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TECHNICAL PAPERS: Fluids/Heat/Transport

# Thin-Film Coupled Fluid-Solid Analysis of Flow Through the Ahmed™ Glaucoma Drainage Device

[+] Author and Article Information
Matthew S. Stay

Department of Biomedical Engineering,  University of Minnesota, Minneapolis, MN 55455

Tingrui Pan, Babak Ziaie

Department of Electrical and Computer Engineering,  University of Minnesota, Minneapolis, MN 55455

J. David Brown

Department of Opthalmology,  University of Minnesota, Minneapolis, MN 55455

Victor H. Barocas1

Department of Biomedical Engineering,  University of Minnesota, Minneapolis, MN 55455

1

To whom correspondence should be addressed.

J Biomech Eng 127(5), 776-781 (May 09, 2005) (6 pages) doi:10.1115/1.1993662 History: Received April 07, 2004; Revised May 09, 2005

## Abstract

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 $12mmHg$ 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 $4.2MPa$. Simulation results compared favorably with previous experimental studies and our own pressure-drop∕flow-rate data. For an in vitro flow of $1.6μL∕min$, we calculated a pressure drop of $5.8mmHg$ and measured a pressure drop of $5.2±0.4mmHg$. As flow rate was increased, pressure drop rose in a strongly sublinear fashion, with a flow rate of $20μL∕min$ giving a predicted pressure drop of only $10.9mmHg$ and a measured pressure drop of $10.5±1.1mmHg$. The AGV model was then applied to simulate in vivo conditions. For an aqueous humor flow rate of $1.5–3.0μL∕min$, the calculated pressure drops were 5.3 and $6.3mmHg$.

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## Figures

Figure 1

The AGV. Cartoon (a) shows where the AGV is attached to the eye, and how the valve inlet tube is used to redirect aqueous humor around the trabecular meshwork. Cartoon (b) shows the basic AGV components construction: AH is fed through an inlet tube into a channel formed by two opposing sheets of silastic material. Drawing (c) defines the dimensions of the two-dimensional channel formed by the silastic sheets (or leaflets).

Figure 2

The Ahmed valve in vitro experimental setup. The experimental setup consists of a syringe pump, a pipe stand and manometer, and an AGV sealed in a saline bath. The saline viscosity is 1.1cP, and tubing size was chosen so that its resistance was negligible compared to the AGV.

Figure 3

Predicted in vitro results: Physiologically low AH flow. For a 1.6μL∕min flow rate, subfigure (a) shows the displacement of the midplane surface and the contours of the transverse displacement w. (b) plots the pressure contours of AH as it moves the through the valve.

Figure 4

Predicted in vitro results: Severe overfiltration. For a 20.0μL∕min flow rate, subfigure (a) shows the displacement of the midplane surface and the contours of the transverse displacement w. (b) plots the pressure contours of AH as it moves the through the valve.

Figure 5

In vitro AGV performance. (a) compares the predicted RVK model results against the in vitro experimental measurements. Error bars show the range of measured results for the three experimental runs. (b) shows a power curve fit to the experimental data. The power fit exponent is 0.23, a favorable match to the RVK model value of 0.25. The simulations were performed for an AH viscosity of 1.1cP, a Poisson’s ratio of 0.45, and a Young’s modulus of 4.2MPa.

Figure 6

Predicted in vivo AGV valve performance. AGV performance from Fig. 5 is affected by increased temperature, due to decreased AH viscosity and increased leaflet stiffness. The predicted in vivo pressure-drop∕flow-rate results are plotted along with valve resistance (R=ΔP∕F) for a range of physiological flow rates.

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