  We introduce a discrete mathematical model for the mechanical behaviour of a
planar slice of human corneal tissue, in equilibrium under the action of
physiological intraocular pressure (IOP). The model considers a regular
(two-dimensional) network of structural elements mimicking a discrete number of
parallel collagen lamellae connected by proteoglycan-based chemical bonds
(crosslinks). Since the thickness of each collagen lamella is small compared to
the overall corneal thickness, we upscale the discrete force balance into a
continuum system of partial differential equations and deduce the corresponding
macroscopic stress tensor and strain energy function for the micro-structured
corneal tissue. We demonstrate that, for physiological values of the IOP, the
predictions of the discrete model converge to those of the continuum model. We
use the continuum model to simulate the progression of the degenerative disease
known as keratoconus, characterized by a localized bulging of the corneal
shell. We assign a spatial distribution of damage (i. e., reduction of the
stiffness) to the mechanical properties of the structural elements and predict
the resulting macroscopic shape of the cornea, showing that a large reduction
in the element stiffness results in substantial corneal thinning and a
significant increase in the curvature of both the anterior and posterior
surfaces.
