Mathematical Modeling of Applanation and Impression Tonometry after Surgical Correction of Vision

Abstract

Abstract—Mathematical modeling of applanation and impression tonometry (according to Maklakoff and Schiotz, respectively) was performed for the eye with artificially induced strong inhomogeneity of the elastic properties of the cornea. Such inhomogeneity occurs as a result of surgical correction of vision. Corneal weakening was considered for either the apical area (correction of myopia) or the peripheral annular zone lying close to the sclera (correction of hyperopia). A two-component model of the eyeball was used, where the cornea is represented by a momentless, deformable, linearly elastic surface and the scleral area is represented by an elastic element that responds to changes in intraocular pressure by changing its volume. Within this representation, the mechanical properties of the cornea are characterized by effective stiffness, which is a parameter that contains both the elastic properties of the cornea material and the corneal thickness. The relationships employed in the standard processing of tonometry data, as well as simulation results obtained previously for the case of a homogeneous cornea, were tested for applicability to operated eyes with significant inhomogeneity of the elastic properties of the cornea. The bias caused by inhomogeneity was found to be the most significant for Schiotz tonometry with an apical weakening and a rather high intraocular pressure. For Maklakoff tonometry, inhomogeneity exerted a less significant effect on the calculation of the true pressure in either type of corneal weakening.