Mathematical modelling of Maklakoff elastotonometry in the case of artificially created cornea inhomogeneity

Abstract

The mechanical response of the eye to cornea loading by wide flat stamps of different weights (Maklakoff elastotonometry) is studied in the case of artificially created strong inhomogeneity of the elastic properties of the cornea, which is formed due to vision correction surgery. The weakening of the cornea in the apical region or in the peripheral annular zone that lies a short distance from the sclera but is not adjacent to it is considered. The first case corresponds to correction of myopia and the second one to that of hyperopia. The cornea is modeled by a momentless, linearly elastic surface and the scleral region by an elastic reservoir that responds to changes in volume by changes in pressure. Within this representation, the mechanical properties of the cornea are characterized by the effective stiffness, a parameter that reflects both the elastic properties of the cornea material and the corneal thickness. It is shown that for moderate corneal stiffness the dependence of the tonometric pressure on the tonometer weight remains, similar to the case of homogeneous cornea, almost linear, which makes it possible to introduce the pressure difference coefficient as the slope of the corresponding straight line. The dependence of this coefficient on parameters that characterize the distribution of the elastic properties of the cornea is studied for various true pressures and scleral stiffnesses. The corneal inhomogeneity effect turned out to be qualitatively different for apical and peripheral weakening but insignificant. In the latter case, the effect is less expressed and, moreover, practically indiscernible. Thus, for operated eyes with moderately stiff corneas, the earlier developed methods of clinical estimation of elastotonometry results can be used.