Mathematical Models of Fluid Flows in the Human Eye

Fluids in the eye have many important functions, such as regulating the intraocular pressure, delivering nutrients to the avascular intraocular tissue of the cornea and the lens, and contributing to adhesion forces between the sensory retina and the retinal pigment epithelium. Failure of these functions may lead to a number of pathological conditions. Studying fluid flows in the eye is therefore relevant to improve our understanding of the physiology of the organ and to prevent or treat certain eye diseases. This thesis consists of two main parts. In the first part we propose mathematical models of the dynamics of the aqueous humour in the anterior segment of the eye. The problems considered are in the area of fluid mechanics and our approaches are based on the use of lubrication theory that is applicable for flows in thin domains. The second part is related to fluid transport across the retinal pigment epithelium and it concerns a multiphysics problem, which couples fluid and ion transport.