Development of a complex of mathematical models of the cornea biomechanical parametrs with diagnosed keratoconus before and after treatment with corneal collagen crosslinking

This study is aimed at creation of 3-D geometrical and mechanical finite-element models of the cornea and numerical analysis of its stress-strain state and mechanical behavior under conditions of intraocular pressure and external air jet pressure when diagnosing patients at different stages of keratoconus as well as after treatment with corneal collagen cross-linking. There is created a geometrical model of the cornea in a form of spatial segment of thin-shell convex structure where shell thickness is variable and form of anterior and posterior surfaces is determined arbitrarily by extrapolation of experimental data of corneal topographic study of a specific patient with keratotopograph Pentacam AXL. Material, used for emulation of the cornea, is regarded as heterogeneous, isotropic and nonlinearly elastic. Its coefficients of rigidity are assigned basing on the known experimental data and are adjusted by correlation of parameters on corneal deformation under airflow impulse resulting from numerical modeling and their true estimation by noncontact tonometer Corvis ST. To describe airflow impact occurring in course of tonometry a distributed impulse strain, with parameters corresponding to the settings of airflow impulse of the applied equipment, is effectuated to a part of anterior surface of the emulated shell. If ectatic process is present adjacent to the corneal region in question, local segments with diminishing coefficients of rigidity (from periphery to the center) are applied. Dimensions, form, place, quantity of such regions and character of rigidity decrease inside them are derived from solution of inverse problems aimed at minimization of difference between the results of emulation and experimental measurement of keratotopometric and deformational parameters in specific points of the cornea. To simulate corneal collagen crosslinking procedure, an additional circular zone with enhanced rigidity coefficients is provided. Modification of rigidity characteristics by depth and radius of this zone, is set in accordance with experimental data on photosensitive agent distribution in course of its diffusion within the cornea and flux density of UV emission.