Effect of Nonlinearity of Elastic Properties of the Cornea on the Results of Schiøtz Tonometry: Estimation Based on a Two-Component Mathematical Model

Abstract

During Schiøtz tonometry, the eye cornea preliminarily loaded with a concave heavy stamp (footplate) is additionally loaded with a rod (plunger), by immersion depth of which the value of intraocular pressure is estimated. A mathematical modeling of this process was done on the basis of an efficient model of the eyeball, previously developed and tested by the authors. Unlike the basic (physically linear) version of this model, the elastic properties of the system are characterized here not by two but by three essential parameters, one of which is responsible for the nonlinearity of elastic behavior of the cornea. The influence of such nonlinearity on a tonometric difference (an excess of the tonometric pressure (in the eye loaded with the tonometer) over the true one (before loading)) is numerically analyzed. The possibility of a nonmonotonic dependence of the tonometric difference from true pressures (when the latter are small), which is absent in the linear model, was found. A correction to the calculation of the true pressure from the tonometric one, introduced by nonlinearity, was estimated. This correction has a different sign depending on the true pressure and is significant for sufficiently high values of this quantity: in this case, taking into account the nonlinearity reduces the tonometric difference. However, the dependence on both stiffnesses present in the model (corneal and scleral) is more significant in most cases than the effect of nonlinearity. The use of the average values of these stiffnesses instead of individual ones in the calculation of the true pressure can lead to fatal errors for the eyes, the stiffness of which deviates greatly from the average, which, particularly, occurs in glaucoma. The dependences used in the clinic during the standard processing of Schiøtz tonometry data can give the correct results with practical accuracy with some values of elastic parameters but deviate significantly from the calculated ones even at the average values of these constants, and the deviations are more noticeable when the greater is the weight of the plunger. A completely correct approach to estimating the mechanical state and mechanical characteristics of the eye should include several measurements with at least two different tonometers, followed by numerical processing of the results.