Russell L. McCally

Numerical modeling of the cornea’s lamellar structure and birefringence properties

A model of the corneas lamellar structure is proposed that is capable of explaining experimental results obtained for the transmission of normal-incidence polarized light through rabbit and bovine cornea. The model consists of a large number of planar lamellae, each approximated as a uniaxial birefringent layer, stacked one upon another with various angular orientations. Polarized light transmission through the composite system is modeled theoretically by use of the Jones matrix formalism. The light transmission is calculated numerically for a large number of model lamellae arrangements, each generated from a statistical description, and histograms are constructed of various properties of the light transmission, including the minimum and maximum cross-polarized output intensities. It is demonstrated that various structural and optical parameters of the lamellae arrangements of actual corneas may be estimated by comparison of the calculations with detailed experimental data. Certain characteristics of the histograms are identified that permit a clear distinction between random and partially ordered systems. Comparisons with previously published experimental data provide strong evidence that the lamellae orientations are not entirely random, but rather a significant fraction are oriented in a fixed, preferred direction.

Direct summation of fields for light scattering by fibrils with applications to normal corneas

A statistical analysis based on a direct summation of electric fields scattered by individual fibrils is developed to calculate corneal scattering from the fibril distributions shown in electron micrographs. Unlike previous analyses, the method of direct summation of fields can be used for swollen and scarred corneas as well as normal corneas. The method is tested by applying it to the case of the normal rabbit cornea. The results are in good agreement with those obtained using the radial distribution formulation.

Structural implications of small-angle light scattering from cornea

Abstract Small angle light scattering (SALS) patterns are recorded from the central region of rabbit and bovine corneas. These measurements differ from those of other investigators in that an applied transcorneal pressure maintains the corneas curvature. The experiment shows, for the first time, that rabbit and bovine SALS have the same essential features and the same behavior with increasing pressure. We also fixed corneas under an applied transcorneal pressure for electron microscopy and confirmed that this treatment flattens the usually undulating lamellae. Thus, we explain the form of the SALS patterns and their behavior with pressure in terms of scattering from corrugated lamellae which become straight upon application of a differential hydrostatic pressure. The wavelength of the corrugations is approximately constant as their amplitude decreases and a small amount of waviness remains even at normal intraocular pressure. The experiments show that the collagen fibrils are optically anisotropic, with their polarizability at 45° with respect to the fibril axis. The results also suggest that the orientation directions of the corneal lamellae are not random; rather there are either: one preferred direction or two preferred directions which are orthogonal, although some lamellae are evidently oriented in every direction. The preferred directions are correlated with the overall corneal geometry and do not vary among different corneas.

Light Scattering from Cornea and Corneal Transparency

Understanding the properties of the cornea that are essential to vision—its structural stability and transparency—is a long-standing endeavor that continues to intrigue a variety of researchers ranging from ophthalmologists to physicists.1–12 The transparency of a normal cornea results directly from the fact that the cornea does not absorb visible light, and the light that it scatters is minimal. The small amount of scattered light, however, carries information about the internal structural elements from which the light is scattered. Therefore measurements of this scattered light can be used to probe structures in fresh (unfixed) corneal tissue.

Calculated and measured endothelial temperature histories of excised rabbit corneas exposed to infrared radiation

Abstract This paper reports calculation of the endothelial and epithelial temperature increases caused by exposing the cornea to radiation from three infrared laser systems: CO2 holmium and erbium. Data are presented for a variety of exposures and beam diameters. The calculations assume that the lasers are operated with a Gaussian beam intensity profile and the radiation is absorbed according to the Beer-Lambert law. We show that the absorption lengths of some of these laser lines are sufficiently long that the endothelial temperature rise is very close to that of the epithelium. The efficacy of the theoretical model is tested by comparing the calculations with measurements on excised corneas exposed to CO2 laser radiation. Both a liquid crystal technique and a thermocouple were used to measure the temporal and spatial variations of endothelial temperature. The experimental and theoretical values are in resonable accord which gives added confidence in the calculations for other laser systems and exposures. The results presented here show that infrared laser exposure safety standards should address the possibility of endothelial damage.

Effects of fibril orientations on light scattering in the cornea

It is generally assumed that the collagen fibrils in the stroma are the primary scatters of light in the nearly transparent cornea of the eye. We derive a scaling relationship between scattering angle and light wavelength that should hold if this hypothesis is valid. The derivation accounts for the corneas layered nature and the azimuthal orientations of the fibrils in the different layers. The fibrils are treated as finite-length cylinders, and the scaling relation is obtained in both the far- and the intermediate-field zones. The predicted relationship is verified experimentally for normal-thickness rabbit corneas.

Stromal damage in rabbit corneas exposed to CO2 laser radiation

Threshold damage to the cornea from CO2 lasers is confined to the epithelium. Exposures well above the threshold for epithelial damage produce bowl-shaped stromal wounds. Light and electron microscopy and slit-lamp photographs all show a sharp demarcation between the damaged and undamaged regions 48 hr after exposure. The micrographs also show that the damaged region is accellular. Calculations of the expected temperature increases combined with analyses of slit lamp photographs show that the wound boundary corresponds to a surface of equal peak temperature increase. Comparisons with epithelial and endothelial damage conditions suggest that stromal, endothelial and epithelial cells have essentially the same thermal damage mechanism.

Propagation of polarized light through two- and three-layer anisotropic stacks

The extended Jones formulation is used to investigate propagation at nonnormal incidence through two- and three-layer systems of birefringent material in which the optic axes of the individual layers are in the plane of the layers. Such systems are equivalent to two optical elements in series-an equivalent retardation plate and a polarization rotator. Analytical solutions are obtained for the equivalent retardation and rotation. The major finding is that, in general, there are two nonnormal incidence directions for which the retardation vanishes; therefore these two directions are optic axes of the composite system. These simple layered systems therefore behave in a manner similar to biaxial crystals. Moreover, the results illustrate the fact that even if the optic axes of individual layers in composite systems are in the plane of the layers, the optic axes of the system are, in general, out of this plane.

ON THE INTERPRETATION OF DEPTH DEPENDENT LIGHT SCATTERING MEASUREMENTS IN NORMAL CORNEAS

In recent studies other investigators have presented traces of “light scattering” versus depth into the cornea. The present investigation demonstrates that these traces do not measure the actual light scatter intensity and that a proper interpretation of such traces shows that most of the scattering is from within the stroma.