albuminsolution. Note that hyaluronidase significantly reducedthe albumin diffusion coefficient at each DC. Also hyal-uronidase reduced but did not eliminate the concentra-tion-dependent increase in the albumin diffusion coeffi-cient.

Table 1. Effect of albumin concentration difference (DC)and hyaluronidase (HSE) on albumin diffusion coefficient(D) measured in rabbit mesentery

DC(g/dL)

D (albumin) × 108

(cm2/s)D (HSE) × 108

(cm2/s)

0 1.38 ± 0.36 (5)* —0.1 2.77 ± 1.14 (12) —0.5 1.98 ± 1.19 (13) 0.80 ± 0.76 (6)1.5 3.08 ± 0.92 (6) —5 4.88 ± 1.52 (21) 2.51 ± 0.86 (8)

10 5.88 ± 1.08 (5) 2.58 ± 1.39 (4)

*Mean ± SD (n). n 4 number of samples.

Diffusion across rabbit mesenteryS Parameswaran et al.

122

proximately threefold from 2.2 × 10−8 ± 1.2 × 10−8

(average value in the range 0–0.5% DC) cm2/s to 5.9× 10−8 ± 1.1 × 10−8 cm2/s as the albumin concen-tration difference increased from ∼ 0–0.5 g/dL to 10g/dL. Degradation of mesentery hyaluronan (andother glycosaminoglycans that are degraded by hy-aluronidase) by hyaluronidase reduced the albumindiffusion coefficient by ∼ 60% at albumin concen-tration differences between 0.5 and 10 g/dL. Hyal-uronidase reduced, but did not eliminate the in-crease in albumin diffusion with albumin concentra-tion.

Methods

The measurement of the diffusion coefficient of al-bumin across mesentery membrane was based onFick’s law for steady-state diffusion [Eq. (1)]. Thisentailed several assumptions and features that wouldaffect accuracy. First, we assumed that the tracer125I-albumin and solute albumin were of identicalmolecular weight and conformational geometry sothat in a well-mixed solution, they have identicaldiffusional rates. This is a reasonable assumptionbecause the molecular weight of albumin (66,000) is500-fold greater than that of iodine (125). Thus, themass of tracer albumin was representative of themass of albumin.

Second, we assumed that DC, the albumin concen-tration difference across the membrane, was con-stant during the 9–10 hour experiment. The mass ofalbumin that diffused through the membrane wasless than 8% of the albumin in the outer chamber.Thus, DC decreased by less than 16% at the end ofthe experiment and a 16% reduction in DC wouldresult in an 8% underestimate of the diffusion coef-ficient.

Third, the presence of unstirred layers in the solutionin contact with the membrane would reduce the ef-fective value of DC and result in an underestimationof diffusion coefficient (25). The permeability of anunstirred layer (Ds/Ls) is given by the ratio of solutediffusivity (Ds) to thickness (Ls) of the unstirred lay-ers. The ratio of the actual solute concentration dif-ference across the membrane (DCm) to that acrossthe two chambers (DCm/DC) is related to Ls/Ds andLm/Dm by the following equation:

DCm/DC = ~Lm/Dm!/@~2Ls/Ds! + ~Lm/Dm!# (4)

Given a typical unstirred layer thickness Ls of 100mm (25), membrane thickness (Lm) of 30 mm andestimated ratio of free diffusion coefficient (Ds) tomembrane diffusion coefficient (Dm) of 20, DCm/DCis 0.75. This results in an underestimate of mem-

brane diffusion coefficient of 25%. This indirect es-timate might be affected by a solute concentrationinduced change in Ls. This is a maximum error be-cause the solution was stirred continuously to mini-mize the thickness of the unstirred layer.

Fourth, although the unbound 125I was only a frac-tion (< 2%) of the radioactive tracer 125I-albumin,its effect on the diffusion measurements was virtu-ally eliminated from the steady-state response of thediffused tracer by carrying out the experiment over arelatively long time scale (9 hours). Over this timescale, the diffusion of all the unbound 125I across themesentery occurred as an initial transient lasting for∼ 20 minutes. This was consistent with the 23-foldfaster diffusion of 125I compared to albumin, basedon D that is proportional to M−1/2, with the molecu-lar weights (M) of iodine (125) and albumin(66,000). The relatively long time scale over whichthe steady state diffusion was calculated also en-sured that the radioactivity emitted from the un-bound 125I was a small fraction of that from the125I-albumin that diffused through the membrane.

Finally, the linear response in the diffusion of albu-min measured over 9.5 hours after adding hyaluron-idase (Fig. 7) provided evidence that the amount ofhyaluronidase used in each experiment (0.02 g/dL ×1.8 mL 4 3.6 × 10−4 g) was sufficient to degrade theglycosaminoglycan (1.7 × 10−2 g/g wet weight) pre-sent in the mesentery tissue (∼ 2.1 × 10−5 g 4 1.7 ×10−2 g/g × 1.25 × 10−3 g tissue). Here we used thetotal glycosaminoglycan measured in rabbit mesen-tery by Iozzo and Muller-Glauser (9): hyaluronan, 5× 10−3 g/g wet weight; chondroitin sulfate, 2 x 10−3

g/g wet weight; dermatan sulfate, 10−2 g/g wetweight. Hyaluronidase had no measurable effect ontissue mass because tissue mass measured in experi-ments without hyaluronidase (1.25 ± 0.5 mg, n 412) was not significantly (P 4 0.66) different fromthat with hyaluronidase (1.13 ± 0.7 mg, n 4 11).

Finally, we determined whether the reduced albu-min diffusion coefficient measured with hyaluroni-dase was caused by degradation of albumin by aprotease contamination of the hyaluronidase. Wemeasured albumin concentration (Lowry method) of2 and 5 g/dL albumin solutions containing 0.02%hyaluronidase after 9 hours. The measured valuesdiffered from control values without hyaluronidaseby < 3%, indicating that the addition of hyaluroni-dase did not degrade the albumin in solution.

Comparison with Other Studies

The diffusion coefficient (2.2 × 10−8 − 5.9 × 10−8

cm2/s) for albumin measured in rabbit mesentery in

Diffusion across rabbit mesenteryS Parameswaran et al.

123

this study was ∼ tenfold smaller than the free diffu-sion coefficient of albumin (6 × 10−7 cm2/s, ref. 28).Our values of albumin diffusion coefficient in rabbitmesentery were near to those (1.6 × 10−8 cm2/s)measured in the intact perfused rat mesentery (4)and in the rabbit ear chamber preparation (18). Ourvalues are also consistent with values of the perme-ability-surface area product (PS) measured in stripsof canine pleural membrane (24), but is an order ofmagnitude greater than PS values measured in rab-bit parietal pleura in situ (17). By contrast, otherstudies in isolated subcutaneous tissue (5), humanumbilical cord (6), rat diaphragm interstitium (27),and rat mesentery (26) have indicated albumin dif-fusion coefficients that were close (30–100%) to thefree diffusion coefficient. In the latter study (26),diffusion coefficient of albumin increased with tem-perature.

Since the original results of Day’s studies (3) showedthat hyaluronidase increased the hydraulic conduc-tivity of skin fascia, similar effects of hyaluronidasehave been demonstrated in hydrated lung intersti-tium (29), rabbit mesentery (23), and synovial lin-ing (28). Similar studies have shown that the bulk(convective) flow of albumin solution relative to thatof lactated Ringer solution through hydrated lunginterstitium increased with albumin concentration(12). Because this effect was partly eliminated byhyaluronidase, the increased flow of albumin solu-tion relative to that of Ringer solution with albuminconcentration was attributed to a reduced excludedvolume from albumin by interstitial hyaluronan.

The diffusion coefficient of albumin measured in so-lution was either constant (30) or decreased withincreasing albumin concentration (10). In the latterstudy, the diffusion coefficient of albumin increased3% per °C between 25 and 37°C, comparable to theeffects observed in mesentery (26). In other studies,the diffusion of serum albumin in solution decreasedas the concentration of hyaluronan increased (19). Asimilar trend was observed at a fixed hyaluronanconcentration as albumin concentration increased.The partitioning of a diffusible macromolecule, suchas albumin, between solutions of hyaluronan andbuffer has been attributed to steric exclusion of themacromolecular solute from a solution containingrandomly coiled hyaluronan chains (20). The os-motic pressure of albumin and hyaluronan in solu-tion was found to be greater than the sum of theosmotic pressures of the constituents measured sepa-rately at the same concentrations (13). This in-creased osmotic pressure of albumin and hyaluronanin solution increased with either albumin or hyaluro-

nan concentration and was interpreted in terms of anexclusion of albumin from part of the solution occu-pied by hyaluronan. Similar effects have been mea-sured in albumin and collagen solutions (31).

In contrast to the reduced diffusion of albumin withconcentration measured in solutions containing bothalbumin and hyaluronan, the diffusion of albuminacross the mesentery measured in the present studyincreased with concentration (Fig. 6). This behavioris consistent with an albumin-excluded volume thatwas reduced with albumin concentration, opposite tothe effects measured in albumin solutions (21) andin albumin and hyaluronan solutions (21). Also, theincreased diffusion of albumin with concentrationmeasured across the mesentery (Fig. 8) decreasedwith the degradation of tissue hyaluronan (or otherglycosaminoglycans that are degraded by testicularhyaluronidase). This suggests that tissue hyaluronanserved to decrease the volume excluded from albu-min. A similar effect was observed in rat mesenterywhere the volume excluded from albumin increasedafter superfusion with hyaluronidase (22). Accord-ingly, steric exclusion of albumin by hyaluronanmeasured in solution cannot explain the increaseddiffusion of albumin with concentration nor the de-creased diffusion of albumin by hyaluronidase mea-sured in rabbit mesentery. The mechanism by whichalbumin and hyaluronan interact to increase diffu-sion of albumin needs to be elucidated.

Our results also indicated that hyaluronidase re-duced but did not eliminate the increased diffusionof albumin with albumin concentration (Fig. 8).This suggests that the interaction between albuminand interstitial hyaluronan (or other glycosamino-glycans that are degraded by testicular hyaluroni-dase) was not entirely responsible for the increaseddiffusion of albumin with albumin concentration.The interaction between albumin and other intersti-tial constituents, such as collagen, might producesimilar effects on the diffusion of albumin.

Relationship Between Diffusion Coefficient andHydraulic Conductivity

At first sight the postulated reduced-interstitialcross-sectional area for diffusion caused by hyal-uronidase in the present study might appear to runcounter to the hyaluronidase-induced increase in hy-draulic conductivity measured in several studies(3,8,11,12,16, 23,29). The reason for this apparentcontradiction lies in the essential differences betweendiffusion and bulk flow. To illustrate these differ-ences, consider one-dimensional flow of a solutethrough the interstitium made of a number (N) of

Diffusion across rabbit mesenteryS Parameswaran et al.

124

parallel tubes of radius R and length L. Given aconstant L and DC, the diffusive flow of a solute ofdiameter much smaller than the tube diameter byFick’s law [Eq. (1)] is proportional to the cross-sectional area of the tubes, A 4 pNR2. The bulkflow of solution (Q) driven by a hydrostatic pressure(P) gradient (DP/L) is given by Poisseuille’s law:

Q = @NpR4/~8m!#~DP/L! (5)

Here, m is fluid viscosity. Hydraulic conductivity (Q/DP) is given by:

Q/DP ~ NR4/m (6)

Consider the ratio of the bulk flow of albumin solu-tion with hyaluronidase (Qh) to that of albumin so-lution (Qa), subjected to a constant DP and L:

Qh/Qa = ~Nh/Na!~Rh/Ra!4/~mh/ma! = a (7)

Here subscript (h) represent albumin with hyaluron-idase and subscript (a) represents albumin. Thecross-sectional area ratio is then:

Ah/Aa = ~Nh/Na!~Rh/Ra!2 = b (8)

From Eqs. (7) and (8):

Nh/Na = gb2/a, Rh/Ra = @a/~gb!#1/2 (9)

Here mh/ma 4 g. As a specific example, consider thecase where b 4 0.5, that is, the cross-sectional areadecreased by 50% with hyaluronidase causing a50% reduction in diffusion while a 4 2, that is,hydraulic conductivity doubled with hyaluronidase.We assume that hyaluronidase in low concentrations(0.02%) has no effect on viscosity (12) so that g 41. Then from Eq. (9), Nh/Na 4 1/8, Rh/Ra 4 2.Thus, hyaluronidase has the effect of reducing thenumber of tubes (pores) eightfold while doubling thepore radius. The actual situation is far more complexbecause interstitial pores are not uniform and aredistributed nonuniformly in three dimensions. How-ever, this idealized example of parallel tubes illus-trates that diffusion coefficient and hydraulic con-ductivity can change in opposite directions with aconstant change in cross-sectional area dependingon the change in the number of pores and pore ra-dius.

In summary, albumin diffusion coefficient measuredin rabbit mesentery using steady-state flux of radio-active tracer 125I-albumin was approximately ten-fold smaller than the free diffusion coefficient.Albumin diffusion increased with albumin concen-tration and was reduced in the presence of hyaluron-idase. Both these effects were consistent with a re-

duced volume excluded from albumin by the pres-ence of interstitial hyaluronan, a behavior oppositeto the excluded volume effects measured in solutionscontaining albumin and hyaluronan. Further studiesare required to define the mechanism of interactionbetween albumin and interstitial hyaluronan in mes-entery tissue.

REFERENCES

1. Chandra R. (1982). In-vitro radiation detection. In:Introductory Physics of Nuclear Medicine. Lea & Fe-biger. Philadelphia, PA. 123–132.

2. Comper WD. (1984). Interstitium. In: Edema (StaubNC, and Taylor AE, Eds.) Raven. New York. 229–262.

3. Day TD. (1952). The permeability of interstitial con-nective tissue and the nature of the interfibrillary sub-stance. J Physiol Lond 117:1–8.

4. Fox JR, Wayland H. (1979). Interstitial diffusion ofmacromolecules in the rat mesentery. Microvasc Res18:255–276.

5. Granger HJ, Taylor AE. (1975). Permeability of con-nective tissue linings isolated from implanted cap-sules. Circ Res 36:222–228.

6. Granger HJ, Shepherd AP. (1979). Dynamics andcontrol of the microcirculation. In: Advances in Bio-medical Engineering (Brown JHU, Ed.) Academic.New York. 1–63.

7. Harper GS, Comper WD, Preston BN. (1985). Con-centration dependence of proteoglycan diffusion. Bio-polymers 24:2165–2173.

8. Hedbys BO. (1963). Corneal resistance to the flow ofwater after enzymatic digestion. Exp Eye Res 2:112–121.

9. Iozzo RV, Muller-Glauser W. (1985). Neoplasticmodulation of extracellular matrix: Proteoglycanchanges in the rabbit mesentery induced by V2 car-cinoma cells. Canc Res 45:5677–5687.

10. Keller KH, Canales ER, Yum SI. (1971). Tracer andmutual diffusion coefficients of proteins. J PhysicalChem 75(3):379–387.

11. Knepper PA, Farbman AL, Tesler AG. (1984). Exog-enous hyaluronidases and degradation of hyaluronicacid in the rabbit eye. Inv Opthalmol Vis Sci 25:286–293.

12. Lai-Fook SJ, Rochester NL, Brown LV. (1989). Ef-fects of albumin, dextran, and hyaluronidase on pul-monary interstitial conductivity. J Appl Physiol67(2):606–613.

13. Laurent TC, Ogston AG. (1963). The interaction be-tween polysaccharides and other macromolecules. 4.The osmotic pressure of mixtures of serum albuminand hyaluronic acid. Biochem J 89:249–253.

14. Laurent TC, Sundelof LO, Wik KO, Warmegard B.(1976). Diffusion of dextran in concentrated solu-tions. Eur J Biochem 68:95–102.

15. Laurent TC, Preston BN, Comper WD, Checkley GJ,Edsman K, Sundelof LO. (1983). Kinetics of multi-

Diffusion across rabbit mesenteryS Parameswaran et al.

125

component transport by structured flow in polymersolutions. 1. Studies on a poly(vinylpyrrolidone)-dextran system. J Phys Chem 87:648–654.

16. Li J, Lai-Fook SJ, Conhaim RL. (1992). Effect ofhyaluronidase on interstitial cuff and pressure re-sponse to liquid-inflated rabbit lung. J Appl Physiol72(4):1261–1269.

17. Negrini D, Venturoli D, Townsley MI, Reed RK.(1994). Permeability of parietal pleura to liquid andproteins. J Appl Physiol 76(2):627–633.

18. Nugent LJ, Jain RK. (1984). Plasma pharmacokinet-ics and interstitial diffusion of macromolecules in acapillary bed. Am J Physiol 246:H129–H137.

19. Ogston AG, Sherman TF. (1961). Effects of hyal-uronic acid upon diffusion of solutes and flow of sol-vent. J Physiol 156:67–74.

20. Ogston AG, Phelps CF. (1961). The partition of sol-utes between buffer solutions containing hyaluronicacid. Biochem J 78:827–833.

21. Ogston AG, Preston BN, Wells JD. (1973). On thetransport of compact particles through solutions ofchain-polymers. Proc Roy Soc Lond 333:297–316.

22. Parameswaran S, Dutta S, Babbitt RA, Barber BJ.(1996). Unexpected effect of hyaluronidase on albu-min excluded volume fraction. FASEB J 10:A56 (Ab-str).

23. Parameswaran S, Brown LV, Lai-Fook SJ. (1998).Effect of flow on hydraulic conductivity and reflec-tion coefficient of rabbit mesentery. Microcirculation5:265–274.

24. Payne DK, Kinasewitz GT, Gonzalez E. (1988). Com-parative permeability of canine visceral and parietalpleura. J Appl Physiol 65(6):2558–2564.

25. Pedley TJ. (1983). Calculation of unstirred layerthickness in membrane transport experiments: a sur-vey. Quart Rev Biophys 2:115–150.

26. Rasio E. (1970). The permeability of isolated mesen-tery. Effect of temperature. In: Capillary Permeabil-ity (Crone C, and Lassen NA, Eds.) Academic. NewYork. 643–646.

27. Schultz JS. (1976). Transport of solutes across theintact rat diaphragm. In: Microcirculation, Vol. 2(Grayson J, and Zingg W, Eds.) Plenum. New York.106–108.

28. Scott D, Coleman PJ, Mason RM, Levick JR. (1997).Glycosaminoglycan depletion greatly raises the hy-draulic permeability of rabbit joint synovial lining.Exp Physiol 82:603–606.

29. Tajaddini A, Brown LV, Lai-Fook SJ. (1994). Effectof hydration on lung interstitial permeability responseto albumin and hyaluronidase. J Appl Physiol 76(2):578–583.

30. Van Damme M-PI, Comper WD, Preston BN. (1982).Experimental measurements of polymer unidirec-tional fluxes in polymer + solvent systems with non-zero chemical-potential gradients. J Chem Soc Fara-day Trans 78:3357–3367.

31. Wiederhielm CA, Black LL. (1976). Osmotic interac-tion of plasma proteins with interstitial macromol-ecules. Am J Physiol 231:638–641.

Diffusion across rabbit mesenteryS Parameswaran et al.

126