Diffusion-based degeneration of the collagen reinforcement in the pathologic human cornea

We describe a multiphysics model of the collagen structure of the cornea undergoing a progressive localized reduction of the stiffness, preluding to the development of ectasia and keratoconus. The architecture of the stromal collagen is assumed to follow the simplified two-family model proposed in Pandolfi et al. (A microstructural model of cross-link interaction between collagen fibrils in the human cornea. Philos Trans R Soc A 377:20180079, 2019), where the mechanical stiffness of the structure is supplied by transversal bonds within the fibrils of the same family (inter-crosslink bonds) and across the fibrils of the two families (intra-crosslink bonds). In Pandolfi et al. (A microstructural model of cross-link interaction between collagen fibrils in the human cornea. Philos Trans R Soc A 377:20180079, 2019), it was shown that the loss of the spherical shape due to the protrusion of a cone can be ascribed to the mechanical weakening of the intra-crosslink bonds in the central region of the collagen structure. In the present study, the reduction of bond stiffness is coupled to an evolutive pathologic phenomenon, modeled as a reaction–diffusion process of a normalized scalar field. We assume that the scalar field is a concentration-like measure of the degeneration of the chemical bonds stabilizing the structural collagen. We follow the evolution of the mechanical response of the system in terms of shape change, according to the propagation of the degeneration field, and identify the critical loss of mechanical stability resulting in the typical bulging of keratoconus corneas.