Differential tonometry with a Schiotz tonometer: mathematical modeling with account for the nonlinearity of the elastic behavior of the cornea and comparison with clinical data

Mathematical modeling of the diagnostic procedure of differential tonometry based on loading the eye with a Schiotz tonometer using two or more weights of the plunger, one of the two structural elements of this tonometer, is performed. The model of the eyeball developed earlier by the authors is used, based on the representation of the cornea as a momentless two-dimensional elastic surface and the scleral region as a zero-dimensional elastic element that responds with a change in pressure to a change in the volume of the fluid contained in it. Unlike previous works, in which a theoretical study of differential tonometry was carried out based on a physically linear model of the cornea, the nonlinearity of its elastic behavior is taken into account on the basis of an effective approach that made it possible to describe this nonlinearity by means of a single parameter. It is shown that the dependence of the tonometric pressure on the weight of the plunger remains almost linear, which makes it possible to introduce the pressure difference coefficient γ as the slope of the corresponding straight line. This coefficient increases with both scleral and corneal stiffness and decreases with true pressure. Accounting for nonlinearity leads to increase in the calculated values of γ at sufficiently high both true pressures and stiffnesses of the two components of the eyeball, as well as to an expansion of the pressure range for which these values are large. It is shown that two groups of eyes can be distinguished, in one of which, characterized by high values of the pressure difference coefficient, both components of the corneoscleral coat are very rigid, and in the other, where these values are significantly lower, the stiffness of the eye tissues can be considered normal. At the same time, an intermediate range of γ values remains, for which such definite conclusions cannot be drawn only from the result of differential tonometry. However, the ability to isolate a group of very stiff eyes that are particularly likely to have glaucoma makes this procedure useful in diagnosing this disease.