A microstructural model of cross-link interaction between collagen fibrils in the human cornea.

We propose a simplified micromechanical model of the fibrous reinforcement of the corneal tissue. We restrict our consideration to the structural function of the collagen fibrils located in the stroma and disregard the other all-important components of the cornea. The reinforcing structure is modelled with two sets of parallel fibrils, connected by transversal bonds within the single fibril family (inter-cross-link) and across the two families (intra-cross-link). The particular design chosen for this ideal structure relies on the fact that its ability to sustain loads is dependent on the degree of the cross-link and, therefore, on the density and stiffness of the bonds. We analyse the mechanical response of the system according to the type of interlacing and on the stiffness of fibres and bonds. Results show that the weakening of transversal bonds is associated with a marked increase of the deformability of the system. In particular, the deterioration of transversal bonds due to mechanical, chemical or enzymatic reasons can justify the loss of stiffness of the stromal tissue resulting in localized thinning and bulging typically observed in keratoconus corneas. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.