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R A Farrell

Publications and source records attributed to R A Farrell.

36 records · Page 2Linked to original sources

Corneal small-angle light-scattering theory: wavy fibril models.

Small-angle light-scattering (SALS) measurements of the cornea together with electron micrographs of the corneal stroma suggest that the waviness in the stromal collagen fibrils of corneas fixed at zero pressure is the structural feature responsible for the cross-polarized SALS patterns. This paper derives and discusses a Born approximation to the parallel- and cross-polarized SALS patterns expected from lamellae of long, thin, optically anisotropic wavy fibrils whose axes are parallel to each other and are spatially distributed about one another in a quasi-ordered fashion. The predicted scattered intensity depends on three factors: (1) the fibrils within a given lamella wave in unison, which produces scattering that is characteristic of a wavy sheet (as opposed to that characteristic of an isolated wavy fibril); (2) the undulations lead to a diffraction condition for determining the dependence of scattered intensity on scattering angle; (3) the relative orientations of fibril axes in different lamellae and the intrinsic electric susceptibility of a fibril determine the dependence of scattered intensity on azimuthal angle. The patterns predicted for anisotropic fibrils with a random distribution of lamella orientations or with distributions of lamella orientations that have one or two preferred directions superimposed upon a random background agree with the qualitative features of the experimental patterns observed with rabbit corneas. Experimental evidence in support of the distributions with preferred orientations is discussed.

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On corneal transparency and its loss with swelling.

The cornea is the clear front covering of the eye through which we see and is composed of collagen fibrils embedded in an optically homogeneous ground substance. It has long been recognized that these fibrils scatter light and that transparency results from interference effects due to an ordering in the spatial arrangement of the fibrils about one another. The nature of this ordering and of its disruption in abnormal corneas is of great current interest. The present study reviews experimental light scattering and electron microscopic evidence relevant to this problem. This evidence suggests that theoretical attempts to model and understand corneal transparency and its loss during swelling, in terms of ultrastructure, must account for a short-ranged ordering of fibrils in normal healthy corneas and for the formation of regions void of fibrils in swollen corneas.

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Wave-length dependencies of light scattering in normal and cold swollen rabbit corneas and their structural implications.

1. The studies described herein involve the use of light scattering measurements to characterize the ultrastructural arrangement of the constituent collagen fibrils in rabbit corneal stromas.2. Theoretical light scattering techniques for calculating the scattering to be expected from the structures revealed by electron micrographs are discussed, and comparison with the experimental light scattering tests the validity of these structures.3. The wave-length dependence of light transmission and of angular light scattering from normal corneas is in agreement with the short range ordering of collagen fibrils depicted in electron micrographs.4. The transmission measurements on oedematous rabbit corneas indicate that transmission decreases linearly with the ratio of thickness to normal thickness.5. The wave-length dependence of transmission through cold swollen corneas indicates that the increased scattering is caused by large inhomogeneities in the ultrastructure. Electron micrographs do, indeed, reveal the presence of such inhomogeneities in the form of large regions completely devoid of fibrils.

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The transparency of the mammalian cornea.

1. A theoretical and experimental analysis of the relationship of the corneal stromal ultrastructure with light transmission has been made in an attempt to resolve recent contradictory explanations of corneal transparency.2. The spatial distribution of collagen fibrils in electronmicrographs of rabbit corneal stroma has been analysed in terms of a radial distribution function. The results indicate the presence of local order extending to at least 200 nm from individual fibrils.3. The observed spatial distribution of the collagen fibrils was used as a basis to compare the theoretically derived and the experimentally determined values of light transmission. It has been found that the transparency of the normal cornea may be explained by the quasi-random structure revealed by the electronmicroscope.4. Histograms of the collagen fibril diameter in normal rabbit corneal stroma revealed the range to be 12.5-32.5 nm and the mean value to be approximately 20 +/- 1.5 nm. Corneal swelling did not change the collagen fibril diameter significantly.5. It is concluded that the size and distribution of collagen fibrils revealed in electronmicrographs are consistent with the observed transparency of normal stromas.6. A marked heterogeneity in the spatial distribution of collagen fibrils was found in the swollen cornea. This is qualitatively consistent with the observed decrease in transparency.

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Polarized light propagation in corneal lamellae.

The propagation of polarized light through the cornea is affected by the orientations of the corneal lamellae and by the refractive imbalance between the collagen fibrils and the ground substance. Thus, well-designed measurements and analyses of polarized light propagation through the cornea can be used to obtain information regarding the cornea's lamellar and fibrillar structures. This paper shows that, for the rabbit, measured values of the optical parameters strongly suggest that the distribution of lamellae orientations is not random, but has one (or two) preferred orientation directions. Also, there is considerable evidence that collagen is intrinsically anisotropic. The Weiner formula gives the effective birefringence of an assembly of parallel isotropic fibrils and its generalization to the case of anisotropic fibrils is presented. Finally, calculations based on preferred orientation models having lamellae composed of anisotropic fibrils show that comparison with experimental values can yield structural information.

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Small-angle light scattering and birefringence properties of chick cornea.

PURPOSE: Techniques employing polarized light propagation and scattering are useful in examining the cornea's lamellar structure. Recent advances in theoretical methods have significantly increased the ability to relate features of lamellar arrangements to measurements of transmitted polarized light. The chick cornea, because of its hypothesized structure of a gradual helical rotation of lamellar pairs, presents an interesting model for further development of this methodology. METHODS: Small-angle light scattering (SALS) and polarized transmission measurements were made on 7-week-old chick corneas under conditions that closely approximate the physiological state. Birefringence properties were determined from the transmission measurements and compared to the results of model calculations of polarized light propagating through lamellae organized according to the hypothesized structure for chick cornea. RESULTS: The I+ small-angle light scattering pattern had 4 cloverleaf lobes aligned with the crossed polarizer and analyzer axes. The lobes disappeared when the transcorneal pressure was increased from zero to 18 mmHg. Retardation measured at 18 mmHg was very small (approximately 0.01 microm). CONCLUSION: The disappearance of the I+ small-angle light scattering pattern when IOP is increased suggests that the lamellae undulate in their relaxed state and the undulations straighten when IOP is increased. Measured birefringence properties are consistent with the hypothesized lamellar structure.

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