Computer Simulation of Valved Glaucoma Drainage Device Performance: Pre– and Post–Microtube Stent Insertion

Abstract

Abstract: : Purpose: To understand the function and physics of valved glaucoma drainage devices (GDDs), including the Ahmed^TM glaucoma valve (AGV) and the Krupin^TM valve, to determine the mechanical and fluidic performance of aqueous humor flow in these valved implants, and to demonstrate the effect on valve performance of inserting a microtube stent across the valve. Methods: A coupled lubrication–von Karman (LVK) mathematical model was developed to predict the fluid–solid interactions of aqueous humor and the elastic valve leaflets in the AGV pre– and post– microtube stent insertion. The resulting coupled two–dimensional steady–state partial differential equation system was solved with the finite element method, using measured geometric specifications for the AGV and close estimations of the valve membrane properties. Moreover, a mathematical model of the Krupin valve was developed. Calculations based on its specifications and analyses of previous experimental data were used to predict the valve performance. Results: The LVK model predicted a strongly nonlinear relationship between aqueous humor pressure drop and flow rate across the AGV. At flow rates of 2 and 20 µL/min, pressure drops of 6.5 and 11.7 mmHg was shown, respectively. Furthermore, the simulation results showed that the insertion of a microtube between the AGV leaflets eliminates valve resistance to a pressure drop of 0.002 mmHg at a physiological aqueous humor flow rate of 2.5 µL /min. Conclusions: This study analyzes the mechanical and fluidic performance of the valve in the Ahmed and Krupin valved GDDs. It suggests, through a numerical analysis, that a microtube stent placed across the valve will completely eliminate its resistance.

Keywords: clinical (human) or epidemiologic studies: systems/equipment/techniques • clinical laboratory testing • intraocular pressure