Mathematical modelling of eye cornea deformation by external pressure

The deformation of the eyeball under the effect of external pressure applied to the cornea in a limited area, for example, as a result of loading with an air jet, is considered. The cornea is modeled by a homogeneous, isotropic, momentless surface and, in the general case, is considered to be linearly Voigt-type viscoelastic. Its elastic properties are determined by the quadratic dependence of the strain energy on the components of the strain tensor, and viscous by the quadratic dissipative function of the strain rates. The scleral region is described by the differential relationship between the scleral volume and intraocular pressure.The process of slow deformation is considered in detail, when the derivatives of the deformation characteristics with respect to time can be neglected in the constitutive relations. It is shown that, at a certain external pressure, a section is formed in the central region of the zone of its influence, which can be considered to be flat with high accuracy. From the external pressure at which this zone occurs, the true intraocular pressure,i.e., pressure in an unloaded eye, can be determined with good accuracy. The relationship between these pressures is weakly affected by the elastic properties of both the cornea and the scleral region. In the area of external pressures corresponding to “flattening”, the rate of subsidence of the corneal apex at external pressure uniformly increasing changes. Possible generalizations of them ode land the problem formulation are discussed.