Numerical estimation of stress and refractive power maps in healthy and keratoconus eyes

Keratoconus is an eye condition caused by localized thinning of the corneal tissue, which leads to a characteristic cone-shaped protrusion of the cornea. We investigate the mechanical behavior of keratoconus and suspect keratoconus corneas versus healthy corneas by using patient-specific finite element models. Patient-specific geometries of the corneas are obtained from diagnostic images provided by corneal topographer, transformed into solid models, and discretized in hexahedral elements. For the diseased corneas, a suitable reduction of the stiffness is applied within a limited region of the cornea around the conus. After the identification of the stress-free configuration, the models are used to simulate pressurization tests up to 40 mmHg. The material parameters have been estimated within the stress-free configuration identification procedure. As expected, numerical results reveal a more compliant behavior for the diseased corneas in terms of apex displacement plots as a function of the intraocular pressure, with diseased corneas experiencing up to 44% increase in apex displacement compared to healthy corneas. The maps of the stress confirm, for the diseased corneas, a marked increase of the maximum tensile stress, on both anterior and posterior surfaces, to be ascribed mainly to the reduction of the corneal thickness. Stress maps also show, for keratoconus corneas, a marked increase of the ratio between posterior and anterior tensile stress in the conus. Numerical analyses are used to construct the refractive power maps, revealing clearly that the maximum dioptric power in keratoconus corneas is at the center of the cone-shape rather than at the apex.