Hydraulically-induced convective solute transport across the rabbit peritoneum

Kidney International, Vol. 38 (1990), pp. 19—27

LABORATORY INVESTIGATION

Hydraulically-induced convective solute transport across the rabbit peritoneum JEFFREY L. BELL,' JOHN K. LEYPOLDT, RONALD P. FRIGON, and LEE W. HENDERSON Department of Medicine, Veterans Administration Medical Center, San Diego, and Department of Medicine and Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, California, USA

Hydraulically-induced convective solute transport across the rabbit peritoneum. Transport of solutes during osmotically-induced transperitoneal ultrafiltration is less than would be predicted based upon rates of transperitoneal solute diffusion. Previous workers have hypothesized

diffusive solute transport to different capillary pores sizes, with convection occurring through small arteriolar pores and diffusion occurring through large venular pores. Osmotically driven that osmotically-induced convective solute transport occurs only in ultrafiltration occurs preferentially through small pores since small pores at the arteriolar end of peritoneal capillaries, whereas solute

fluid movement can only be induced through pores that are

diffusion occurs only through large venular pores. We tested this similar in size to the osmotic agent employed. Anatomical heteroporosity hypothesis in the eviscerated New Zealand White rabbit evidence for this hypothesis is easily marshalled [3], but rigorby determining sieving coefficients (S) for creatinine, p-aminohippurate

ous experimental tests have not as yet been published. One empirical test of the heteroporosity model of the peritoneum would be a comparison of solute transport rates during for diffusion; therefore S for all solutes should approach unity if the heteroporosity hypothesis is valid. S for creatinine and PAH were osmotically induced ultrafiltration with those during hydraulirespectively 0.72 0.03 and 0.67 0.05, values lower than unity and cally induced ultrafiltration. Preferential ultrafiltration through not different from those previously determined during osmotically small capillary pores induced by low molecular weight osmotic induced ultrafiltration. Mean S for dextran were relatively independent of molecular size, ranging from 0.50 at 13 A to 0.40 at 50 A. Thus, agents would not occur if ultrafiltration is induced by a hydraudextran S were higher than those previously determined during osmot- lic pressure difference. During peritoneal dialysis, however, the ically induced ultrafiltration yet still less than unity. Control experi- hydraulic pressure difference between blood and dialysis fluid is ments (N = 6) suggested that only surface area and not transport normally insignificant when compared with the osmotic prescharacteristics were altered by evisceration. These observations dem(PAH) and neutral dextran during hydraulically-induced transperitoneal ultrafiltration (N = 13). A hydraulically-induced driving force directs convective solute transport through the same capillary pores employed

sure difference [4]. Here, experiments are described using negative abdominal intracavitary pressure to convect solutes

onstrate that the heteroporosity hypothesis fails to completely describe both diffusive and convective transport properties of the peritoneum.'

across the peritoneum. Sieving coefficients for test solutes with widely different molecular sizes were determined during hy-

The existence of a peritoneal transport barrier is exploited draulically induced ultrafiltration and compared with values today as the basis for an effective modality of renal replacement previously reported during osmotically induced ultrafiltration. Moreover, theoretical predictions from a heteroporosity model therapy. As peritoneal dialysis offers superior diffusive clearances for molecules of large molecular size when compared of peritoneal solute transport were compared with hydrauliwith hemodialysis [1], the peritoneum is often conceptualized cally- and osmotically-induced sieving coefficients in addition to as a leaky or highly porous hemodialysis membrane [2]. This peritoneal diffusive permeability properties. construct, however, is inconsistent with low sieving coefficients

that have been measured during osmotically-induced fluid

Methods

movement or ultrafiltration. Noiph et al [3] have suggested that such paradoxical solute transport characteristics result from the heteroporosity of capillary walls contained within the peritoneal

Experimental

microvasculature. This hypothesis relegates convective and Thirteen male New Zealand White rabbits weighing between 2.2 and 3.0 kg underwent hydraulically-induced transperitoneal ultrafiltration. In six of these animals, a hypertonic exchange was performed immediately following ultrafiltration.

'Naval Hospital San Diego. The views expressed in this article are those of the author and do not reflect the official policy or position of the

Under halothane anesthesia, the carotid artery and jugular vein were cannulated for blood sampling and intravenous infusion, respectively. Through a midline incision, the distal

Department of the Navy, Department of Defense, or the US Government. Received for publication March 15, 1989 and in revised form December 27, 1989 Accepted for publication February 2, 1990

sigmoid colon and duodenum were first ligated and divided. The inferior mesenteric artery was ligated and the dorsal reflection of the mesentery was gently divided to the origin of the superior

© 1990 by the International Society of Nephrology 19

20

Bell et al: Convective transport across the peritoneum

mesenteric artery and celiac trunk. These were gathered as a single pedicle, ligated, and divided permitting the removal of the small and large intestines en bloc. All bleeding sites were meticulously cauterized. The stomach and liver were not disturbed. A parabolic wire framework measuring approximately

transport properties of this preparation with previously reported values [5]. Hypertonic dialysis solution, Normosol R

13 cm in length and 10.5 cm in width and covered with a tightly

conventional indicator dilution method [5, 6]. The initial osmo-

containing 7% glucose, was warmed to 37°C and infused into the peritoneal space. The dialysis solution also contained dex-

tran T2000 (Sigma) to measure changes in volume by the

stretched porous polypropylene mesh was placed within the lality of this solution was 650

20 mOsmlkg H20. Initial

peritoneal cavity. A segment of tubing, perforated for 6 to 7 cm dialysate volume was 70 mI/kg body weight in one animal and 40 at its tip, permitted external access via the surgical incision in ml/kg in the remaining five. Each infusion of dialysis solution the anterior abdominal wall. The midline incision was then was mixed thoroughly by repeated barbotage and sampled after closed in a double layer and made airtight by the application of three minutes to calculate the residual volume remaining from cyanoacrylate adhesive. The tubing was connected externally the preceding portion of the experiment [6]. Blood and dialysate to vacuum, and intraperitoneal pressure was modulated using a were sampled at four, equally spaced intervals within the dwell

roller clamp and an in-line manometer. A 5 ml heparinized period to examine the time-dependent equilibration of test solutes between plasma and the dialysis solution. In two sampling trap was also placed in-line. Five hundred eighty-five mg of dextran T40 (Pharmacia Fine experiments the parabolic wire framework was left in place Chemicals, Piscataway, New Jersey, USA), 1755mg of dextran during the hypertonic exchange, and in the remaining four TlO (Pharmacia), 45 to 135 mg of creatinine (Sigma Chemical experiments the device was first removed from the peritoneal

Co., St. Louis, Missouri, USA) and 75 to 225 mg of p-

cavity.

aminohippurate (PAH; Merck, Sharp and Dohme, West Point, Pennsylvania, USA) were dissolved in 20 ml of a 0.9% NaCI solution, warmed to 37°C, and given intravenously as a single bolus. In the first five experiments the entire dextran dose was given as dextran Tb; dextran T40 was added later to improve data resolution at large molecular size. A 5% dextrose solution was then administered as a bolus (20 mI/kg body wt) followed by a maintenance intravenous infusion of saline containing the above test solutes in amounts sufficient to maintain constant plasma concentrations. In addition, urinary losses were quan-

The samples were analyzed for dextran concentrations as described previously [5, 7]. Briefly, dextrans were recovered from plasma and ultrafiltrate samples by picric acid deproteinization, ethanol precipitation of the polymer, lyophilization,

titatively replaced with Normosol R (Abbott Laboratories,

ing dextran into component molecular sizes [5, 7, 8]. The

Chicago, Illinois, USA). Five ml blood samples were taken at the beginning and end of each timed collection of peritoneal

concentration of dextran T2000 was estimated as the chromatogram height at the column void volume, and the concentrations

stored for chemical analysis while the cells were resuspended in lactated Ringer's solution (Travenol Laboratories, Inc., Deerfield, Illinois, USA) and reinfused intravenously. Twenty mm Hg of negative pressure was created within the peritoneal cavity to initiate hydraulically induced ultrafiltration.

chromatogram at the appropriate column retention volume. The

The rabbit remained anesthetized and supine with the peritoneal catheter in the wire framework held in the dependent, paraspinal position. The abdominal wall was partially vented ventrally with a 25 gauge needle allowing any ultrafiltrate generated to be rapidly drained, and so minimized the opportunity for diffusive transport, Following placement of the needle, the vacuum regulator was readjusted to sustain the 20 mm Hg negative pressure within the cavity. Four 30-minute study periods were employed, each yielding approximately 3 ml of ultrafiltrate. In the initial five experiments, negative pressure was applied and collection of ultrafiltrate started within 10 minutes of the bolus dose of the test solutes. The importance of achieving steady state plasma and tissue concentrations of the test solutes prior to beginning ultrafiltration was later considered to be of possible importance. A one hour delay prior to the application of negative intraperitoneal pressure was therefore allowed in the final eight experiments. In all experiments the first collection of ultrafiltrate was discarded, and the second through the fourth were included in the final analysis.

reported data [8—10]

and reconstitution in column buffer (0.15 M ammonium acetate,

0.05 M sodium phosphate, pH 7.4). Dialysate samples were processed identically following threefold concentration by evaporation (Speed VAC Concentrator, Savant Instruments, Inc., Hicksville, New York, USA). Size exclusion chromatography using a TSK-G3000SW column was employed for resolv-

ultrafiltrate and immediately centrifuged. The plasma was of all other dextrans were determined as the height of the

In six experiments a hypertonic exchange of peritoneal dialysis solution was performed following the periods of ultrafiltration in order to compare the diffusive and convective solute

relationship between column retention volume and dextran molecular weight was determined by calibration using dextran fractions of very low polydispersity [8]. The molecular or solute

radii (R) of dextrans in A were computed from previously R = 0.305 M°47

(1)

where M denotes dextran molecular weight. Solute radii for creatinine and PAH were roughly approximated as 3 and 4 A, respectively [11].

Creatinine concentrations were measured by an automated Jaffe rate methodology (Creatinine Analyzer 2, Beckman Instruments, Inc., Fullerton, California, USA). PAH concentrations were measured by the method of Waugh and Beau [12]. Osmolality determination was by freezing point depression (Osmette A, Precision Systems, Inc., Sudbury, Massachusetts, USA). Analysis Solute concentrations in ultrafiltrate (Ce) and plasma (C) were used to compute sieving coefficients (5) for the test solutes during the period of hydraulically induced ultrafiltration by the ratio Cf

(2)

21

Bell et al: Convective transport across the peritoneum

Table 1. Sieving coefficients (S) determined during hydraulically induced ultrafiltration (N = 13)

S SEM

Solute

Creatinine PAH

0.72 0.67

1.5

1.4

0.03 0.05 1.3

1.2 — 1.2 1.0

(1)

0.8

1.1

0.6

1.0

90

60

30

120

Time, minutes

0.4

Fig. 2. Volume of peritoneal dialysate relative to the volume at three minutes (vol/vol') shown as a function of dwell time during the control I SEM, and the asterisk hypertonic exchange. The bars indicate

0.2

denotes a value different from unity (P < 0.05). 0.0 0

10

20

30

40

50

Solute radius, A

Fig. 1. Sieving coefficients determined during hydraulically induced ultrafiltration shown as a function of molecular size. Values for creatinine and PAH are indicated by symbols and those for dextran are 1 SEM. points connected by straight lines. Bars denote

Table 2. Diffusive permeability-area products (PA) and solute reflection coefficients (u) determined during control hypertonic exchanges

Solute Creatinine PAH

1-a-

PA mI/mm

0.51 0.31

0.13 0.06

0.65 0.45

0.17 0.10

Mean values SEM from 6 experiments are shown.

where the plasma concentration was taken as the average of the plasma samples that bracketed the collection period of interest. Diffusive and convective solute transport during the hypertonic exchange was assessed from changes in dialysate volume and concentration with dwell time as described previously [5]. Changes in dialysate volume were calculated from changes in the concentration of dextran T2000 by using indicator dilution methodology [5, 6, 13]. Methods for estimating the diffusive permeability-area product (PA) and the solute reflection coefficient (a-) were identical to those described previously [5]. A single transport parameter was computed for each animal

Sieving coefficients for creatinine, PAH and dextran determined during hydraulically induced ultrafiltration are plotted as

a function of molecular size in Figure 1. Dextran sieving coefficients are lower than those for creatinine and PAH, are less than unity (P < 0.01), and do not decrease appreciably with an increase in molecular size from 13 to 50 A. These values for dextran are, however, considerably higher than 1-if values recently determined during osmotically induced ultrafiltration in the rabbit which all fell below 0.2 [5].

The change in volume with time during the hypertonic by averaging individual estimates from the different study periods. The reported data, mean SEM, therefore represent exchange in six rabbits is shown plotted in Figure 2. The data the average and interanimal variability, respectively. Statistical are expressed as the calculated indicator dilution volume reladifferences were determined using an unpaired Student's I-test. tive to the calculated volume three minutes after infusion and

barbotage (vollvolt), a procedure that corrects for any small residual volume remaining after the period of hydraulically induced ultrafiltration. The increase in peritoneal dialysate Values of sieving coefficient were not altered by permitting an volume with time is considerably smaller here than in previous additional hour of equilibration before ultrafiltrate collection; studies of intact (noneviscerated) rabbits using 7% glucose as the results of all experiments were therefore included for dialysis solution [5, 6]. Only the relative volume after 120 analysis. S values determined during hydraulically induced minutes is significantly different from the starting volume (P < ultrafiltration for creatinine and PAH (Table 1, Fig. 1) are 0.05). Results

PA and 1-if values for creatinine and PAH determined during different from unity (P < 0.01) and similar to 1-if values recently reported in the rabbit during osmotically induced ultrafiltration the control hypertonic exchanges are shown in Table 2. The PA (S for creatinine of 0.82 0.20, S for PAH of 0.86 0.14 [5]). values are considerably lower than those determined previously The value for creatinine is also similar to that reported for the in rabbits with an intact peritoneum (PA for creatinine of 2.26 human peritoneum of 0.57 0.09 [14], although the latter value 0.59 mllmin, PA for PAH of 1.42 0.25 mi/mm [5]). The 1-if was determined by a different methodology. and S values for creatinine and PAH are similar for both

22

Bell et a!: Convective transport across the peritoneum 0.7

I

I

I

I

0.6 —

0.5 —

I Fig. 3. Diffusive permeability-area product (PA) shown as a function of molecular size for eviscerated rabbits compared with previously published results [5J. Eviscerated rabbit values for creatinine and PAH are indicated by symbols and those for dextran are points connected by straight lines. Bars denote I SESI. The hatched area denotes the range of previously published results for dextran in the intact animal.

fthI/,/Im,..

' I,,,, 74/

0.0 0

10

30

20

SQIyte rcdiu8 A

10,000

1000

100

0

10

20

30

Solute radius, A

osmotically and hydraulically induced ultrafiltration. In both instances, significant rejection by the pentoneum is observed. The dependence of PA values on molecular size is shown in Figure 3. Here, PA values for dextran between 13 and so A are compared with the those previously reported for rabbits with an intact peritoneum [5]. Dextran PA values are considerably less than those reported previously, but the dependence of PA on molecular size is similar. The similar molecular size dependence of diffusion across the intact and eviscerated peritoneum is further illustrated in Figure 4 where the permeability-area

40

50

Fig. 4. D(lfusive permeability-area product divided by the solution diffusion coefficient (PAID) on a logarithmic scale shown as a function of molecular size in eviscerated rabbits compared with previously published results for the intact animal [5]. Eviscerated rabbit values for creatinine and PAH are indicated by symbols and those for dextran are points connected by straight lines. Bars denote 1 SEM. The hatched area denotes the range of previously published results.

product divided by the solution diffusion coefficient (PA/D) is plotted as a function of molecular size. In intact and eviscerated rabbits the PAID values do not depend appreciably on molecular size; in each case values for both small and large solutes are virtually identical.

The values of 1-a (or S) for creatinine, PAH and dextran determined during the hypertonic exchange are shown as a function of molecular size in Figure 5. Also shown are previously reported l-o values determined in rabbits with an intact peritoneum [5]. The 1-a- values for dextran are lower than for

1

Bell et al: Convective transport across the peritoneum

0.8 -

23

I

0.6 -

0.40.2 — h

0

40

10

50

Solutn rarlills

Fig. 5. One minus solute reflection coefficient (1-cr) or sieving coefficient (S) shown as a function of molecular size for eviscerated rabbits compared with previously published results [5]. Eviscerated rabbit values for creatinine and PAH are indicated by symbols and those for dextran are points connected by I SEM. The straight lines. Bars denote hatched area denotes the range of previously published results.

creatinine and PAH; moreover, the relationship between i-cr values during peritoneal dialysis, however, depends on achievand molecular size is preserved in both intact and eviscerated ing high ultrafiltration rates during a hypertonic exchange [20], rabbits. and it is difficult to induce high ultrafiltration flow rates using Discussion

The peritoneum displays diffusive and convective solute transport properties that are paradoxical. While albumin and other plasma proteins can readily diffuse across the peritoneum,

small solutes and ions do not appear in osmotically-induced

peritoneal ultrafiltrate at concentrations equal to those in plasma [4]. Recent studies in the rabbit using neutral dextrans as test solutes have indeed demonstrated that such transport properties reflect the unique structural and biological properties of the peritoneum [5]. The concept that the peritoneum behaves as a heteroporous membrane, although qualitatively consistent with these data [3], has yet to be experimentally tested. Paradoxical solute transport properties are not an intrinsic feature of a heteroporous membrane; they are displayed only when a mechanism exists to direct transport through a particular size of pore. For example, solute transport by diffusion

high molecular weight osmotic agents that require prohibitively

large quantities of solute mass to be added to the dialysis

solution [4]. An alternative approach, also previously employed

for examining solute transport across artificial kidney membranes [21], is that described in the present study where a comparison between sieving coefficients using osmotic and hydraulic pressure driving forces is performed. A hydraulic pressure driving force does not permit a selection of pores that occurs during osmotically induced ultrafiltration with low molecular weight osmotic agents. Thus, the peritoneal capillary pores employed during hydraulically induced ultrafiltration should be identical to those employed during transperitoneal solute diffusion.

A hydraulic pressure driving force was employed in the present experiments to collect peritoneal ultrafiltrate by creat-

ing a negative pressure within the peritoneal cavity of the rabbit. Preliminary experiments in the intact animal proved

across a heteroporous membrane is determined only by the unsuccessful because of frequent failure to drain fluid from the relative numbers and sizes of pores [15—18]. All pores likewise peritoneal cavity. By means of evisceration and structural participate in convective solute transport when induced by a support of the peritoneal cavity with its investing parietal hydraulic pressure difference. According to theory [17], para- peritoneum intact, a reasonably steady flow of ultrafiltrate was doxical convective solute transport can occur across a hetero- obtained. For the small test solutes, creatinine and PAH, porous membrane only when ultrafiltration can be induced to significant restriction to hydraulically-induced convective solflow preferentially through certain pores, such as when using ute transport was evident (Table 1, Fig. 1) and S values were low molecular weight osmotic agents during peritoneal dialysis. similar to those previously determined during osmotically inThere are two possible approaches to test whether a hetero- duced ultrafiltration [5]. For dextrans, sieving coefficients durporosity model completely describes the observed paradoxical transport properties of the peritoneum. One approach would be

ing hydraulically induced ultrafiltration ranged from 0.5 at 15 A to 0.4 at 50 A (Fig. 1); these values are midway between unity to use a high molecular weight osmotic solute to induce and the near zero values of 1-cr that were previously determined ultrafiltration through both small and large pores. This approach during osmotically induced ultrafiltration [5]. These experimenhas been employed by Twardowski et al [19] to examine the tal results likely reflect a degree of capillary wall heteroporos-

effect of heteroporosity on convective solute transport across ity; however, a more detailed analysis is required to test synthetic artificial kidney membranes. The accuracy of 1-cr whether these sieving coefficient values are quantitatively con-

24

Bell et a!: Convective transport across the peritoneum 1.000

1.2 1.0

0.100

0.8 Q'

0.6

0.010

0.4

0.2

0.001

0.0

0

10

20

30

40

50

Solute radius, A

Fig. 6. Sieving coefficients predicted from a two-pore membrane model of the peritoneum during both hydraulically induced (solid lines)

and osmotically induced (dashed lines) ultrafiltration shown as a

50 20 30 40 Solute radius, A Fig. 7. Normalized values of PAID on a logarithmic scale predicted 0

10

from a two-pore membrane model of the peritoneum shown as a function of molecular size. The pore radii are assumed as 20 and 300 A.

function of molecular size. The pore radii are assumed as 20 and 300 A.

explain experimental sieving coefficients during osmotically induced ultrafiltration (Figs. 5 and 6). During hydraulically induced ultrafiltration, experimental sieving coefficients are more consistent with a 300: 1 small to large pore area ratio tal results and a heteroporosity model, the pentoneum is (Figs. 1 and 6). In contrast, the independence of PAID on envisioned as a membrane containing two different types of molecular size, either in the intact or the eviscerated rabbit, is pores; the pore areas and sizes are in general arbitrary. The more closely similar to that for the membrane with a 4:1 ratio of mathematical equations employed in these theoretical calcula- small to large pore area (Figs. 4 and 7). The inability of the data sistent with those predicted by a heteroporosity model of the peritoneum. To examine the consistency between the present experimen-

tions have been previously developed [15—18] and are detailed in the Appendix. For simplicity, however, we assume that the peritoneum has pores with radii of 20 and 300 A. The total pore

to conform to a single combination of pore size and area

area is arbitrary and is taken to be proportioned such that the small to large pore area ratio is either 4: 1 or 300: 1. Figure 6 shows theoretical sieving coefficients that would be obtained from these membranes during both osmotically and hydraulically induced ultrafiltration. During osmotically induced ultrafiltration, it is assumed that solute convection occurs only through the small pores; therefore, the predictions for either pore combination are identical and equal to that which would occur across an isoporous membrane containing pores with radii of 20 A. During hydraulically induced ultrafiltration, sieving coefficients for the alternative pore combinations differ

cal model can be interpreted alternatively as follows. The

considerably. For the membrane with a pore area ratio of 300: 1, hydraulically-induced sieving coefficients are higher than during osmotically induced ultrafiltration. When the pore area ratio is

4: 1, S values are near unity because solute transport occurs almost exclusively through the numerous large pores. Figure 7 shows theoretical values of PAID, normalized for changes in total membrane area, that would occur with these hypothetical membranes, When the small to large pore area ratio is 300: 1, PA/D values decrease dramatically with increasing molecular size until about 20 A, after which the values decrease only slightly. Values of PAID for the membrane with a small to large pore area ratio of 4: 1 decrease much less between 0 and 20 A compared with the membrane containing predominantly small pores.

indicates a lack of fit of the two-pore membrane model. This comparison between experimental results and theoretiknown independence of PAID on molecular size suggests that the peritoneum can be modeled as a heteroporous membrane with a 4: 1 ratio of small to large pore area when the small and large pore radii are assumed as 20 and 300 A, respectively. One would therefore predict that sieving coefficients during hydraulically induced ultrafiltration should approach unity (> 0.9) for all solutes less than 50 A in molecular radius (Fig. 6). Sieving

coefficients that were measured in the present study during hydraulically induced ultrafiltration, however, were all significantly lower than unity. This inconsistency between experimental results and theoretical predictions indicates similarly a lack of fit. It should be noted that considering different pore size and area combinations in this two-pore membrane model changes only the numerical values predicted but not the overall conclusions (unpublished observations). Moreover, it can be shown that theoretical membrane models containing more than two different pore sizes would also not permit significantly better agreement with the experimental data. Finally, these conclusions are not altered by the inclusion of a hydraulic pressure gradient on the high pressure (arteriolar) side of the membrane,

as has been previously proposed as applicable to the peritoneum [3]. Based upon these theoretical considerations, therefore, it is concluded that peritoneal capillary heteroporosity

These combinations of pore size and area were chosen to alone is sufficient to completely describe the observed diffusive and convective solute transport properties of the peritoneum. Hydraulically-induced sieving coefficients are nevertheless experimental results. Either pore combination is sufficient to permit easy comparison between theoretical predictions and the

25

Bell et al: Convective transport across the peril oneum

higher than 1-cr values previously determined during osmotically induced ultrafiltration. These observations either reflect a degree of capillary wall heteroporosity that is likely present or alternatively are an artifact of the preparation. In the present work evisceration was necessary due to technical considerations, and sieving coefficients were determined only for the parietal peritoneum. Values of 1-cr determined during peritoneal dialysis in intact animals, however, include contributions from the entire peritoneum. Although regional ultrastructural and vascular differences in the peritoneum are known [22, 23], the relative contribution of the visceral and parietal surfaces to fluid and solute transport remains uncertain [24]. It should be noted that although the visceral peritoneum is often postulated to be the predominant diffusive transporting surface [21, recent work actually suggests the contrary [25, 261. Another source of artifact from evisceration could be damage to peritoneal capillaries sufficient to alter their transport properties. While red blood cells were occasionally found in hydrau-

molecular size very similar to that reported here for dextrans of comparable size (36 A and 55 A, respectively). The present work demonstrates that a new model of perito-

neal transport is needed. Noiph and Twardowski [2] have suggested several alternatives to the heteroporosity model of peritoneal transport, but little work has been devoted to their study. Our recent work has suggested that the observed trans-

port properties of the peritoneum may arise from different elements of the transport barrier separately governing solute diffusion and convection [5]. Further experimentation is necessary to more completely characterize both diffusive and convective solute transport properties of the pentoneum. Acknowledgments This work was presented at the 20th Annual Meeting of the American Society of Nephrology, Washington, D.C., 13—16 December 1987 and has been published in abstract form [29]. This work was supported by

Veterans Administration and National Institutes of Health grant lically-induced peritoneal ultrafiltrate, the quantity of cells the DK35862. The authors thank Sharon N. Okamoto for technical assisfound in these cases was small and insufficient to explain tance. sieving coefficients of 0.4 or 0.5; the peritoneum remained

semi-permeable.

To experimentally examine possible changes in the peritoneum resulting from the extreme nature of the preparation, we performed a hypertonic exchange in six of the rabbits that had previously undergone evisceration and hydraulically-induced transperitoneal ultrafiltration. The rates of osmotically induced ultrafiltration and solute diffusion obtained in these animals are markedly lower than those in intact animals [5]. Although the values of PAID are lower in eviscerated animals, this parameter retains the same independence on molecular size as in intact animals. In addition, the solute reflection coefficients deter-

mined using an osmotic pressure driving force are also in reasonable agreement with those recently published [5]. It should be noted, however, that rates of osmotically induced ultrafiltration in the present experiments are very low, and this condition precludes very accurate determinations of the solute reflection coefficient [201. Nevertheless, the present observations are most compatible with the hypothesis that evisceration results in a loss of approximately two-thirds of transport surface area without a significant alteration in parietal permeability.

The present observations are in contrast with those recently reported by Rubin et al [25, 26].

Previous work by others is consistent with the present observations during hydraulically induced ultrafiltration. Aune [27] measured the transport of serum albumin from plasma to

Reprint requests to J.K. Leypoldt, Ph.D., Renal Section (lIH), VA Medical Center, 500 Foothill Blvd., Salt Lake City, Utah 84148, USA.

Appendix

Theoretical predictions of transperitoneal solute transport were derived by envisioning the pentoneum as a heteroporous membrane containing cylindrical pores; the number of pores of type i per unit membrane area are indicated by n1, and the radii of pores of type i by r1. The principles for computing solute transport parameters from such a heteroporous membrane have been previously described by others [15—18]. The overall sieving coefficient for the heteroporous membrane (S) was calculated using the sieving coefficient for each pore type (S1) by the following equation n1A1L,1S

s=:

(Al) n1A1L

where A1 denotes the cross sectional area of a pore of type i and

denotes the hydraulic conductivity of a pore of type i. An

the empty peritoneal cavity in the intact rabbit under more

analogous expression could also be written for the solute

physiologic conditions. Using three different methods for collecting naturally-occurring peritoneal ultrafiltrate, he determined the rate of ultrafiltrate formation to be 0.13 mI/mm. Moreover, the ratio of albumin in peritoneal ultrafiltrate to that in plasma averaged 0.50 0.02 in 10 rabbits. This value for the

P = n1A1P1

intact rabbit is practically identical to that determined for

reflection coefficient. Similarly, the overall diffusive permeability for the heteroporous membrane (P) was calculated from the diffusive permeability for each pore type (P1) by the following equation (A2)

dextran in the present experiments on eviscerated rabbits. In a

somewhat different context, Henriksen et al have studied As emphasis was placed on the dependence of the diffusive protein transport from plasma to the peritoneal cavity in pa- permeability divided by the solution diffusion coefficient (P/D) tients with ascites, and have reported that the ascitic fluid to on molecular size, it was convenient to express this parameter plasma concentration ratio (or sieving coefficient) for albumin normalized by the corresponding value for a reference solute

(P0/D0). If the reference solute is chosen as a very small for proteins are similar to and show an independence on molecule, then the ratio (PID)/(P0/D0) can be expressed as and IgG averaged 0.30 and 0.31, respectively [28]. These values

26

Bell et a!: Convective transport across the peritoneum

induced ultrafiltration and the imposed transperitoneal hydraulic pressure employed during hydraulically induced ultrafiltration.

n1A1(P1/D) (P/D)/(P0/D0) = _________ (A3)

References

since the permeability of this reference solute in all pore types is its solution diffusion coefficient (D0). Equations (Al) and (A3) can be simplified by noting that both the pore cross sectional area and hydraulic conductivity are proportional to the square of the pore radius. This assumption leads to the following expressions n1r1S1

s=

(A4)

nr1

I. Popovici-i RP, MONCRIEF JW: Transport kinetics (Chapt 5), in Peritoneal Dialysis, edited by NOLPH KD, Boston, Martinus Nij2.

hoff, 1985, PP. 115—158 NOLPH KD, TWARDOWSKI ZJ: The peritoneal dialysis system

(Chapt 2), in Peritoneal Dialysis, edited by NOLPH KD, Boston, Martinus Nijhoff, 1985, pp. 23—50 3. NOLPH KD, MILLER FN, PYLE WK, PoPovIcH RP, S0IUIN MI: An hypothesis to explain the ultrafiltration characteristics of peritoneal dialysis. Kidney mt 20:543—548, 1981 4. HENDERSON L: Ultrafiltration with peritoneal dialysis (Chapt 6), in Peritoneal Dialysis, edited by NOLPH KD, Boston, Martinus Nijhoff, 1985, pp. 159—177 5. LEYPOLDT JK, PARKER HR, FRIGON RP, HENDERSON LW: Molec-

ular size dependence of peritoneal transport. J Lab Clin Med

njrj2(Pj/D) (P/D)/(PWD0) = ________

110:207—216, 1987 6. PUST AH, LEYPOLDT JK, FRIG0N RP, HENDERSON LW: Peritoneal

dialysate volume determined by indicator dilution measurements. (A5)

nr12

Kidney tnt 33:64—70, 1988 7. LEYPOLDT JK, FRIGON RP, DEVORE KW, HENDERSON LW: A

rapid renal cleance methodology for dextrans. Kidney mt 31: 855—860, 1987

To complete these theoretical predictions, it was necessary to compute the sieving coefficient and diffusive permeability for each pore type. Such values were obtained by using previous hydrodynamical calculations from membrane pore theory that assume solutes behave as rigid spheres passing through cylindrical holes in the membrane [16, 181. The following equations were employed in the present calculations [16] Si =

(1 — A)2[2

—

(1

—

A)2](l

—

A/3)

1 — A13 + 2A213

(1 — A)912

= 1

—

0.3956A + l.0616A2

(A6)

8. FRIGON RP, LEYPOLDT JK, UYEJI S, HENDERSON LW: Disparity

between Stokes radii of dextrans and proteins as determined by retention volume in gel permeation chromatography. Anal Chem 55:1349—1354, 1983

9. GRANATH KA: Solution properties of branched dextrans. J Colloid Sd 13:308—328, 1951

10. GRANATH KA, KVIST BE: Molecular weight distribution analysis by gel chromatography on Sephadex. J Chromatogr 28:69—81, 1967

11. AUNE S: Transperitoneal exchange. I. Peritoneal permeability studied by transperitoneal plasma clearance of urea, PAH, inulin, and serum albumin in rabbits, Scand J Gastroent 5:85—97, 1970 12. WAUGH WH, BEALL PT: Simplified measurement of p-aminohip-

purate and other arylamines in plasma and urine. Kidney tnt

'A7

where A denotes the ratio of solute to pore radii. By assuming combinations of pore size and area, it was thus possible to calculate the overall sieving coefficient and diffusive permeability of a heteroporous membrane by using equations (A4) through (A7). It is important to note that the overall sieving coefficient predicted using the above method is that occurring during hydraulically induced ultrafiltration. When the osmotic

5:429—436, 1974 13. LEYPOLDT JK, PUST AH, FRIG0N RP, HENDERSON LW: Dialysate

volume measurements required for determining peritoneal solute transport. Kidney mt 34:254-261, 1988 14. RUBIN J, KLEIN E, BOWER JD: Investigation of the net sieving coefficient of the peritoneal membrane during peritoneal dialysis. asaiof5:9—15, 1982 15. WENDT RP, MASON LA, BRESLER EH: Effects of heteroporosity on flux equations for membranes. Biophys Chem 4:237—247, 1976 16. MASON LA, WENDT RP, BRESLER EH: Similarity relations (dimen-

sional analysis) for membrane transport. J Membr Sci 6:283—298,

pressure driving force is comparable in magnitude to the

1980 17. WENDT RP, MASON LA, BRESLER EH: Effect of heteroporosity on membrane rejection coefficients. J Membr Sci 8:69—90, 1981

hydraulic pressure driving force, then theoretical predictions of the sieving coefficient require additional assumptions regarding the flow distribution through each type of pore.

18. CURRY FE: Mechanics and thermodynamics of transcapillary exchange (Chapter 8), in Handbook of Physiology, Section 2: The Cardiovascular System, Vol. IV, Microcirculation, edited by RENKIN EM, MICHEL CC, Bethesda, American Physiological Society,

It is also relevant to note that the transperitoneal solute transport simulations recently reported by Rippe and Stelin [30]

1984, pp. 309—374 19. TWARDOWSKI Z, NOLPH KD, POPOVICH R, HOPKINS CA: Compar-

ison of polymer, glucose, and hydrostatic pressure induced ultraffiare not directly applicable to the present experiments. These tration in a hollow fiber dialyzer: Effects on convective solute workers predicted transperitoneal solute transport rates using a transport. J Lab Clin Med 92:619—633, 1978 two-pore membrane model, but the flow distribution through 20. LEYPOLDT JK: Determining ultrafiltration properties of the peritoneum. Trans Am Soc Artif Intern Organs (in press) each type of pore was determined by the prevailing transcapillary oncotic and hydraulic pressures present during CAPD 21. NOLPH KD, HoPKINs CA, NEW D, ANTWILER GD, POPOvICH RP: Differences in solute sieving with osmotic vs. hydrostatic ultrafilusing isotonic dialysis solution. These pressure driving forces tration. Trans Am Soc Artif Intern Organs 22:618—626, 1976

were neglected in the present theoretical predictions, since they 22. GOTLOIB L, SHUSTAK A, BAR-SELLA P, EIALI V: Heterogeneous are small compared with the osmotic pressure generated when density and ultrastructure of rabbit's peritoneal microvasculature.

using hypertonic glucose concentrations during osmotically

tnt J Artif Organs 7:123—125, 1984

Bell et al: Convective transport across the peritoneum 23. DOBBIE JW, ZAKI M, WILSON L: Ultrastructural studies on the

peritoneum with special reference to chronic ambulatory peritoneal dialysis. Scott Med J 26:213—223, 1981 24. MILLER FN: The peritoneal microcirculation (Chapter 3), in Pentoneal Dialysis, edited by NOLPH KD, Boston, Martinus Njjhoff, 1985, pp. RUBIN J, JONES Q, PLANCH A, RUSHTON F, BOWER J: The 51—93

25.

of the abdominal viscera to peritoneal transport during peritoneal dialysis in the dog. Am J Med Sci 292:203—208, 1986 26. RUBIN J, JONES Q, PLANCH A, STANEK K: Systems of membranes involved in peritoneal dialysis. J Lab C/in Med 110:448—453, 1987 27. AUNE 5: Transperitoneal exchange, III. The influence of transperiimportance

27

toneal fluid flux on the pentoneal plasma clearance of serum albumin in rabbits. Scand J Gastroent 5:161—168, 1970 28. HENRIKSEN JH, LASSEN NA, PARVING H, WINKLER K: Filtration

as the main transport mechanism of protein exchange between plasma and the peritoneal cavity in hepatic cirrhosis. Scand J C/in Lab Invest 40:503—5 13, 1980 29. BELL JL, LEYPOLDT JK, FRIGON RP, HENDERSON LW: Hetero-

porosity model of peritoneal transport is not supported by hydraulically-driven convective transport. (abstract) Kidney mt 33:243, 1988

30. RIPPE B, STELIN G: Simulations of peritoneal solute transport during CAPD. Application of two-pore formalism. Kidney mt 35:1234—1244, 1989