Corneal biomechanics: A mathematical model for keratoconus

This paper aims to determine the surface patterns of corneal diseases under the effects of swelling, such as in keratoconus (KC). Swelling is a mechanism that responds to changes in pressure within a medium. The cornea allows aqueous humor to flow from the stroma into the anterior chamber, following the laws of mechanics to reach mechanical equilibrium. The geometry of the cornea is altered to change its curvature, and it is reformed through the process of inflating and shearing. The theory of shells is divided into two theories: membrane theory and bending theory. These theories are used to determine stress and its corresponding shell deformation, providing solutions for bending, changes in shell thickness, and axially symmetrical load deformation, respectively. The change in corneal shape due to swelling is calculated and demonstrated under constant intraocular pressure (IOP) and the corneal load. This estimates the potential deformations of the corneal structure in response to the pressure and load imposed by the equilibrium equations. Moreover, the model can estimate the tensile properties of corneal tissue, such as its elastic modulus and stiffness. This model helps understand the mechanical stress–strain relations, permanent structural changes, and surface patterns of corneal deformations.