A generalised plate with kinematically independent thickness for modelling shapes of corneas affected by keratoconus before and after penetrating keratoplasty

A two-dimensional (2D) reduced-order generalised continuum model within the framework of the three-dimensional (3D) deformations is deduced from a 3D Cauchy continuum model by imposing a micro-macro kinematical map, which is linear in the direction normal to the corneal surface. This kinematical assumption is plausible as the cornea thickness is much smaller than its diameter. We use the obtained 2D generalised continuum that incorporates a kinematically independent thickness to model the changes of shape induced in corneas: (1) by the changes of cornea mechanical properties whose aetiology can be found in the complex (and not completely understood yet) pathogenic process causing keratoconus, (2) by penetrating keratoplasty, and (3) degeneration of both patient residual corneal tissue and transplanted corneal tissue after transplant. We postulate that growth and regeneration phenomena occurring in the cornea shape it following the “elastic” solutions, which we have calculated. The preliminary obtained predictions seem to promise significant applicative developments and are in good qualitative agreement with experimental results: future investigations will need to improve the presented model by considering explicitly the remodelling phenomena and a more detailed analysis of the evolution of metabolically driven mechanical damage of corneal tissue and its visco-plasticity.