JOURNAL
OF U L T R A S T R U C T U R E
RESEARCH
61, 100-114 (1977)
Striations of Light Scattering in the Corneal Stroma BETTY GALLAGHER AND DAVID MAURICE Division of Ophthalmology, Stanford University Medical Center, Stanford, California 94305 Received April 8, 1977 When the rabbit cornea is stressed in various ways, light focused on the stroma is scattered back in the form of striations. Light and electron microscopy reveal t h a t the striations correspond to a waveform assumed by the collagen fibrils in the stroma when the tension on them is relaxed. The waves act as reflectors for the light, which is a consequence of the light-scattering properties of the fibrils themselves, rather than a result of interfaces opening up between the lamellae.
The transparency of the corneal stroma is generally agreed to result from the regular arrangement of the collagen fibrils which leads to the destructive interference of the light they individually scatter (17). It is not certain how strict this regularity must be in order to obtain the observed degree of clarity, and what must be the nature and extent of the disorganization required to produce the clouding that is observed when the tissue is swollen or stressed. Several theoretical studies of the problem have been published (1, 8, 10, 25), but the choice among the models proposed will most probably depend on experimental determinations of the angular and wavelength dependence of the light scattering of the collagenous lamellae. These determinations are not easy to make without ambiguity, for it is evident from observation of the cornea in the slit-lamp microscope that much of the light scattering takes place from numerous discrete points which can be identified as the stromal keratocytes. Attempts in this laboratory to make scattering measurements on microscopic elements of tissue between the keratocytes led to results for which no ready interpretation could be provided and made it necessary to examine the distribution of scattered light on the microscopic scale in more detail. To this end an instrument named the scanning slit microscope (SSM) was devel-
oped, whose construction has been described elsewhere (20). This instrument allows photographs to be made of optical sections through the tissue by what is effectively dark field microscopy. These photographs reveal that under many conditions light is scattered from the stroma in the form of striations. More often than not, the striations are doubled t o give a tramline effect. This paper shows these striations to be related to the formation of waves in the stromal lamellae when the normal tension on them is relaxed. An optical explanation of the appearance of the striations in the SSM is derived out on the basis of the angular distribution of the light scattered from individual fibrils. MATERIALS AND METHODS The SSM works on the principle of focusing a very narrow illuminated slit through one-half of a 40 x water-immersion objective while recording on film the light returned by scattering or reflection up the other half of the objective. The film is placed behind an identical parfocal slit mounted in the eyepiece plane. The specimen is gradually displaced through the image of the slit, and the film is moved at a corresponding speed in the opposite direction so t h a t the image formed on it remains in register. In this way an optical section only a few microns thick is reproduced on the film. New Zealand White rabbits were killed, and the eyes were enucleated after their orientation in the orbit was marked. In some cases the enucleated intact eye was glued to a metal ring behind the
100 Copyright © 1977by Academic Press, Inc. All rights of reproduction in any form reserved.
ISSN 0022-5320
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STRIATIONS IN CORNEA equator with cyanoacrylate cement (Eastman 910). The weighted globe was then immersed in saline or silicone oil at room temperature. Intraocular pressure (IOP) was regulated by means of an elevated saline-filled reservoir connected through a 20-gauge needle into the posterior vitreous humor; preliminary experiments had shown that a needle inserted near the corneal limbus was itself sufficient to cause the appearance of striations. In other cases the cornea was excised and mounted in a chamber so as to avoid distortion of the tissue and to distend it to its proper shape under the normal IOP (5). Various corneal preparations were examined: normal, swollen, under reduced intraocular pressure, with a cut in the stroma, and with a needle penetrating just outside the limbus. Corneas were made to swell by refrigerating the intact eye, by scraping away the epithelial cell layers and placing saline on the bare stromal surface, or by bathing its posterior surface with 0.133 M NaHCO3. The corneas were swollen to between 150 and 200% of their original thickness as measured by the fine focus control of the microscope (5). To demonstrate the relationship between fibril relaxation and striations, cuts approximately 200 t~m deep were made near the center of the cornea in the intact globe by means of a razor blade fitted with a guard, and were either parallel or perpendicular to the superior-inferior axis. Initially, observations were made under saline. Local edema complicated interpretation, and in subsequent experiments the tissue was covered with silicone oil during scanning slit microscopy. The stromas were photographed with the SSM near the apex of the tissue unless otherwise noted. They were then prepared for electron microscopy. The fixative consisted of 1% glutaraldehyde-0,3% formaldehyde in a NaHCO3 or PO4 buffer at pH 7.4. Each was adjusted to be isotonic or slightly hypotonic to blood. This was applied to both surfaces of the cornea except when the anterior surface had been cut and covered with oil, in which case fixative was applied only to the posterior surface. The thickness of the cornea was checked after fixation and in 13 cases was 0.97 _+ 0.1 of its fresh value. Specimens were postfixed in osmium, stained en bloc with uranyl acetate (13), and embedded in Epon-Araldite. Specimens were cut on a Porter Blum MT-2 ultramicrotome and stained with 0.5% phosphotungstic acid. Thin sections parallel to the surface were prepared by trimming to the center of the concentric circles which appear in the block face on cutting tangentially into the cornea. Sections were viewed and photographed in a Philips 200 electron microscope calibrated with Dow latex particles. Thick sections for light microscopy (LM), either cross or tangential, were cut from the same block a n d stained with basic fuchsin and methylene blue (12).
RESULTS
Normal Cornea The general appearance of the mammalian stroma both in the light and electron microscopes is described in many texts (7, 11, 18), but it is convenient to recall some salient features at this point. The tissue is built up by the supraposition of ribbomlike lamellae, each about 2 t~m thick, which run from limbus to limbus. When a fresh rabbit cornea is fixed under normal intraocular pressure, the lamellae are generally seen in cross section as almost smooth arcs, both by LM and low power electron microscopy (EM) (Figs. 1 and 2). However, undulations of low amplitude can be distinguished, particularly in the posterior cornea. The lamellae do not interweave except possibly in the anterior layers, which are less well organized. Each lamella is made up of uniform collagen fibrils about 30 nm in diameter and 60 nm between centers. The fibrils in a lamella run parallel to each other and to its surface, but in adjacent lamellae they make large angles with each other. A cross section of the cornea will occasionally cut through a lamella in the direction of the fibrils and include lengths of them within it. Generally, the slice will cut across the fibrils, and they will appear in the EM as circles, ellipses, or linear segments according to the angle of the section. In sections cut parallel to the surface, the central lamellae are seen in the electron micrographs to be formed by sheets of straight, parallel fibrils whose appearance suggests an absence of appreciable waving. The junction between two lamellae is recognized as an abrupt change in direction of the collagen fibrils (Fig. 3). The image of the undisturbed stroma as seen by the SSM is a dark background against which fibroblast nuclei and nerves and other linear structures of uncertain nature, possibly cell processes or elastic fibers, appear as light-scattering elements
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(Fig. 4). Striations are not seen in photographs made from such tissue.
Striations When the organization of the stroma is disturbed, parallel white lines against a dark background are recorded by the SSM, which commonly appear as tramlines (Fig. 5). The periodicity, defined as the distance between alternate lines whether tramlines were present or not, ranged from 8 to 15 t~m. The striations show no marked preference in their orientation with respect to the superior-inferior axis of the eye. When a cornea is rotated about the optical axis, the striations change direction by a corresponding angle, but their general appearance does not alter. When the SSM is focused down between photographs in order to produce serial optical sections, the pattern of striations is found to be constant over a considerable depth (Fig. 6). On either side of this range the pattern becomes unrecognizable, and the direction of the striations may undergo a large rotation.
Waves Scanning electron microscopy (SEM) of an isolated cornea shattered while frozen reveals the interface of a lamella to be a corrugated sheet (Fig. 7). In histological sections prepared as is customary from eyes fixed in the absence of intraocular pressure, the many lamellae are seen to be wavy in outline. Others have a banded appearance as if they were rippling in and out of the section. The form of the waves can be made out more clearly in low power electron micrographs where the individual
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collagen fibrils can be distinguished. In cross sections, the fibrils occasionally lie flat in the plane of the section, but more generally the section cuts across them, giving rise to alternating bands of segments of different lengths. In many places the plane of the waves appears to be perpendicular to the section, and the surfaces of the lamellae may be free of undulations. On other occasions fluctuations in the thickness of a lamella occur, and its two surfaces may form waves which are partially or completely out of phase with one another. In general, however, the wave peaks remain in phase over depths of several microns (Fig. 8). The appearance of the fibrils in tangential sections is consistent with that in cross sections. Bands of linear segments are separated by circular segments of collagen fibrils, as one would expect from waves of collagen fibrils running together in phase (Fig. 9). Occasionally, where the waves are parallel to the surface, they lie within the section, and long continuous lengths of the fibrils can be seen. Although the fibrils tend to form planar waves, the patterns of the segments are frequently irregular. We sought for helical wave forms by comparing angles between linear segments from adjacent bands. Helical patterns did not appear to be maintained over any number of wavelengths, however. This corresponds to the results in tendon (4, 23), where the waves were found to be planar. In the following sections, the appearance of the waves will be compared to t h a t of the striations in each of the disturbed states of the cornea.
FIG. 1. Light micrograph (LM) of rabbit cornea fixed under normal intraocular pressure. Lamellae approximate to smooth arcs. Fro. 2. Electron micrograph (EM) of rabbit cornea in cross section fixed under normal intraocular pressure, Within each 'lamella, the collagen fibrils have a uniform appearance indicating an absence of appreciable waving in and out of the section. Fro. 3. EM of a tangential section of the normal cornea. An underlying lamella is seen as an area whose fibrils make large angles with those of the sheet above it.
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FIG. 4. Scanning specular micrograph (SSM) of the normal stroma. The fibroblast nuclei appear bright against a dark background. FIG. 5. SSM of a cornea stressed by a needle. Striations appear as tramlines superimposed on the image of the normal stroma.
FIG. 6. A series of SSM sections at different levels. The pattern of striations persists although the focus passes through cellular elementsl FIG. 7. Scanning electron micrograph of a freeze-fractured cornea. The split passes between the waves in the lamellar surface. Fibers running at different orientations conform to the corrugations. FIG. 8. EM cross section of swollen cornea. Waves are in phase through many lamellae. 105
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Swollen Cornea Scanning slit microscopy of swollen corneas commonly reveals regular striations in the posterior cornea (Fig. 10). Often, however, t h e light scattered from the anterior regions of the cornea reduces the contrast to such an extent that they are not visible. Photographs of striations in the anterior layers of the swollen stroma have never been obtained. Light microscope observations of swollen corneas in cross section always show lamellar waves, beginning with waves of small amplitude in the middle stroma which become more pronounced towards the posterior surface (Fig. 11). By EM, collagen fibrils in the posterior layers can be seen as waves in the plane of the section (Fig. 8) as well as oblique to that plane (Fig. 12). Waves are not seen near the anterior surface. Thin sections of the posterior cornea parallel to the surface usually show the bands of linear segments typifying fibrils which wave in and out of the section. On occasion, the plane of the wave corresponds to that of the section so that entire fibrillar waves are seen.
Low Intraocular Pressure When the intraocular pressure is lowered behind corneas of normal thickness, striations of a very irregular pattern can be seen in the SSM across the entire thickness (Fig. 13). The lamellae are noticeably wavy at all levels of the stroma when it is examined by LM or low power EM.
Cut Cornea Corneas with superficial cuts show linear striations in the anterior layers simi-
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lar in appearance to those in Fig. 5. The striations are always parallel to the cut and more distinct near it. Cross sections of these corneas show the uncut lamellae to be straight and the cut lamellae to be wavy (Fig. 14). The lamella at the interface shows great disorganization, presumably because of the considerable shear in this plane. The waves become less pronounced with distance from the cut. In tangential sections examined in the electron microscope the bands that correspond to the wave fronts are parallel to the cut; that is, they take the same direction as the striations seen in the SSM.
Needle Eyes in which a needle has been inserted at the limbus show striations in the SSM with particular clarity. These, when viewed at the apex, are directed towards the point of insertion. In the electron microscope the direction of the striations and of the bands seen in tangential sections is the same.
Periodicity A comparison was made between the periodicity of the striations photographed by the SSM and of the waves seen in electron micrographs (Table I). For the latter measurement, sections parallel to the surface were used, because here the axis of the fibril wave lies in the plane of the section. This is rarely true of cross sections, in which the measured wavelength would generally be longer than the true wavelength. The periodicity of the striations has already been defined. In the case of the electron micrographs one period was
FIG. 9. T a n g e n t i a l E M o f s w o l l e n c o r n e a . The collagen fibrils in a single lamella wave in and out through the section, forming bands composed of linear segments (cf. Fig. 3). FIG. 10. SSM of swollen cornea. Striations appear whose pattern is less regular than that caused by stress (cf. Fig. 5). The cellular elements appear to have increased in area, probably because the cytoplasm is scattering light. FIG. 11. LM of swollen cornea. The anterior layers are free of waves, but in the deeper stroma waves are found whose amplitude increases towards the rear surface (cf. Fig. 1).
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FIG. 12. EM cross section of swollen cornea in posterior layers. The presence of s e g m e n t s of different l e n g t h s within one l a m e l l a shows t h a t fibrils are forming waves oblique to the section. FIG. 13. S S M o f n o r m a l c o r n e a u n d e r l o w i n t r a o c u l a r p r e s s u r e . Striations form a very i r r e g u l a r pattern. FIG. 14. Anterior cut in cornea. The cut surface (arrow) retracts, t h r o w i n g t h e lamellae into waves of large amplitude. The u n c u t lamellae are smooth as in t h e n o r m a l cornea. 108
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S T R I A T I O N S IN C O R N E A TABLE I
PERIODICITIES OF STRIATIONS SEEN IN SCANNING SPECULAR MICROSCOPE AND WAVES SEEN IN ELECTRON MICROSCOPE UNDER VARIOUS CONDITIONS
Periodicity (tLm) -+ SD S c a n n i n g s p e c u l a r microscope
E l e c t r o n microscope
Swollen c o r n e a s 14.2 -+ 0.5 (12) a {4}° Cut corneas 9.8 ± 1.9 (42) {14} Needle 12.0 + 1.9 (15) {5}
15.2 -+ 3.0 (38) {3} 11.5 _+ 3.8 (26) {3} 12.8 ± 1.9 (4) {1}
a N u m b e r of m e a s u r e m e n t s . N u m b e r of corneas.
defined as the distance between alternate bands of linear segments of collagen. Cut corneas give a shorter spacing b y both methods, probably as a result of the larger amplitude of the waves in this condition. In can be seen that the two methods give similar values for the wavelength. DISCUSSION
Waves and Striations In every experimental situation detailed above, there is a close relationship between the appearance of the striations in the SSM and the form of the waves as seen in the light and electron microscopes. The direction of striations corresponds to the direction of the wave fronts observed in the electron microscope. There is good agreement in periodicity between striations and waves. Striations are not recorded when the waves are too flat to be easily made out in electron micrographs.
Waves and Relaxation Rat tail tendon observed under polarized light shows a system of light and dark bands which result from a release of tension on the formation of waves in the collagen fibers (23). Although the periodicity of these bands, 300 t~m, clearly separates them from the striations seen in the cornea, the results of the present study are compatible with the view that corneal striations also result from a release of tension in the stroma. Normally, the intraocular pressure stretches the fibrils into nearly wave-free circular arcs. Any relaxation of the fibril tension permits waves to
be developed in the lamellae. Thus, when the intraocular pressure is dropped to a very low level, all lamellae are released and waves are generated in an irregular pattern through the thickness of the tissue.
A superficial incision in the cornea relaxes the tension only in the cut lamellae, and, correspondingly, waves and striations are noted only in these layers. Corneas submerged in oil and in saline give the same result, demonstrating that it is not the introduction of saline through the cut into the stroma which causes the waves, but relaxation alone. In swollen corneas waves appear only in the posterior levels. Presumably this is because the fibrils are virtually inextensible so that the tissue is forced to swell inward. This causes relaxation in the posterior lamellae, while the strain is taken up by the anterior ones. The arrangement of the waves in the normal cornea stressed by a needle may be considered analogous to the puckering that can be seen around the point where an inflated plastic bag is indented with a finger. The weight of the needle pulls on fibrils running through the point of insertion and eases those which cross them. Wave fronts always line up perpendicular to the relaxed fibrils and therefore follow the direction of greater tension. Striations are not evident in the cornea of normal thickness under normal IOP. This indicates that the tension is such t h a t none of the lamellae are relaxed enough to form significant waves. The tension in the
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cornea appears, therefore, to be distributed throughout all the layers of the stroma and not restricted to one or the other surface, as has been suggested by Goldmann and Schmidt (9).
Quantitative Aspects of Swelling If a fully extended fibril relaxes to a sine wave of wavelength h and amplitude a, its fractional reduction in length can be approximated by (rra/h)2 (see Appendix). In the posterior lamellae of corneas swollen to approximately double their normal thickness, a was measured to be of the order of 1 tLm while ~ was 14 t~m. Accordingly, the fibrils should be about 5% shorter than their fully extended length. The shortening t h a t should occur if the stroma swelled inward from a fully stretched layer on the anterior surface can be determined by geometrical considerations. Two alternative swelling modes can be envisaged. In the first, the cornea is assumed to expand inward uniformly from limbus to center. In this case the shortening of the posterior fibrils is given by the ratio of the change in thickness to the radius of curvature. For an expansion of 350 tLm in a cornea of 7-mm radius of curvature, the fibrils will be shortened by 4.5%. If, on the other hand, it is supposed t h a t the inward expansion of the cornea is prevented at the limbus, only the center will move inward, increasing the radius of curvature. Using 13 mm as the diameter of the corneal segment, the change in arc length is calculated to be 3%. Given the uncertainty of the measurements, these results are compatible with the estimate arrived at from the amplitude of the waves.
Packing In the normal cornea the lamellae lie closely on top of one another so that no spaces exist between them. When the tension on the lamellae is released, they are thrown into waves, and problems in pack: ing arise t h a t require consideration. Ob-
servations on single isolated lamellae suggest t h a t the natural relaxed form is t h a t of a corrugated sheet (18) with the corrugations perpendicular to the direction of the collagen fibrils. In the intact cornea, lamellae generally do not adopt this form when relaxed, since in adjacent lamellae the fibrils make large angles with one another and grooves devoid of fibrils would appear between every wave peak. Such spaces are not observed in the electron microscope. Indeed, at the greatest swelling we studied, twice normal thickness, the lamellae do not separate from one another, nor is there a frequent appearance of collagen-free volumes which could correspond to the lakes whose existence has been proposed by Benedek (1) to account for the clouding of the tissue. It is evident, therefore, that some distortion of the natural shape of the lamellae must occur to account for their continued close packing in swollen corneas. Furthermore, since the waves remain in register over several lamellae, it is difficult to see how each set of fibrils can maintain its natural wavelength as it runs at a different angle across the wave pattern. We could not find a complete solution to this problem. When the direction of the undulations undergoes a change, the problem arises more acutely. It is probable that in intermediate lamellae the fibril waves lie in a plane which is parallel to the corneal surface, resulting in a smooth lamellar face. Regular thickening and thinning of a lamella provides further opportunities for its fibrils to redistribute themselves into potentially collagen-free volumes. Local changes in stress could produce changes in amplitude and therefore wavelength t h a t could further help the lamellae accommodate to one another. Finally, the frequent irregularity of the path followed by the fibrils was already noted.
Stress-Strain Relationship It has been suggested that both in the eye (7) and in tendon (23), the waviness of
STRIATIONS IN CORNEA the collagen fibrils is an elastic system which absorbs sudden stresses which might otherwise rupture them. The relationship between tension and extension in an elastic rod bent in the form of a sine wave has been treated theoretically by Comninou and Yannas (3), and more simply by Maurice (21), who has shown experimentally that the rabbit cornea obeys the derived equation:
T \ZU _I]
-1
where T is the tension in the cornea, l represents the length of the fibril, and lo and l~ are its values in the unstressed and fully extended states. These measurements indicate that the fibrils in a totally relaxed state should have an amplitude a of 1.2 t~m. When the intraocular pressure is raised to 5 cm H20, they should be 60% of their way to total extension and a should be 0.8 t~m, and when the intraocular pressure is 20 cm H20 the corresponding figures are 90% and 0.4 tLm. Amplitude measurements from electron micrographs can be made on cross sections in places where it appears that the fibrils lie in the plane of the section. The variability is great, but from 45 measurements of a cornea fixed at an IOP of 5 cm the mean value of a is 0.7 _+ 0.3 tLm. In the paired cornea at an IOP of 20 cm the mean value of a was 0.2 _+ 0.1 t~m. It was observed (21) that though the elasticity due to waviness is a feature of the rabbit's cornea it is absent in the rabbit sclera and over the whole fibrous tunic of the human eye. Its role as an absorber of shock may perhaps not be so important as appeared previously.
Optical Basis of Striations When this problem was first considered, two explanations based on the lamellar organization presented themselves, but they can readily be disposed of. In the first, it was proposed that only
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one lamella out of very few would scatter light. Striations would be caused by the intersection of the focal plane of the SSM with this lamella, and tramlines would result from the intersections becoming closer near the peaks of the waves. Apart from the difficulty of explaining why occasional lamellae should scatter more strongly than others, this hypothesis would not be consistent with the persistence of the pattern of tramlines at different depths of focus. The second explanation is that light is reflected back from the interlamellar interspaces at the peaks and troughs of the waves; here tramlines would be an effect of parallax. However, there is nothing in the structure of the interface as shown by the electron microscope to account for such reflections. Furthermore, since the thickness of the optical section is about 4 ~m, comparable to that of the lamellae, there should be considerable areas over which it does not intersect interlamellar boundaries at their peaks, and striations should not be present. On making the optical section thicker by widening the slits, fresh boundaries should be included and the striations should become more frequent; this is not seen to happen. A true explanation of the striations appears to lie in the scattering properties of the fibrils themselves. A thin, straight rod, long compared to the wavelength of light, will scatter incident coherent light in a conical distribution, where the apical angle of the cone is equal to that of the incident light upon the rod (Fig. 15). An array of parallel rods should give rise to a similar distribution of light, although the intensity around the conical shell may undergo variations as a result of the interference of the components scattered by the individual rods in the array. Under the specular microscope the array should appear bright only when the cone of scattered light happens to strike the half of the objective which is used for observation (Fig. 16). Geometrical considerations show
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SCATTERED LIGHT
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they run at an angle to this plane, tramlines are to be expected (Fig. 18b). Further tilting of the tissue should lead to single striations of double the normal periodicity, and then to their disappearance. This was tested by photographing striations in a stressed cornea at the apex and at several millimeters before and beyond it, so that the natural curvature of the tissue provided the necessary angle. This showed the predicted features: Near the apex the
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that this will only occur when the rods lie in a plane perpendicular to the optical axis of the microscope (Fig. 17). They should therefore appear bright in the SSM only where the lamellae run perpendicular to its axis. To a first approximation the collagen fibrils of the cornea may be considered straight rods, since the wavelength of their undulations is large compared to the wavelength of light. It may be emphasized that though the light behaves as if it were reflected from the tissue, this is not the case, but is a result of scattering from within the thickness of the lamellae. When the waves run in the focal plane of the microscope, the tendency will be to form uniform striations (Fig. 18a), but if
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FIG. 17. Fibrils continue to scatter light into the objective when rotated in the focal plane. FIG. 18. The pattern of scattered light depends upon the angle which the waves make with the optical axis. (a) A wave lying in the focal plane produces striations of uniform periodicity. (b) Tilting of the wave causes the striations to form tramlines.
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Fro. 19. A cornea photographed at different angles to the fibrillar waves. At the apex, the striations are nearly uniform, at 9° tramlines predominate and at 21° the striations become less distinct and more separated.
striations tended to be regular, at moderate tilts tramlines developed, and a less distinct, larger periodicity showed up as the angle increased (Fig. 19). If this is the correct explanation for the formation of the striations, the normal cornea should scatter more light into the SSM at the apex, where the fibrils all run parallel to the surface, than towards the periphery, where they are tilted. This was checked experimentally using a photometer in the eyepiece of an instrument which was provided with an automatic vertical scan (15). The tracings showed that the scattered light intensity from a freshly enucleated eye maintained at normal IOP was about five times greater at the apex than near the periphery. The ratio is prevented from being higher because much of the light comes from the nuclei and other structures which may not scatter in a specular fashion (Fig. 4).
Previous Observations Observations of whole thickness corneas in transmitted or reflected polarized light (22) or by phase microscopy (18) show networks or lines corresponding in periodicity to the striations described in the present article. Kikkawa (14) claims that optical diffraction figures are obtained from isolated rabbit cornea which correspond to a diffraction grating spacing of 13-15 t~m. Apart from this, regular optical inhomogeneities of unspecified periodicity have been observed by the slit lamp in the intact eyes of humans and animals under a variety of normal and pathological circumstances (16, 18, 22, 26, 28) which may correspond to the striations under consideration. It is worthy of recall that Vogt noted and photographed the tramline patterns similar to those we have described, both from within the stroma and from its posterior surface (26). He explained these
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as a result of reflection, which is true in the latter case, but missed the correct explanation in the former. Apart from these regular patterns, there are reports of more widely spaced striae in the human cornea, either normally (2, 24), or after contact lens wear (2 7). These cannot correspond to the regular lamellar waves seen in rabbit corneas, although it is possible they may appear as a result of light scattering from occasional folds in a lamellae. Halos around lights corresponding to a 15-~m spacing have been described (19), which could result from the waves in the stroma. These halos are, however, less prominent than those which are generally noticed and that correspond to a 9-t~m spacing arising from the epithelial cells of the cornea (6). Although the presence of striations causes no major subjective visual effects, their presence should be borne in mind in interpreting light-scattering measurements, which are often used in order to gain insight into the relationship between corneal structure and transparency. Similarly, caution should be exercised in ignoring the contribution of the cells and other formed structures in the stroma to the scattered light. This work was supported by NIH Grant EY 00431. APPENDIX
Derivation of Extended Length of Sine Wave Consider a fiber of inextensible material bent into a wave: 27TX
y = a sin-
If d s is length of an infinitesimal element
of fiber d s 2 = d x 2 + d y 2.
Total length s of one wavelength may be approximated by
s ~- ~
1+
cos2
dx,
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which gives the solution: 8 -- ~
a2~ 2
h
k2
REFERENCES 1. BENEDEK, G. B., Appl. Opt. 19, 459 (1971). 2. BRON, A. J., Brit. J. Ophthal. 59, 133 (1975). 3. COMNINOU, M., AND YANNAS, I. V., J. Biomechan. 9, 427 (1976). 4. DIAMANT, J., KELLER, A., BAER, E., LITT, M., AND ARRIDGE, R. G. C., Proc. R. Soc. Lond. B. 180, 293 (1972). 5. DIKSTEIN, S., AND MAURICE, D., J. Physiol. 221, 43 (1971). 6. DRUAULT,A., Arch. Ophthalrnol. (Paris) 40,458, 536 (1923). 7. DUKE-ELDER, W. S. System of Ophthalmology, Volume VII. The Anatomy of the Visual System, p. 88. C. V. Mosby, St. Louis, 1961. 8. FEUK, W., IEEE Trans. BME-17, 186 (1970). 9. GOLDMANN, H., AND SCHMIDT, Th., Ophthalmologica 134, 221 (1957). 10. HART, R. W., AND FARRELL, R. A., J. Opt. Soc. Amer. 59, 766 (1969). 11. HOGAN, M., ALVARADO, J., AND WEDDELL, J., Histology of the Human Eye. W. B. Saunders Co., Philadelphia, 1971. 12. HUEER, J. D., PARKER, F., AND ODLAND, G. F., Stain Techno[. 43, 83 (1968). 13. KARNOVSKY,M. J., J. CellBiol. 35, 213 (1967). 14. KIKXAWA,Y., Japan J. Physiol. 8, 138 (1958). 15. KLYCE, S. D., AND MAURICE, D. M., Invest, Ophthal. 15, 550 (1976). 16. KOEPPE, L., Arch. Ophthal. 102, 4 (1920). 17. MAURICE,D. M., d. Physiol. 136, 263 (1957). 18. MAURICE,D. M. The Cornea and Sclera in DAVSON, H. (Ed.), The Eye Vol. 1. Academic Press, New York 1969. 19. MELLERIO,J., AND PALMER, D. A., Vis, Res. 10, 515 (1970). 20. MAURICE,D. M. Invest. Ophthal. 13, 1033 (1974). 21. MAURmE, D. M. (In preparation). 22. MISHIMA, S. Advan. Ophthal. 10, 23 (1960). 23. RIGBY, B. J., HIRAI, N., SPIKES, J. D., AND EYRING, H., J. Gen. Physiol. 43, 265 (1959). 24. STURROCK, G., Arch. Klin. Exp. Ophthal. 188, 245 (1973). 25. TWERSKY,V., d. Opt. Soc. Amer. 65, 524 (1975). 26. VOGT, A., '*Atlas of the Slitlamp Microscopy of the Living Eye." Springer, Berlin, 1921. 27. WECHSLER, S., Amer. J. Optom. Physiol. Opt. 51, 852 (1974). 28. WILSON, M. J. Vis. Res. 10, 519 (1970).
OF U L T R A S T R U C T U R E
RESEARCH
61, 100-114 (1977)
Striations of Light Scattering in the Corneal Stroma BETTY GALLAGHER AND DAVID MAURICE Division of Ophthalmology, Stanford University Medical Center, Stanford, California 94305 Received April 8, 1977 When the rabbit cornea is stressed in various ways, light focused on the stroma is scattered back in the form of striations. Light and electron microscopy reveal t h a t the striations correspond to a waveform assumed by the collagen fibrils in the stroma when the tension on them is relaxed. The waves act as reflectors for the light, which is a consequence of the light-scattering properties of the fibrils themselves, rather than a result of interfaces opening up between the lamellae.
The transparency of the corneal stroma is generally agreed to result from the regular arrangement of the collagen fibrils which leads to the destructive interference of the light they individually scatter (17). It is not certain how strict this regularity must be in order to obtain the observed degree of clarity, and what must be the nature and extent of the disorganization required to produce the clouding that is observed when the tissue is swollen or stressed. Several theoretical studies of the problem have been published (1, 8, 10, 25), but the choice among the models proposed will most probably depend on experimental determinations of the angular and wavelength dependence of the light scattering of the collagenous lamellae. These determinations are not easy to make without ambiguity, for it is evident from observation of the cornea in the slit-lamp microscope that much of the light scattering takes place from numerous discrete points which can be identified as the stromal keratocytes. Attempts in this laboratory to make scattering measurements on microscopic elements of tissue between the keratocytes led to results for which no ready interpretation could be provided and made it necessary to examine the distribution of scattered light on the microscopic scale in more detail. To this end an instrument named the scanning slit microscope (SSM) was devel-
oped, whose construction has been described elsewhere (20). This instrument allows photographs to be made of optical sections through the tissue by what is effectively dark field microscopy. These photographs reveal that under many conditions light is scattered from the stroma in the form of striations. More often than not, the striations are doubled t o give a tramline effect. This paper shows these striations to be related to the formation of waves in the stromal lamellae when the normal tension on them is relaxed. An optical explanation of the appearance of the striations in the SSM is derived out on the basis of the angular distribution of the light scattered from individual fibrils. MATERIALS AND METHODS The SSM works on the principle of focusing a very narrow illuminated slit through one-half of a 40 x water-immersion objective while recording on film the light returned by scattering or reflection up the other half of the objective. The film is placed behind an identical parfocal slit mounted in the eyepiece plane. The specimen is gradually displaced through the image of the slit, and the film is moved at a corresponding speed in the opposite direction so t h a t the image formed on it remains in register. In this way an optical section only a few microns thick is reproduced on the film. New Zealand White rabbits were killed, and the eyes were enucleated after their orientation in the orbit was marked. In some cases the enucleated intact eye was glued to a metal ring behind the
100 Copyright © 1977by Academic Press, Inc. All rights of reproduction in any form reserved.
ISSN 0022-5320
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STRIATIONS IN CORNEA equator with cyanoacrylate cement (Eastman 910). The weighted globe was then immersed in saline or silicone oil at room temperature. Intraocular pressure (IOP) was regulated by means of an elevated saline-filled reservoir connected through a 20-gauge needle into the posterior vitreous humor; preliminary experiments had shown that a needle inserted near the corneal limbus was itself sufficient to cause the appearance of striations. In other cases the cornea was excised and mounted in a chamber so as to avoid distortion of the tissue and to distend it to its proper shape under the normal IOP (5). Various corneal preparations were examined: normal, swollen, under reduced intraocular pressure, with a cut in the stroma, and with a needle penetrating just outside the limbus. Corneas were made to swell by refrigerating the intact eye, by scraping away the epithelial cell layers and placing saline on the bare stromal surface, or by bathing its posterior surface with 0.133 M NaHCO3. The corneas were swollen to between 150 and 200% of their original thickness as measured by the fine focus control of the microscope (5). To demonstrate the relationship between fibril relaxation and striations, cuts approximately 200 t~m deep were made near the center of the cornea in the intact globe by means of a razor blade fitted with a guard, and were either parallel or perpendicular to the superior-inferior axis. Initially, observations were made under saline. Local edema complicated interpretation, and in subsequent experiments the tissue was covered with silicone oil during scanning slit microscopy. The stromas were photographed with the SSM near the apex of the tissue unless otherwise noted. They were then prepared for electron microscopy. The fixative consisted of 1% glutaraldehyde-0,3% formaldehyde in a NaHCO3 or PO4 buffer at pH 7.4. Each was adjusted to be isotonic or slightly hypotonic to blood. This was applied to both surfaces of the cornea except when the anterior surface had been cut and covered with oil, in which case fixative was applied only to the posterior surface. The thickness of the cornea was checked after fixation and in 13 cases was 0.97 _+ 0.1 of its fresh value. Specimens were postfixed in osmium, stained en bloc with uranyl acetate (13), and embedded in Epon-Araldite. Specimens were cut on a Porter Blum MT-2 ultramicrotome and stained with 0.5% phosphotungstic acid. Thin sections parallel to the surface were prepared by trimming to the center of the concentric circles which appear in the block face on cutting tangentially into the cornea. Sections were viewed and photographed in a Philips 200 electron microscope calibrated with Dow latex particles. Thick sections for light microscopy (LM), either cross or tangential, were cut from the same block a n d stained with basic fuchsin and methylene blue (12).
RESULTS
Normal Cornea The general appearance of the mammalian stroma both in the light and electron microscopes is described in many texts (7, 11, 18), but it is convenient to recall some salient features at this point. The tissue is built up by the supraposition of ribbomlike lamellae, each about 2 t~m thick, which run from limbus to limbus. When a fresh rabbit cornea is fixed under normal intraocular pressure, the lamellae are generally seen in cross section as almost smooth arcs, both by LM and low power electron microscopy (EM) (Figs. 1 and 2). However, undulations of low amplitude can be distinguished, particularly in the posterior cornea. The lamellae do not interweave except possibly in the anterior layers, which are less well organized. Each lamella is made up of uniform collagen fibrils about 30 nm in diameter and 60 nm between centers. The fibrils in a lamella run parallel to each other and to its surface, but in adjacent lamellae they make large angles with each other. A cross section of the cornea will occasionally cut through a lamella in the direction of the fibrils and include lengths of them within it. Generally, the slice will cut across the fibrils, and they will appear in the EM as circles, ellipses, or linear segments according to the angle of the section. In sections cut parallel to the surface, the central lamellae are seen in the electron micrographs to be formed by sheets of straight, parallel fibrils whose appearance suggests an absence of appreciable waving. The junction between two lamellae is recognized as an abrupt change in direction of the collagen fibrils (Fig. 3). The image of the undisturbed stroma as seen by the SSM is a dark background against which fibroblast nuclei and nerves and other linear structures of uncertain nature, possibly cell processes or elastic fibers, appear as light-scattering elements
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(Fig. 4). Striations are not seen in photographs made from such tissue.
Striations When the organization of the stroma is disturbed, parallel white lines against a dark background are recorded by the SSM, which commonly appear as tramlines (Fig. 5). The periodicity, defined as the distance between alternate lines whether tramlines were present or not, ranged from 8 to 15 t~m. The striations show no marked preference in their orientation with respect to the superior-inferior axis of the eye. When a cornea is rotated about the optical axis, the striations change direction by a corresponding angle, but their general appearance does not alter. When the SSM is focused down between photographs in order to produce serial optical sections, the pattern of striations is found to be constant over a considerable depth (Fig. 6). On either side of this range the pattern becomes unrecognizable, and the direction of the striations may undergo a large rotation.
Waves Scanning electron microscopy (SEM) of an isolated cornea shattered while frozen reveals the interface of a lamella to be a corrugated sheet (Fig. 7). In histological sections prepared as is customary from eyes fixed in the absence of intraocular pressure, the many lamellae are seen to be wavy in outline. Others have a banded appearance as if they were rippling in and out of the section. The form of the waves can be made out more clearly in low power electron micrographs where the individual
103
collagen fibrils can be distinguished. In cross sections, the fibrils occasionally lie flat in the plane of the section, but more generally the section cuts across them, giving rise to alternating bands of segments of different lengths. In many places the plane of the waves appears to be perpendicular to the section, and the surfaces of the lamellae may be free of undulations. On other occasions fluctuations in the thickness of a lamella occur, and its two surfaces may form waves which are partially or completely out of phase with one another. In general, however, the wave peaks remain in phase over depths of several microns (Fig. 8). The appearance of the fibrils in tangential sections is consistent with that in cross sections. Bands of linear segments are separated by circular segments of collagen fibrils, as one would expect from waves of collagen fibrils running together in phase (Fig. 9). Occasionally, where the waves are parallel to the surface, they lie within the section, and long continuous lengths of the fibrils can be seen. Although the fibrils tend to form planar waves, the patterns of the segments are frequently irregular. We sought for helical wave forms by comparing angles between linear segments from adjacent bands. Helical patterns did not appear to be maintained over any number of wavelengths, however. This corresponds to the results in tendon (4, 23), where the waves were found to be planar. In the following sections, the appearance of the waves will be compared to t h a t of the striations in each of the disturbed states of the cornea.
FIG. 1. Light micrograph (LM) of rabbit cornea fixed under normal intraocular pressure. Lamellae approximate to smooth arcs. Fro. 2. Electron micrograph (EM) of rabbit cornea in cross section fixed under normal intraocular pressure, Within each 'lamella, the collagen fibrils have a uniform appearance indicating an absence of appreciable waving in and out of the section. Fro. 3. EM of a tangential section of the normal cornea. An underlying lamella is seen as an area whose fibrils make large angles with those of the sheet above it.
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FIG. 4. Scanning specular micrograph (SSM) of the normal stroma. The fibroblast nuclei appear bright against a dark background. FIG. 5. SSM of a cornea stressed by a needle. Striations appear as tramlines superimposed on the image of the normal stroma.
FIG. 6. A series of SSM sections at different levels. The pattern of striations persists although the focus passes through cellular elementsl FIG. 7. Scanning electron micrograph of a freeze-fractured cornea. The split passes between the waves in the lamellar surface. Fibers running at different orientations conform to the corrugations. FIG. 8. EM cross section of swollen cornea. Waves are in phase through many lamellae. 105
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Swollen Cornea Scanning slit microscopy of swollen corneas commonly reveals regular striations in the posterior cornea (Fig. 10). Often, however, t h e light scattered from the anterior regions of the cornea reduces the contrast to such an extent that they are not visible. Photographs of striations in the anterior layers of the swollen stroma have never been obtained. Light microscope observations of swollen corneas in cross section always show lamellar waves, beginning with waves of small amplitude in the middle stroma which become more pronounced towards the posterior surface (Fig. 11). By EM, collagen fibrils in the posterior layers can be seen as waves in the plane of the section (Fig. 8) as well as oblique to that plane (Fig. 12). Waves are not seen near the anterior surface. Thin sections of the posterior cornea parallel to the surface usually show the bands of linear segments typifying fibrils which wave in and out of the section. On occasion, the plane of the wave corresponds to that of the section so that entire fibrillar waves are seen.
Low Intraocular Pressure When the intraocular pressure is lowered behind corneas of normal thickness, striations of a very irregular pattern can be seen in the SSM across the entire thickness (Fig. 13). The lamellae are noticeably wavy at all levels of the stroma when it is examined by LM or low power EM.
Cut Cornea Corneas with superficial cuts show linear striations in the anterior layers simi-
107
lar in appearance to those in Fig. 5. The striations are always parallel to the cut and more distinct near it. Cross sections of these corneas show the uncut lamellae to be straight and the cut lamellae to be wavy (Fig. 14). The lamella at the interface shows great disorganization, presumably because of the considerable shear in this plane. The waves become less pronounced with distance from the cut. In tangential sections examined in the electron microscope the bands that correspond to the wave fronts are parallel to the cut; that is, they take the same direction as the striations seen in the SSM.
Needle Eyes in which a needle has been inserted at the limbus show striations in the SSM with particular clarity. These, when viewed at the apex, are directed towards the point of insertion. In the electron microscope the direction of the striations and of the bands seen in tangential sections is the same.
Periodicity A comparison was made between the periodicity of the striations photographed by the SSM and of the waves seen in electron micrographs (Table I). For the latter measurement, sections parallel to the surface were used, because here the axis of the fibril wave lies in the plane of the section. This is rarely true of cross sections, in which the measured wavelength would generally be longer than the true wavelength. The periodicity of the striations has already been defined. In the case of the electron micrographs one period was
FIG. 9. T a n g e n t i a l E M o f s w o l l e n c o r n e a . The collagen fibrils in a single lamella wave in and out through the section, forming bands composed of linear segments (cf. Fig. 3). FIG. 10. SSM of swollen cornea. Striations appear whose pattern is less regular than that caused by stress (cf. Fig. 5). The cellular elements appear to have increased in area, probably because the cytoplasm is scattering light. FIG. 11. LM of swollen cornea. The anterior layers are free of waves, but in the deeper stroma waves are found whose amplitude increases towards the rear surface (cf. Fig. 1).
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FIG. 12. EM cross section of swollen cornea in posterior layers. The presence of s e g m e n t s of different l e n g t h s within one l a m e l l a shows t h a t fibrils are forming waves oblique to the section. FIG. 13. S S M o f n o r m a l c o r n e a u n d e r l o w i n t r a o c u l a r p r e s s u r e . Striations form a very i r r e g u l a r pattern. FIG. 14. Anterior cut in cornea. The cut surface (arrow) retracts, t h r o w i n g t h e lamellae into waves of large amplitude. The u n c u t lamellae are smooth as in t h e n o r m a l cornea. 108
109
S T R I A T I O N S IN C O R N E A TABLE I
PERIODICITIES OF STRIATIONS SEEN IN SCANNING SPECULAR MICROSCOPE AND WAVES SEEN IN ELECTRON MICROSCOPE UNDER VARIOUS CONDITIONS
Periodicity (tLm) -+ SD S c a n n i n g s p e c u l a r microscope
E l e c t r o n microscope
Swollen c o r n e a s 14.2 -+ 0.5 (12) a {4}° Cut corneas 9.8 ± 1.9 (42) {14} Needle 12.0 + 1.9 (15) {5}
15.2 -+ 3.0 (38) {3} 11.5 _+ 3.8 (26) {3} 12.8 ± 1.9 (4) {1}
a N u m b e r of m e a s u r e m e n t s . N u m b e r of corneas.
defined as the distance between alternate bands of linear segments of collagen. Cut corneas give a shorter spacing b y both methods, probably as a result of the larger amplitude of the waves in this condition. In can be seen that the two methods give similar values for the wavelength. DISCUSSION
Waves and Striations In every experimental situation detailed above, there is a close relationship between the appearance of the striations in the SSM and the form of the waves as seen in the light and electron microscopes. The direction of striations corresponds to the direction of the wave fronts observed in the electron microscope. There is good agreement in periodicity between striations and waves. Striations are not recorded when the waves are too flat to be easily made out in electron micrographs.
Waves and Relaxation Rat tail tendon observed under polarized light shows a system of light and dark bands which result from a release of tension on the formation of waves in the collagen fibers (23). Although the periodicity of these bands, 300 t~m, clearly separates them from the striations seen in the cornea, the results of the present study are compatible with the view that corneal striations also result from a release of tension in the stroma. Normally, the intraocular pressure stretches the fibrils into nearly wave-free circular arcs. Any relaxation of the fibril tension permits waves to
be developed in the lamellae. Thus, when the intraocular pressure is dropped to a very low level, all lamellae are released and waves are generated in an irregular pattern through the thickness of the tissue.
A superficial incision in the cornea relaxes the tension only in the cut lamellae, and, correspondingly, waves and striations are noted only in these layers. Corneas submerged in oil and in saline give the same result, demonstrating that it is not the introduction of saline through the cut into the stroma which causes the waves, but relaxation alone. In swollen corneas waves appear only in the posterior levels. Presumably this is because the fibrils are virtually inextensible so that the tissue is forced to swell inward. This causes relaxation in the posterior lamellae, while the strain is taken up by the anterior ones. The arrangement of the waves in the normal cornea stressed by a needle may be considered analogous to the puckering that can be seen around the point where an inflated plastic bag is indented with a finger. The weight of the needle pulls on fibrils running through the point of insertion and eases those which cross them. Wave fronts always line up perpendicular to the relaxed fibrils and therefore follow the direction of greater tension. Striations are not evident in the cornea of normal thickness under normal IOP. This indicates that the tension is such t h a t none of the lamellae are relaxed enough to form significant waves. The tension in the
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cornea appears, therefore, to be distributed throughout all the layers of the stroma and not restricted to one or the other surface, as has been suggested by Goldmann and Schmidt (9).
Quantitative Aspects of Swelling If a fully extended fibril relaxes to a sine wave of wavelength h and amplitude a, its fractional reduction in length can be approximated by (rra/h)2 (see Appendix). In the posterior lamellae of corneas swollen to approximately double their normal thickness, a was measured to be of the order of 1 tLm while ~ was 14 t~m. Accordingly, the fibrils should be about 5% shorter than their fully extended length. The shortening t h a t should occur if the stroma swelled inward from a fully stretched layer on the anterior surface can be determined by geometrical considerations. Two alternative swelling modes can be envisaged. In the first, the cornea is assumed to expand inward uniformly from limbus to center. In this case the shortening of the posterior fibrils is given by the ratio of the change in thickness to the radius of curvature. For an expansion of 350 tLm in a cornea of 7-mm radius of curvature, the fibrils will be shortened by 4.5%. If, on the other hand, it is supposed t h a t the inward expansion of the cornea is prevented at the limbus, only the center will move inward, increasing the radius of curvature. Using 13 mm as the diameter of the corneal segment, the change in arc length is calculated to be 3%. Given the uncertainty of the measurements, these results are compatible with the estimate arrived at from the amplitude of the waves.
Packing In the normal cornea the lamellae lie closely on top of one another so that no spaces exist between them. When the tension on the lamellae is released, they are thrown into waves, and problems in pack: ing arise t h a t require consideration. Ob-
servations on single isolated lamellae suggest t h a t the natural relaxed form is t h a t of a corrugated sheet (18) with the corrugations perpendicular to the direction of the collagen fibrils. In the intact cornea, lamellae generally do not adopt this form when relaxed, since in adjacent lamellae the fibrils make large angles with one another and grooves devoid of fibrils would appear between every wave peak. Such spaces are not observed in the electron microscope. Indeed, at the greatest swelling we studied, twice normal thickness, the lamellae do not separate from one another, nor is there a frequent appearance of collagen-free volumes which could correspond to the lakes whose existence has been proposed by Benedek (1) to account for the clouding of the tissue. It is evident, therefore, that some distortion of the natural shape of the lamellae must occur to account for their continued close packing in swollen corneas. Furthermore, since the waves remain in register over several lamellae, it is difficult to see how each set of fibrils can maintain its natural wavelength as it runs at a different angle across the wave pattern. We could not find a complete solution to this problem. When the direction of the undulations undergoes a change, the problem arises more acutely. It is probable that in intermediate lamellae the fibril waves lie in a plane which is parallel to the corneal surface, resulting in a smooth lamellar face. Regular thickening and thinning of a lamella provides further opportunities for its fibrils to redistribute themselves into potentially collagen-free volumes. Local changes in stress could produce changes in amplitude and therefore wavelength t h a t could further help the lamellae accommodate to one another. Finally, the frequent irregularity of the path followed by the fibrils was already noted.
Stress-Strain Relationship It has been suggested that both in the eye (7) and in tendon (23), the waviness of
STRIATIONS IN CORNEA the collagen fibrils is an elastic system which absorbs sudden stresses which might otherwise rupture them. The relationship between tension and extension in an elastic rod bent in the form of a sine wave has been treated theoretically by Comninou and Yannas (3), and more simply by Maurice (21), who has shown experimentally that the rabbit cornea obeys the derived equation:
T \ZU _I]
-1
where T is the tension in the cornea, l represents the length of the fibril, and lo and l~ are its values in the unstressed and fully extended states. These measurements indicate that the fibrils in a totally relaxed state should have an amplitude a of 1.2 t~m. When the intraocular pressure is raised to 5 cm H20, they should be 60% of their way to total extension and a should be 0.8 t~m, and when the intraocular pressure is 20 cm H20 the corresponding figures are 90% and 0.4 tLm. Amplitude measurements from electron micrographs can be made on cross sections in places where it appears that the fibrils lie in the plane of the section. The variability is great, but from 45 measurements of a cornea fixed at an IOP of 5 cm the mean value of a is 0.7 _+ 0.3 tLm. In the paired cornea at an IOP of 20 cm the mean value of a was 0.2 _+ 0.1 t~m. It was observed (21) that though the elasticity due to waviness is a feature of the rabbit's cornea it is absent in the rabbit sclera and over the whole fibrous tunic of the human eye. Its role as an absorber of shock may perhaps not be so important as appeared previously.
Optical Basis of Striations When this problem was first considered, two explanations based on the lamellar organization presented themselves, but they can readily be disposed of. In the first, it was proposed that only
111
one lamella out of very few would scatter light. Striations would be caused by the intersection of the focal plane of the SSM with this lamella, and tramlines would result from the intersections becoming closer near the peaks of the waves. Apart from the difficulty of explaining why occasional lamellae should scatter more strongly than others, this hypothesis would not be consistent with the persistence of the pattern of tramlines at different depths of focus. The second explanation is that light is reflected back from the interlamellar interspaces at the peaks and troughs of the waves; here tramlines would be an effect of parallax. However, there is nothing in the structure of the interface as shown by the electron microscope to account for such reflections. Furthermore, since the thickness of the optical section is about 4 ~m, comparable to that of the lamellae, there should be considerable areas over which it does not intersect interlamellar boundaries at their peaks, and striations should not be present. On making the optical section thicker by widening the slits, fresh boundaries should be included and the striations should become more frequent; this is not seen to happen. A true explanation of the striations appears to lie in the scattering properties of the fibrils themselves. A thin, straight rod, long compared to the wavelength of light, will scatter incident coherent light in a conical distribution, where the apical angle of the cone is equal to that of the incident light upon the rod (Fig. 15). An array of parallel rods should give rise to a similar distribution of light, although the intensity around the conical shell may undergo variations as a result of the interference of the components scattered by the individual rods in the array. Under the specular microscope the array should appear bright only when the cone of scattered light happens to strike the half of the objective which is used for observation (Fig. 16). Geometrical considerations show
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SCATTERED LIGHT
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they run at an angle to this plane, tramlines are to be expected (Fig. 18b). Further tilting of the tissue should lead to single striations of double the normal periodicity, and then to their disappearance. This was tested by photographing striations in a stressed cornea at the apex and at several millimeters before and beyond it, so that the natural curvature of the tissue provided the necessary angle. This showed the predicted features: Near the apex the
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that this will only occur when the rods lie in a plane perpendicular to the optical axis of the microscope (Fig. 17). They should therefore appear bright in the SSM only where the lamellae run perpendicular to its axis. To a first approximation the collagen fibrils of the cornea may be considered straight rods, since the wavelength of their undulations is large compared to the wavelength of light. It may be emphasized that though the light behaves as if it were reflected from the tissue, this is not the case, but is a result of scattering from within the thickness of the lamellae. When the waves run in the focal plane of the microscope, the tendency will be to form uniform striations (Fig. 18a), but if
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FIG. 17. Fibrils continue to scatter light into the objective when rotated in the focal plane. FIG. 18. The pattern of scattered light depends upon the angle which the waves make with the optical axis. (a) A wave lying in the focal plane produces striations of uniform periodicity. (b) Tilting of the wave causes the striations to form tramlines.
STRIATIONS IN CORNEA
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Fro. 19. A cornea photographed at different angles to the fibrillar waves. At the apex, the striations are nearly uniform, at 9° tramlines predominate and at 21° the striations become less distinct and more separated.
striations tended to be regular, at moderate tilts tramlines developed, and a less distinct, larger periodicity showed up as the angle increased (Fig. 19). If this is the correct explanation for the formation of the striations, the normal cornea should scatter more light into the SSM at the apex, where the fibrils all run parallel to the surface, than towards the periphery, where they are tilted. This was checked experimentally using a photometer in the eyepiece of an instrument which was provided with an automatic vertical scan (15). The tracings showed that the scattered light intensity from a freshly enucleated eye maintained at normal IOP was about five times greater at the apex than near the periphery. The ratio is prevented from being higher because much of the light comes from the nuclei and other structures which may not scatter in a specular fashion (Fig. 4).
Previous Observations Observations of whole thickness corneas in transmitted or reflected polarized light (22) or by phase microscopy (18) show networks or lines corresponding in periodicity to the striations described in the present article. Kikkawa (14) claims that optical diffraction figures are obtained from isolated rabbit cornea which correspond to a diffraction grating spacing of 13-15 t~m. Apart from this, regular optical inhomogeneities of unspecified periodicity have been observed by the slit lamp in the intact eyes of humans and animals under a variety of normal and pathological circumstances (16, 18, 22, 26, 28) which may correspond to the striations under consideration. It is worthy of recall that Vogt noted and photographed the tramline patterns similar to those we have described, both from within the stroma and from its posterior surface (26). He explained these
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as a result of reflection, which is true in the latter case, but missed the correct explanation in the former. Apart from these regular patterns, there are reports of more widely spaced striae in the human cornea, either normally (2, 24), or after contact lens wear (2 7). These cannot correspond to the regular lamellar waves seen in rabbit corneas, although it is possible they may appear as a result of light scattering from occasional folds in a lamellae. Halos around lights corresponding to a 15-~m spacing have been described (19), which could result from the waves in the stroma. These halos are, however, less prominent than those which are generally noticed and that correspond to a 9-t~m spacing arising from the epithelial cells of the cornea (6). Although the presence of striations causes no major subjective visual effects, their presence should be borne in mind in interpreting light-scattering measurements, which are often used in order to gain insight into the relationship between corneal structure and transparency. Similarly, caution should be exercised in ignoring the contribution of the cells and other formed structures in the stroma to the scattered light. This work was supported by NIH Grant EY 00431. APPENDIX
Derivation of Extended Length of Sine Wave Consider a fiber of inextensible material bent into a wave: 27TX
y = a sin-
If d s is length of an infinitesimal element
of fiber d s 2 = d x 2 + d y 2.
Total length s of one wavelength may be approximated by
s ~- ~
1+
cos2
dx,
J0
which gives the solution: 8 -- ~
a2~ 2
h
k2
REFERENCES 1. BENEDEK, G. B., Appl. Opt. 19, 459 (1971). 2. BRON, A. J., Brit. J. Ophthal. 59, 133 (1975). 3. COMNINOU, M., AND YANNAS, I. V., J. Biomechan. 9, 427 (1976). 4. DIAMANT, J., KELLER, A., BAER, E., LITT, M., AND ARRIDGE, R. G. C., Proc. R. Soc. Lond. B. 180, 293 (1972). 5. DIKSTEIN, S., AND MAURICE, D., J. Physiol. 221, 43 (1971). 6. DRUAULT,A., Arch. Ophthalrnol. (Paris) 40,458, 536 (1923). 7. DUKE-ELDER, W. S. System of Ophthalmology, Volume VII. The Anatomy of the Visual System, p. 88. C. V. Mosby, St. Louis, 1961. 8. FEUK, W., IEEE Trans. BME-17, 186 (1970). 9. GOLDMANN, H., AND SCHMIDT, Th., Ophthalmologica 134, 221 (1957). 10. HART, R. W., AND FARRELL, R. A., J. Opt. Soc. Amer. 59, 766 (1969). 11. HOGAN, M., ALVARADO, J., AND WEDDELL, J., Histology of the Human Eye. W. B. Saunders Co., Philadelphia, 1971. 12. HUEER, J. D., PARKER, F., AND ODLAND, G. F., Stain Techno[. 43, 83 (1968). 13. KARNOVSKY,M. J., J. CellBiol. 35, 213 (1967). 14. KIKXAWA,Y., Japan J. Physiol. 8, 138 (1958). 15. KLYCE, S. D., AND MAURICE, D. M., Invest, Ophthal. 15, 550 (1976). 16. KOEPPE, L., Arch. Ophthal. 102, 4 (1920). 17. MAURICE,D. M., d. Physiol. 136, 263 (1957). 18. MAURICE,D. M. The Cornea and Sclera in DAVSON, H. (Ed.), The Eye Vol. 1. Academic Press, New York 1969. 19. MELLERIO,J., AND PALMER, D. A., Vis, Res. 10, 515 (1970). 20. MAURICE,D. M. Invest. Ophthal. 13, 1033 (1974). 21. MAURmE, D. M. (In preparation). 22. MISHIMA, S. Advan. Ophthal. 10, 23 (1960). 23. RIGBY, B. J., HIRAI, N., SPIKES, J. D., AND EYRING, H., J. Gen. Physiol. 43, 265 (1959). 24. STURROCK, G., Arch. Klin. Exp. Ophthal. 188, 245 (1973). 25. TWERSKY,V., d. Opt. Soc. Amer. 65, 524 (1975). 26. VOGT, A., '*Atlas of the Slitlamp Microscopy of the Living Eye." Springer, Berlin, 1921. 27. WECHSLER, S., Amer. J. Optom. Physiol. Opt. 51, 852 (1974). 28. WILSON, M. J. Vis. Res. 10, 519 (1970).
