Download - Permeability of the Corneal Endothelium to Nonelectrolytes · Permeability of the corneal endothelium to nonelectrolytes Saiichi Mishima and Sterling M. Trenberih* The endothelial

Permeability of the corneal endothelium tononelectrolytes

Saiichi Mishima and Sterling M. Trenberih*

The endothelial surface of the isolated rabbit cornea was perfused with modified KEI medium,according to the method reported previously. This in vitro cornea maintained its thicknesswithin the normal range even after the epithelium ivas removed. The endothelial permeabilityof these in vitro corneas to tritiated water, 1J>C-labeled urea, sucrose, and inulin teas determined.The reflection coefficients of the endothelium calculated according to the physical interpreta-tion of Kedem and Katchalsky were in fair agreement with those determined previously fromosmotic fluid flow across the endothelium. Perfusion of the corneal endothelium with calcium-free KEI medium resulted in a corneal swelling with an increased endothelial permeability.Perfusion with KEI medium containing ouabain (10~s and 10~5 moles per liter) induced acorneal swelling with normal endothelial permeability.

In vitro perfusion of the endothelial sur-face of the isolated rabbit cornea withmodified KEI medium was recently foundto maintain thickness of the cornea withina normal range, even after removal of theepithelium from the cornea.1 It was con-

From the Department of Ophthalmology, Collegeof Physicians and Surgeons, Columbia Universi-ty, New York, N. Y.

This investigation was supported by the UnitedStates Public Health Service Research GrantNB 06309 and also by Grant NB 04968(Cornea Center) from the National Institute ofNeurological Diseases and Blindness. This workwas also supported by a Grant-in-Aid from theNational Society for the Prevention of Blindness,Inc., New York.

This paper was presented at the Eastern SectionMeeting of the Association for Research inOphthalmology, March 10-11, 1967, in Wash-ington, D. C.

* United. States Public Health Service Ophthalmol-ogy Training Grant 5 TI NB 05164 from theNational Institute of Neurological Diseases andBlindness. Present address: Jules Stein Eye In-stitute, UCLA Center for the Health Sciences,Los Angeles, Calif.

eluded, therefore, that the endothelium isof major importance in maintaining normalcorneal thickness. The method of this invitro perfusion will therefore offer a verygood system to study endothelial functionin the maintenance of the corneal thickness.This endothelial function may be classifiedin two categories, namely: (1) activeprocesses which require metabolic energyand (2) the function as a physical barrier.Some experimental evidence has been re-ported14 suggesting that aerobic metabo-lism of the endothelium is required for themaintenance of normal thickness. The sec-ond aspect, namely, the function as aphysical barrier, has been the object of thepresent study.

The physical properties of a membraneinvolved in transport are characterized bythree independent coefficients,5 i.e., thehydraulic conductivity, the reflection co-efficients, and the permeability to solutes.The hydraulic conductivity of the endo-thelium and its reflection coefficients tovarious solutes were the subject of the

34

Downloaded From: http://iovs.arvojournals.org/pdfaccess.ashx?url=/data/journals/iovs/932998/ on 04/19/2017

Volume 7Number 1

Perfusion of cornea! endothelium 35

previous investigation.0 The permeabilityof the endothelium to various solutes hastherefore been of primary interest in thisstudy. Endothelial permeability to variouselectrolytes was studied very extensivelyby Maurice.7'8 Donn, Miller, and Mallett9

determined diffusional flux of tritiatedwater across the rabbit cornea and esti-mated the endothelial permeability to thissubstance. In the present investigation, thepermeability of the endothelium perfusedin vitro to non electrolytes has been de-termined, with the use of "C-labeled urea,sucrose, and inulin, as well as tritiatedwater. The advantage of using these non-electrolytes is that they are not consumedby the tissue and that permeation will notbe modified by cellular activities.

A marked swelling of the cornea occurredfollowing the perfusion of the endothelialsurface with either the modified KEI medi-um free of calcium or with the mediumcontaining ouabain. The endothelial perme-ability of these swelling corneas was com-pared with that of corneas having a main-tained thickness, and two different swellingswere demonstrated, namely, one with in-creased permeability and the other withnormal permeability of the endothelium.

Materials and methodsThe experiments were divided into two parts,

namely: (1) determination of isotope efflux fromthe cornea and (2) determination of distributionratio of the isotopes between the cornea and themedium.

Albino rabbits weighing 2 to 3 kilograms wereused without regard to sex. The eyes were enucle-ated under anesthesia with pentobarbital. Thecornea was isolated and perfused in vitro accordingto the method of Mishima and Kudo.1

Efflux experiments.Perfusion of the isolated cornea. The cornea with

its scleral rim was isolated and clamped in a luciteperfusion chamber. This chamber was then placedin a larger moist chamber within a constant tem-perature water bath; the corneal surface was incontact with air saturated over 0.9 per cent saline.The endothelial surface was perfused with themodified KEI medium. The temperature of thecornea was 34° C. and the intraocular pressurewas maintained between 10 and 20 mm. Hg byadjusting the height of the outlet tube of the

perfusion system. The details of the preparationand perfusion were reported previously.1

Perfusing medium. The basic perfusate was themodified KEI medium. This medium was madecalcium free by substituting sodium for calcium.Details of the preparation and the composition ofthese media were reported elsewhere.1

Rate of perfusion. Since the exact rate of perfu-sion was necessary for the calculation of endo-thelial permeability, the rates were individuallycalibrated. The outlet tube of the perfusion systemwas connected to a graduated capillary pipette(0.01 ml. per division) and the time was measuredduring which the front meniscus of the perfusingmedium traveled through 0.01 ml. The rate usedfor perfusion of 14C-labeled compounds was ap-proximately 20 /*L per minute and the rate fortritiated water was approximately 40 /xL perminute.

Removal of the epithelium. After normal cornealthickness was attained and maintained for aboutone-half to one hour of perfusion, the epitheliumwas removed. It was crushed with a fine grainsand paper driven by a small electric motor. Thecrushed epithelium was then removed with a smallscalpel. This method of removal caused very littlestress to the cornea.

The measurement of corneal thickness. Cornealthickness was measured through the transparentdoor of the moist chamber with a Maurice-Giardini10 pachometer attached to a Haag-Streitslit lamp (Model 360). Ten readings for the cen-tral region of the cornea were averaged in eachdetermination.

Isotope solutions and application to the cornea.14C-labeled urea (sp. act. 2 to 10 me. per milli-mole), sucrose (sp. act. 1 to 5 me. per millimole)and inulin (sp. act. 1 to 3 me. per gram) wereobtained in crystalline form (New England NuclearCorporation, Boston, Mass.). The isotopes weredissolved in distilled water to a concentration of0.1 fie per microliter. Tritiated water (sp. act.250 fie per gram) was obtained from the samesource. Fluorescein was added to these isotopesolutions to the concentration of 0.1%.

Approximately 1 /xL of the isotope solution wasaspirated into a fine polyethylene tube (Intra-medic PE 10, Clay-Adams, New York) with amicrometer syringe. The tube was calibrated tocontain 0.81 - 0.01 /iL per 10 mm. The solutionwas then applied on the bare stromal surface ofthe isolated cornea as evenly as possible. Thedistribution of fluorescein in the corneal stromaindicated the evenness of application.

Sampling of the perfusing medium The per-fusing medium was sampled at the outlet of theperfusion system in vials (Fig. 1) after the ap-plication of the isotopes to the corneal stroma.Sampling was done every 3 minutes for tritiatedwater, every 10 minutes for 1IC urea and su-


36 Mishima and Trenberth Investigative OphthalmologyFebruary 1968

ISOTOPE

Fig. 1. Application of isotope on the cornealstroma and sampling of the perfusing medium atthe outlet.

GASMIXTURE

Fig. 2. Reservoir-type chamber for the incubationof isolated rabbit cornea. For gas mixture, seetext.

crose, and every 15 minutes for " C inulin. Twelveto fifteen samples were collected for each experi-ment.

Assay of the isotope activity. Activities of theradioisotopes in the samples were assayed witha liquid scintillation counter (Packard, Tri-CarbLiquid Scintillation Spectrometer, Model 3003,Packard Instrument Co., Downers Grove, 111.).

Determination of distribution ratio. The dis-tribution ratio of the isotopes between the cornealstroma and the medium was necessary to calculatethe permeability of the endothelium. The ratiosfor urea and sucrose were therefore determinedexperimentally. Experimental determinations werenot done for tritiated water and inulin.

Bathing of the endothelial surface. The cornea,with its scleral rim, was isolated as describedpreviously and clamped in a lucite chamber as

shown in Fig. 2. The whole specimen was placedin a small moist chamber described previously.In this reservoir-type chamber the modified KEImedium bathing the endothelial surface was re-circulated by bubbling a warm wet gas mixture(7 per cent oxygen, 5 per cent carbon dioxide,88 per cent nitrogen). The rate of circulation wasapproximately 3 ml. per minute, insuring goodmixing of the medium. The total amount of me-dium bathing the endothelial surface was approxi-mately 4 ml. The gas mixture maintained the pHof the medium at 7,3 throughout the experiment.The temperature of the main water bath wascontrolled to approximately 38° C. so that thetemperature of the medium behind the corneawas maintained at 34° C.

Application of the isotope and sampling. Whennormal corneal thickness had been maintainedduring incubation for one-half to one hour, 20 fiL.of isotope solution were added to the medium.Rapid mixing was revealed by the distributionof fluorescein mixed into the isotope solution. Atthe end of the incubation, 10, 20, and 100 /tLof the medium were sampled with Lang-Levymicropipettes and were subjected to the assayof the isotope activity.

Assay of isotope activity in the corneal stroma.At the termination of the incubation, the corneawas removed from the incubation chamber, rinsedbriefly with nonradioactive medium and blotted.The epithelium and endothelium were then re-moved with a razor blade and the stroma wassandwiched between two parafilms. The previousprocedures were carried out in a transfer cham-ber saturated with moist air over 0.9 per centsaline. A stromal button of 9 mm. diameter wasthen punched out. It was weighed and dried invacuo to a constant weight at 60° C. over phos-phorus pentoxide. The dry weight was deter-mined, and the amount of the stromal water cal-culated. The dry cornea was then extracted in1 ml. of distilled water by vigorous shaking forat least 7 hours. This time was chosen sinceOtori11 reported that sodium, potassium, and chlo-ride were almost completely extracted after 5hours. After the extraction, 400 fiL of the extractwas sampled with the Lang-Levy micropipetteand the activity was assayed.

Mathematical methods. The time course of theconcentration changes of the isotopes in the per-fusing medium at the outlet sampling site wasthe function of the rate of perfusion, permeabilityof the corneal endothelium, volume of the anteriorchamber, volume of the cornea, and area of thecorneal endothelium. A mathematical relationamong these factors was formulated in order tocalculate the permeability of the corneal endo-thelium.

Calculation of endothelial permeability. In theperfusion system, shown in Fig. 1, let us assume


Volume 7Number 1

Perfusion of corneal endothelium 37

that most of the resistance to diffusion of thesubstance in the cornea is in the endothelium andthat the anterior chamber and the corneal stromawere well stirred. The former assumption maybe substantiated by the fact that the cornealstroma has very low resistance to diffusion com-pared with that of the endothelium (less than1/200, Maurice7-s). The latter assumption ofwell-stirred corneal stroma was not correct inthese experiments; the error caused by this as-sumption will be treated in the next section.

The basic equation for the solute flux acrossthe unit area of the endothelium under the pre-vious assumption and the steady state conditionswere obtained as follows, according to the the-ory of membrane permeability (Kedem andKatchalskyf').

Js = <oRT ( C - r C«) + (1 - o) c Jv (1)

where symbols are defined in the following:Js = Rate of net solute flow per unit area

(moles per second per square centimeter), Jv =Rate of volume flow per unit area (cubic centi-meter per second per square centimeter), wRT =Permeability coefficient of the endothelium (centi-meter per second), C = Concentration of thesolute in the anterior chamber (moles per cubiccentimeter), CK = Concentration of the solute inthe cornea (moles per cubic centimeter), r =Distribution ratio of solute between the anteriorchamber and the cornea, a = Reflection coeffi-cient, c = Average concentration of the solutein the endothelium, i.e., c = (rCc + Cn)/2.By dividing Equation 1 by the volume of thecornea (Vc) and applying the equation for theentire area of the endothelium (A), one can ob-tain the following:

— = — (ICC. - rK: Cc) (2)dt Vc

Tvwhere K, = «RT + (1 - a) — and IG = «RT -

2

For the concentration of the anterior chamber(Cn), one can write:

dC,

dt

(AJS + V, C.)

Va(3)

where Vo is anterior chamber volume, and Vi israte of anterior chamber perfusion. This equationcan be transformed to more practical form byusing Equation 1:

dC. _ {AK3rCe - (AKi + vi) C.}

dt ~ V,,(4)

assume that the rate of volume flow, namely,of corneal swelling (Jv), is constant0 and thatthe change of the corneal volume during the ex-periment is not large so that the steady state ofthe system can be approximated.f The solutionof these equations is the following:

G. = M (e"x t - e"yt) (5)

where M is a constant given by the amount ofisotoj^e applied, and x and y are given by thefollowing equations:

x and v —

= ( •

AKi

Va

v,—V.

AK:r\

d =VnVc

(6)

Since y is larger than x, the second term of Equa-tion 5 will be negligible after a certain time inter-val, and therefore the value of x will be obtainedgraphically from semilogarithmic plotting of theCn-time relations.

By solving Equation 6 in terms of the permea-bility coefficient of the endothelium (wRT), oneobtains:

coRT = (7)

VaVc Vn

( rVi x rx\

VnVc Va Vc/

When the cornea does not swell, the second termof the numerator becomes zero, and the calcula-tion becomes simplified.

Calculations of dimensions. At the end of eachexperiment, the distance between the corneal apexand the base of the anterior chamber was mea-sured by the use of a caliper to the accuracy of0.05 mm. The depth of the anterior chamber ( d )is obtained by subtracting the corneal thickness.Since the diameter of the cornea clamped to theperfusion chamber was 11 mm., the radius of thecorneal curvature ( r ) in millimeters was calcu-lated, assuming that the cornea had a single curva-ture throughout.

(5 .5 ' + d a )

2d(8)

Volume of the anterior chamber (VB) and thearea of the cornea (A) are, respectively,

*In corneas perfused with calcium-free KEI medium (Fig.4) and also treated with ouabain (see reference 17), theswelling was found to be practically linear in the first2 to 3 hours.

Equations 2 and 4 may be solved, if one can fSee Results, the permeability of the swelling cornea.



/ cl \

V. = •* (r - y )A = 27rrd

Volume of the cornea, with its solid mass ex-cluded, is obtained by

V c = A (q - 0.08)

where q is the corneal thickness in millimetersand 0.08 mm. corresponds to the thickness of thesolid mass.0

The calculations of these dimensions lead to asolution of Equation 7 to yield uRT values forthe corneal endothelium.

Correction for unstirred layer. Since the as-sumption used in the preceding section that the

corneal stroma is well stirred does not hold, onemust correct for the errors resulting from thisassumption. Correction for the apparent permea-bility coefficient for unstirred layer was studied byGinzberg and Katchalsky.12 Their equation wasmodified to give the following equation:

«RT u'RT0.D'

(9)

where wRT is the permeability of the endotheliumcorrected (centimeters per second), u'RT is theapparent permeability (centimeters per second)calculated from equation 7, Q is the thickness ofthe stroma (centimeters), and D' is the diffusioncoefficient of the solute for unit thickness of the

-g 0.40 rE

| 035

cc8 0-30

0 1 2 3 4 5 6TIME (Hr.)

Fig. 3. Corneal thickness during the efflux experiment: the perfusion with the modified KEImedium. E, Epithelium was removed. /, Isotope solution (^C sucrose) applied on thestromal surface.

0.55 r

0.50

¥ 0.45

0.40

E I

0 1 2 3 4 5

TIME (Hr.)

Fig. 4. Corneal thickness during the efflux experiment: perfusion with Ca free medium. E,Epithelium was removed. /, Isotope solution ( "C inulin) applied on the stromal surface.


Volume 7Number 1

Perfusion of cornea! endothelium 39

corneal stroma (square centimeters per second).For actual calculation, D' was assumed to beapproximately half of the free diffusion in theaqueous medium for the given solute. Diffusioncoefficients of sodium, tritiated water, and othersmall ions in the corneal stroma were found tobe about one half of their free diffusion."-9

Results

Corneal thickness during the experiments.Perfusion with the modified KEI medi-

um. When the isolated cornea with itsepithelium removed was perfused with themodified KEI medium, the cornea couldmaintain constant thickness for severalhours. This observation, made in more than10 perfusions, confirmed the previous find-ing of Mishima and Kudo.1

When an isotope solution of sucrose,inulin, or tritiated water was applied tothe stromal surface, the cornea swelled toless than 5 per cent of its thickness (Fig. 3).When urea was applied, however, swellingto about 10 per cent of the thickness wasmeasured. During the subsequent perfu-sion, the thickness initially tended to reducetoward the original value, and then tomaintain constant thickness during the re-mainder of the experimental period. Simi-larly, when the cornea was incubated inthe reservoir-type chamber, the cornealthickness remained constant for more than6 hours of incubation.

Perfusion with Ca free medium. Theisolated cornea was first perfused with the

modified KEI medium and then with theCa free medium. Slight corneal swellingwas noticed after about one hour, followedby remarkable swelling, again confirmingthe previous results of Mishima and Kudo.1

The rate of swelling was 0.08 ± 0.03 mm.per hour (5 corneas) when the epitheliumwas present and 0.07 ± 0.02 mm. per hour(11 corneas) without the epithelium. Thepresence of the epithelium did not alterthe rate of swelling.

When definite swelling of the cornea wasmeasured, isotope solution was appliedevenly on the bare corneal stroma. Afterthe isotope application, swelling continuedwithout change of rate (Fig. 4).

Distribution ratio of urea and sucrosebetween the corneal stroma and the medi-um. The isolated cornea was incubated forvarious lengths of time after the isotopewas mixed in the medium. The activity inthe corneal water was expressed as theratio with that in the medium. When ureawas used, the ratio was found to be steadybetween 2 and 6 hours of incubation.The average of ratios in 6 experimentsincubated for this time period was re-garded as the distribution ratio; it was0.95 ± 0.07.

The ratios of the activity in the stromalwater to that in the medium at variousintervals after sucrose application wereplotted in Fig. 5. Considerable scatteringof the data was noticed, but the result was

i.o

0.5

3 4

TIME (Hr)

Fig. 5. Concentration ratio of 3!C sucrose between the corneal stroma and the medium. Solidline, average time course of the change in ratio.



compatible with the assumption that thedistribution ratio was practically unity.

For tritiated water, the ratio of one wasused without experimental determination.For inulin, the ratio was assumed to beunity without experiment. It was not possi-ble to incubate the cornea long enough(more than 12 hours) without the risk ofdamage to the endothelium, to make theactual determination for inulin which istaken up very slowly by the cornea.

Calculation of the permeability coef-ficients.

Permeability for the cornea with a main-tained thickness. When normal cornealthickness had been maintained for one-half to one hour of perfusion, the epitheli-um was removed. After a certain period toallow recovery of the cornea from evapora-tion during the procedure, the isotope solu-tion was applied on the bare stromal surfaceand the perfusing medium was sampled atthe outlet of the perfusion system at inter-vals (Fig. 1). The activity of the isotope

lOV

io4

I03

10'18

TIME Imin.)27 36

Fig. 6. Time course of the activity change (tri-tiated water) in the perfusing medium at theoutlet.

in the samples was plotted semilogarithmi-cally, as shown in Figs. 6 and 7. The activitychanges can be expressed by double expo-nential equation, as expected from themathematical analysis. The time requiredfor maximum activity to be reached in theperfusing medium became longer and thesubsequent decrease of activity slower asthe size of the test molecules increased.The rate of the activity decrease after themaximum was reached was determinedgraphically and the permeability coefficientscalculated. The results are given in Table I.

Since the assumption for this calculation,that the corneal stroma constitutes a well-stirred compartment, does not hold, correc-tions were made for this unstirred layer bythe method described in the previous sec-tion. The error was approximately 40 percent for tritiated water and about 10 percent for urea. The corrected values aregiven in Table I. The error was negligiblefor sucrose and inulin.

Diffusion coefficients of these moleculesin the aqueous medium at 34° C. werecalculated from previous sources13"10 andare given in Table I. The ratios of thepermeability coefficients for the endotheli-um and the diffusion coefficients in aqueousmedium were calculated on the assumptionthat the endothelial thickness was 5 /.<,.These results are also given in Table I.

Permeability for the swelling cornea.When corneal swelling was definitely no-ticed in the perfusion with Ca free medi-um, the epithelium was removed. After thecorneal thickness had recovered fro?ntemporary thinning because of evaporationduring the removal of the epithelium, theisotopes were applied on the stromal surface(Fig. 4). The perfusing medium was thensampled and the activity counted. Thepermeability coefficients were calculatedfor urea and inulin. The calculation withthe obtained swelling rate of the corneashowed that the second term of Equation7, which is due to the corneal swelling, wasnegligible (less than 5 per cent of thepermeability value at the maximum). Thesubsequent calculation was therefore made


Volume 7Number 1


10V

id1

10s

30 60 90 120TIME( min.

150 180 210

Fig. 7. Time course of the activity change in the perfusing medium at the outlet: solid circles,urea; open circles, sucrose; crosses, inulin.

Table I

Testmolecule

Tritiatedwater

UreaSucroseInulin

uRT x 10«cm./sec.0

164 ±52 (6)2 1 + 2 . 2 ( 6 )

6.5 ± 1.7 (5)1.25 ± 0.45(6)

10f'cm.-'/soc.

3.0§1.7110.651f0.29#

D350 c. T

coRT x AX

3601,6002,0004,400

acalculated

-0.770.820.92

measuredt

-0.60.9T O O

Ca free mediumuRT x 10"

cm./sec.

43 ± 1 2 (5)

7.2 ± 2.7 (6 )

Ouabain 10-s,10~5 mole/L.

aRT x 106

cm./sec.

20.6 ±4.5 (11)8.8 ±2.5 (11)

-

°AH data are presented as average ± standard deviation (number of experiments).f Ax: thickness of the endothelium was assumed to be 5 fi.JFrom Mishima and Hedbys (1967).§Wang, Robinson, and Edelman13 (1953).|| Longworth1" 1954).IFLongworth14 (1953).#Calculated from Einstein-Stokes equation assuming radius for sucrose 5.3 A, inulin 12 A (Durbin,18 1960).ooFor ra Hi nose.

by neglecting this swelling rate and byusing an average corneal volume* duringthe experimental period. The permeabilitycoefficients of the endothelium of the corneaswelling during perfusion with Ca freemedium are listed in Table I. The perme-ability of the endothelium is found to beconsiderably increased over normal values.

"For mathematical analysis, the volume change during theexperimental period was assumed to be negligible. Whenaverage volume was used, errors caused by this assumptionwere less than 10 per cent.

In another investigation,17 it was foundthat the perfusion with ouabain-containingmedium (10"3 and 10"5 moles per liter)resulted in a corneal swelling; the endo-thelial permeability of these swelling cor-neas was determined. The permeabilitycoefficients for these corneas to urea andsucrose are given in Table I for compari-son. The coefficients in these cases are notsignificantly different from those values forcorneas with a maintained thickness.


42 Mishima and Trenberth In vestigative OphthalmologyFebruary 1968

Discussion

Direct determination of corneal endo-thelial permeability to the nonelectrolytesused in this investigation is not found inthe literature. The present data may becompared, however, with estimated valuesfor tritiated water (Donn and co-workers9)and with determined values for small ions(Maurice7-s). Donn and others measureddiftusional flux of tritiated water across thewhole layer of rabbit corneas, cornea withepithelium removed, and the cornea withthe endothelium removed. From their data,endothelial permeability of tritiated watermay be calculated, assuming that the diffu-sion coefficients in swollen stroma remainedvirtually unchanged from those in normalstroma. A calculation from their data in-dicated that the obstruction of the endo-thelium to tritiated water (ratio betweenthe endothelial permeability and free diffu-sion) was about the order of 1/250, whichis in fair agreement with 1/360 of thepresent study.

The permeability coefficient found forurea in this study was almost the same asthose found for sodium and other smallions in the living cornea (Maurices). Inthe previous investigation,0 it was foundthat both urea and sodium chloride hadabout the same reflection coefficients tothe corneal endothelium. Since the reflec-tion coefficients are the function of waterand solute permeabilities across the mem-brane, these results indicate that the endo-thelium of the perfused cornea has beenkept practically intact as in these previousinvestigations.

The reflection coefficients may be ex-pressed by using the available area of themembrane for diffusion of solute and water,according to the physical interpretation ofKedem and Katchalskyls:

_ « As

A w

where v is the partial molar volume of thesolute, Lp is the hydraulic conductivity ofthe membrane, and As and Aw are, area ofthe membrane available for diffusion of the

solute and water, respectively. It is, there-fore, of interest to calculate the value of a-from the present permeability values andto compare this with the values of a de-termined previously from osmotic fluid flowacross the endothelium. The results arelisted in Table I. The calculated and thedetermined values may be regarded to bein fair agreement, when it is realized thatthe determination of hydraulic conductivityand the permeability coefficient, especiallyof tritiated water, were subject to ratherlarge standard deviation of the values.

A comparison of the permeability valuesfor the swelling cornea with those forcorneas with maintained thickness bringsout an interesting point concerning mech-anisms of the comeal swelling. The per-fusion with Ca free medium resulted in aswelling with markedly increased perme-ability of the endothelium. In the other in-vestigation,19 it was found that the perfu-sion with Ca free medium resulted in adissolution of the terminal bar and separa-tion of the endothelial cells. Wide inter-cellular separation obviously increased thepermeability of this layer and fluid wasimbibed through this impaired endotheli-um by the imbibition pressure of the cor-neal stroma.-0

The cornea also showed a marked swell-ing after the endothelial surface was bathedwith the medium containing ouabain.17 Theswelling occurred with ouabain concentra-tion between 10~5 and 10~3 moles per literat the maximum rate of about 0.04 mm.per hour. A slower rate of swelling occurredwith lower concentrations of ouabain andthe half rate of maximum swelling wasobtained with an ouabain concentration of3 x 10"7 moles per liter. The averagepermeability of the endothelium to ureaand sucrose is given in Table I for thesecorneas swelling in the presence of 10~3 and10~5 moles per liter ouabain. It is foundthat endothelial permeability remainedpractically the same as normal corneas dur-ing the swelling.

It is thus clear that one can demonstratetwo types of corneal swellings: (1) swell-


Volume 7Number 1


ing with increased permeability, as in thecase of perfusion with Ca free medium,and (2) swelling with practically normalpermeability, as in the case of ouabainapplication.

The authors are very grateful to Dr. D. M.Maurice and Dr. I. Flatt for their helpful criticismduring this investigation. Acknowledgment is alsodue to Miss L. E. Valentin and Miss Susana Li-maco for their skillful technical assistance.

REFERENCES1. Mishima, S., and Kudo, T.: In vitro incuba-

tion of the rabbit cornea, INVEST. OPHTHAL.4: 329, 1967.

2. Harris, J. E., and Gruber, L.: The hydrationof the cornea. II. The influence of the epithe-lium, Am. J. Ophth. 42: 333, 1956.

3. Harris, J. E.: The physiologic control ofcorneal hydration, Am. J. Ophth. 44: 262,1957.

4. Takahashi, G. H., and Mishima, S.: Effectof anoxia upon corneal hydration, INVEST.OPHTH. In press.

5. Kedem, O., and Katehalsky, A.: Thermo-dynamic analysis of the permeability of bio-logical membranes to non-electrolytes, Bio-chim. et biophys. acta 27: 229, 1958.

6. Mishima, S., and Hedbys, B. O.: The per-meability of the corneal epithelium and en-dothelium to water, Exper. Eye Res. 6: 10,1967.

7. Maurice, D. M.: The permeability to sodiumions of the living rabbit's cornea, J. Physiol.112: 367, 1951.

8. Maurice, D. M.: The use of permeabilitystudies in the investigation of submicroscopicstructure, in Smelser, G. K., editor: Thestructure of the eye, New York, 1961, Aca-demic Press, Inc., p. 385.

9. Donn, A., Miller, S. L., and Mallett, N. M.:Water permeability of the living cornea, Arch.Ophth. 70: 515, 1963.

10. Maurice, D. M., and Giardini, A. A.: Asimple optical apparatus for measuring thecorneal thickness and the average thicknessof the human cornea, Brit. J. Ophth. 35: 169,1951.

11. Otori, T.: Electrolyte content of the rabbitcorneal stroma, Exper. Eye Res. 6: 356, 1967.

12. Ginzburg, B. Z., and Katehalsky, A.: Thefrictional coefficients of the flows of non-elec-trolytes through artificial membranes, J. Gen.Physiol. 47: 403, 1963.

13. Wang, J. H., Robinson, C. V., and Edelman,I. S.: Self-diffusion and structure of liquidwater. III. J. Am. Chem. Soc. 75: 466, 1953.

14. Longsworth, L. G.: Diffusion measurementat 25° C. of aqueous solutions of amino acids,peptides and sugars, J. Am. Chem. Soc. 75:5705, 1953.

15. Longsworth, L. G.: Temperature dependenceof diffusion in aqueous solutions, J. Phys.Chem. 58: 770, 1954.

16. Durbin, R. P.: Osmotic flow of water acrosspermeable cellulose membranes, J. Gen.Physiol. 44: 315, 1960.

17. Trenberth, S. M., and Mishima, S.: The ef-fect of ouabain on the rabbit corneal endo-thelium, INVEST. OPHTH. 7: 44, 1968.

18. Kedem, O., and Katehalsky, A.: A physicalinterpretation of the phenomenological coeffi-cients of membrane permeability, J. Gen.Physiol. 45: 143, 1961.

19. Kaye, G. I., Mishima, S., Cole, J. D., andKaye, N. W. Studies on the cornea. VII.Effects of perfusion with a Ca++-free mediumon the corneal endothelium, INVEST. OPHTH.7: 53, 1968.

20. Hedbys, B. O., Mishima, S., and Maurice, D.M.: The imbibition pressure of the cornealstroma, Exper. Eye Res. 2: 99, 1963.


Download - Permeability of the Corneal Endothelium to Nonelectrolytes · Permeability of the corneal endothelium to nonelectrolytes Saiichi Mishima and Sterling M. Trenberih* The endothelial

Top Related