Mechanical-mathematical model of intrastromal shape correction of the cornea in keratoconus

A mechanic-mathematical model of the cornea keratoconus correction is proposed that allows one to numerically simulate the deformation and change in the shape of the cornea when introducing a flexible annular implant into a pre-prepared microchannel. Implants are two ring segments with a radius greater than the radius of the prepared channels. The implant material is polymetamethylcrylate. Using this surgical procedure it is possible to smooth out the defect of the cornea (keratoconus). In the mechanical-mathematical model of keratoconus correction, the problem of joint contact deformation of flexible annular segments and the cornea is solved. The measurements taken before and after the correction of keratoconus in patients of the eye microsurgery clinic were used to create a 3D geometric model of the cornea. The coordinates of the real surfaces of the cornea were represented in the form of Zernike polynomials. Based on this model, a software package has been developed that allows calculating of the cornea shape after implantation. The proposed method of the keratoconus correction modeling makes it possible to evaluate and optimize the mechanical properties and geometric parameters of the annular implant in order to achieve the desired effect - smoothing of the corneal defect in the eye.