altered permeability ofthe peritoneal membrane using...

Altered Permeability of the Peritoneal Membrane

after Using Hypertonic Peritoneal Dialysis Fluid

LEE W. HENDERSONand KARLD. NOLPH

From the Renal-Electrolyte Section, Department of Medicine, University ofPennsylvania School of Medicine, Philadelphia, Pennsylvania 19104

A B S T R A C T Previous work has shown that use ofhypertonic peritoneal dialysis fluid (7% glucose) re-sults in ultrafiltration and enhanced urea transfer acrossthe peritoneal membrane. Simultaneous creatinine stud-ies showed a similar enhancement with hypertonic fluidwhich persisted in lesser degree during subsequent iso-tonic exchanges. The mechanism of solvent drag hasbeen shown to contribute significantly to the increasedurea removal with ultrafiltration. In the present study,the role of altered diffusive permeability of the peri-toneal membrane as suggested by the creatinine datawas evaluated as a possible additional mechanism. Hy-pertonic exchanges were bracketed by isotonic (1.5%glucose) exchanges during 11 studies in four patients.During six other studies in four patients, isotonic ex-changes only were performed. A mathematical modelfor peritoneal solute transport by diffusion was devel-oped and a method to distinguish alterations in peri-toneal membrane permeability from changes in mem-brane area proposed. The method incorporates the de-termination and comparison of transport characteristicsfor two test solutes of widely different molecularweights. Alterations in inulin and urea transperitonealtransport characteristics in the above studies indicatea significant increase in membrane permeability afterexposure to hypertonic solutions that persists duringsubsequent isotonic exchanges. Varying patterns ofmembrane area and permeability changes occurred dur-ing repeated exposure to only isotonic exchanges. The

An abstract of this work was presented at First AnnualMeeting, American Society of Nephrology, 1967, and pub-lished in the Proceedings of the 1st Annual Meeting of theAmerican Society of Nephrology, 1967. 50.

Dr. Henderson is a Scholar in Academic Medicine, Johnand Mary R. Markle Foundation. Dr. Nolph completed hiswork during National Institutes of Arthritis and MetabolicDiseases Fellowship 1-F2-AM 32,683.

Received for publication 6 September 1968 and in revisedform 21 January 1969.

findings are discussed in regard to recent concepts ofpassive transcapillary transport.

INTRODUCTION

Previous work had demonstrated that ultrafiltrationacross the peritoneal membrane in response to dialysissolutions made hypertonic by the addition of 7.0% glu-cose results in the enhanced removal of urea (1). Sol-vent drag has been identified as one of the mechanismsresponsible for this enhancement. A slight but consistentincrease in the removal rate of creatinine with the useof isotonic solutions after exposure of the peritonealmembrane to hypertonic dialysis fluid suggested that analteration in the passive transport characteristics of themembrane may have resulted from exposure to hyper-tonic solutions. Inulin and urea were used as test solutes,and their dialysances across the peritoneal membranewere calculated. Inulin dialysance increased more thanurea, but both increased significantly after exposure tohypertonic solutions.

METHODSInulin with a molecular weight of about 5200 and urea witha molecular weight of 60 were selected as test solutes be-cause of their widely differing molecular size and neutralcharge.

Previously described dialysis techniques and equipmentwere employed (1) to carry out 17 peritoneal clearancestudies in six oliguric patients coming to dialysis for renalfailure. Urine volume for all patients was less than 400 cc/24hr, with endogenous creatinine clearances of less than 5 ml/min. The study was conducted during the first 10 exchangesof the dialysis. Inulin, 0.1 g/kg of body weight, was giveniv. before the dialysis was initiated. The inulin was per-mitted to equilibrate for at least 2 hr, after which a singlewashout exchange was conducted to insure the technicalacceptability of the procedure and to empty any collectionof peritoneal fluid which might be present. Blood was drawnat this point and the inulin space calculated. Urea spacewas assumed to be 60% of the total body weight, i.e., total

992 The Journal of Clinical Investigation Volume 48 1969

body water. Fig. 1 is a plot of dialysance vs. body spacefor a variety of equilibration ratios. It is apparent that er-rors of 5-10 liters in body space do not alter dialysance atequilibration ratios below 0.60. After this exchange at leasttwo and usually three control exchanges with 2 liters ofdialysis fluid containing 1.5% glucose ("isotonic") wereconducted using a 70 min exchange time (10 min inflow, 30min dwell, 30 min drain). In protocol A (11 studies in fourpatients) two or three exchanges were then conducted with7% glucose-containing dialysis fluid ("hypertonic"). Inulinand urea were added to the hypertonic dialysis fluid inamounts sufficient to approximate their plasma concentra-tions, and sieving coefficients were measured. The studyconcluded with a second set of isotonic exchanges. In pro-tocol B (six studies in four patients) isotonic solutions wereused throughout. Dialysis fluid was sampled after the drain-age period was completed to obviate the problem of samplingerror due to incomplete mixing of fluid within the peritonealspace. Blood was drawn every second or third exchange,and a concentration vs. time curve was constructed forurea and inulin from which blood values for the clearanceperiods were taken. Urea and osmolality were assayed bymethods previously reported (1). The alkali stable fractionof inulin was determined by the method of Walser, Davidson,and Orloff (2). This method selects for assay a compara-tively larger and more homogeneous molecular weight frac-tion of polymers within the total inulin population. The dif-fusive transport characteristics of the peritoneal membranewere compared before and after the use of 7% glucose-con-taining dialysis fluid (protocol A), and these values werecompared with comparable exchanges when continuous 1.5%exchanges were run (protocol B).

A mathematical model of the system was, set up (SeeAppendix), and peritoneal dialysance in milliliters per min-ute for each exchange was calculated for inulin (Di) andurea (Du) across the peritoneal membrane. The dialysancevalue for a given solute is physiologically a function of theperitoneal membrane properties of area and permeabilityas well as the extramembrane factors of dialysis fluid tem-perature, hydrostatic pressure in the belly, diffusion rate ofthe solute in water, and timing of the various phases of theexchange. Since care was taken to maintain the extramem-brane factors constant from exchange to exchange, the peri-toneal dialysance will reflect changes in membrane areaand permeability. If the dialysance value for two solutes arecompared in ratio fashion, e.g.

Di (permeability to inulin) (membrane area for inulin)Du (permeability to urea) (membrane area for urea)

then alterations in this ratio (Dr) will reflect changes inselective permeability of the peritoneal membrane providedthe membrane area for diffusion of the two solutes con-sidered is the same. Dialysance values for inulin and ureafrom both protocols were calculated for control and ex-perimental exchanges. Sieving coefficients were calculatedfor the hypertonic exchanges of protocol A only if therewas reasonably close agreement between the inulin and ureaconcentrations in the dialysis fluid before inflow and theplasma.

RESULTSTable I is a representative set of data for study L. M.using protocol A. The first and seventh exchanges wereconducted with no dwell time and were for the purpose

Dx03ml/min

60

50.

40.

30 .

20 .

10 .

SD-.70

SD- .60SB

SD: AOSeSD

-:SO.20SB

10 20 30 40 50 60 70

VB (Lifers)

FIGURE 1 Dialysance (D) is plotted against body spaceof distribution (V3) for a variety of equilibration ratios(SD/SB). The dialysance values used to plot these curveswere generated from the equation for dialysance formulatedin the Appendix for a-given equilibration ratio by varyingVB. At a given equilibration ratio the body space was variedand a theoretical dialysance calculated.

of "washing out" the peritoneal space. In the first in-stance this was conducted to insure that there was noascites present and in the second to reduce the likelihoodof any contamination of the experimental exchanges bythe preceding hypertonic solution. The volume returnedin the drainage from both experimental and control iso-tonic exchanges exceeds that infused (2050 cc) by amaximum of 200 cc. This results from the slight osmoticgradient from dialysis fluid to plasma present when"isotonic" 1.5% glucose-containing dialysis fluid is used.Dialysis fluid-to-plasma osmotic ratios (SD osm/SB osm)for the isotonic exchanges (2-4, 8-10) were 1.04-1.06,indicating the equilibration at the close of an exchangeis virtually complete. This small degree of ultrafiltra-tion when present was about equivalent in both controland experimental exchanges. Fig. 2 shows the inulindialysance (Di) values for the Table I study in bargraph form as well as all other studies conducted usingprotocol A. The statistical significance of the differ-ences of the means for each study appears along theabscissa. It is apparent that Di rose in every instanceafter exposure of the membrane to 7% gluocse-contain-ing solution. Fig. 3 is a comparable bar graph plot ofurea dialysance (Du) for all of the values obtained.Once again, it is apparent that in every instance theDu values rose. Finally, Fig. 4 gives the ratio of inulin-

Alterations in Peritoneal Membrane Permeability 993

TABLE IRepresentative Study on L. M. using Protocol A

Inulin UreaReturn

Exchange volume V SDosm/SBosm SB SD/SB Di X 103 SB SD/SB Du X 10' DR

ml ml/min mg/mi mi/min mg/mi ml/min

1 1820 45.5 1.07 0.2565 - 1.010 -2 2200 31.4 1.05 0.2033 0.129 4.0 0.975 0.499 20.3 0.1973 2056 29.3 1.06 0.1980 0.150 4.7 0.950 0.453 17.6 0.2674 2248 32.1 1.06 0.1938 0.130 4.0 0.926 0.486 19.3 0.2075 (7%) 2740 39.1 1.45 0.1990 0.580 0.933 0.8246 (7%) 2930 41.9 1.39 0.2052 0.503 0.942 0.786 - -7 1945 46.3 1.07 0.2030 - 0.9288 2185 31.2 1.04 0.2033 0.189 6.2 0.910 0.540 22.8 0.2719 2090 29.9 1.04 0.2020 0.241 8.1 0.908 0.549 23.4 0.346

10 2108 30.1 1.04 0.2014 0.185 6.0 0.906 0.541 22.8 0.263

V, volume; SDOSm/SBOSm,dialysis fluid-to-plasma osmotic ratio; SB, concentration of a solute S in the body compartment ofits distribution; SD, concentration of the same solute in dialysis fluid; DI, inulin dialysance; Du, urea dialysance; DR, ratio ofinulin-to-urea dialysance.

to-urea dialysance (Dt) in graphic form. There is anincrease in the mean values in all but two instances, andthere is considerable overlap in the ranges for eachstudy. By treating the mean dialysance values for pre-and postexposure to 7% solutions as paired variablesand analyzing the difference for all 11 studies, we de-

DI x 103ml/min

37.5.

rived a P value for the change in Di of less than 0.01,for Du of less then 0.001, and for their ratio (DR) ofless than 0.05 (3). Sieving coefficients for inulin andurea are given in Table II. There were seven inulinand three urea exchanges in which the concentrationsof solute in dialysis fluid and plasma were sufficiently

42.0

Pvalue NS NS1 2 3 4 5 6 7 8

PROTOCOLA STUDY NUMBER

FIGuRE 2 Dialysance values for inulin in control (open bars) and experimental (hatchedbars) exchanges for the studies in protocol A. Paired analysis of all 11 studies gives a Pvalue of less than 0.01 for the difference in control and experimental observations. P valuesfor the significance of the difference of the means for each study is given along the abscissa.

994 L. W. Henderson and K. D. Nolph

Dux 103ml/min

45

40

35

30 I

25

20.

P value N S1

..052

c.02 c.05 NS '.05 NS N S *.02 c.001 N S3 4 5 6 7 8 9 10 11


FIGuRE 3 Dialysance values for urea in control (open bars) and experimental(hatched bars) exchanges for the studies in protocol A. The P value for pairedanalysis of all 11 studies was less than 0.001. See caption to Fig. 2 for furtherexplanation.

close to minimize contributions of solute transfer bydiffusion. The mean values of 0.83 and 0.81 for inulinand urea are very similar.

Table III is a representative set of data for study

DR §27

G. K. using protocol B. During exchanges 5 and 6,1.5% glucose solutions were used, and hence no "wash-out" exchange was required as in protocol A. Di and Duvalues were calculated for all exchanges, but only 2, 3,

.70

.60

s0

Pvalue NS NS NS <.05 N S N S N S NS1 2 3 4 5 6 7 8


CD01 NS NS9 10 11

FIGURE 4 Inulin: urea dialysance ratios in control (open bars) and experimental(hatched bars) exchanges for the studies in protocol A. The P value for paired analysisof all 11 studies was less than 0.05. See caption to Fig. 2 for further explanation.


.0.3,

0

TABLE IISieving Coefficients for Inulin and Urea

Sieving coefficientsUltrafiltrate

Study No. volume Inulin Urea

(cc)5-4 640 1.005-5 680 0.87 0.886-4 624 0.786-5 800 0.93 0.787-4 670 0.827-5 620 0.808-4 800 0.82 -8-5 730 0.60

Mean 695 0.83 0.81

and 4 were used for the control dialysance ratios (DR)and 8, 9, and 10 for the experimental dialysance ratiospresented in Fig. 7. In this study Di increased in theexperimental exchanges. Fig. 5 shows inulin dialysancein this and the remaining studies utilizing protocol B inbar graph form. The significance of the changes isnoted along the abscissa. In contrast to the uniform riseof Di noted in protocol A, these studies showed no par-ticular pattern. Only in study 4 did Di rise, and instudy 5 it fell.

Values for Du and DR in study G. K. are given in Ta-ble III. These values for all six studies are plotted inFigs. 6 and 7. Urea dialysance values were the most con-sistent, showing either an increase or no change. Onlystudy 6 showed a significant increase. DR values, aswould be expected, showed no consistent pattern. Threestudies increased and three decreased. Two of the threestudies that decreased showed a significant change (5

and 6). Only one of the increasing studies was signifi-cant. By treating the difference in pre- and postmeanvalues as nonindependent, paired variables and analyzingthe difference in all six studies as we have done for theprotocol A data, we have found no significant differencefrom zero in the change of Di, Du, and DR.

DISCUSSIONThe peritoneum covers all structures in the peritonealspace and is the membrane through which solute mustmove in order to enter the dialysis fluid. Urea and inu-lin occupy different body spaces. Urea with an intra-cellular distribution has the potential for a larger mem-brane for diffusion into the peritoneal space than doesinulin. Muscle and visceral cells that abut on the peri-toneal mesothelium provide potential membrane avail-able to urea for this diffusion. However, Karnovsky(4) has shown that for "small" solutes (molecularweight of 40,000 or less) such as urea and inulin, themajor path of egress from capillaries is via intercellu-lar channels with no major transcellular transfer oc-curring. Thus, even though urea can traverse the limit-ing plasma membrane of cells, it would be expected to doso at a considerably slower rate than via intercellularchannels. In addition, the urea content of the mesothelialcells is small and would be exhausted promptly exceptfor cells in immediate juxtaposition to a capillary. Thecontribution of urea by other than capillary membranesto the total urea in the dialysis fluid after the first orsecond exchange would be expected to be negligible.Should these theoretical considerations be correct, themajor diffusion path for urea would be the same as forinulin, namely from plasma via intercellular channelsacross the capillary wall to the interstitium and fromthere acros the peritoneal mesothelium. This would im-

TABLE IIIRepresentative Study on G. K. using Protocol B

Inulin UreaReturn

Exchange volume V SDOSm/SBOSm SD/SB Di X 103 SD/SB Du X 103 DR

ml ml/min Ml/min ml/min1 1820 27.2 1.06 - -2 2178 31.1 1.08 0.096 3.1 0.449 17.4 0.1783 2133 30.5 1.07 0.093 2.8 0.431 16.4 0.1704 2105 30.1 1.07 0.087 2.6 0.390 14.3 0.1815 2084 29.8 1.07 0.093 2.8 0.424 16.0 0.1756 2092 29.9 1.07 0.095 2.8 0.404 15.1 0.1857 2060 29.4 1.05 0.106 3.1 0.432 16.4 0.1898 1990 28.4 1.04 0.099 3.0 0.422 16.0 0.1879 2188 31.3 1.03 0.114 3.3 0.435 16.6 0.198

10 2116 30.2 1.03 0.132 4.1 0.441 16.9 0.242

See Table I for explanation of abbreviations.


p1 2 3 4 5 6

PROTOCOLB STUDY NUMBER

FIGURE 5 Dialysance values for inulin in control (open bars) andexperimental (hatched bars) exchanges for the studies in protocol B.Paired analysis of all six studies indicates no significant differencefrom zero for the changes in inulin dialysance. P values for the sig-nificance of the difference of the means is given along the abscissa.

DU x 103mi/mn 21.2

P value


FIGuRE 6 Dialysance values for urea in control (open bars) and experimental(hatched bars) exchanges for the studies in protocol B. Paired analysis for allsix studies indicates no difference from zero for the change in urea dialysance.See caption to Fig. 5 for further explanation.


DR

.36

.32

.28

-24

.20

.16

.12P value N S NS NS <.02 .02 <.02

1 2 3 4 5 6


FIGURE 7 Inulin: urea dialysance ratios in control (open bars) andexperimental (hatched bars) exchanges for the studies in protocolB. Paired analysis for all six studies indicates no difference fromzero-for the change in the dialysance ratio. See caption to Fig. 5 forfurther explanation.

ply that the membrane area for the passive transport ofurea and inulin is virtually' identical.

Experimental support for these considerations isfound in the high dialysance ratios found in the ex-perimental exchanges of protocol A (mean DR for study5 = 0.84). Since the diffusion constant for inulin inwater is less than that for urea, DR must always be lessthan one. A value near one must indicate circumstancesin which no significant difference in either total mem-brane area or permeability exists for the two solutes,and only the diffusion coefficient difference keeps theratio from reaching one. In studies 7 and 10 of protocolA no detectable change in DR occurs in the face of sub-stantial increases in both components of the ratio.This indicates an increase in area for passage of bothinulin and urea with no detectable alteration in perme-ability. Such a response points away from an initialdisparity in membrane area available for inulin andurea transport. A larger urea membrane in the con-trol situation would result in a larger proportional in-crease in the experimental inulin membrane with an in-creased DR. Finally, the sieving coefficients for inu-lin and urea across the peritoneal membrane in responseto hypertonic solutions are frequently quite comparable(Table II). The high sieving coefficients for inulin

1 The area of peritoneal membrane served by a givencapillary would be larger for urea than for inulin in pro-portion to the ratio of the diffusion constants for thetwo solutes.

point away from a significant contribution of intra-cellular water to the ultrafiltrate. The sieving coeffi-cients for urea given in Table II agree with previouslypublished figures (1). All of these experimental ob-servations support the second assumption of the mathe-matical model in which the urea and inulin membranesare considered to be the same.

Examination of the data from protocol A shows thatin every instance the individual dialysance values forinulin and urea increase after exposure of the peri-toneal membrane to hypertonic dialysis fluid. This asdiscussed can result from either an increase in the areaof membrane participating in the diffusion process, oran increase in membrane permeability, or any combina-tion of the two. On looking at the dialysance ratios,however, it is apparent that Di rises more than Du re-sulting in a significant (P < 0.05) increase in DR.Three mechanisms could result in a selective increasein transfer of inulin as noted with the rising DR valuesin protocol A. First, a selective increase in the areaof membrane available for inulin transfer could resultin an increase in DR, provided that urea membrane areaexceeded inulin membrane area initially. Such an in-crease in shared membrane area could be pictured asan increased total area available for shared transferroutes or an increased number of pores per unit area ofmembrane available for diffusion of both solutes withno change in pore size or shape. The result would be agreater proportional increase in total inulin transport

998 L. W. Henderson and K. D. Noiph

pathways than in urea transport pathways. As discussedthere are several reasons to reject this explanation.

A second mechanism to explain a greater increase ininulin dialysance would be an increasing inulin space.If the volume of distribution of a solute increases, thetrue dialysance (clearance at time -> 0) does not change,but the solute concentration gradient will fall lessrapidly, and a greater clearance rate will persist dur-ing the exchange. At time t there will be a greaterSD/SB ratio (see Appendix) and, if the former smallervolume of solute distribution is used to calculate dialy-sance, this calculated dialysance will be falsely increased.Several factors minimize this mechanism. Finkenstaedt,O'Meara, and Merrill (5) have shown that inulin spaceis quite stable in anuric patients during the period ofour study (8 hr). Wehave confirmed that observationin three of our patients. It must also be expected thatwith some ultrafiltration and perhaps some shift of wa-ter into cells during dialysis, inulin space would be morelikely to decrease causing calculated inulin dialysanceto fall. Most important, however, as shown in Fig. 1, isthe fact that errors in the space of distribution of 5-10liters account for very little error in calculated dialy-sance in the volume ranges at which we are working.

Thirdly, an alteration in pore configuration couldalso explain the data. An increase in mean pore radiuswould result in a greater reduction in steric hindrancefor inulin than for urea. Should the over-all pore areaincrease as a result of this change in configuration, thenthe individual dialysance values for these solutes wouldbe expected to rise in conjunction with their ratio.Should no change in over-all pore area occur with achange in pore configuration, we would speculate thatDi and DR would increase with no change in Du. Pro-tocol A showed no such results. In study 4 of protocol B,however, such a pattern is observed. Of the three ex-planations available alterations in pore configuration,and thereby selective membrane permeability, seems tobest explain the observation of an increase in DR notedwith protocol A. In view of the slight osmotic gradientfrom dialysis fluid to plasma present with isotonic solu-tions solvent drag was examined as a possible explana-tion for the observed changes in equilibration ratio forinulin and urea. Calculations assuming bulk flow ofplasma water with inulin or urea for the discharge ofthe small osmotic gradient observed point up this ex-planation as unsatisfactory on quantitative grounds.The amount of solute delivered would be a factor of20 too low.

The six studies in protocol B provide an interestingcontrast to those in protocol A. There is no constant pat-tern of change in Di or DR, which may increase or de-crease in any given study. Du generally shows onlyslight increase. In study 4, Di and DR increase signifi-

cantly, while Du does not change. This change in selec-tive permeability of the membrane only is best explainedas a change in pore configuration such that steric hin-drance to the passage of inulin is reduced, but no al-teration occurs in the over-all area available for thediffusion of urea. Of particular interest is study 6 inwhich DR falls significantly in spite of a rising Di andDu. This could be interpreted anatomically as an in-crease in the pore area available for diffusion and, inaddition, as an alteration in the pore configuration suchthat the permeability for inulin is somewhat less. It isapparent that under more physiologic conditions inwhich only isotonic solutions are used, changes in mem-brane area and permeability show no constant rela-tionship and behave as independent variables in theircontribution to solute transport.

Several reasonable speculations as to why thesechanges occur should be considered. Clearly any factorinfluencing blood flow to the peritoneum will influencesolute transfer across the membrane. Increased bloodflow might influence solute transfer by the delivery ofmore solute to the blood side of the membrane, therebymaintaining the blood-to-dialysis fluid concentrationgradient at a maximum. In addition, this might reducethe capillary endothelial stagnant fluid film. Also, an in-crease in blood flow might clearly be expected to ex-pand the capillary bed and provide greater membranearea by opening previously unperfused capillaries anddistending capillaries already perfused. The work ofHare, Valtin, and Gosselin (6) suggests the importanceof vasoactive compounds acting on the splanchnic bed.With the reasonable supposition that neither of thesecompounds is blood flow limited, all of the mechanismscited would result in a proportional increase in bothDi and Du. Should distention of a capillary also openpores of larger diameter then the ratio will rise.Protocol A in which solutions with over twice normalosmolality are used could well be expected to produceperitoneal irritation with a postexposure reactive dila-tation of the capillary bed. Protocol A always producedan increase in dialysance of both solutes, but the dialy-sance ratio did not always rise. If vasodilatation is thebasis for the increase, there would have to be two com-ponents involved to explain the data, namely an increasein the number of capillaries perfused (area) and sec-ond, an increase in capillary membrane pore size (per-meability).

In protocol B as contrasted with A no consistent pat-tern developed. The lack of consistent relationship be-tween changes in Di and DR point away from a com-mon factor causing these changes. Variations in themembrane probably result more from physiologic vari-ables rather than from the dialysis procedure. A rea-sonable speculation as to why these changes occur would


be that membrane area and pore configuration are inde-pendently mediated by nervous and (or) hormonalstimuli.

APPENDIXSolute movement across the peritoneal membrane when1.5% glucose-containing dialysis fluid is used can be treatedas a problem of simple diffusion in a two compartment sys-tem. Peritoneal membrane is here defined to mean any mem-brane, visceral or parietal, and its stagnant fluid films,separating blood from dialysis fluid. Changes in the pas-sive transport characteristics of the peritoneal membranefor solutes of differing size may result in either propor-tional or disproportional changes in the transfer of the vari-ous solutes. Any proportional changes in solute transfer areconsidered to represent an alteration in membrane area,while any disproportional changes are considered to repre-sent alteration in the selective permeability of the membrane.It is recognized that discrete anatomical pores are not une-quivocally implicated in the mechanisms for solute and wa-ter transfer across biological membranes. In most instances,however, the functional behavior of such membranes can bemost satisfactorily described and understood using the ana-tomical concept of pores and classical pore theory (7-9).

Four simplifying assumptions have been made. Firstly,diffusion is considered to proceed smoothly throughout theexchange starting at the time of inflow and stopping at thetermination of the exchange 70 min later. It is recognizedthat variations in the volume of dialysis fluid present inthe peritoneal space occur during inflow and outflow. As aresult, solute does not cross the peritoneal membrane smoothlybut rather at a rate which would be primarily a reflectionof the area of membrane exposed. As each exchange wasconducted with the same inflow and outflow times, the er-ror introduced into the model is a constant factor that woulddrop away when isotonic control exchanges are comparedwith postultrafiltration, isotonic experimental exchanges.It is recognized that by making this assumption, the absoluterate of solute transfer is in error.

Secondly, the total membrane surface area available forurea diffusion is the same as that for inulin (see Discussion).

Thirdly, it is assumed that there is no ultrafiltration,either osmotic or hydrostatic, from blood to dialysis fluidduring 1.5% glucose exchanges. Contributions of solute bybulk flow or solvent drag mechanisms would thereby beeliminated, and all solute movement could then be ascribedto simple diffusion. At times slightly more (100 cc) dialysisfluid returns on drainage than was introduced. The errorintroduced by this assumption is not considered significant.

Finally, it is also assumed that the volume of distributionin the body for each solute is homogeneous and does notchange significantly during the study.

Inulin space was measured during each study after the2 hr equilibration period. The work of Finkenstaedt,O'Meara, and Merrill (5) on the stability of the inulin spacein oliguric man over 24 hr was confirmed by three studiesof our own. Urea space was estimated as 60% of bodyweight. All patients were essentially anuric, and any fall inblood concentration of the study solutes or body weight wasconsidered to result from dialysis. In some studies, a 1-2liter total ultrafiltration loss of volume occurred. Changesof such magnitude (1-2 liters) have no significant effecton the calculated dialysance (Fig. 1).

With these assumptions solute movement across the peri-toneal membrane can be expressed with a standard equa-

tion (10) for the dissipation of a concentration gradient bydiffusion.

d(SB- SD) -K(S - SD) (1)

where

SB = the concentration of a solute S in the body compart-ment of its distribution at any t

SD = the concentration of the same solute in dialysis fluidat any t

t = the time in minutes from the beginning of theexchange

K = a first-order rate constant with units of reciprocalminutes. K incorporates the factors of temperaturegradient (patient to dialysis fluid), cycle patterns ofthe exchange, total membrane surface area, thevolumes of solute distribution in the body and peri-toneal cavity, and permeability. All factors but thetotal area and permeability of the membrane can beheld constant.

Equation 1 can be expressed in exponential form:

SB - SD = Ce-Kt whereC = a constantt =0

SD 0SB = C, thus, since SB does not change significantly

during one exchange

SB -SD = SBe-Kt (2)Now since

dSD dSB ( dSD dSB VB\dt * VD = - dt dt dt VD

where

VB = the volume of distribution for a solute within thebody and outside the peritoneal space

VD = the 2 liter volume of dialysis fluid returned at the endof an exchange

and

then

or

and

d(SB - SD)_ dSB dSDdt dt dt

d(SB -SD) dSB / dSB VBdt dt dt VD,

dSB I+VB)=dt lVDJdSB _ d(SB - SD) VDdt dt VD + VBI

or substituting from equation 1dSB _ K(B-S) VDdt = - K(SB -SD) VD + VB

then substituting from equation 2 we have

dSB - K(SBeKt) VD + VB (3)


The actual clearance rate of solute at any time t is expressed as

Actual clearance rate = dB VBdt SB

or by substituting - -Ke-KtVBVDfrom equation 3 VD + VB

The total volume of extracellular fluid cleared of solute aftertime t is the integral of equation 4 or

ft VBVD= - Ke-Kt VD+ VB dt

t VBVD e-Kt-OVD + VB

VBVDVD+VB}(e-Kt (5)

The total cleared can also be expressed as

thus

SDVDSB

SDVD _ VBVDSB VD + VB

e-t SDVDVD+ VB1+1e t = [ _ SB VB*VV J

Taking the natural log of each side and rearranging terms wehave

In [1 SD(VD+Vs)] (6)t

Note that VB appears in both numerator and denominator,and that VB changes produce very little change in K (seeDiscussion).

It can be seen in equation 4 that the clearance rate at thestart of an exchange (t -> 0) in a diffusion system in whichthe starting sink solute concentration is zero is equivalent todialysance. Using the simple form of the dialysance equation(dialysance = QA V

where Q equals machine blood flowA-BPin milliliters per minute and A, V, and B are the given soluteconcentrations in artery, vein, and bath, respectively) it canbe seen that at t = 0, then B = 0, and dialysance equalsclearance. - K(VB-VD)/(VB + VD) is thus referred to asdialysance (D). (Di = inulin dialysance, Du = ureadialysance.)

Dividing dialysance by total membrane area would yield avalue with the characteristic units of a permeability constantand would represent the initial clearance rate per exchangeper unit area of total membrane.

-KVIB -VDKVB -= dialysance = permeability -area

If the total surface area available for diffusion of inulin andurea are assumed to be the same, and if volumes of distributionare assumed to change insignificantly in relation to oneanother, then changes in the ratio DI/Du measured duringidentical exchanges must reflect functional membrane altera-tions affecting one solute proportionately more than the other,i.e., a permeability change.

DI .. inulin permeability= dialysance ratio (DR) = iDUrea urea permeability

"Permeability" would be determined by the diffusion rate ofthe solute through the membrane and (or) through solvent-filled pores therein and would be influenced by such factors asmolecular weight, charge, and hydrated radius of the soluteparticle. The effective "pore" radius, length of diffusion path,and fixed membrane charge, as well as the influence of stag-nant fluid films at the membrane surface would also be im-portant. Since the solutes examined in the present study areuncharged, variations in the individual dialysance values fromcontrol to experiment would reflect variation in pore configu-ration or changes in total membrane area with or without asso-ciated changes in pore configuration. Variation in pore size orshape while altering the true area for diffusion and hence theindividual dialysance values would also be expected to alter thepassage of inulin more strikingly than urea. Such an alterationin mean pore radius can be identified by a change in DR, i.e.,a disproportional change in solute transfer. Changes in dialy-sance values due to area change alone would change Di andDu but would not alter DR.

ACKNOWLEDGMENTSThe authors are indebted to Drs. Lewis W. Bluemle andMartin Goldberg for their criticism and support of thiswork as well as to Miss Helaine Kandel for technical as-sistance.

This work was supported in part by Clinical ResearchCenter Grant 5 MO1FR 40, Division of Research Facili-ties, National Institutes of Health, and by U. S. PublicHealth Service Grants 5 RO1 HE 00340 and 5 RO1 HE07284.

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