Multi-physics modeling and finite element formulation of corneal UV cross-linking

The UV cross-linking technique applied to the cornea is a popular and effective therapy for eye diseases such as keratoconus and ectatic disorders. The treatment strengthens the cornea by forming new cross-links via photochemical reactions and, in turn, prevents the disease from further developing. To better understand and capture the underlying mechanisms, we develop a multi-physics model that considers the migration of the riboflavin (i.e., the photo-initializer), UV light absorption, the photochemical reaction that forms the cross-links, and biomechanical changes caused by changes to the microstructure. Our model is calibrated to a set of nanoindentation tests on UV cross-linked corneas from the literature. Additionally, we implement our multi-physics model numerically into a commercial finite element software. We also compare our simulation against a set of inflation tests from the literature. The simulation capability allows us to make quantitative predictions of a therapy's outcomes in full 3-D, based on the actual corneal geometry; it also helps medical practitioners with surgical planning.