Modeling and Simulation of the Aqueous Humor Flow for Healthy, Glaucomatous and Treated Eyes with Stokes and Darcy Equations

In old age some people fall ill with glaucoma. In some cases glaucoma can lead to blindness. The primary risk factor for the development of the vision loss in glaucoma is an increased intraocular pressure (IOP) and lowering the IOP is currently the only therapeutic option with proven efficiency. To understand the behavior of the aqueous humor flow and of the IOP in the anterior chamber of the human eye, a mathematical model is developed. This model is given by Stokes and Darcy equations. The Stokes equation describes the aqueous humor flow in the anterior chamber and the Darcy equation describes the pressure in the trabecular meshwork which is a porous medium. With the help of the Darcy equation the mean pressure value in the Darcy domain is computed. This mean pressure value is incorporated into the Robin boundary condition of the Stokes equation. The characteristic physical properties are given by the inflow rate of the aqueous humor at the ciliary body, the pressure of the episcleral veins and it is assumed that the cornea, the lens, the iris and the zonules are impermeable. Geometries for healthy, pathological and treated eyes are considered. Numerical simulations using the Finite Element method are performed in three dimensions. In the computation, mixed finite elements (e.g. Taylor Hood finite elements for the Stokes equation) are used and the solutions of the equations are generated with deal.ii software. The simulations cover the dependence of the IOP to specific changes of certain model and geometric parameters. Moreover, medical applications concerning IOP changes due to cataract surgery, stent insertion as well as trabeculectomy are discussed. For instance, the model shows a postoperative decrease in IOP about 18.32% in a case of partial occlusion of the trabecular meshwork and the initial IOP of 28.37 mmHg. In addition, the model illustrates linear dependence between the episcleral venous pressure and the IOP