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Structural alterations affecting transparency in swollen human corneas Jerome N. Goldman, 9 George B. Benedek, Claes H. Dohlman, and Barbara Kravitt A simple discussion of the theory of the diffraction and scattering of light is presented. This theory is used to explain corneal transparency in terms of microscopic structure, and leads to the prediction that characteristic morphological changes ivould be found in swollen, opaque corneas. Specifically, it is to be expected that opaque corneas will show marked fluctuations in the index of refraction over distances comparable to, or larger than, the wavelength of light. Examination of all layers of pathological surgical specimens demonstrated morphological changes which were consistent with predictions of this theory. From the Department of Cornea Research, Insti- tute of Biological and Medical Sciences, Retina Foundation, Boston, Mass.; the Cornea Service, Massachusetts Eye and Ear Infirmary, Boston, Mass.; and the Department of Physics, Massa- chusetts Institute of Technology, Cambridge, Mass. This work was supported in part by United States Public Health Service Research Grant NB- 02220, by United States Public Health Service Training Grant NB-05518, and by special fel- lowship NB-1275 0 from the National Institutes of Neurological Diseases and Blindness, United States Public Health Service; in part by a Fight for Sight Grant-in-Aid of the National Council to Combat Blindness, Inc., New York, N. Y.; and in part by the Massachusetts Lions Eye Research Fund, Inc. The Phillips 200 Electron Microscope was ob- tained with the support of United States Public Health Service Ceneral Research Grant FR- 05527 awarded to the Retina Foundation. This work was presented at the Spring Meeting of the Association for Research in Ophthalmol- ogy, April 28, 1968. "Address reprint requests to: Department of Oph- thalmology, George Washington University School of Medicine, 239 Warwick Clinic, 2300 K St. N.W., Washington, D. C. 20037. T -Lr .ransparency of the cornea is explicable in terms of its microscopic structure. Light passing through the cornea interacts with the corneal constituents. The result of this interaction is the sideward scattering of some of the light. Transparency implies that the total scattered intensity is much smaller than the incident intensity. To describe the interaction between light and the structural components of the corne- al stroma, it must be recognized that the collagen fibers are very small (diameter — 300 Angstrom units [A]) and that their spacings are also small (— 550 A) com- pared with the wavelength of light (— 5,000 A). Since geometrical optics is not adequate to describe the interaction be- tween the light and the corneal constitu- ents when such conditions exist, we must apply the theory of diffraction. According to diffraction theory, the in- cident light induces an oscillating dipole in each of the collagen fibers. Each ener- gized fiber then radiates a spherically spreading wavelet. The summation of the individual wavelets determines the ampli- 501

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Structural alterations affecting transparencyin swollen human corneas

Jerome N. Goldman,9 George B. Benedek, Claes H. Dohlman, andBarbara Kravitt

A simple discussion of the theory of the diffraction and scattering of light is presented. Thistheory is used to explain corneal transparency in terms of microscopic structure, and leads tothe prediction that characteristic morphological changes ivould be found in swollen, opaquecorneas. Specifically, it is to be expected that opaque corneas will show marked fluctuationsin the index of refraction over distances comparable to, or larger than, the wavelength of light.Examination of all layers of pathological surgical specimens demonstrated morphologicalchanges which were consistent with predictions of this theory.

From the Department of Cornea Research, Insti-tute of Biological and Medical Sciences, RetinaFoundation, Boston, Mass.; the Cornea Service,Massachusetts Eye and Ear Infirmary, Boston,Mass.; and the Department of Physics, Massa-chusetts Institute of Technology, Cambridge,Mass.

This work was supported in part by United StatesPublic Health Service Research Grant NB-02220, by United States Public Health ServiceTraining Grant NB-05518, and by special fel-lowship NB-12750 from the National Institutesof Neurological Diseases and Blindness, UnitedStates Public Health Service; in part by aFight for Sight Grant-in-Aid of the NationalCouncil to Combat Blindness, Inc., New York,N. Y.; and in part by the Massachusetts LionsEye Research Fund, Inc.

The Phillips 200 Electron Microscope was ob-tained with the support of United States PublicHealth Service Ceneral Research Grant FR-05527 awarded to the Retina Foundation.

This work was presented at the Spring Meetingof the Association for Research in Ophthalmol-ogy, April 28, 1968.

"Address reprint requests to: Department of Oph-thalmology, George Washington UniversitySchool of Medicine, 239 Warwick Clinic, 2300K St. N.W., Washington, D. C. 20037.

T-Lr

.ransparency of the cornea is explicablein terms of its microscopic structure. Lightpassing through the cornea interacts withthe corneal constituents. The result of thisinteraction is the sideward scattering ofsome of the light. Transparency impliesthat the total scattered intensity is muchsmaller than the incident intensity.

To describe the interaction between lightand the structural components of the corne-al stroma, it must be recognized that thecollagen fibers are very small (diameter— 300 Angstrom units [A]) and that theirspacings are also small (— 550 A) com-pared with the wavelength of light (—5,000 A). Since geometrical optics is notadequate to describe the interaction be-tween the light and the corneal constitu-ents when such conditions exist, we mustapply the theory of diffraction.

According to diffraction theory, the in-cident light induces an oscillating dipolein each of the collagen fibers. Each ener-gized fiber then radiates a sphericallyspreading wavelet. The summation of theindividual wavelets determines the ampli-

501

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502 Goldman et al. Invcstigatice OphthalmologyOctober 1968

tude and the direction of the light scat-tered to the side. A portion of the incidentbeam continues in the forward direction.In both cases the light wave amplitude isdetermined by the summation of the scat-tered wavelets and the incident excitinglight.

The application of the diffraction theoryto this problem can be expressed in theterminology of geometrical optics. To dothis, one may describe the cornea as acontinuous medium whose index of refrac-tion may vary from one region to another.According to the theory of diffraction,periodic fluctuations in the index of refrac-tion over distances small compared withthe light wavelength do not produce lightscattering. This result can be understoodqualitatively by recognizing that the lightwave itself has a characteristic dimension:its wavelength. It cannot resolve structuressubstantially smaller than this dimension.To be quantitative, if the periodic fluctua-tions in the index of refraction take placeover linear dimensions (d) smaller thanone half the wavelength of light in themedium (X/2n), these fluctuations willnot produce scattering. In the cornea thischaracteristic dimension is — 2,000 A. Ap-preciable scattering can occur only if thecornea contains fluctuations in its refractiveindex which are distributed over distanceslarger than this critical dimension.

We have used these considerations toshow that a lattice arrangement is not anecessary condition for the transparency ofthe corneal stroma.1 An example of ex-treme disorganization of corneal collagenfibers is found in Bowman's layer of thestroma of the dogfish shark, Sqiialus acan-thias. Although this random array of fibersconstitutes 15 per cent of the stromal thick-ness, the dogfish cornea is transparent.2 Inthis case, transparency exists because Bow-man's zone is optically homogeneous overdistances greater than half the wavelengthof light. Similar considerations will explainthe transparency of the fiberless layers ofthe cornea—the epithelium and the endo-thelium—and of Descemet's membrane.

If we are correct, we would expect thatopaque corneas will exhibit refractive indexfluctuations of the appropriate dimensions.We have looked for regions which mightrepresent such inhomogeneities in electronmicrographs of swollen, opaque corneas.There is no certainty, of course, that thedifferences in electron density found inthin sections of fixed, embedded, andstained tissue are proportional to differ-ences in index of refraction. Nevertheless,we can confidently expect that structuralalterations such as substantial changes inthe number density of collagen fibers willproduce fluctuations in the index of refrac-tion.

To examine this hypothesis, we per-formed electron microscopic examination of8 corneal specimens (obtained at kerato-plasty) in which transparency was suffi-ciently compromised to justify the surgicalreplacement. It was anticipated that alter-ations in morphology would create fluctua-tions in refractive index over dimensionsexceeding 2,000 A. In addition, we exam-ined several corneas with retrocornealmembrane. We found that both the swollencorneas and the opaque retrocorneal mem-branes exhibited morphology compatiblewith our hypothesis.

Materials and methodsPathological human corneas were placed into

3 per cent glutaraldehyde solution, pH 7.4 (caco-dylate buffer) at room temperature. Simultaneous-ly, normal corneas (either the fellow to the donoreye or a portion of the donor cornea taken fromoutside the trephine area) were processed on eachoccasion.

After 5 or 10 minutes, the partially fixed speci-mens were cut into pieces smaller than 1 mm.2

and were returned to the glutaraldehyde for anadditional 20 minutes. The glutaraldehyde wasdecanted, and 1 per cent aqueous osmic acid wasadded to the unrinsed tissue fragments. After 30to 45 minutes in this solution, the tissue wasrapidly dehydrated with increasing concentrationsof ethanol. It was then rinsed with propyleneoxide. After infiltration with a propylene oxide-Epon 812 mixture for 2 to 15 hours, the tissuewas embedded in Epon 812 (Luft's 1:1 mixture).

Sectioning was performed with glass and dia-mond knives on an LKB Ultramicrotome, Model8802A, and mounted directly onto copper grids.

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Fig. 1. Normal superficial epithelium. The diaphanous layer on the surface into which the villous processes project may representthe tear film. Although celhilar degeneration is apparent in the superficial cell, the intercellular space (arrows) is very smalland the desmosomes (d) are intact. Endoplasmic reticulum (er) also has normal appearance. (Original magnification xl5,000.)

OlOw

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504 Goldman et ah Investigative OphthalmologyOctober 1968

Electron micrographs were made with a Phillips200 electron microscope operated at 60 kv. Kodakmedium contrast Projector Slide plates and KodakElectron Image plates were both used.

Some corneas which had been graft failuresbecause of retrocomeal membrane formation wereexamined after similar preparation.

Observations

Because there are variations in the elec-tron microscopic appearance even of nor-mal tissue processed and examined by dif-ferent investigators, we will compare thepathological tissue with our own normalcontrol ones throughout this description.

Epithelium and its basement membrane.The normal human corneal epithelium iscovered by a tear film which may berepresented by the finely particulate layerfrequently seen on electron microscopic ex-amination into which the villous processesof the superficial squamous cells project.3

This layer probably corresponds to a com-bination of the elements of the tear filmdescribed by Mishima.1 Cellular degenera-tion is evident in the superficial cells priorto desquamation, but the membranes ofthe adjacent cells are in close appositionuntil the cell peels off (Fig. 1).

Control corneas in this study were allfrom postmortem eyes from the BostonEye Bank. These eyes had been refriger-ated (4° C.) for several hours. At thistemperature, the enucleated eye developsepithelial edema quickly. There are no sig-nificant spaces between the epithelial cellsin normal human and rabbit corneas. Underexperimental conditions which bring aboutswelling, the cellular membranes separatefrom one another. The width of the inter-cellular spaces increases as the epitheliumswells.*

The epithelium was missing from someof the specimens studied. In every casewhere it was present, the outstanding struc-tural change was a distension of the inter-cellular spaces. The degree of distensionwas significantly greater in our pathologicalspecimens than in the Eye Bank controlones. These spaces were extremely perine-

°Goldman and Klyce (unpublished results).

Fig. 2. Early epithelial edema. The intercellularspaces (arrows) are moderately distended at alllevels of the epithelium. In this specimen, theepithelium rested directly on Bowman's layer (B)of the stroma. The basement membrane, whichis usually present at the junction of the epitheliumand Bowman's layer, is absent in this case. Asteriskindicates region magnified in Fig. 6. (Originalmagnification x7,280.)

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Light diffraction and scattering 505

Fig. 3. Moderate epithelial edema. The distended intercellular spaces and intact desmosomesare more striking at this higher magnification of another specimen. • i ~ \/2n —~- 2,000A. (Original magnification xl93500.)

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506 Goldman et al. Inoestigative OphthalmologyOctober 1968

Fig. 4. At a yet higher magnification of a portion of Fig. 2, the fine structure of an intactdesmosome (d) is visible keeping cells in apposition at fixed points; t = tonofibrils, r = ribo-somes, and > i = >>./2n ^ 2,000 A. (Original magnification x60,OQO.)

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Volume 7Ntnnbet 5

Light diffraction and scattering 507

able to the electron beam. Their dimensionswere frequently greater than 2,000 A. With-in these spaces, portions of retracted cellu-lar interdigitations and amorphous granularmaterial were seen. Even when the disten-sion was marked, the desmosomes appeared

to be unchanged in their fine structure(Figs. 2, 3, and 4). The tear film was pres-ent in only two of the pathological corneas.

In general, the intercellular components,including nuclei, tonofibrils, glycogen gran-ules, mitochondria, and the endoplasmic

Fig. 5. Normal junction between epithelium and Bowman's layer. Basement membrane (b) iscontinuous between basal cell above and Bowman's (B); h = hemidesmosome, t = tonofibrils,g = glycogen, and arrow = intercellular space. (Original magnification x50,000.)

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508 Goldman et al. Investigative OphthalmologyOctober 1968

reticulum, appeared normal in structureand frequency.

The usual orientation of the low colum-nar basal cells of the normal human cornealepithelium is perpendicular to the base-ment membrane and the corneal surface.In several of the pathological specimens,the anterior portions of these cells weredisplaced laterally.

In the normal cornea, the basementmembrane is continuous. It runs parallel tothe straight surface provided by the mostposterior cell membranes of the basal cellsin the central portion of the cornea. Pe-ripherally, the basement membrane followsthe more convoluted surface of the corre-sponding cellular membranes. Hemides-mosomes appear as frequent, but irregular-ly spaced, condensations on the posteriorcell membrane of the basal cells (Fig. 5).

In the swollen specimens, the basement

membrane was frequently absent or frag-mented. Hemidesmosomes were only seenwhere basement membrane was present(Figs. 6 and 7). Although bullae werevisualized in some of the preoperative eyes,no tissue separation was seen which wasthought to correspond to clinical bullae. Insome of the pathological tissue, the epithe-lium was separated from the underlyingtissue during processing. It may be that thedimensions of the bullae exceeded those ofour tissue fragments.

Pannus and Bowman's layer. Normally,Bowman's layer underlies the basementmembrane of the epithelium. This layeris about 10 to 12 p thick in the centralcornea, and consists of randomly oriented,tightly packed collagen fibers. It is acellu-lar. Posteriorly, the collagen fibers of Bow-man's layer are continuous with those ofthe anterior lamellae of the stroma. The

Fig. 6, Higher magnification of region in Fig. 2 marked by the asterisk. Basal cell, above,rests directly on Bowman's layer (B). Basement membrane and hemidesmosomes are absent.The usual columnar orientation of the basal cells is displaced laterally. Arrows indicate inter-cellular space. Double arrows indicate swollen mitochondrion which is sometimes found innormal tissue subjected to prolonged fixation, d = Desmosome. (Original magnificationx33,000.)

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Light diffraction and scattering 509

most superficial keratocytes are found inthese anterior lamellae.

In several of the pathological specimens,what is referred to histopathologically aspannus had insinuated itself between theepithelium and Bowman's layer. Therewere many projections of epithelium ex-tending into the pannus. In one case, sucha projection was very large and extendedwell below the inferior surface of thebasal cells into the pannus (Fig. 8).

The pannus is composed of irregularlydistributed collagen fibers. Large fluctua-tions in the number density of collagenfibers seem to be the primary characteristicof pannus. This is in contrast to the uni-form density of the randomly arrangedfibers of Bowman's zone (Fig. 9). Withinthe pannus, fibroblasts, polymorphonuclearleukocytes, and other wandering cells werefound. In further distinction to the tightlypacked, acellular Bowman's layer, the pan-

h

Fig. 7. Base of epithelium overlying collagen fibers of connective tissue pannus (p). Hemides-mosomes (h) appear only where basement membrane material {*) is present. Dense granules(arrows) appear in distended intercellular spaces. (Original magnification x31,000.)

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510 Goldman et at Investigative OphthalmologyOctober 1968

Fig. 8. A low magnification view of the connective tissue pannus (p) which has insinuateditself between the Bowman's layer and the slightly edematous epitheliinii. A wandering cellcontaining large amounts of endoplasmic reticulum appears in the lower left anterior to aportion of epithelium (e) which has projected into the pannus. The large fluctuations in thenumber density of the collagen fibers are apparent even at this magnification. Basementmembrane material appears intermittently at the junction of pannus and epithelium. Densegranules are present in the distended intercellular spaces. (Original magnification x83640.)

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Light diffraction and scattering 511

f

Fig. 9. Junction between pannus and intact Bowman's layer. The mature collagen fibers ofthe pannus (p) have large fluctuations in their number density. Fibroblasts (f) are seen bothwithin the pannus and in the space (*) anterior to Bowman's (B). > < = \/2n —~* 2,000A. (Original magnification x30,000.)

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512 Goldman et al. Investigative OphthalmologyOctober 1968

Fig. 10. A portion of a keratocyte between lamellae in posterior normal human cornealstroma. Dense granular material (*) fills space between cellular membrane and adjacentlamella anterior to it. (Original magnification x60,000.)

nus contained regions of various dimen-sions, many of which exceeded 2,000 A,which were devoid of mature collagenfibers. In some cases, these regions werefilled with an amorphous substance of lowelectron density. Other regions in the pan-nus contained granular or fibrillar materialwhose diameter was less than 100 A.

In several specimens, the distended in-tercellular spaces of the basal epithelialcells were filled with round structures

whose diameter was also less than 100 A.These structures were never seen in longi-tudinal section and had greater electrondensity than the comparable fibrillar struc-tures in the pannus (Figs. 7 and 8).

Bowman's layer did not undergo anystructural change which we were able todetect. The entire Bowman's layer sep-arated from the epithelium as a unit. Usu-ally there was a wide channel with onlyfragments of collagen fibers, and a some-

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Light diffraction and scattering 513

Fig. 11. A tangential section of a normal keratocyte. Very fine fibrils extend from the cellularmembrane. The mature collagen fibers are not closely applied to the cell in this plane.(Original magnification x40,000.)

what continuous layer of cells of the fibro-blast series between the anterior border ofthe Bowman's layer and the pannus (Fig.9).

Stroma. The anterior third of the normalcentral human corneal stroma contains in-terwoven bundles of collagen fibers whosenumber density is less than that of thefibers in the posterior stroma. In this an-terior portion, it is not unusual to findkeratocytes within as well as between thelamellae. Posteriorly, the more tightlypacked collagen fibers are also more reg-ularly organized into lamellae. Here, thekeratocytes are almost exclusively foundbetween lamellae.

The lamellae in the posterior portion ofthe cornea behave as a structural unitwhose anterior and posterior boundariesdo not always conform rigorously to theundulating cell membranes of the kerato-

cytes. In meridional section, the centralportion of the keratocyte, which containsthe nucleus, is much thicker than the pe-ripheral extensions of the cells, the pro-cesses. The collagen fibers are alwaysclosely applied to the cell membrane in thecentral portion. This application of fibersis usually found in the vicinity of the pro-cesses as well, but occasionally moderatelylarge spaces may be seen between the cellboundaries and the mature collagen fibersof the lamella near the peripheral portionsof the normal keratocyte. Within thesespaces, a rather dense granular material isfrequently distinguishable (Fig. 10). Fi-brillar concentrations extend peripherallyfrom the processes. These are particularlywell seen in tangential sections of normalkeratocyte processes. They seem to extendfrom the cellular membranes. In this hori-zontal plane, the mature collagen fibers are

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514 Goldman et at Investigative OphthalmologyOctober 1968

Fig. 12. Low magnification of normal and swollen corneal stroma. A, Normal central stroma;k = keratocyte. (Original magnification xl9,000.) Interruptions in the collagen pattern ofthis specimen (single arrows) occur in senescence, and are easily distinguishable from theaggregates of lakes (double arrows) found in B, swollen central stroma. (Original magnifica-tion x20,000.) • i = ^/2n —-2,000 A.

seldom closely applied to the cell. The fi-brillar extensions from the keratocyte pro-cesses were first described by Kuwabara*(Fig. 11).

In swollen corneas, we observed markedirregularities in the number density of col-lagen fibers both within and between la-mellae. Those irregularities within thelamellae took the form of lakes withinwhich no mature collagen fibers were ap-parent. In the least swollen corneas, the

•Kuwnbara, T. (unpublished results).

lakes were small (—1,500 to 2;000 A) andisolated. In more advanced states of swell-ing, the lakes increased in size, and clus-tered together to form aggregates (Figs.12 and 13).

The keratocyte processes were retractedin the swollen corneas. There was no evi-dence of the fibrillar material extendingfrom their processes. Granular material orno material at all was frequently found inthe wide interlamellar spaces. The colla-gen lamellae were separated even from thethick central portions of the keratocytes.The anteroposterior dimension of the la-

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Light diffraction and scattering 515

iFig. 13. Advanced, chronic stromal edema. A, Disorganized collagen with fluctuations in thenumber density of their fibers. • i = h/2n —. 2,000 A. The two cells in the superiorportion of the photograph are probably keratocytes. (Original magnification x30,000.) B,Another specimen of advanced stromal edema demonstrating the lamellar separations whichmust contribute strongly to opacity. Invading cells appear in the lamellar interspaces.> i = \/2n ^ 2,000 A. (Original magnification xl6,000.)

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516 Goldman et al. Investigative OphthalmologyOctober 1968

Fig. 14. A fixed fold of Descemet's membrane in a chronically swollen cornea with retro-corneal membrane. Fluctuations in the number density of collagen fibers are apparent bothanterior ( *) and posterior (* *) to Descemet's (D). The cells posterior to Descemet's are poly-morphonuclear leukocytes. Rectangle indicates region depicted in Fig. 15. (Original magnifi-cation x3,600.)

mellar separations varied; the lamellaetook on an undulating appearance. Inva-sion of polymorphonuclear leukocytes andwandering cells occurred through thesewidened spaces (Fig. 13).

Descemet's membrane and endothelium.The normal structure of Descemet's mem-brane and the warty excrescences whichappear on it with aging have been ade-quately described by others.0' " These de-scriptions are consistent with our own find-ings. Several, of the pathological corneashad fixed folds of Descemet's membrane.In connection with this folding, we foundtissue spaces both anterior and posteriorto the membrane. These veiy large spaceswere virtually fiberless, and would there-fore reflect and refract light according togeometrical optics and in so doing willreduce transparency. None of the patho-logical specimens included in our studycontained endothelium (Fig. 14).

Retrocorneal membrane. In addition tothe 8 corneas examined, we studied severalwhich had undergone previous kerato-plasty which had failed because of theformation of a connective tissue membraneposterior to the cornea. In each of thesecases, the endothelium. was absent. A morecomplete description of retrocorneal mem-branes will be published. For our presentpurposes, it is sufficient to observe thatthere were very substantial fluctuations inthe collagen fiber number density overdistances (d) larger than the light wave-length, X. This is what we would expectto be the condition since the retrocornealmembrane is opaque (Fig. 15).

Discussion

In undertaking this electron microscopicstudy of swollen human corneas with im-paired transparency, it was our purpose toexamine the hypothesis that appreciable

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Light diffraction and scattering 517

Fig. 15. Higher magnification of retrocorneal membrane posterior to fixed fold in Descemet'smembrane seen in Fig. 14. At this magnification, the fluctuations in collagen fiber numberdensity are striking. > i — \/2n ^ 2,000 A. (Original magnification xl9,000.)

light scattering occurs when the corneacontains fluctuations in its refractive indexwhich are distributed over distances (d)which are larger than one half the wave-length of light (X/2n). In the cornea, thecritical value for d is <~^ 2,000 A.

We have mentioned previously thatthere is no certainty that differences inelectron density are strictly proportionalto differences in the index of refraction ofthe tissue components. It is, however, quitereasonable to assume that a region of thestroma which is devoid of fibers has a dif-ferent refractive index than one in whichmany collagen fibers are present. It is alsoreasonable to assume that the edema fluidwhich fills the intercellular spaces of theswollen epithelium differs in index of re-

fraction from the material within the cell.Under this assumption, we have studiedswollen corneas to see whether they pos-sess structural alterations with dimensionslarger than A/2n (—> 2,000 A). Our photo-graphs show that such alterations do occurin the stroma, pannus, and retrocornealmembrane, and in the intercellular spacesof the epithelium.

Our criterion for the required size of thescattering fluctuations in the index of re-fraction within the cornea is based on thefollowing considerations: As the light wavepasses through the cornea, scattering isproduced by even the smallest of its con-stituents. To calculate the total intensityof the scattered light, one must first calcu-late the sum of the scattered fields, includ-

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518 Goldman et ah Investigative OphthalmologyOctober 1968

ing the phases of each of the scattered sec-ondary wavelets. The summation will pro-duce a zero net scattered field if the scat-tering particles are spaced by distancesthat are small compared with the wave-length of the incident light.

Maurice, in his treatise on corneal trans-parency, recognized the importance of therelative phases of the secondary waveletsin producing a destructive interference.He was able to make an explicit calcula-tion of this destructive interference in thespecial case in which the collagen fiberswere arranged with perfect regularity. Theperfect regularity of collagen fibers inMaurice's description essentially producesa medium whose index of refraction ishomogeneous over dimensions comparableto the wavelength of light.

The term "homogeneity" has meaningonly when the scale of the region studiedis specified. On a small enough scale, nomedium is homogeneous, since it is madeup of atoms and molecules. Nevertheless,we do not hesitate to treat normal aqueoushumor, for example, as a homogeneous me-dium. We know that aqueous humor con-tains electrolytes, proteins, and water mole-cules, yet we treat this medium as if itwere homogeneous. We can do this be-cause the spacing between these units isvery small compared with the wavelengthof light. The scale which is relevant to thequestion of light scattering by assemblagesof small particles is the wavelength oflight, A. When the scattering particles arespaced by distances that are small com-pared with A, their scattered wavelets willinterfere destructively even if they areirregularly arranged. This has been pointedout with special reference to the Bowman'szone of the shark.

The present approach to transparencywhich focuses attention on optical homo-geneity over distances (d) larger or smallerthan A/2n provides a more comprehensiveapproach in that it is useful in the explana-tion of the transparency and scattering inthe areas of the cornea which are not com-posed of mature collagen fibers (i.e., epi-

thelium, Descemet's membrane, kerato-cytes, and endothelium).

The question now arises as to how weexplain the opacity of the swollen cornea.In the swollen stroma, we observed bothindividual and aggregates of "lakes" inwhich no mature collagen fibers were pres-ent. These lakes were generally larger thanA/2n. They would scatter light effectively.This is explainable either by treating eachof them as an individual scatterer whosescattering power is roughly proportionalto the square of its volume or by recogniz-ing that assemblages of these lakes repre-sent fluctuations in the optical homoge-neity whose dimensions are of such magni-tude as to satisfy the condition of Braggreflection.* Similar considerations apply tothe rapid appearance of distended inter-cellular spaces in early epithelial swelling.

When the dimensions of the refractiveindex fluctuations are very large (—10 /x),the laws of refraction and reflection applyand geometrical optics is appropriate.Thus, when the interlamellar spaces in thestroma or the intercellular epithelial spacesbecome as large as •—' 50,000 A (5 fx), theyact like an assemblage of partially reflect-ing surfaces which, in the epithelium par-ticularly, appear to be arranged at arbi-trary angles relative to the incident light.This multitude of reflections will substan-tially reduce transparency.

In connection with scattering in the epi-thelium, we would like to note the per-sistence of the epithelial desmosomes inthe face of marked distension of the inter-cellular spaces. The desmosomes appear toserve as binding sites which tend to main-tain the approximation of the cell mem-branes of adjacent cells. The spaces appearwith even small amounts of epithelialswelling, and seemingly serve as a reservoirof considerable capacity for edema fluid.From the structural point of view, onewould anticipate that, as long as desmo-somal integrity is maintained, epithelial

°In a subsequent publication, one of us (G. B. B.) willapply the principles of Bragg reflection (which is centralto the theory of x-ray diffraction) to the problem of lightscattering in the cornea.

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edema is reversible. The clinical reversi-bility of epithelial edema is consistent withthis interpretation.

The altered structure of the posteriorepithelial border was also of clinical inter-est. In all of the pathological specimens,the basement membrane, which was nor-mally continuous and punctuated with theirregular placement of hemidesmosomes,was either fragmentary or absent overlarge segments. Hemidesmosomes werefound only where basement membrane waspresent. We have found this abnormalityin a case of recurrent epithelial erosion ina human being.* The relationship betweenthe adhesiveness of the epithelium andthe presence of basement membrane hasbeen recently demonstrated experimen-tally.8 The ease with which the epitheliumis lifted from its bed in bullous keratopathyis probably a reflection of the basementmembrane deficiency.

REFERENCES1. Maurice, D. M.: The structure and transpar-

ency of the cornea, J. Physiol. 136: 263, 1957.2. Goldman, J. N., and Benedek, G. B.: The re-

lationship between morphology and transparen-cy in the nonswelling corneal stroma of theshark, INVEST. OPHTH. 6: 574, 1967.

3. Bliimcke, S., and Morganroth, K., Jr.: Thestereo ultrastructure of the external and in-ternal surface of the cornea, J. Ultrastruct.Res. 18: 502, 1967.

4. Mishima, S.: Some physiological aspects of theprecorneal tearfilm, Arch. Ophth. 73: 233,1965.

5. Kayes, J., and Holmberg, A.: The fine struc-ture of the cornea in Fuch's endothelial dys-trophy, INVEST. OPHTH. 3: 47, 1964.

6. Jakus, M.: Further observations on the finestructure of the cornea, INVEST. OPHTH. 1:202, 1962.

7. Duke-Elder, S.: System of ophthalmology,The eye in evolution, Vol. 1, St. Louis, 1958,The C. V. Mosby Company.

8. Khodadoust, A. A., Silverstein, A. M., Kenyon,K. R., and Dowling, J. E.: Adhesion of regen-erating corneal epithelium—The role of base-ment membrane, Am. J. Ophth. 65: 339, 1968.

"Goldman, Dohlman, and Kravitt, to be published.