On the Connection Between Geometry and Statically Determined Membrane Stresses in the Human Cornea

Under the action of the intraocular pressure (IOP), the human cornea is stressed and deforms acquiring a quasi-spherical configuration. If the stressed configuration is known, and the cornea is regarded as a membrane, disregarding flexural behaviors with an equilibrium analysis only is possible to estimate the distribution of the average stress across the thickness. In the cornea, the action of the intraocular pressure is supported by collagen fibrils, immersed into an elastin-proteoglycan matrix, and organized in a very precise architecture to provide the necessary confinement and transparency to the light. With the goal of understanding the static consequences of shape modifications due to pathological dilatation (ectasia), we present a simplified stress analysis of the human cornea modeled as a membrane. A numerical investigation over 40 patient-specific corneas (20 normal and 20 ectatic) is carried out to establish a relationship between the physiological geometry and the distribution of the membrane stresses, and to assess the possibility to obtain information on the stress state based on topographic images only. Comparative analyses reveal that, with respect to normal corneas, in ectatic corneas the pattern of the principal stress lines is modified markedly showing a deviation from the hypothetical dominant orientation of the collagen fibrils. The rotation of the principal stress with respect to the fibril orientation can be thought as responsible of the transmission of a large amount of shear stresses onto the elastin-proteoglycan matrix. The anomalous loading of the matrix could be correlated to the evolution of time-dependent shape modifications leading to ectasia.