Mathematical modeling of corneal hysteresis

Mathematical modeling of the deformation of the eyeball under the external pressure applied to the cornea in a bounded area and gradually increasing and then decreasing according to a given law is performed. This relationship corresponds to the change in applied pressure in the ocular response analyzer (ORA) used in clinic. An approach previously developed by the authors is applied, based on representing the cornea as a soft two-dimensional surface and the scleral region as a zero-dimensional element. Since the process under consideration occurs very quickly (lasting several tens of milliseconds), it cannot be considered as purely elastic. The Voigt viscoelasticity of the cornea is taken into account, the smallness of the strain relaxation time allowing us to consider the solution as a correction to a similar purely elastic problem considered at the previous stage of research. The behavior of two parameters characterizing the asymmetry of the system's response to a symmetrical action is studied. These are the delay time of the moment of maximum flattening of the cornea in the apical region during unloading compared to the moment of its flattening during loading and the difference in external pressures at which these flattenings are reached (corneal hysteresis). Their values obtained from the simulation are of the same order as the same values determined experimentally. It is shown that hysteresis increases with increasing strain relaxation time and with increasing maximum external pressure.