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Effect of a Gradient Distribution of Cross-Links on the Deformation Behaviors of Corneal Stroma: Theoretical Model and Finite Element Simulation

In this work, both theoretical model and finite element simulation are combined to address the influence of gradiently distributed cross-links on the underlying deformation mechanisms of corneal stroma. Theoretically, a hyperelastic model is developed that involves the strengthening contributions of ultraviolet A (UVA)-induced cross-links, collagen fibers and matrix materials. Thereinto, the influence of collagen cross-linking (CXL) is characterized by a mechanism-based strain energy function, which not only explicitly depends on the density of cross-links (as a function of the corneal thickness and UVA irradiation dose), but also relies on the discrepant distribution of cross-links in the proteoglycan matrix and along the fibers. Moreover, the developed constitutive laws are incorporated into the subroutine UMAT of ABAQUS to simulate the expansion deformation of porcine cornea with/without the treatment by CXL. It is noticed that the simulated results can fit well with the experimental data, and are able to predict the macroscopic intraocular pressure (IOP)-apex displacement relations at different UVA irradiation doses. Corresponding stiffening and strengthening behaviors induced by cross-links, fibers and the matrix are systematically compared at different corneal surfaces along the thickness direction in order to obtain a sophisticated comprehension of the fundamental deformation mechanisms, which may theoretically help design and guide the operation of CXL in clinics.