Corneal lamellar birefringence - effects of fibril anisotropic permittivity on retardation

Purpose. The retardation, A, of polarized light as it traverses the cornea has been analyzed by others in terms of the Wiener formula describing form birefringence.¹ This formula does not account for known comeal intrinsic birefringence which arises from the fibrils having anisotropic permittivity and it is only valid for a single lamella. The purpose of this study was to extend the single lamella model by accounting for intrinsic birefringence and the possibility of fibril diameter varying with corneal hydration. Methods. We considered a model with parallel anisotropic fibrils embedded in an isoiropic ground substance. The fibrils were assumed to have different pcrmittivites (equivalently-refractive indices) parallel and perpendicular to ihe geometric axis. The resulting equation was analyzed for two models, (1) and (2): in (1) the fibril hydration remained fixed as the cornea hydration, H=wi of H2U/dry wt. changed; and In (2), which was based on x-ray data, the fibril hydration remains fixed down to H=HCI=\, and then varies so that the fibrils are dry at H=0. Results. The effect of fibril anisotropy adds a constant, which is the difference between the parallel and perpendicular fibril permittivities, to the Wiener formula. This can be cither positive or negative. In model {1),4 decreases to a minimum as H decreases and then rises very sharply. The value of H at the minimum depends on the assumed value of fibril hydration. In (2), A also decreases .but does not reach a minimum until H~0. Conclusions. These results show promise for distinguishing between models of fibril properties and for obtaining optical properties which are ultimately related to fibrillar ultrastructure. The model must be extended to account for the multilamellar corneal stroma.