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

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 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 microL/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 microL/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 microL/min, the calculated pressure drops were 5.3 and 6.3 mm Hg.

A New Design and Application of Bioelastomers for Better Control of Intraocular Pressure in a Glaucoma Drainage Device

“…The Young's modulus of the commercially purchased PLC was noted to be 32.5 MPa before degradation, which is higher than the reported value of 12 MPa due to differences in synthesis 23. The Young's modulus of Si was found to be 4 ± 0.3 MPa, which is close to the reported value of 5 MPa 24. Figure 5d shows a plot of Young's modulus against time for PLC films during the degradation study.…”

“…Thus, any biodegradable material chosen to perform within the AGV must satisfy the following requirements: a) it must be elastomeric, that is, it must be easily stretched and be able to maintain the strain for a specified period (4–6 weeks); this implies minimal creep or stress relaxation in this time period. b) Its modulus should be in the region of 5–10 MPa, based on the silicone modulus 15. c) Its biodegradation rate must be such that substantial relaxation occurs in 4–6 weeks, which is the period associated with capsule formation in vivo.…”

Gekoppelte Analyse der Fluid-Struktur-Interaktion eines mikromechanischen Ventils für Glaukomdrainageimplantate

“…5,6 × 10 −3 mmHg/µl • min −1 (iStent ® inject) vorliegt [26]. Auch das Membranventil des Ahmed™ GDI wurde bereits mithilfe von FSI-Analysen untersucht [21][22][23]. Die beschriebenen numerischen Modelle ermöglichen eine Untersuchung der nicht linearen Volumenstrom-Druckdifferenz-Charakteristik des Implantats.…”

“…Im Rahmen von Parameterstudien, z. B. durch Variation des Membranmaterials, der Membrandicke oder -länge, kann so die Einstellung einer gewünschten Volumenstrom-Druckdifferenz-Charakteristik realisiert werden [21,22]. Das im Rahmen der vorliegenden Arbeit beschriebene numerische Modell ermöglicht eine wechselseitig gekoppelte FSI-Analyse dreidimensionaler mikromechanischer Ventilmodelle für GDI.…”

“…Unabhängig davon ist eine Validierung der Simulation anhand experimenteller Ergebnisse unabdingbar. In der Literatur wurde bereits die FSI-Analyse des Ventils des kommerziellen Ahmed™ GDI (New World Medical Inc., USA) beschrieben [21][22][23]. Im Rahmen der vorliegenden Arbeit erfolgt die FSI-Analyse eines eigenentwickelten mikromechanischen Ventils.…”