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We introduce a discrete mathematical model for the mechanical behaviour of aplanar slice of human corneal tissue, in equilibrium under the action ofphysiological intraocular pressure (IOP). The model considers a regular(two-dimensional) network of structural elements mimicking a discrete number ofparallel collagen lamellae connected by proteoglycan-based chemical bonds(crosslinks). Since the thickness of each collagen lamella is small compared tothe overall corneal thickness, we upscale the discrete force balance into acontinuum system of partial differential equations and deduce the correspondingmacroscopic stress tensor and strain energy function for the micro-structuredcorneal tissue. We demonstrate that, for physiological values of the IOP, thepredictions of the discrete model converge to those of the continuum model. Weuse the continuum model to simulate the progression of the degenerative diseaseknown as keratoconus, characterized by a localized bulging of the cornealshell. We assign a spatial distribution of damage (i. e., reduction of thestiffness) to the mechanical properties of the structural elements and predictthe resulting macroscopic shape of the cornea, showing that a large reductionin the element stiffness results in substantial corneal thinning and asignificant increase in the curvature of both the anterior and posteriorsurfaces.

A discrete-to-continuum model for the human cornea with application to keratoconus