Thin-film coupled fluid-solid analysis of flow through the Ahmed™ glaucoma drainage device

The Ahmed™ glaucoma valve (AGV) is a popular glaucoma drainage device, allowing maintenance of normal intraocular pressure in patients with reduced trabecular outflow facility. The uniquely attractive feature of the AGV, in contrast to other available drainage devices, is its variable resistance in response to changes in flow rate. As a result of this variable resistance, the AGV maintains a pressure drop between 7 and 12 mm Hg for a wide range of aqueous humor flow rates. In this paper, we demonstrate that the nonlinear behavior of the AGV is a direct result of the flexibility of the valve material. Due to the thin geometry of the system, the leaflets of the AGV were modeled using the von Kármán plate theory coupled to a Reynolds lubrication theory model of the aqueous humor flow through the valve. The resulting two-dimensional coupled steady-state partial differential equation system was solved by the finite element method. The Poisson's ratio of the valve was set to 0.45, and the modulus was regressed to experimental data, giving a best-fit value 4.2 MPa. Simulation results compared favorably with previous experimental studies and our own pressure-drop/flow-rate data. For an in vitro flow of 1.6 μL/min, we calculated a pressure drop of 5.8 mm Hg and measured a pressure drop of 5.2 ± 0.4 mm Hg. As flow rate was increased, pressure drop rose in a strongly sublinear fashion, with a flow rate of 20 μL/min giving a predicted pressure drop of only 10.9 mm Hg and a measured pressure drop of 10.5 ± 1.1 mm Hg. The AGV model was then applied to simulate in vivo conditions. For an aqueous humor flow rate of 1.5-3.0 μL/min, the calculated pressure drops were 5.3 and 6.3 mm Hg.