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

Abstract

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.