Mathematical modelling of applanation loading of the eyeball with account for the nonlinearity of the cornea

Abstract

Mathematical modelling of the deformation of the eyeball loaded by a heavy stamp with a flat base is performed, which corresponds to Maklakoff tonometry. The modelling is carried out within the framework of the general approach developed by the authors, which represents the eyeball as a set of a deformable two-dimensional surface (cornea) and a zero-dimensional element that responds with a change in volume to changes in intraocular pressure (scleral region). The behavior of both components is assumed to be elastic: linear for the scleral region and non-linear for the cornea. For the latter, an exponential model developed by the authors was used, in which the nonlinearity of the elastic properties of the cornea is characterized by a single parameter. The calculations were carried out in the range of values of the nonlinearity parameter, estimated on the basis of data on tension of an isolated cornea by pressure. It is shown that taking into account the nonlinearity leads to an increase in the difference between the pressures in a loaded and unloaded eye (tonometric difference) and an increase in the slope of the dependence of tonometric pressure on the tonometer weight (pressure difference coefficient) during elastotonometry. The calculated corrections make it possible to propose refinements for the procedure of processing clinical measurement data. However, such conclusions should be considered as preliminary: there are no final estimates of the nonlinearity parameter for living eyes and they should be obtained as a result of comparing the calculation results with clinical studies. In particular, it is necessary to find out to what extent the values of this parameter are individual and may differ for different eyes.